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BOOK 5
FIXED INCOME ,
DERIVATIVES, AND ALTERNATIVE
INVESTMENTS
-
Reading Assignments and Learning Outcome Statements
Study Session 15 - Fixed Income: Basic Concepts
........................................
.................................................
Study Session 16- Fixed Income: Analysis and Valuation
87
186
...........................................................................
191
Study Session 18- Alternative Investments
........................................................
278
............................................
309
............................................................................................................
312
.................................................................................................................
314
Self-Test - Derivatives and Alternative Investments
Formulas
Index
11
.................................................................
Self-Test - Fixed Income Investments
Study Session 17- Derivatives
....................................
3
SCHWESERNOTES™
2013
CPA
LEVEL
I
BOOK
5:
FIXED
INCOME,
DERIVATIVES, AND ALTERNATIVE INVESTMENTS
©20 12 Kaplan, Inc. All rights reserved.
Published in 2012 by Kaplan Schweser.
Printed in the United States of America.
ISBN: 978-1-4277-4265-0 1-4277-4265-0
PPN: 3200-2848
I
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republished from 2013 Learning Outcome Statements, Level I, II, and III questions from CFA® Program
Materials, CFA Institute Standards of Professional Conduct, and CFA Institute's Global Investment
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Disclaimer: The SchweserNotes should be used in conjunction with the original readings as set forth by
CFA Institute in their 2013 CFA Level I Study Guide. The information contained in these Notes covers
topics contained in the readings referenced by CFA Institute and is believed to be accurate. However,
their accuracy cannot be guaranteed nor is any warranty conveyed as to your ultimate exam success. The
authors of the referenced readings have not endorsed or sponsored these Notes.
Page 2
©2012 Kaplan, Inc.
READING ASSIGNMENTS AND
L EARNING OUTCOME STATEMENTS
The following material is a review ofthe Fixed Income, Derivatives, andAlternative
Investments principles designed to address the learning outcome statements setforth by
CPA Institute.
STUDY SESSION 15
Reading Assignments
CFA Program 2013 Curriculum, Volume 5 (CFA Institute,
2012)52. Features of Debt Securities
page
11
53.54. Risks
Associated
with
Investi
n
g
in
Bonds
page
25
page
ew ofnBond
page 4669
55. Overvi
Understandi
g YielSectors
d Spreadsand Instruments
Equity and Fixed Income,
STUDY SESSION 16
Reading Assignments CFA Program 2013 Curriculum, Volume 5 (CFA Institute,
2012)56. Introduction to the Valuation of Debt Securities
page
87
page
101
57.58. Yield
Measures,to theSpotMeasurement
Rates, and Forward
RatesRate Risk
Introduction
of
Interest
page
134
page 157
59. Fundamentals of Credit Analysis
Equity and Fixed Income,
STUDY SESSION 17
Reading Assignments
CFA Program 2013 Curriculum, Volume 6
(CFA60.Institute,
2012)
page
Deri
v
ati
v
e
Markets
and
Instruments
191
page 213
61.62. Forward
MarketsandandContracts
Contracts
197
page
Futures
Markets
page
226
63.64. Swap
OptioMarkets
n MarketsandandContracts
Contracts
page
254
page 268
65. Risk Management Applications of Option Strategies
Derivatives and Alternative Investments,
STUDY SESSION 18
Reading Assignments
CFA Program 2013 Curriculum, Volume 6
(CFA66.Institute,
2012)
Introductionin Commodities
to Alternative Investments
page 278
67. Investing
page
303
Derivatives and Alternative Investments,
©20 12 Kaplan, Inc.
Page 3
Book 5 - Fixed Income, Derivatives, and Alternative Investments
Reading Assignments and Learning Outcome Statements
LEARNING OUTCOME STATEMENTS (LOS )
The CPA Institute Learning Outcome Statements are listed below. These are repeated in each
topic review; however, the order may have been changed in order to get a betterfit with the
flow ofthe review.
STUDY SESSION 15
The topical coverage corresponds with the following CPA Institute assigned reading:
ofdate should be able to:
The
candi
a. expl
a
i
n
the
purposes
of
a
bond'
s
i
n
denture
and
describe
affi
r
mati
v
e
and
negati
v
e
covenants.the(page
11)features of a bond, the various coupon rate structures, and the
b. describe
basic
structure
of floating-rate
securities.
(pageclean12)price. (page 14)
n
e
accrued
i
n
terest,
ful
l
price,
and
c.d. defi
ain thecommon
provisions
for redemption
anda bond
retirement
of bonds.the(page
14)
e. expl
identify
options
embedded
in
issue,
explain
importance
ofbondholder.
embedded(page
options,16) and identify whether an option benefits the issuer or the
describe
methods
used by (i.institutional
investors
in repurchase
the bond market
to finance
the
purchase
of
a
security
e
.
,
margi
n
buyi
n
g
and
agreements).
(page 17)
52. Features
Debt Securities
f.
The topical coverage corresponds with the following CPA Institute assigned reading:
53. Risks Associated with Investing in Bonds
The
candidate
should
be able to:with investing in bonds. (page 25)
a
i
n
the
ri
s
ks
associated
a.b. expl
identify
the
rel
a
tions
among
a
bond'
s
coupon
rate,
the
yield
required
by
the
market,
and
the(pagebond'27)s price relative to par value (i.e., discount, premium, or
equal
to
par).
ain howratea bond
maturity,
coupon, embedded options and yield level affect
c. iexpl
t
s
interest
risk.
(page
27)
d. bond
identifyandthetherelprice
ationofofthetheembedded
price of a callable
bond(page
to the29)price of an option-free
call
option.
a
i
n
the
interest
rate
risk
of
a
fl
o
ati
n
g-rate
security
and
why
its
price
may
e. expl
dicalculate
ffer fromandparinterpret
value. (page
29) and dollar duration of a bond. (page 30)
the
duration
describrisk.
e yiel(page
d-curve32)risk and explain why duration does not account for yield­
g. curve
ain34)the disadvantages of a callable or prepayable security to an investor.
h. expl
(page
identify
the
factors
that
affect
the
reinvestment
risk
of
a
security
and
explain
why
prepayable
amortizingsecurities.
securities(page
expose34)investors to greater reinvestment
risk
than
nonamortizing
types of risk
creditandriskwhyanditthemightmeaning
and roletoofinvestors
credit ratings.
(page
35)
k. describe
expl
a
i
n
liquidity
be
important
even
if
they
expect to hold a security to the maturity date. (page 36)
f.
1.
)·
Page 4
©2012 Kaplan, Inc.
Book 5 Fixed Income, Derivatives, and Alternative Investments
Reading Assignments and Learning Outcome Statements
-
describe
thecurrency.
exchange(pagerate37)risk an investor faces when a bond makes payments in
a
forei
g
n
explaaiinn how
inflatiyield
on risk.volatil(pageity affects
37) the price of a bond with an embedded option
m.n. expl
and
how(pagechanges
in volatility affect the value of a callable bond and a purable
bond.
37)
o. describe sovereign risk and types of event risk. (page 38)
Overview
of
Bond
Sectors
and
Instruments
The
candidatefeatures,
shouldcredit
be ableriskto:characteristics, and distribution methods for
describe
a. government
securities.
(page
46)
b. describe
typesbonds,
of securities
issued
byprotection
the U.S. Department
of thedistinguish
Treasury
(e.between
g., bills,theon-the-run
notes,
and
infl
a
tion
securities),
and
andTreasury
off-the-run
Treasury
securities.and(page
47) between
describe strihowps stripped
securities
are
created
di
s
tinguish
c. coupon
and and
principal
strips. c(page
49) issued by U.S. federal agencies.
d. describe
the
types
characteristi
s
of
securities
(page
49)
theowtypes
and characteristi
cfors ofeachmortgage-backed
securities and explain
e. describe
the
cash
fl
and
prepayment
risk
type.
(page
50)
expl
ain52)the motivation for creating a collateralized mortgage obligation.
(page
thebetween
types oftax-backed
securities issued
by municipalities
in(page
the United
States and
g. describe
distinguish
debt
and
revenue
bonds.
53)
the
characteristi
c
s
and
moti
v
ation
for
the
various
types
of
debt
issued
h. bydescribe
corporations
(inclpaper,
udingnegotiable
corporateCDs,
bonds,andmedium-term
notes, structured
notes,
commercial
bankers
acceptances).
(page e55)
defi
n
e
an
asset-backed
security,
describe
the
rol
e
of
a
special
purpose
vehicl
in issue
an asset-backed
security'security,
s transaction,
state thethe types
motivatiofoexternal
n for a corporation
toenhancements
an asset-backed
and
describe
credit
for
asset-backed
securities.
(page
59)
describe
col
l
aterali
z
ed
debt
obligations.
(page
60)
mechanithesmsprimary
availableandforsecondary
placing bonds
market61)and
k. describe
distinguishthebetween
marketsin theforprimary
bonds. (page
Understanding
Yield Spreads
The
candi
d
ate
should
berateablepolicy
to: tools available to a central bank. (page 69)
identify thea yieldinterest
a.b. describe
curve
andofthethevarious
shapes ofoftheinyield
curve.
(pagedescribe
70) the
a
i
n
the
basic
theories
term
structure
terest
rates
and
c. expl
implications
of
each
theory
for
the
shape
of
the
yi
e
l
d
curve.
(page
71)
ne a spot
rate.
(pageyield
73) spread measures. (page 74)
e.d. defi
calculate
and
compare
describe credi(page
t spreads
and relationships between credit spreads and economic
conditions.
75)
describe
howliembedded
options
affectaffects
yieldthespreads.
(page 76)of a bond relative to
h.g. expl
a
i
n
how
q
uidity
and
issue-size
yield
spread
other similar securities. (page 76)
I.
54.
The topical coverage corresponds with the following CFA Institute assigned reading:
f.
1.
J·
55.
The topical coverage corresponds with the following CFA Institute assigned reading:
f.
©20 1 2 Kaplan, Inc.
Page 5
Book 5 Fixed Income, Derivatives, and Alternative Investments
Reading Assignments and Learning Outcome Statements
-
1.
)·
calculate thesecurity.
after-tax(page
yield77)of a taxable security and the tax-equivalent yield of a
tax-exempt
defi
n
e
and
explain
its
importance
to
funded
investors
who
borrow
short
term. (page 78)
LIBOR
STUDY SESSION 16
The topical coverage corresponds with the following CFA Institute assigned reading:
56. The candidate should be able to:
aibnesteps
inofthebonds
bondforvalwhiuation
process. (page
87) cash flows is difficult.
descri
types
c
h
estimating
the
expected
b.a. expl
(page
87)
c.d. calculate
the thevaluepriceof aofbond
(coupon
andifzero-coupon).
(pagechanges
88) and as the
expl
a
i
n
how
a
bond
changes
the
discount
rate
bond
its maturi
tyofdate.a bond(pagegiven
91) a change in its discount rate.
calculateapproaches
the
change
i
n
value
e. (page
92)and demonstrate the use of the arbitrage-free valuation approach and
expl
a
i
n
descri
b
e
how
a
dealer
can
generate
an
arbitrage
profi
t
i
f
a
bond
i
s
mispriced.
(page 94)
57. The candidate should be able to:
describe theandsources
of traditional
return fromyield
investimeasures
ng in a forbond.fixed-rate
(page 10bonds
1) and
b.a. expl
calculate
interpret
aiinn thei
rreilimitations
and
assumptions.
(pagein calculating
101) yield to maturity
c. expl
a
the
n
vestment
assumption
implicit
describeandtheinterpret
factorsthethatbond
affectequivalent
reinvestment
risk.
(page
1 08) bond and the
d. and
calculate
yield
of
an
annual-pay
annual-paytheyield
of a semiannual-pay
bond.Treasury
(page 110)
e. the
describe
cal
c
ulation
of
the
theoretical
spot rate curve and calculate
val
u
e
of
a
bond
using
spot
rates.
(page
111)
f. expl
ain these
nominal,
zero-vol
aoption
tility, and
option-adjusted
spreads and the relations
among
spreads
and
cost.
(page
115)
a
i
n
a
forward
rate
and
cal
c
ul
a
te
spot
rates
from
forward
rates,
forward
rates
g. expl
from spot rates, and the value of a bond using forward rates. (page 118)
58. The candidate should be able to:
ntheguishduration/convexi
between the fullty approach
valuationforapproach
(theinterest
scenariorateanalysis
approach)
a. disti
and
measuring
risk,
and
expl
ibnethetheadvantage
of usingcharacteri
the fulslticsvaluation
approach.callable,
(page 134)prepayable,
b. and
descriaputable
price
volatility
for
option-free,
bondsconvexi
whentinterest
ratesvchange.
(page
136)their relation to bond
describeandpositive
y
and
negati
e
convexi
t
y,
and
c. price
yield. (page 136)
Introduction to the Valuation of Debt Securities
f.
The topical coverage corresponds with thefollowing CFA Institute assigned reading:
Yield Measures, Spot Rates, and Forward Rates
The topical coverage corresponds with the following CFA Institute assigned reading:
Introduction to the Measurement of Interest Rate Risk
Page 6
©2012 Kaplan, Inc.
Book 5 Fixed Income, Derivatives, and Alternative Investments
Reading Assignments and Learning Outcome Statements
-
d.
e.
f.
g.
h.
calculate
and interpret
thel increase
effectiveandduration
offora bond,
gichanges
ven information
about
how
the
bond'
s
price
wil
decrease
gi
v
en
i
n
interest
rates.
(page
139)
calculate durati
the approximate
percentage
priceinchange
for a bond,
given the bond's
effective
o
n
and
a
specifi
e
d
change
yield.
(page
141)
distinguish
among
the
alternati
v
e
defi
n
itions
of
duration
and
explain
why
effective
durationoptions.
is the most
appropriate
measure of interest rate risk for bonds
with
embedded
(page
142)
calculate
the duration
of atheportfolio,
givenoftheportfolio
durationduration.
of the bonds
comprising
the
portfolio,
and
explain
limitations
(page
144)
describe
the convexity
measure
of a bondandandconvexi
estimatety and
a bond'
s percentage
price
change,
given
the
bond'
s
duration
a
speci
fied change in
(page 145)
idistinguish
nterest rates.between
modifi
eadbasis
convexi
tyt and
effective
convexi
titsy. relationship
(page 147) to
calculate
the
price
val
u
e
of
poi
n
(PVBP),
and
explai
n
(pageimpact
147)of yield volatility on the interest rate risk of a bond.
k. duration.
describe
the
(page 148)
1.
)·
The topical coverage corresponds with the following CFA Institute assigned reading:
59. Fundamentals of Credit Analysis
The
candidatecredishould
beandablcredi
e to:t-related risks affecting corporate bonds. (page 157)
a.b. describe
t
ri
s
k
descri
b
e
seniority
ranki
n
gs
of
corporate
debt
and
expl
a
i
n
the
potential
violation
of the prioritybetween
of claimscorporate
in a bankruptcy
proceeding.
(page
158)
issuer
credit
rati
n
gs
and
issue
credit ratings and
c. distinguish
descri
b
e
the
rati
n
g
agency
practice
of
"notching".
(page
159)
explaaiinn theriskscomponents
in relying onofratitraditional
ngs fromcredit
creditanalysis.
rating agencies.
(page 160)
d.e. expl
(page
161)
calculate
and
interpret
fi
n
ancial
ratios
used
in
credi
t
analysis.
(page
163)
evaluatekeythefincredit
quali
tsyforofthea corporate
bondthe issuer
and(page
a bond167)of that issuer,
g. given
anci
a
l
rati
o
issuer
and
industry.
factors
thatimpact
influenceof spread
the levelchanges.
and vol(page
atility169)
of yield spreads. (page 169)
h. describe
calculate
the
return
explain special
consideratidebt
ons when
credi172)
t of high yield,
sovereign,
and municipal
issuersevalanduating
issues.the(page
f.
1.
)·
STUDY SESSION 17
The topical coverage corresponds with the following CFA Institute assigned reading:
60. The candidate should be able to:
ne a derivatives.
derivative and(pagedistinguish
between exchange-traded and over-the­
a. defi
counter
191)
contrast
forwardcontracts,
commitments
andcontracts,
contingentoptions
claims.(calls(pageand191)
c.b. defi
n
e
forward
futures
puts), and swaps
and
compare
their
basi
c
characteristics.
(page
192)
purposes
of
and
controversies
related
to
deri
v
ati
v
e
markets.
(page
192)
d.e. describe
explain
arbitrage and(pagethe 193)
role it plays in determining prices and promoting
market efficiency.
Derivative Markets and Instruments
©20 1 2 Kaplan, Inc.
Page 7
Book 5 Fixed Income, Derivatives, and Alternative Investments
Reading Assignments and Learning Outcome Statements
-
The topical coverage corresponds with the following CPA Institute assigned reading:
61. The candidate should
andbeContracts
abl
e
to:
ain delcontract.
ivery/settl(page
ement197)and default risk for both long and short positions in
a. aexplforward
bation
e the procedures
for settling
aaffect
forwardcredicontract
at expiration,
and how
b. descri
termi
n
prior
to
expiration
can
t
ri
s
k.
(page
198)
nguish
between
a dealer
andequityan end
user contracts
of a forwardandcontract.
(page 199)on
d.c. disti
descri
b
e
the
characteristi
c
s
of
forward
forward
contracts
zero-coupon
and
coupon
bonds.
(page
200)
beandthe Euribor.
characteristics
of202)the Eurodollar time deposit market, and define
e. descri
LIBOR
(page
forward
rate
agreements
(FRAs)
and
cal
c
ul
a
te
the
gain/loss
on
a
FRA.
f. describe
(page 203)and interpret the payoff of a FRA and explain each of the component
g. terms
calculate
payoff formula.
203)forward contracts. (page 205)
cs of(page
currency
h. describeof thethe characteristi
62. The candidate should
and Contracts
be ablecsto:of futures contracts. (page 213)
the
characteristi
a.b. describe
compare
contracts
andin forward
contracts.
(pageand213)margin in the futures
c. markets,
disti
nguishfutures
between
margin
the
securities
markets
andsettlement
explain theinrolefutures
of initrading.
tial margin,
maintenance
margin, variation
margin,
and
(page
214)
d. descri
b
e
price
limits
and
the
process
of
marki
n
g
to
market,
and
cal
c
ul
a
te
and
ithenterpret
theprice.
margi(page
n balance,
given the previous day's balance and the change in
futures
216)
how a futures contract can be terminated at or prior to expiration.
e. describe
(page
218)
describe thebill,characteristi
s of the folbond,
lowinstock
g typesindex,
of futures
contracts.(page 219)
f. Treasury
Eurodollar,cTreasury
and currency.
Forward Markets
The topical coverage corresponds with the following CPA Institute assigned reading:
Futures Markets
The topical coverage corresponds with thefollowing CPA Institute assigned reading:
63. The
Optioncandidate should
and Contracts
be abloptions.
e to: (page 226)
call
and
put
a.b. describe
distinguitheshconcept
betweenofEuropean
andofAmerican
options.
(page 227)
moneyness
an
option.
(page
228)
c.d. define
compare
exchange-traded
options
and
over-the-counter
options.
(page
229)
theinterest
typesrateof options
inwithtermsforward
of therateunderlying
instruments.
(page230)
229)
e. identify
compare
options
agreements
(FRAs).
(page
interest
rate caps,option
floors,payoffs
and collars.
(pageain231)
calculate
and
interpret
and
expl
how
i
n
terest
rate
options
h.g. define
differnefrom
othervalue
typesandof time
options.value,(pageand233)
defi
intrinsic
explainof their
relationship.
(page 234)
determine
the
minimum
and
maximum
values
European
options
and
canandoptions.
(pagethe237)lowest prices of European and American calls and
k. Ameri
calculate
interpret
puts based on the rules for minimum values and lower bounds. (page 238)
Markets
f.
1.
j.
Page 8
©2012 Kaplan, Inc.
Book 5 Fixed Income, Derivatives, and Alternative Investments
Reading Assignments and Learning Outcome Statements
-
expl
ain how(page
option242)prices are affected by the exercise price and the time to
expiration.
m. explain
put-call
parity
for
European
options,
and
explain
how
put-cal
l
parity
is
atedain tohowarbicashtragefloandws onthetheconstruction
ofassetsynthetic
options.l pari
(pagety 243)
n. relexpl
underlying
affect
put-cal
and the
lower
bounds
of
option
prices.
(page
245)
o. determine
an option'stheprice.directional
(page 246)effect ofan interest rate change or volatility change on
I.
The topical coverage corresponds with the following CFA Institute assigned reading:
64. The candidate should be able to:
a. describe
the
characteristi
c
s
of
swap
contracts
and
expl
a
i
n
how
swaps
are
terminated.calculate,
(page 255)
nterpretswaps.
the payments
b. describe,
interest rate swaps, and
and iequity
(page 256)of currency swaps, plain vanilla
65. The candidate should be able to:
determine underl
the valyuinge atprice
expiration,
the profit,andmaximum
profioft,themaxistrategi
mum eloss,
a. breakeven
at
expiration,
payoff
graph
sfor
ofinvestors
buyingusing
and selthese
ling strategi
calls andes. puts
and
determine
the
potential
outcomes
(page
268)
b. breakeven
determine underl
the valyuinge atprice
expiratatiexpiration,
on, profit, maximum
profi
t, maximum
loss,
and
payoff
graph
of
a
covered
calapplication
l strategyofandeacha protective
put
strategy,
and
explain
the
ri
s
k
management
strategy. (page 272)
Swap Markets and Contracts
The topical coverage corresponds with the following CFA Institute assigned reading:
Risk Management Applications of Option Strategies
STUDY SESSION 18
The topical coverage corresponds with the following CFA Institute assigned reading:
66. The candidate should be able to:
compare categories
alternativeofinalvestments
wiinvestments.
th traditional(pageinvestments.
(page 278)
b.c.a. describe
t
ernati
v
e
278)
describe
potential
benefits
of alternative investments in the context of portfolio
management.
(page
279)
hedge
funds, private
equity,asrealapplicable,
estate, commodities,
and other
d. describe
alternati
v
e
i
n
vestments,
incl
u
ding,
strategies,
sub-categories,
potential
benefi
t
s
and
ri
s
ks,
fee
structures,
and
due
diligence.
(page
280)
e. describe
issuesestate,in valuing,
and calculating
returns
on, hedge funds, private
equity,
real
and
commodities.
(page
280)
descri
b
e,
calculate,
and
i
n
terpret
management
and
i
n
centi
v
e
fees
and
net-of-fees
funds. (pageof alternati
292) ve investments. (page 294)
describetoriskhedge
management
g. returns
Introduction to Alternative Investments
f.
©20 12 Kaplan, Inc.
Page 9
Book 5 Fixed Income, Derivatives, and Alternative Investments
Reading Assignments and Learning Outcome Statements
-
The topical coverage corresponds with the following CPA Institute assigned reading:
67. The
Investing
inateCommodities
candi
d
should
be
able
to:
ain the relationship
between (page
spot prices
and expected future prices in terms
a. ofexplcontango
and
backwardation.
303)
bone thea portfolio
sources ofof return
andan allocation
risk for a commodity
investment
and the
b. descri
effect
adding
to
commodities.
(page
304)
ain why (page
a commodity
c. expl
investment.
305) index strategy is generally considered an active
Page 10
©2012 Kaplan, Inc.
The following is a review of the Analysis of Fixed Income Investments principles designed to address the
learning outcome statements set forth by CFA Institute. This topic is also covered in:
FEATURES OF DEBT SECURITIES
Study Session 15
EXAM FOCUS
xeda giincome
securities,of years
historical
lythen
, wererepay
promises
tooanpayamount
a streamat ofthesemiannual
payments
forFicontract
vbetween
en number
and
the
l
maturi
t
y
date.
The
the borrower
andthatthethelender
(the
indenture)
canofrealcontracts
ly be desithat
gnedareto have
any
payment
stream
or
pattern
parti
e
s
agree
to.
Types
frequently have specific names, and there is no shortage of those (for you to learn) here.used
You
specialof these)
attention
to how/when
how the periodic
payments
ared (calls,
determined
(fixed,ng
flfunds,
oatishould
ng,amortization,
andpayvariants
and
to
the
principal
is
repai
puts,
sinki
andwhen
prepayments).
These
features
all affectsecurities
the valueandofcompare
the securities
and
will
come
up
again
you
learn
how
to
value
these
their
risks, both at Level I and Level II.
LOS 52.a: Explain the purposes of a bond's indenture and describe affirmative
and negative covenants.
CFA® Program Curriculum, Volume 5, page 294
The contract
that specifiis called
es all thethe rights and obligations
of the issuerdefiandnes thetheowners
of a
fixed
income
security
The
indenture
obligations
of and restrictions
on theandborrower
and These
forms thecontract
basis provisions
for all futurearetransactions
between
the
bondholder
the
issuer.
known as
and include(actions
both that the borrower (prohibitions
on
the
borrower)
and
promises to perform) sections.
include
restrictionsnegative
on assetplesales
(thecollateral
company(thecan'company
t sell assetscan't
that
have
been
pledged
as
collateral),
dge
of
claimadditional
that theborrowings
same assets (the
backcompany
several debtcan'issues
simultaneously),
and unless
restrictions
onfinancial
t
borrow
additional
money
certain
conditions are met).
include
the For
maintenance
ofthecertain
financial
ratios
andtothemaintain
timely
payment
of
principal
and
interest.
example,
borrower
mi
g
ht
promise
theis notcompany'
s
current
ratio
at
a
value
of
two
or
higher.
If
thi
s
val
u
e
of
the
current
ratio
maintained, then the bonds could be considered to be in (technical) default.
bond indenture.
covenants
affirmative
negative covenants
covenants
Negative covenants
Affirmative covenants
©20 12 Kaplan, Inc.
Page 1 1
Study Session 1 5
Cross-Reference to CFA Institute Assigned Reading #52
-
Features of Debt Securities
LOS 52.b: Describe the basic features of a bond, the various coupon rate
structures, and the structure of floating-rate securities.
CPA® Program Curriculum, Volume 5, page 295
A6% (option-free)
bond
iyears
s the from
simplesttodaycase.in Consider
a Treasury
bondThisthatbondhas ias a
and
fi
v
e
the
amount
of
$1,000.
promise
. Treasury)
of thefrom$1,0today.
00
(i.e., $60)
each yearbyforthefive years(theandU.toSrepay
the $1,to0pay
00 fi6%ve years
Wi
t
h
Treasury
bonds
and
almost
all
U.
S
.
corporate
bonds,
the
annual
interest
is
paid
in(onetwoevery
semiannual
installments.
Therefore,
this bondof wi$1,ll0make
nineparcoupon
payments
si
x
months)
of
$30
and
a
fi
n
al
payment
30
(the
value
pl
us thethe final
coupon
payment)
at
the
end
of
five
years.
This
stream
of
payments
is
fixed
when
bonds are issued and does not change over the life of the bond.
Note
that aseachan semiannual
coupon
is one-half
thewhicoupon
rate (whichcalled
is alwtheays
expressed
annual
rate)
ti
m
es
the
par
value,
c
h
i
s
sometimes
or payment of $4,An0008%every
Treasury
note wiandth aafacefinalvalpayment
ue of $100,
000 wi000ll make
amaturity.
coupon
six months
of $104,
at
AotherU.Scurrenci
. Treasuryes bond
is The
denominated (of course) in U.S.of adollars.
BondsbycanthebeMexican
issued in
as
well.
bond
issued
government
kely be Mexican pesos. Bonds can be issued that promise to make
payments in wianyll licurrency.
straight
coupon
matures
issuer
par value
foce
value
maturity value.
currency denomination
Coupon Rate Structures: Zero-Coupon Bonds, Step-Up Notes, Deferred­
Coupon Bonds
arenterestbondsresults
thatfrom
do notthepayfactperiodic
interest. They
payaretheinitially
par value
atsoldmaturi
t
y
and
the
i
that
zero-coupon
bonds
at a pricewe below
(i.e., theywitharenosoldexpliat caitsignifi
Sometimes
will calparl debtvaluesecurities
interestcantpayments
at a specified rate. The increase
may take placehave
one orcoupon
more rates
timesthatduringincrease
the lifover
e oftithemeissue.
carry
coupons,accrue,
but atthea initial
couponrate,payments
aredeferral
deferredperiodfor
some
period.
The
coupon
payments
compound
over
the
andpassed,
are paidthese
as a lump
sum
atregulthearendcoupon
of thatinterest
period.forAfter
the initial
deferment
period
has
bonds
pay
the
rest
of
the
l
i
f
e
of
the
issue
(to maturity).
Zero-coupon bonds
discount to par value) .
pure discount
securities.
Step-up notes
Deferred-coupon bonds
Page 12
©2012 Kaplan, Inc.
Study Session 1 5
Cross-Reference to CFA Institute Assigned Reading #52 - Features of Debt Securities
Floating-Rate Securities
svary
c r based
i s areonbonds
forewhich
the rate
coupon
interest
payments
over
the life
ofinterest
the security
a
specifi
d
i
n
terest
or
i
n
dex.
For
example,
if
market
rateshave
are movi
ng up,thatthearecoupons
on straight(normally
floaters willeveryrise3,as6,wellor. 12In months)
essence,
these
bonds
coupons
reset
periodically
based on prevailing market interest rates.
The
mostchcommon
procedure
for setting
the, thecoupon
rates
on U.floSating-rate
securities
is
one
whi
starts
wi
t
h
a
(e.
g
.
rate
on
certain
.
Treasury
securities
or the London
Interbank
Offeredrate.RateThe[LIBOR])
and
thenn mayaddsalsoor vary
subtracts
atimstated
to
or
from
that
reference
quoted
margi
over
e
according
to a scheduleThus,
that istostated
ascoupon
the formula:
find thein thenewindenture.
coupon rate,Theyouschedul
woulde isuseoftenthe referred
followintog
new coupon rate reference rate quoted margin
Just
th a fixed-coupon bond, a semiannual coupon payment will be one-half the
(annualas wi) coupon
is aratefloating-rate
securityinterest
with a coupon
formulaandthatviactuall
yA
icoupon
ncreasesformul
the coupon
when
a
reference
rate
decreases,
c
e
versa.
a such as coupon rate = 12% - reference rate accomplishes this.
Some
fl
o
ating-rate
securities
have
coupon
formulas
based
on
infl
a
tion
and
are
referred
bond with
a coupon
of 3%security.
annual change in
theto asConsumer Price Index is anAexampl
e of such
an inflformula
ation-linked
The
parties toratethebybondplacing
contract
canandlimloitwertheilimits
r exposure
tocoupon
extremerate.fluctuations
in
thelimit,reference
upper
on
the
The
upper
whi
c
h
is
called
a
puts
a
maximum
on
the
interest
rate
paid
by
the
borrower/
issuer. Thepayments
lower limit,
callbyed thea lender/security
puts a minimum
onWhen
the periodic
coupon
interest
received
owner.
both
limits
are present
simultaneously, the combination is called a
Consider
a
fl
o
ati
n
g-rate
security
(fl
o
ater)
with
a
coupon
rate
at
issuance
of
5%,
a
7%
cap, theandborrower
a 3% floor.wilIfl paythe (lender
coupon will
ratereceive)
(referenceonlyrate7%plusfortheas long
margin)
risescoupon
aboverate,
7%,
as
the
accordingwilto lthepayformula,
remains
attheor above
7%.rate,If according
the coupontoratethe falls
belowremains
3%, the
borrower
3%
for
as
long
as
coupon
formula,
at or below 3%.
Floating-rate e
u
it e
reference rate
margin
coupon formula.
±
=
rate.
An inverse floater
+
inflation-indexed bonds.
cap,
floor,
collar.
©20 12 Kaplan, Inc.
Page 1 3
Study Session 1 5
Cross-Reference to CFA Institute Assigned Reading #52
-
Features of Debt Securities
LOS 52.c: Define accrued interest, full price, and clean price.
CFA® Program Curriculum, Volume 5, page 301
When
bondthetrades
between
coupon
dates,
thetheselldate
er is ofentitltheedsale.to recei
vies any
interest
earned afrom
previous
coupon
date
through
This
known
as
and isofantheamount
that
is payable
byof thethe next
buyercoupon
(new owner)
of and
the will
bond.
The
new
owner
bond
wi
l
l
recei
v
e
all
payment
then
recover
any
accrued
i
n
terest
pai
d
on
the
date
of
purchase.
The
accrued
i
n
terest
i
s
calculated as the fraction of the coupon period that has passed times the coupon.
InthethebondUnited
States,
the
convention
i
s
for
the
bond
buyer
to
pay
any
accrued
interest
to
sel(theler. The amountplusthatanytheaccrued
buyer pays
to theIn selthelerUnited
is the agreed-upon
price
of
the
bond
interest.
States,
bonds
trade
withethright
the next
coupon
attached,is said
whictoh beis termed
A bond
traded
without
to
the
next
coupon
trading
The
total
amount
paid,
including
known as the
of the bond. The full
price = cleanaccrued
price interest,
accruedis interest.
If the issuertheof thebondbondwillistrade
in default
., has notinterest,
made periodic
coupon
payments),
without(i.eaccrued
and it is obligatory
said to be tradingflat.
accrued interest
clean price)
cum coupon.
ex-coupon.
+
full (or dirty) price
LOS 52.d: Explain the provisions for redemption and retirement of bonds.
CFA® Program Curriculum, Volume 5, page 301
The
redemptiontheprovisions
circumstances
principal forwillabebondrepaid.refer to how, when, and under what
Coupon
Treasury
bonds
andatmostwhichcorporate
bonds
arepar or face value isthat
is, they
pay
onl
y
interest
until
maturity,
ti
m
e
the
enti
r
e
repaid.
This
repayment
structure
is referred
toprincipal
as a be repaidor through a series Alternati
vely,over
the
bond
terms
may
specify
that
the
of
payments
time
or
al
l
at
once
prior
to
maturity,
at
the
option
of
ei
t
her
the
bondholder
or
the
issuer
(putable and callable bonds).
make
periodic
payments
over
the
life
of
the
bond.
A conventional
mortgageconsists
is anofexampl
e of an interest
amortizingpayment
loan; theandpayments
are
allof aequal,
and
each
payment
the
periodic
the
repayment
portion
of
the
original
principal.
For
a
fully
amortizing
loan,
the
fi
n
al
(l
e
vel)
payment
automobileat maturity
loan). retires the last remaining principal on the loan (e.g., a typical
options
giThese
ve theoptions
issuer/borrower
theinrimortgages
ght to accelerate
the principal
repayment
on
a
loan.
are
present
and
other
amortizing
loans.
Amorti
z
i
n
g
loans
require
a
series
of
equal
payments
that
cover
the
periodic
i
n
terest
and
reduce
the
outstanding
principal
each
ti
m
e
a
payment
is
made.
When
a
person
gets
a
home
or anIfautomobile
any thetime,
in wholemortgage
or in part.
the borrowerloan,sellsshetheoften
homehasor theauto,rightshetois prepay
requiredittoat pay
nonamortizing;
bullet bond
Amortizing securities
interest and principal
Prepayment
Page 14
bullet maturity.
©2012 Kaplan, Inc.
Study Session 1 5
Cross-Reference to CFA Institute Assigned Reading #52 - Features of Debt Securities
loan off in full. Thesecurity
signifiicsance
oftherea prepayment
option
to an investor
in acashmortgage
or
mortgage-backed
that
i
s
additional
uncertainty
about
the
fl
o
ws
to
be received compared to a security that does not permit prepayment.
Call
provisions
give
the
issuer
the
ri
g
ht
(but
not
the
obligation)
to
retire
all
or
a
part
of
an issue prior
tobonds
maturity.
If thecallbonds
are called,thethebonds
bondholders
have
no choice
buttheyto
surrender
their
for
the
pri
c
e
because
qui
t
payi
n
g
interest
when
arecoupon
called.bonds
Callwifeatures
give the issuer
th lower-coupon
issues.the opportunity to replace higher-than-market
Typical
l
y,
there
is
a
period
of
years
after
issuance
during
whi
c
h
the
bonds
cannot
be
called.a This
is termed
the period
ofthe period (if any)because
thel protection
bondholderhas ispassed,
protected
from
call
over
this
period.
After
of
cal
the
bonds are referred to as
There mayly,bewhen
severala bond
call dates
specionfiedtheinfitherst indenture,
each
with athelowercall calpricel price.
Customari
is
called
permissible
call
date,
is
above
theoverpartime
value.accordi
If thenbonds
areschedule.
not calForled example,
entirely ora notcall called
at all,maythespecifY
call price
decl
i
nes
g
to
a
schedule
that
acall20-year
bond
can
be
call
e
d
after
fi
v
e
years
at
a
pri
c
e
of
110
(110%
of
par),
wi
t
h
the
price declining to 105 after ten years and 100 in the 15th year.
Nonrefundable
bondsThus,prohibit
themaycallbeofcallan aisblsuee butusinnotg therefundable.
proceeds from
a lothat
wer is
coupon bondhasissue.
a
bond
A
bond
absolute
priorother
to maturi
y. In contrast, a callable
but
bond protection
can be calledagaifornstanya callreason
than trefunding.
When
bondsbondsarearecalledsaidthrough
a call optionIf a orlowerthrough
theissue
provisions
oftoaprovide
sinkingthe
fund,
the
to
be
redeemed.
coupon
i
s
sol
d
funds to call the bonds, the bonds are said to be refunded.
Sinking
fund
provisions
provi
d
e
for
the
repayment
of
principal
through
a
series
of
payments
overmaythe requi
life ofrethethatissue.
For example,
a 20-miyllion
ear issue
wiprincipal
th a face amount
of
$300
million
the
issuer
reti
r
e
$20
of
the
every
year
beginning in the sixth year. This can be accomplished in one of two
or
The
issuer
may
deposit
the
required
cash
amount
annually
with
the
issue's trustee
whong wia selection
ll then retimethod
re the such
applicable
proportion
of bondssele(1/15
inthethis
example)
by
usi
as
a
l
o
ttery.
The
bonds
cted
by
trustee are typically retired
at
par.
The
issuerred may
purchase
bonds
with aandtotaldeliparvervalue
equal
to
thetrusteeamount
that
i
s
to
be
reti
i
n
that
year
i
n
the
market
them
to
the
who will retire them.
Ifis thethe less
bondsexpensive
are tradialntgernative.
below parIf thevalue,bondsdelivery
of
bonds
purchased
i
n
the
open
market
ares thetrading
above thewaypartovalue,
deliveri
ng
cash
to
the
trustee
to
reti
r
e
the
bonds
at
par
i
less
expensive
satisfY
the
sinking fund requirement.
call protection
currently callable.
noncallable
nonrefundable
ways-cash
delivery:
•
Cash payment.
•
Delivery ofsecurities.
©20 12 Kaplan, Inc.
Page 1 5
Study Session 1 5
Cross-Reference to CFA Institute Assigned Reading #52
-
Features of Debt Securities
Anthanaccelerated
sinking
fundspecifi
provision
allosinki
ws theng issuer
the choice ofAsretianringexample,
more
the
amount
of
bonds
e
d
in
the
fund
requirement.
thechooseissuerto retire
may beuprequired
to
redeem
$5
million
par
val
u
e
of
bonds
each
year
but
may
to $10 million par value of the issue.
Regular and Special Redemption Prices
When
bonds
are asredeemed
under the callandprovisions
specifi
eared inreferred
the bondto asindenture,
these
are
known
regular
redemptions,
the
call
prices
regular
redemption
prices.
However,of awhen
bondssalearemandated
redeemedbytogovernment
comply withauthority,
a sinkingthe
fund
provisi
o
n
or
because
property
redemption
prices
(typically
par
value)
are
referred
to
as
special
redemption
prices.
Asset
sales
maybybeantitrust
forced byauthori
a regultieastoryor through
authoritya governmental
(e.g., the forcedunit'divesti
thtureofofeminent
an operating
divi
s
ion
s
ri
g
domain).
Exampl
essalofe sales
forced through
theforgovernment'
selright
ofutilieminent
domain
woul
d
be
a
forced
of
privately
held
land
erection
of
e
ctric
t
y
lines
or
for
construction of a freeway.
LOS 52.e: Identify common options embedded in a bond issue, explain the
importance of embedded options, and identify whether an option benefits the
issuer or the bondholder.
CPA® Program Curriculum, Volume 5, page 302
The
fol
l
o
wing
are
exampl
e
s
of
embedded
i
n
the
sense
that
they
are
anoptions
integralare part
of the bond
contract
andtheareissuer
not aofseparate
securiandty.some
Someareembedded
exercisable
at
the
option
of
the
bond,
exercisable
at the option of the purchaser of the bond.
Security
ownerty options.
In thegranted
following
cases,
the option
embedded
ingithevesfiadditional
xed­
income
securi
is
an
option
to
the
security
holder
(lender)
and
value to the security, compared to an otherwise-identical straight (option-free) security.
embedded options,
grants shares
the holder
of
a
bond
the
right
to
convert
the
bond
i
n
to
a
1. Afixed number of common
ofis thesimilar
issuer.butThisallowschoice/option
hasthevaluebondforintothe a
bondhol
d
er.
An
exchange
option
conversion
of
security other than the common stock of the issuer.
2. specified pricegipriveobondholders
the
ri
g
ht
to
sell
(put)
the
bond
to
the
issuer
at
a
rortoclose
maturito tpar.y. TheIf interest
put priceratesis generally
parand/or
ifthethebonds were
original
l
y
issued
at
have
ri
s
en
creditworthiness
of thetheissuer
has deteriorated
so that
the market
priceoption
of suchandbonds
has
fall
e
n
below
par,
bondholder
may
choose
to
exerci
s
e
the
put
require the issuer to redeem the bonds at the put price.
3. couponsetratea minimum
on theeachcoupon
ratebasedforona floating-rate
bond,usually
a bonda short-term
with a
that
changes
period
a
reference
rate,
rate such as LIBOR or the T-bill rate.
conversion option
Put provisions
Floors
Page 16
©2012 Kaplan, Inc.
Study Session 1 5
Cross-Reference to CFA Institute Assigned Reading #52 - Features of Debt Securities
Security
issuerof the
options.
Inincome
these security.
cases, theSecurities
embeddedwhere
optiontheisissuer
exercisabl
e atwhether
the option
ofto theexercise
issuer
fi
x
ed
chooses
the
embedded
option
wi
l
l
be
priced
less
(or
wi
t
h
a
hi
g
her
coupon)
than
otherwise identical securities that do not contain such an option.
1. maturity. The detai
give lthes ofbond
ht to redeem
a callissuer
featurethearerigcovered
later in(paythisoff)topithec reviissueew.prior to
2. by mortgages or carareloans.included
in many amortizing
securities,
such as thosethebacked
A
prepayment
option
gi
v
es
the
borrower/issuer
riLoans
ght to
prepay
the
loan
bal
a
nce
pri
o
r
to
maturi
t
y,
i
n
whole
or
i
n
part,
wi
t
hout
penal
t
y.
may bein prepaid
of a mortgage
drop
interest forratesa vari
or theetysalofereasons,
of a homesuchprioras theto itsrefinancing
loan maturity
date. due to a
are proportion
embedded options
heldthan
by theis required
issuer thatbyalthelow
thesinkiissuer
to
(annually)
reti
r
e
a
l
a
rger
of
the
issue
ng fund provision, up to a specified limit.
setrate
a maximum
on theeachcoupon
ratebasedfor ona floaating-rate
bond,usually
a bonda wishort-term
th a
coupon
that
changes
period
reference
rate,
rate such as LIBOR or the T-hill rate.
Callprovisions
Prepayment options
3. Accelerated sinkingfundprovisions
4.
Caps
Professor's Note: Caps andfloors do not need to be "exercised" by the issuer or
bondholder. They are considered embedded options because a cap is equivalent
to a series of interest rate call options and a floor is equivalent to a series of
interest rate put options. This will be explained further in our topic review of
Option Markets and Contracts in the Study Session covering derivatives.
Toto calsummarize,
the(2)follanoaccel
wingerated
embedded
options
favor the issuer/borrower:
(1)option,
the rightand
l
the
issue,
si
n
king
fund
provision,
a
prepayment
(4)borrower/issuer.
a cap on the floating
coupon
rate
that
limi
t
s
the
amount
of
interest
payable
by
the
theseumoptions
higher option-free
market yieldbonds.
s since
bondholders willBonds
requirewitha premi
relativewitoll tend
otherwito have
se identical
The
ng embedded
options
favorinterest
the payment to theconversion
provisions,
(2) aafolflputolorowioption.
that
guarantees
a
minimum
bondholder,
andbe lower
The
market
yields
on
bonds
with
these
options
will
tend
to
than
attractiotherwise
ve. identical option-free bonds since bondholders will find these options
(3)
bondholders: (1)
(3)
LOS 52.f: Describe methods used by institutional investors in the bond market
to finance the purchase of a security (i.e., margin buying and repurchase
agreements).
CFA® Program Curriculum, Volume 5, page 308
Marginthebuying
involves
borrowing
fundscollateral
from aforbroker
or a bankloan.to purchase
securities
where
securities
themsel
v
es
are
the
the
margin
The
margi
n
amount
(percentage
of
the
bonds'
val
u
e)
i
s
regulated
by
the
Federal
Reserve
i
n
the
United States, under the Securities and Exchange Act of
1934.
©20 12 Kaplan, Inc.
Page 17
Study Session 1 5
Cross-Reference to CFA Institute Assigned Reading #52
-
Features of Debt Securities
(repo) toagreement
is anat arrangement
bya whi
cheand (higher)
institutionprice.sellsThea security
wiA repurchase
th a commitment
buy
it
back
a
l
a
ter
date
at
specifi
is
greater
than
the
sell
i
ng
price
and
accounts
for
the
interest
charged
by
the buyer,
who
is, intheeffect, lendingwhifunds
to theannuali
sellezr.edThepercentage
interest ratedifference
impliedbetween
by the
two
prices
i
s
called
c
h
i
s
the
theagreement
two prices.
A
repurchase
agreement
for
one
day
is
called
an
and
an
a wouldThe
customarilycovering
less thana thelongerrateperiod
a bankisorcalled
brokerage
chargeinterest
on a cost
margiofn aloan. is
Most bond-dealer
financing
is achieagreements
ved througharerepurchase
agreements
rather than
through
margin
loans.
Repurchase
not
regulated
by
the
Federal
Reserve,
and
the
collateral
position
of
the
lender/buyer
in
a
repo
is
better
i
n
the
event
of
bankruptcy
ofn totheselldealiteback
r, sinceat thethe price
securityspecifi
is owned
by therepurchase
lender. The
lender hasratheronly
the
obligati
o
e
d
i
n
the
agreement,
than simply having a claim against the assets of the dealer for the margin loan amount.
repurchase price
repo rate,
overnight repo,
term repo.
Page 18
©2012 Kaplan, Inc.
repo
Study Session 1 5
Cross-Reference to CFA Institute Assigned Reading #52 - Features of Debt Securities
KEY CONCEPTS
ALOS
bond'ors buyer
indenture
contains the obligations, rights, and any options available to the
issuer
of a bond.
Covenants
arevethecovenants
specific specify
conditionsactionsof thethatobligation:
Affi
r
mati
the
borrower/issuer
must
perform.
Negative covenants prohibit certain actions by the borrower/issuer.
LOS have the following features:
Bonds
Maturity-the
term of the loan
agreement.
Par
value
(
f
ace
value)-the
principal
amount
of
the
fi
x
ed
income
security
that
the
bond
issuerrate-the
promisesratetoused
pay theto determine
bondholdersthe over
the liinterest
fe of thetobond.
Coupon
periodic
be paid on onthethe
principal
amount.
Interest
can
be
pai
d
annually
or
semiannual
l
y
,
depending
terms. Coupon rates may be fixed or variable.
TypesOption-free
of coupon (straight)
rate structures:
bonds pay periodic interest and repay the par value at
maturi
t
y.
Zero-coupon
bonds
pay
no
expli
c
it
periodic
interest
and
are
sold
at
a
discount
to
par
value.
Step-up notes have a coupon rate that increases over time according to a specified
schedule.
Deferred-coupon
bonds
initialof thely make
no coupon
payments
(they(compound)
are deferredinterest
for a
period
of
time).
At
the
end
deferral
period,
the
accrued
s flpaid,
makehasregul
ar coupon
payments
unti
l maturity.
Ai(usually
oatingandLIBOR)
(varitheabonds
ble)andrateathen
bond
a
coupon
formula
that
i
s
based
on
a
reference
rate
quoted
margin.coupon
A caprateis athemaxibondholder
mum coupon
rate
theve onissuerany
must
pay,
and
a
fl
o
or
i
s
a
minimum
will
recei
coupon date.
LOS
Accrued
interestto aisbond
the interest
a bond buyer
seller. earned since the last coupon payment date and is paid by
Clean price is the quoted price of the bond without accrued interest.
Full price refers to the quoted price plus any accrued interest.
52.a
•
•
52.b
•
•
•
•
•
•
•
•
52.c
©20 12 Kaplan, Inc.
Page 1 9
Study Session 1 5
Cross-Reference to CFA Institute Assigned Reading #52
-
Features of Debt Securities
LOS
52.d
BondAmortizing
retirementsecurities
(payoff) make
provisions:
periodic
payments
that
include
both
interest
and
principal
paymentsoccurs.
so that the entire principal is paid off with the last payment
unless
prepayment
Ato prepayment
option
is
contained
in
some
amortizing
debt
and
allows
the
borrower
pay offfundprincipal
at anyrequire
time prior
topartmaturity,
in whole
or reti
in part.
Sinking
provisions
that
a
of
a
bond
issue
be
red at specified
dates,
typical
l
y
annuall
y
.
Cal
l
provi
s
ions
enable
the
borrower
(issuer)
to
buy
back
the
bonds
from
the
iCalnvestors
(redeem
them) at abonds
call price(s)
specifi
eprior
d in theto maturity,
bond indenture.
l
abl
e
but
nonrefundable
can
be
call
e
d
their rate.
redemption cannot be funded by the issuance of bonds with a lowerbutcoupon
LOS
52.e options that benefit the issuer reduce the bond's value (increase the yield) to
Embedded
a bondCallpurchaser.
Examples are:
provisions.
Accelerated
sinking
fund
provisions.
Caps (maximum interest rates) on floating-rate bonds.
Embedded
optionspurchaser.
that benefit
bondholders
increase the bond's value (decrease the
yield)Conversion
to a bond
Examples
are:
optisocommon
ns (the option
of bondholders to convert their bonds into shares of
thePut bond
i
s
suer'
stock).
options (theprice).
option of bondholders to return their bonds to the issuer at a
predetermined
Floors (minimum interest rates) on floating-rate bonds.
LOS
52.
f
Institutions
can
financeprice,secondary
market
bond
purchases
by) or,margi
n buying
(borrowi
ng
some
of
the
purchase
using
the
securi
t
i
e
s
as
coll
a
teral
more
commonl
y
,
by
repurchase
(repo)to agreements,
ananarrangement
inhigher
whichprice
an institution
sells date
a security
with
a
promise
buy
it
back
at
agreed-upon
at
a
specified
i
n
the
future.
•
•
•
•
•
•
•
•
•
•
•
Page 20
©2012 Kaplan, Inc.
Study Session 1 5
Cross-Reference to CFA Institute Assigned Reading #52 - Features of Debt Securities
CONCEPT CHECKERS
s indenture:
1. AA. bond'
contains
i
t
s
covenants.
the same
C.B. isrelates
onlyastoaitsdebenture.
interest and principal payments.
2. Asemiannual
bond haslya. parWhatvaluisetheof $5,dollar000amount
and a coupon
rate of 8. 5 %coupon
payablepayment?
of
the
semiannual
A.B. $238.
$212.353.0.
$425.00.
3. would
From theaddperspective
of the bondholder,
which
of the following pairs of options
value
to
a
straight
(option-free)
bond?
A.B. Put
Calloption
optionandandconversion
conversionoption.
option.
C. Prepayment option and put option.
4. Aby10-year
bond
pays
no
interest
for
three
years,
then
pays
$229.
2
5,
foll
o
wed
payments
ofs bond
$35 semiannually
for seven years and an additional $1,000 at
maturi
t
y.
Thi
i
s
a:
A.B. step-up
bond.
bond.bond.
C. zero-coupon
deferred-coupon
a $11 andmilJuly
lion semiannual-pay,
floating-raterateissue
where theLIBOR,
rate isandreset
5. Consider
ontheJanuary
1
each
year.
The
reference
is
6-month
stated
margin
is
+
1.25%.
If
6-month
LIBOR
i
s
6.5%
on
July
1,
what
wil
l
semiannual
coupon be on this issue?
A.theB. next
$38,
7
50.
$65,
0
00.
$77,500.
of thehavefollcapsowinandg statements
is
with regard to floating-rate
6. Which
issues
that
fl
o
ors?
A. AiSSUer.
cap is an advantage to the bondholder, while a floor is an advantage to the
B. AiSSUer.
floor is an advantage to the bondholder, while a cap is an advantage to the
C. Aa diflsoadvantage
or is an advantage
to
both
the
issuer
and
the
bondholder,
whi
l
e
a
cap
i
s
to both the issuer and the bondholder.
investorcoupon
paid adates,
full priandceaccrued
of $1,059.interest
04 eachwasfor$23.10054bonds.
TheWhat
purchase
was
7. Anbetween
per
bond.
is
each
bond'
s
clean
price?
A.B. $1,$1,035.
000.050.0.
$1,082.58.
c.
c.
most accurate
c.
©20 12 Kaplan, Inc.
Page 2 1
Study Session 1 5
Cross-Reference to CFA Institute Assigned Reading #52
-
Features of Debt Securities
of the following statements is
with regard to a call
8. Which
provision?
A.B. AA callable
call provision
will
benefit
the
issuer
i
n
times
of
declining
interest
rates.
bond will trade at a higher price than an identical noncallable
bond.
C. Anoncallable
nonrefundabl
e
bond
provides
more
protection
to
the
bondholder
than
a
bond.
ofy callable
the follobond?
wing
describes the maximum price for a
9. Which
currentl
A.B. The
Its parcallvalue.
C. The presentprice.value of its par value.
and
Consider
$1,are000,cal0lable
00 parandvalue,
10-year,
6.n5g%fundcoupon
bondsTheissuedmarket
on January
1,sim2005.
The
bonds
there
i
s
a
sinki
provision.
rate
for
bonds is currently 5.7%. The main points of the prospectus are summarized as follows:ilar
Call dates and prices:
2005
through 1,2009:
After January
2010:103.102.
Additional information:
The
bonds
are
non-refundable.
The
sinkingamount
fund provision
requires
that theundercompany
redeem
$100,
000 fund
of the
principal
each
year.
Bonds
called
the
terms
of
the
sinking
provision
will
be
redeemed
at
par.
The credit rating of the bonds is currently the same as at issuance.
10. A.Usingtheonlybondsthedopreceding
information,
Gould should conclude that:
not
have
call
protection.
issuedtheatbonds
and currentl
B.C. githevenbonds
currentwererates,
will likelyy trade
be calatleda premium.
and new bonds issued.
11. Which
of the following statements about the sinking fund provisions for these
bonds
is
A. Anof theinvestor
would
benefit from having his bonds called under the provision
sinking
fund.
B. Anunderinvestor
will recei
vethea premium
if the bond is redeemed prior to maturity
the
provisi
o
n
of
sinki
n
g
fund.
C. The bonds do not have an accelerated sinking fund provision.
12. AnA. investor
buying
bonds
on
margin:
interestbyongovernment
a loan. regulation of margin lending.
B.C. actually
imust
s notpayrestricted
lends the bonds to a bank or brokerage house.
most accurate
most accurately
Use the following information to answer Questions 10
•
•
•
•
•
most accurate?
Page 22
©2012 Kaplan, Inc.
11.
Study Session 1 5
Cross-Reference to CFA Institute Assigned Reading #52 - Features of Debt Securities
13. byWhich
of the following is
a provision for the early retirement of debt
the
issuer?
A.B. AA conversion
option.
C. A call
sinkingoption.
fund.
is loan.
14. A.A mortgage
a
col
l
ateralized
B.C. characterized
subject to earlbyy retirement.
highly predictable cash flows.
least likely
least likely:
©20 12 Kaplan, Inc.
Page 23
Study Session 1 5
Cross-Reference to CFA Institute Assigned Reading #52 - Features of Debt Securities
ANSWERS - CONCEPT CHECKERS
1.
A
An indenture is the contract between the company and its bondholders and contains the
bond's covenants.
2.
A
The annual interest is 8.5% of the $5,000 par value, or $425. Each semiannual payment
is one-half of that, or $212.50.
3.
B
A put option and a conversion option have positive value to the bondholder. The other
options favor the issuer and result in a lower value than a straight bond.
4.
C
This pattern describes a deferred-coupon bond. The first payment of $229.25 is the
value of the accrued coupon payments for the first three years.
5.
A
The coupon rate is 6.5 + 1 .25 7.75. The semiannual coupon payment equals
(0.5)(0.0775)($1 ,000,000) $38,750.
=
=
6.
B
A cap is a maximum on the coupon rate and is advantageous to the issuer. A floor is a
minimum on the coupon rate and is, therefore, advantageous to the bondholder.
7.
B
The full price includes accrued interest, while the clean price does not. Therefore, the
clean price is 1 ,059.04 - 23.54 $ 1 ,035.50.
=
Page 24
8.
A
A call provision gives the bond issuer the right to call the bond at a price specified in the
bond indenture. A bond issuer may want to call a bond if interest rates have decreased so
that borrowing costs can be decreased by replacing the bond with a lower coupon issue.
9.
B
Whenever the price of the bond increases above the strike price stipulated on the call
option, it will be optimal for the issuer to call the bond. So theoretically, the price of a
currently callable bond should never rise above its call price.
10. A
The bonds are callable in 2005, indicating that there is no period of call protection.
We have no information about the pricing of the bonds at issuance. The company may
not refond the bonds (i.e., they cannot call the bonds with the proceeds of a new debt
offering at the currently lower market yield) .
11. C
The sinking fund provision does not provide for an acceleration of the sinking fund
redemptions. With rates currently below the coupon rate, the bonds will be trading at a
premium to par value. Thus, a sinking fund call at par would not benefit a bondholder.
12. A
Margin loans require the payment of interest, and the rate is typically higher than
funding costs when repurchase agreements are used.
13. A
A conversion option allows bondholders to exchange their bonds for common stock. The
option is held by the boldholder, not the issuer.
14. C
A mortgage can typically be retired early in whole or in part (a prepayment option), and
this makes the cash flows difficult to predict with any accuracy.
©2012 Kaplan, Inc.
The following is a review of the Analysis of Fixed Income Investments principles designed to address the
learning outcome statements set forth by CFA Institute. This topic is also covered in:
RISKS ASSOCIATED WITH
INVESTING IN B ONDS
Study Session 1 5
EXAM FOCUS
This
topic
review
introduces
variousThesources
of here
risk that
investors "areTheexposed
to when
investi
n
g
i
n
fi
x
ed
income
securities.
key
word
i
s
"introduces.
most
important
source
interest rateafterrisk,thehasmaterial
its ownonfullthetopic
reviewofinfixedStudyincome
Sessionsecurities.
16 and
iPrepayment
s moreoffulrisk,
lyriskdeveloped
valuation
has
i
t
s
own
topic
review
at
Level
II,
and
credit
risk
and
reinvestment
risk
revisitedsome
to a significant
extent in other
partsriskofmeasures
the LevelandI curriculum.
In factors
this revithat
ew,
wearewillpresent
worki
n
g
definitions
of
the
identify
the
affect
theseassured
risks.thatTo your
avoidunderstanding
unnecessary repetition,
some ofwilthel bemateri
aleteis abbreviated
here,
but
be
of
this
material
compl
by
the
time
you work through this Study Session and the one that follows.
LOS 53.a: Explain the risks associated with investing in bonds.
CFA® Program Curriculum, Volume 5, page 320
refers interest
to the effect
ofrischanges
in uthees prevaili
ngismarket
rate ofof interest
interest
onratebond
values.
When
rates
e,
bond
val
fall.
This
the
source
risk which is approximated by a measure called
Yield
arirelati
ses from
the possibility
of changes
in the shape
of duration
the yield curve
(whi
c
h
shows
the
o
n
between
bond
yields
and
maturity).
While
is achanges
useful
measure
of
i
n
terest
rate
risk
for
equal
changes
in
yi
e
ld
at
every
maturi
t
y
(paral
l
el
indifferent
the yieldamounts
curve),forchanges
in
the
shape
of
the
yiel
d
curve
mean
that
yields
change
by
bonds with different maturities.
arises
fromreturned
the factandthatmustwhenbe reinvested
interest ratesat thefall,new
a callable
bond
investor'
s
principal
may
be
lower
rates.
Certainly
bonds thatratesarearenotmorecallavolatile,
ble havecallnoacall
risk, andhavecalrell protecti
omore
n reduces
calsk lbecause
risk. When
interest
ble
bonds
a
ti
v
ely
cal
l
ri
of
an
increased probability of yields falling to a level where the bonds will be called.
ions similar
to calllorisk.
Prepayments
areaprincipal
repayments
in excess
ofprepayments
those required
amortizing
ans,
such
as
residenti
l
mortgages.
If
rates
fall,
causing
to
increase,
an
investor
must
rei
n
vest
these
prepayments
at
the
new
l
rate. Just as with call risk, an increase in interest rate volatility increases prepaymentowerrisk.
refers
to
the
fact
that
when
market
rates
fall,
the
cash
fl
o
ws
(both
interest and principal) from fixed-income securities must be reinvested at lower rates,
Interest rate risk
duration.
curve risk
Call risk
Prepayment risk
Reinvestment risk
©20 12 Kaplan, Inc.
Page 25
Study Session 1 5
Cross-Reference to CFA Institute Assigned Reading #53
-
Risks Associated With Investing in Bonds
reducing
the returns anrisk.investor
wiofll these
earn. Note
that
reinvestment
risk ofis related
to cash
call
rifloskwsandat lprepayment
In
both
cases,
it
is
the
reinvestment
principal
o
wer
rates
than
were
expected
that
negati
v
ely
i
m
pacts
the
investor.
Coupon
bonds
that contain
neitherthecallcoupon
nor prepayment
provisionsmustwillbealsoreibenvested
subjectas tothey are
reinvestment
risk,
because
interest
payments
received.
that investors
can be faced
wihasthnoa choice
betweenrisreik novervestment
riskbecause
and price
risk.
ANote
noncallable
zero-coupon
bond
rei
n
vestment
its
life
there
are
nointerest
cash rate
flowsriskto reithannvest,a coupon
but a zero-coupon
bondmaturity.
(as we wilTherefore,
l cover shortly)
has morebond
bond
of
the
same
the
coupon
will have more reinvestment risk and less price risk.
risk that
the creditworthiness
of a fixed-income
s issuer will
deteriorate, iisnthecreasing
the requi
red return and decreasing
the securisecurity'
ty's value.
has
to
do
wi
t
h
the
ri
s
k
that
the
sale
of
a
fi
x
ed-income
security
must
be
made Treasury
at a pricebonds
less thanhavefaiexcellent
r market livalue
because
of a lack
ofmillion
liquiditydollars
for a worth
particular
issue.
q
uidity,
so
selling
a
few
atof
thethe prevailing
market
price
can
be
easily
and
quickly
accomplished.
At
the
other
end
liquidity
spectrum,
a
valuabl
e
painting,
collectible
anti
q
ue
automobile,
or
unique
and
expensiprefer
ve home
may
be quiteto less,
difficult
to selliquickly
at fais rliquidity
-market value.
Since its
investors
more
l
i
quidity
a
decrease
n
a
security'
will
decrease
price, as the required yield will be higher.
arises
fromofthehis uncertainty
aboutcurrency.
the valueWhileof foreign
currency bicashll
fl(T-bill)
ows to may
an investor
in
terms
home-country
a
U.S.
Treasury
be considered
quite linvestor
ow risk orwileven
risk-freebyto aa depreciation
U.S.-based investor,
the
valU.Su.e dolof lthear'sT-bill
to
a
European
l
be
reduced
of
the
value relative to the euro.
mipurchasing-power
ght be better described
as a $10,000inflzero-coupon
ation risk andTreasury
even morebond
descri
p
ti
v
ely
as
risk.
While
can
provide
a payment
of $10,and000services
in thethatfuture$10,wi0t00h near
certaiatnty,thethere
is date.
uncertainty
about
the
amount
of
goods
wil
l
buy
future
This
uncertai
n
ty
about
the
amount
of
goods
and
services
that
a
security'
s
cash
fl
o
ws
wi
ll
purchase is referred to here as inflation risk.
i
s
present
for
fi
x
ed-income
securities
that
have
embedded
options,
such
as calltheoptions,
prepayment
options,
orthus,putaffect
options.the Changes
isecurities
n interest wirateth volembedded
atility
affect
val
u
e
of
these
options
and,
val
u
es
of
options.
encompasses
outside takeovers.
the risks of financial markets, such as the risks
posed by natural
disasterstheandriskscorporate
the credit risk of a sovereign bond issued by a country other
than the investor'is essentially
s home country.
Credit risk
Liquidity risk
Exchange-rate risk
Inflation risk
unexpected
Volatility risk
Event risk
Sovereign risk
Page 26
©2012 Kaplan, Inc.
Study Session 1 5
Cross-Reference to CFA Institute Assigned Reading #53 - Risks Associated With Investing in Bonds
LOS 53.b: Identify the relations among a bond's coupon rate, the yield
required by the market, and the bond's price relative to par value (i.e.,
discount, premium, or equal to par).
CFA® Program Curriculum, Volume 5, page 320
When
coupon
on a thebondcoupon
is equalratetoonitsbonds
marketisyitypicall
eld, they setbondat orwilnear
l tradetheat
iprevail
ts itheng market
Whenyirateeissued,
ld
on
similar
bonds
so
that
the
bonds
trade
initially
at
or
near
their
par
Ifwithell yifalelldandrequired
intradethe atmarket
for thetobond
subsequently
rises,Thetherequi
pricered
ofyieldthevalue.
bond
i
t
will
a
(below)
its
par
value.
cantoincrease
becausefor theinterest
rates
havehasincreased,
because
the theextrarisyiel
dtheinvestors
require
compensate
bond'
s
risk
increased,
or
because
k
of
bond
has increased
was issued.
the bond price
will
increase andsincetheit bond
will tradeConversel
at a y, if the required
to (above)yieldits parfalls,value.
The relation is illustrated in Figure 1.
1:
8%
par value.
discount
premium
Figure
Market Yield vs. Bond Value for an
Coupon Bond
Bond
Value
Premium
to Par
Par Value
I
- - - - - -------------------
�
-------------------
------------------
Discount to Par
'------''- Market
Yield
7%
6%
8%
9%
10%
Professor's Note: This is a crucial concept and the reasons underlying this
relation will be clear after you cover the material on bond valuation methods in
the next Study Session.
LOS 53.c: Explain how a bond maturity, coupon, embedded options and yield
level affect its interest rate risk.
CFA® Program Curriculum, Volume 5, page 322
Interest
rate
risk,
as
we
are
using
i
t
here,
refers
to
the
sensitivity
of
a
bond'
s
value
to
changes
n market
interestprirates/yields.
thereprices
is an inverse
between iyield
and bond
ces-when yiRemember
elds increase,thatbond
decrease.relationship
The term we
©20 12 Kaplan, Inc.
Page 27
Study Session 1 5
Cross-Reference to CFA Institute Assigned Reading #53
-
Risks Associated With Investing in Bonds
interestfor rate
is in yield.which gives us a good approximation
ofusea forbond'thes measure
change inofprice
a givenriskchange
duration,
� Professor's Note: This is a very important concept. Notice that the terms "interest
� rate risk, " "interest rate sensitivity, " and "duration" are used interchangeably.
We
s concepttobyinterest
simplyratelooking
at how a bond's maturity and coupon
affectintroduce
its price thisensitivity
changes.
If twogreater
bondsduration
are identical
except
forl havematuria greater
ty, thepercentage
one with thechange
longerinmaturity
hasa
the
because
i
t
wil
val
u
e
for
giForventwochange
in yield.identical bonds, the one with the higher coupon rate has the
otherwise
lower
gher coupon
coupon bond
rate wiwill lchange
for a giduration.
ven changeTheinprice
yieldofthanthethebondpricewitofh thethe hilower
. less
The
presence
of
embedded
options
also
affects
the
sensi
t
i
v
ity
of
a
bond'
s
value
to
interest
rate
changes
duration).
Pricesofofstraiputable
and callablebonds
bondswill.
will react differently to
changes
in yie(iltds than
the prices
ght (option-free)
Adecline;
call feature
limits
theng,upside
priceprimovement
ofriasebond
when
interest
ratesThis leads
loosely
speaki
the
bond
c
e
wi
l
l
not
above
the
call
price.
to thechanges
conclusion
that
the valueidentical
of a callable
bond wibond.
ll be less sensitive to interest
rate
than
an
otherwise
option-free
Arisput
feature
li
m
i
t
s
the
downside
price
movement
of
a
bond
when
interest
rates
e;conclusion
loosely speaking,
thevaluebondofprice
will notbondfallwibelow
thesensi
put tprice.
This
leadsrateto
thechanges
that
the
a
putable
l
l
be
less
i
v
e
to
i
n
terest
than an otherwise identical option-free bond.
The relations we have developed so far are summarized in Figure 2.
•
•
•
•
Figure 2: Bond Characteristics and Interest Rate Risk
Characteristic
Interest Rate Risk
Duration
Maturity up
Interest rate risk up
Duration up
Coupon up
Interest rate risk down
Duration down
Add a call
Interest rate risk down
Duration down
Add a put
Interest rate risk down
Duration down
Professor's Note: We have examined several factors that affect interest rate risk,
but only maturity is positively related to interest rate risk (longer maturity,
higher duration). To remember this, note that the words "maturity" and
"duration" both have to do with time. The other factors, coupon rate, yield,
and the presence ofputs and calls, are all negatively related to interest rate risk
(duration). Higher coupons, higher yields, and embedded options all decrease
interest rate sensitivity (duration).
Page 28
©2012 Kaplan, Inc.
Study Session 1 5
Cross-Reference to CFA Institute Assigned Reading #53 - Risks Associated With Investing in Bonds
LOS 53.d: Identify the relation of the price of a callable bond to the price of an
option-free bond and the price of the embedded call option.
CFA® Program Curriculum, Volume 5, page 322
Asbondwe relati
notedveearlto ianer,otherwise
a call optionidentical
favorsoption-free
the issuer andbond.decreases
the
value
of
a
call
a
bl
e
The
issuer anownsoption-free
the call. bond
Essentiall
y
,
when
you
purchase
a
callable
bond,
you
have
purchased
but
en a call option
ssuer. Theequalvalueto ofthethevalcaluelable
less than the
valuhave
e of angivoption-free
bondtobythean iamount
of thebondcall isoption.
This relation can be shown as:
callable bond value = value of option-free bond - value of embedded call option
Figure
shows
thisfalls,relationship.
Theinvalue
ofbetween
the callaoption
is bond
greaterandat laocallable
wer yieldsbondso
that
as
the
yield
the
di
f
ference
price
straight
Increases.
3
Figure Price-Yield Curves for Callable and Noncallable Bonds
Pr ice
call
pnce
3:
call op rion
value �
j
t
- ��::- - - - - - - - ----
T
----
- - -
---
i
------- --�-----
,
callable bond
value
o
roo-fc" bood "'""'
L------'--
y'
Yield
LOS 53.e: Explain the interest rate risk of a Boating-rate security and why its
price may differ from par value.
CFA® Program Curriculum, Volume 5, page 324
Recalbased
l that flonoating-rate
securities havereference
a couponrate.rateThethatobjecti
floats,ve iofn that
it is periodically
reset
a
market-determined
the
resetting
mechanism
i
s
to
bring
the
coupon
rate
in
l
i
ne
wi
t
h
the
current
market
yield
so
the
bond
sells at ortonearchanges
its parinvalue.
Thisyiewill
makea fixed-coupon
the price of a bond
floating-rate
security
muchThat'lesss
sensitive
market
lds
than
of
equal
maturity.
the point of a floating-rate security, less interest rate risk.
Between
dates, there
is a timhappens
e lag between
in market
yield andthe
a change coupon
in the coupon
rate (which
on theanynextchangedate).
The longer
reset
©20 12 Kaplan, Inc.
Page 29
Study Session 1 5
Cross-Reference to CFA Institute Assigned Reading #53
-
Risks Associated With Investing in Bonds
tiflmuctuation.
e period between
thewetwocandates,
the thegreater
the (shorter)
amount ofthepotential
bondthepricegreater
In
general,
say
that
longer
reset
period,
(less) the interest rate risk of a floating-rate security at any reset date.
long
as
the
required
margin
above
the
reference
rate
exactly
compensates
for
the
bond'
s risk, thethe price
ofrate
a floating-rate
security
wilsecurity
return istovery
par atsmalleachasreset
date. date
For
this
reason,
interest
ri
s
k
of
a
fl
o
ating-rate
the
reset
approaches.
There
are presence
two primary
reasons
that a bond'
s pricerate)maycandiffer
fromtheparinterest
at its coupon
resetof
date.
The
of
a
cap
(maximum
coupon
i
n
crease
rate
risk
a floating-rate
securi
ty. If theyields
reference
rate increases
enough
thatWhen
the captheratemarket
is reached,
further
increases
i
n
market
will
decrease
the
fl
o
ater'
s
price.
yield
iextent
s abovethatits thecapped
coupon
rate,
a
fl
o
ating-rate
security
will
trade
at
a
discount.
To
the
cap
fi
x
es
the
coupon
rate
on
the
fl
o
ater,
i
t
s
price
sensitivity
to
changes
i
n
market yield will be increased. This is sometimes referred to as cap risk.
Aissuance.
floater'sConsider
price canaalsofirmdiffer
fromissued
par duefloating-rate
to the factdebtthatwith
the margi
n is fiformula
xed at of
that
has
a
coupon
LIBORty.+If2%.the This
2%credimargin
shouldimproves,
reflect thethecredit
riskisandlessliquidity
riskwilloftrade
the at
securi
fi
r
m'
s
t
worthiness
fl
o
ater
ri
s
ky
and
amarket'
premium
to rpar.ed yield
Evenpremium
if the firm'fors credi
trworthi
nkesslevelremains
constant,
a change
infltheoater
s
requi
the
fi
m'
s
ri
s
wi
l
l
cause
the
value
of
the
to differ from par.
As
LOS 53.f: Calculate and interpret the duration and dollar duration of a bond.
CPA® Program Curriculum, Volume 5, page 326
Bychanges
now you
knowSpecifical
that duration
is abemeasure
of theasprice
sensitivity of aofsecurity
to
i
n
yield.
l
y,
it
can
interpreted
an
approximation
the
change
in
the
security
price
for
a
change
in
yield.
We
can
al
s
o
interpret
duration
as
the of the percentage change in price to the change in yield in percent.
This relation is:
change in bond price
duration percentage
yield change in percent
When
calcularelated.
ting theIfdiyourection
of theapriratece decrease,
change, remember
thatshould
yieldsindicate
and prices
areincrease.
inversely
are
given
your
resul
t
a pritoceits
Also
note
that
the
durati
o
n
of
a
zero-coupon
bond
i
s
approximately
equal
years
to
maturi
t
y,
and
the
duration
of
a
fl
o
ater
i
s
equal
to
the
fraction
of
a
year
until
the
next reset date.
percentage
1%
ratio
Page 30
©2012 Kaplan, Inc.
Study Session 1 5
Cross-Reference to CFA Institute Assigned Reading #53 - Risks Associated With Investing in Bonds
Let's consider some numerical examples.
Example: Approximate price change when yields increase
Ifapproximate
a bond haspercentage
a duration change
of 5 andinthetheyield
bondincreases
price. from 7% to 8%, calculate the
Answer:
-5decreased.
1 o/o = -5%, or a 5% decrease in price. Because the yield increased, the price
x
Example: Approximate price change when yields decrease
Aapproximate
bond has apercentage
duration ofchange
7 .2. Ifithen theyielbond
d decreases
from
8.3%
to
7
.
9
%,
calculate
the
price.
Answer:
-7.2 (-0.4%) = 2. 88%. Here the yield decreased and the price increased.
x
The
formula
for
what
we
just
did
(because
duration
is
al
w
ays
expressed
as
a
positive
number and because of the negative relation between yield and price) is:
percentage price change = -duration (yield change in o/o)
Sometimes
the interest
rate risk ofprice
a bondchange
or portfoli
o isinexpressed
astoitsa dollar
duration,
whi
c
h
i
s
simply
the
approximate
in
dollars
response
change
in
yiel
d
basis points
o/o). Withthea duration
of 5.2 andas 5.a2bond
value=of$62,400.
$1.of 100
2 million,
we can(1calculate
dollar duration
% $1.market
2 million
Now let's dochange
it in reverse
and calculate
in the bond'
s price. the duration from the change in yield and the
Example: Calculating duration given a yield increase
If a bond's yield rises from 7% to 8% and its price falls 5%, calculate the duration.
Answer:
change in price -5.0% = 5
duration = percentage
+ l.Oo/o
change in yield
x
x
percentage
©20 12 Kaplan, Inc.
Page 3 1
Study Session 1 5
Cross-Reference to CFA Institute Assigned Reading #53
Example: Calculating duration given a yield decrease
Ifduration.
a bond's yield decreases by 0.1% and its price increases by 1.5%, calculate its
Answer:
change in price -- 1.5 % -1 5
duratton -- percentage
change in yield
-0.1%
.
Risks Associated With Investing in Bonds
_
_
---
_
Professor's Note: Because bond price changes for yield increases andfor yield
decreases are typically different, duration is typically calculated using an average
ofthe price changes for an increase and for a decrease in yield. In a subsequent
reading on interest rate risk we cover this calculation of "effective duration. "
Here we simply illustrate the basic concept ofduration as the approximate
percentage price change for a change in yield of I %.
Example: Calculating the new price of a bond
A8. 5bond
at $1,calculate
034.50,thehasnew
a yieldpriceof7.of3the8%,bond.
and has a duration of
. If theis currently
yield risestrading
to 7.77%,
Answer:
The change in yield is 7.77% - 7.38% = 0.39%.
The approximate price change is -8.5 0.39% = -3.315%.
Since the yield
the price will decrease by this
The new price is (1 - 0.03315) $1,034.50 = $1,000.2 1.
x
increased,
percentage.
x
LOS 53.g: Describe yield-curve risk and explain why duration does not account
for yield-curve risk.
CPA® Program Curriculum, Volume 5, page 327
The
for a portfolio
of bonds
hasinthe same interpretation
aschange
for a single
bond;
itDuration
is theduration
approximate
percentage
change
value
for
a
1%
i
n
yields.
the sensitivity of a portfolio's value to an equal change
in yield forforallatheportfoli
bondso measures
in the portfolio.
AThegraphyieldofcurve
the relationship
and yieldownward
d is knownsloping,
as a yieldflacurve.
can have anybetween
shape: maturity
upward sloping,
t, or some
portfolio
Page 32
©2012 Kaplan, Inc.
Study Session 1 5
Cross-Reference to CFA Institute Assigned Reading #53 - Risks Associated With Investing in Bonds
combination
slopes. oChanging
shapes leadbytotheyield
curvemeasure.
risk, the
interest rate riofskthese
of a portfoli
of bondsyielthatd icurve
s not captured
duration
Inincrease,
Figurea4,paral
we lilellustrate
that thelel shiyieldft. curve might shift when interest rates
shift andtwoa ways
non-paral
Figure 4: Yield Curve Shifts
Yield
�------
A non-parallel shift
Yield Curve
Maturity
The theduration
of a bondof theportfol
ioportfol
can beiocalculated
from intheeachindividual
bond durations
and
proportions
total
value
invested
of
the
bonds.
That
is,
thethe portfolio
duration
is a market-wei
ghtedchange
averagebyofthethesame
individual
bond'percent
s durations.
If
yields
on
al
l
the
bonds
in
the
portfolio
absolute
amount,
wesensiterm
parallelioshift.
Portfolioshifduration
is an curve.
approximation of the price
tivitythatof aa portfol
to parallel
ts of the yield
For
a
non-paral
l
el
shi
f
t
in
the
yield
curve,
the
yields
on
di
f
ferent
bonds
in
a
portfoli
o
byondithefferent
amounts,
and duration
alone
cannot
capture
the effectvalueof afrom
yican
echanges
ldchange
change
value
of
the
portfolio.
This
ri
s
k
of
decreases
in
portfolio
is termedinyitheeld shape
curve ofrisk.the yield curve (i.e., from non-parallel shifts in the yield curve)
Considering
the
non-parall
e
l
yiel
d
curve
shift
i
n
Figure
4,
the
yield
on
short
maturity
bonds hasinincreased
byconsequence.
a small amount,
andmaturity
they wilbonds
l havehaveexperiexperienced
enced onlya asignifi
smallcant
decrease
value
as
a
Long
increase in yieldofandthesisensitivity
gnificant decreases
in value
as a result.
Duration
can beeal shifts
poor in
approximation
of
the
value
of
a
bond
portfolio
to
non-parall
the yield curve.
To estimate
the whi
impact
of non-parall
el shitivity
fts, ofbondtheportfolio
managers
calculate
key
rate
durations,
c
h
measure
the
sensi
portfol
i
o
'
s
value
to
changes
i
n yielinds
fordetailspecifi
c
maturiti
e
s
(or
portions
of
the
yield
curve).
Key
rate
durati
o
n
is
described
at Level II.
©20 12 Kaplan, Inc.
Page 33
Study Session 1 5
Cross-Reference to CFA Institute Assigned Reading #53
-
Risks Associated With Investing in Bonds
LOS 53.h: Explain the disadvantages of a callable or prepayable security to an
investor.
CPA® Program Curriculum, Volume 5, page 331
Compared
to
an
option-free
bond,
bonds
wi
t
h
call
provisions
and
securities
wi
t
h
prepayment
less certainofcashcallable
flow and
stream.prepayabl
This uncertainty
the
timing ofoptions
cash flooffer
ws isaonemuchdisadvantage
e securities.about
Aprepayments
second disadvantage
stemssecurities
from thearefactboththatmore
the calprobable
l of a bond
andinterest
increased
of
amortizing
when
rates
have
decreased.
The
di
s
advantage
here
i
s
that
more
principal
(all
of
the
principal,
i
n
the
case of a callare) islessreturned
whenWhen
the opportunities
foryoureigetnvestment
of theseback
principal
repayments
attractive.
rates
are
l
o
w,
more
principal
that must
bearereinvested
at
the
new
lower
rates.
When
rates
ri
s
e
and
opportunities
for
reinvestment
better, less principal is likely to be returned early.
Asecurities
third disadvantage
i
s
that
the
potential
pri
c
e
appreciation
of
callable
and
prepayable
from
decreases
icalln market
yieldstheis callessl price
than that
ofanoption-free
securi
tiebond'
s of liske
maturi
t
y.
For
a
currently
a
ble
bond,
puts
upper
limit
on
the
pritheceffect
e appreciation.
Whi
l
e
there
is
no
equival
e
nt
price
limit
on
a
prepayable
securi
t
y,
prepayment
similatorlyfallto iangcalmarket
l featureyields.
and reduces the
appreciationof thepotential
of the option
securitiesoperates
in response
related uncertainty about
the yields
atOverall
which, thefundsriskscanofbeearlreiynreturn
vested ofareprincipal
termed and the and
respectively.
call risk
prepayment risk,
LOS 53.i: Identify the factors that affect the reinvestment risk of a security
and explain why prepayable amortizing securities expose investors to greater
reinvestment risk than nonamortizing securities.
CPA® Program Curriculum, Volume 5, page 331
Asmaturity
noted from
in ourcoupon
earlier interest
discussionpayments,
of reinvestment
risk,principal
cash flowspayments
prior toonstated
bond
calls,
amortizing
securities,
and prepayments
all subject
securityrateholders
todecreases
reinvestment
risk. Remember,
acompared
lower coupon
increases
duration
(interest
risk)
but
reinvestment
risk
to an otherwise identical higher coupon issue.
A security has reinvestment risk under the following conditions:
The
coupon
is higher. so that interest cash flows are higher.
ItIt has
a
call
feature
an amortizing
securityoption
. .
It iscontai
ns a prepayment
Asreturnnotedof earli
er, when
interest ratessecurities.
decline, The
thereearlis any return
increased
probabilityincreases
of thetheearly
principal
for
prepayable
of
principal
amount that must be reinvested at lower prevailing rates. With prepayable securities,
more
•
•
•
•
Page 34
©2012 Kaplan, Inc.
Study Session 1 5
Cross-Reference to CFA Institute Assigned Reading #53 - Risks Associated With Investing in Bonds
the uncertainty
about theratesbondholder'
return ofriprincipal
and the
prevai
ling reinvestment
when it iss return
returneddue(i.toe., early
reinvestment
sk) is greater.
LOS 53.j: Describe types of credit risk and the meaning and role of credit
ratings.
CPA® Program Curriculum, Volume 5, page 332
Aprobability
bond's of itsisissuer
used tonotindicate
itstimrelelyativeinterest
probability
of default,payments
which isasthepromised
maki
n
g
and
principal
in the bondofindenture.
A bond
rating
of AAbondis ians lessindication
thatof thean Aexpected
probability
default
over
the
l
i
f
e
of
the
than
that
rated
bond,
whi
c
h
has
a
lower
expected
probability
of
default
than
a
BBB
(triple
B)
rated
bond, and
sori k,onthethrough
the
lower
ratings.
We
can
say
that
l
o
wer-rated
bonds
have
more
riskor principal
that a bondpayments).
will fail toBecause
make promised/scheduled
payments
(eithera lower­
interest
payments
investors
prefer
less
ri
s
k
of
default,
rated
i
s
sue
must
promise
a
higher
yi
e
ld
to
compensate
i
n
vestors
for
taki
n
g
on
a
greater
probability of default.
The
di
f
ference
between
the
yi
e
ld
on
a
Treasury
security,
which
is
assumed
to
be
default
ricredi
sk-free,
t and the yield on a similar maturity bond with a lower rating is termed the
yield on a risky bond = yield on a default-free bond + credit spread
to the even
fact that
thee thedefault
riskTreasury
premiumsecurities
requiredofinsimilar
the market
formaturity
a givenremains
rating unchanged.
canrefersincrease,
whi
l
yi
e
l
d
on
An
i
n
crease
i
n
thi
s
credit
spread
increases
the
required
yield and decreases the price of a bond.
is
the
ri
s
k
that
a
credi
t
rati
n
g
agency
wi
l
l
lower
a
bond'
s
rating.
The
resulthetinbond.
g increase
inngtheincrease
yield required
byaninvestors wiandll lead
tohavea decrease
in theeffect,
price
ofdecreasing
A
rati
is
termed
will
the
opposite
the required yield and increasing the price.
Rating
agenciof thees girivsekbonds
ratingsWhilwhiectheh areratings
meantaretoprimarily
give bondbased
purchasers
anfinancial
indication
of
default.
on
the
strength
ofratings
the company,
difonferentdifferences
bonds ofinthecollateral
same company
can havein theslightlpriority
y of
different
depending
or
di
ff
erences
theseniorbondholders'
cl
a
i
m
(e.
g
.
,
junior
or
subordinated
bonds
may
get
lower
ratings
than
ratingsprobabi
are notlityabsolute
but ratherandgibonds.
ve an
indicatibonds).
on of theBondrelative
of defaultmeasures
across theof default
range ofrisk,companies
For
ratijudged
ngs gitovenhaveby Standard
andsk ofPoor'failing
s Corporation,
apromised
bond ratedinterest
AAA and
(triplprincipal
e-A) has
been
the
l
e
ast
ri
to
make
i
t
s
payments
(defaul
t
i
n
g)
over
i
t
s
life.
Bonds
with
greater
risk
of
defaulting
on
promised
payments
havesecurities
lower ratings
AA (double-A),
A (single-A),
BBB,anBB,AAAandrating.
so on.
U.S. Treasury
and asuch
smallasnumber
of corporate
bonds receive
rating
default
s
spread.
Credit spread risk
Downgrade risk
upgrade
©20 12 Kaplan, Inc.
Page 35
Study Session 1 5
Cross-Reference to CFA Institute Assigned Reading #53
-
Risks Associated With Investing in Bonds
Plusesa and
minuses
arethanusedAA,towhich
indicateis better
differences
in default
riskratedwithiAAAn categories,
with
AA+
better
rating
than
AA-.
Bonds
through
BBB
areandconsidered
and
bonds
rated
BB
and
below
are
considered
specul
a
ti
v
e
sometimes
termed
or,ativemoreandpositi
vely,rated D are currentlBonds
rated
CCC,
CC,
and
C
are
highl
y
specul
bonds
y
in
default.
Moody'
s
Investor
Services,
Inc.
,
another
prominent
issuer
of
bond
ratings,
classi
f
i
e
s
bonds
siwimthilarllower
y butratings
uses AalcarryashiS&P
usespromised
AA+, Aa2
as inAA,theAa3market
as AA-,because
and soinvestors
on.
Bonds
g
her
yields
exposed greater
to moredefault
defaultrisrik.sk require a higher promised return to compensate them for
bearing
investment grade
junk bonds
high-yield bonds.
LOS 53.k: Explain liquidity risk and why it might be important to investors
even if they expect to hold a security to the maturity date.
CPA® Program Curriculum, Volume 5, page 336
We
described
liquidity
earlier
and
noted
that
i
n
vestors
prefer
more
liquidity
to
less.
This
means
that diinfvestors
willbetween
requirethea prihigher
yielddealforerslessareliquid
securities,
other
things(the
equal
.
The
ference
c
e
that
wil
l
i
n
g
to
pay
for
a
security
bid) and the priceTheat bid-ask
which dealers
areis anwilinlidingcatitooselln ofa thesecurity
(theity ofask)theismarket
called thefor a
spread
l
i
qui
d
securi
ty. Ifand
traditheng activi
in a particularto besecurity
declines, the bid-ask spread will widen
(increase),
issue tisy considered
less liquid.
Ifincrease
investorsthearebid-ask
planning
to sellleadatosecurity
prior
toprice,maturiandty,cana decrease
intheliquidity
wionllthe
spread,
a
l
o
wer
sal
e
decrease
returns
position.
Even
i
f
an
i
n
vestor
plans
to
hold
the
security
until
maturi
t
y
rather
than
trade
it, poor
liquidityvaluescan tohaveportfolio
adversesecurities.
consequences
stemming
from theisneed
to periodically
assi
gn current
This
periodic
valuation
referred
to bidas
When
a
security
has
little
liquidity,
the
vari
a
ti
o
n
i
n
dealers'
prices
or the absence
ofordealpriecrinbidsg servialtogether
makesto establi
valuation
difficultvalue.
and Ifmaythisrequi
ree
that
a
valuation
model
c
e
be
used
s
h
current
val
u
is low, institutional investors may be hurt in two situations.
1. portfoli
Institutional
investors
may
need
to
mark
their
holdings
to
market
to
determine
their
o's value
for periodic
reportiingnmarket
g and performance
measurement
purposes.
If
thesecurity
market
is
illiquid,
the
prevail
price
may
misstate
the
true
value
of
the
and can reduce returns/performance.
2. Marki
n
g-to-market
i
s
also
necessary
wi
t
h
repurchase
agreements
to
ensure
that
the
colcanlateral
is adequate
the funds being
lead tovalue
a higher
cost oftofundssupport
and decreasing
portfolborrowed.
io returns.A lower valuation
bid-ask spread.
marking-to-market.
Professor's Note: CPA Institute seems to use "Low Liquidity" and "high Liquidity
risk" interchangeably. I believe you can treat these (liquidity and Liquidity
risk) as the same concept on the exam, although you should remember that Low
Liquidity means high Liquidity risk.
Page 36
©2012 Kaplan, Inc.
Study Session 1 5
Cross-Reference to CFA Institute Assigned Reading #53 - Risks Associated With Investing in Bonds
LOS 53.1: Describe the exchange rate risk an investor faces when a bond makes
payments in a foreign currency.
CFA® Program Curriculum, Volume 5, page 338
Ifreturns
a U.Son. investor
purchases
a
bond
that
makes
payments
in
a
forei
g
n
currency,
dollar
the investment
will depend
on thein value)
exchangeof therateforeibetween
the dolwilarll andreducethe
foreign
currency.
A
depreciation
(decrease
g
n
currency
theflowsreturns
to
a
dollar-based
investor.
Exchange
rate
risk
i
s
the
risk
that
the
actual
cash
the investment
may be worth less in domestic currency than was expected
when from
the bond
was purchased.
LOS 53.m: Explain inflation risk.
CFA® Program Curriculum, Volume 5, page 338
Inflation
risk
refers
to
the
possibility
that
prices
of
goods
and
servi
c
es
in
general
will
moreincome,
than anexpected.
Because
filexveled-coupon
bonds
pay a constant
periodicandstream
ofincrease
i
n
terest
increasing
pri
c
e
decreases
the
amount
of
real
goods
services
that
bond
payments
will
purchase.
For
thi
s
reason,
infl
a
ti
o
n
risk
is
sometimes
referred
toin asnominal
purchasing
power
risk.redWhen
expected
inflationthe valincreases,
the resulting
increase
rates
and
requi
yiel
d
s
wi
l
decrease
u
es
of
previousl
y issued
fixed-income securities.
LOS 53.n: Explain how yield volatility affects the price of a bond with an
embedded option and how changes in volatility affect the value of a callable
bond and a putable bond.
CFA® Program Curriculum, Volume 5, page 339
Without
any
volatil
i
t
y
in
interest
rates,
a
cal
l
provi
s
ion
and
a
put
provision
have
littl
e
value,
if any,inassumi
ng no changes
initycredit
qualityincreases
that affect
market
values.
In general,
anandincallcrease
the
yield/price
vol
a
ti
l
of
a
bond
the
val
u
es
of
both
put
options
options.
We
alreadyoption-free
saw that the(straight)
value ofbonda callbyablethebond
isoflessthethan
theoptionvaluebecause
of an otherwise­
identical
value
call
the
cal
l
option is retained by the issuer, not owned by the bondholder. The relation is:
value of a callable bond = value of an option-free bond -value of the call
Anmarket
increase
in
yi
e
ld
volatil
i
ty
i
n
creases
the
val
u
e
of
the
call
option
and
decreases
the
value of a callable bond.
A put option is owned by the bondholder, and the price relation can be described by:
value of a putable bond = value of an option-free bond + value of the put
©20 12 Kaplan, Inc.
Page 37
Study Session 1 5
Cross-Reference to CFA Institute Assigned Reading #53
-
Risks Associated With Investing in Bonds
Anvaluincrease
in yieldbond.
volatility increases the value of the put option and increases the
e of a putable
Therefore,
we conclude
thatbonds
increases
in interestways.rateVolatility
volatilityriskaffectforthecallable
pricesbonds
of is
call
a
bl
e
bonds
and
putable
in
opposite
thevolarisk
lity will increase, and volatility risk for putable bonds is the risk that
tilitythatwillvolati
decrease.
LOS 53.o: Describe sovereign risk and types of event risk.
CFA® Program Curriculum, Volume 5, page 339
Event
risk
occurs
when
something
signifi
c
ant
happens
to
a
company
(or
segment
of
the
market)
thatg valhasue aofsudden
and substanti
al riimpact
onrespect
its financial
condition
andmany
on the
underl
y
i
n
an
i
n
vestment.
Event
s
k,
wi
t
h
to
bonds,
can
take
forms:
(e.
g
.
,
hurricanes,
earthquakes,
or
industrial
accidents)
impair
the
ability
ofexample,
a corporation
to meetcompany'
its debtsobligations
if thedebtdisaster
reducesmaycashbeflaffected
ow. For by
an
insurance
ability
to
make
payments
property/casualty insurance
payments
in
the
event
of
a
di
s
aster.
[e.g., ofspin-offs,
leveraged
buyouts
(LBOs),
and mergers]
mays
have
an
impact
on
the
value
a
company'
s
debt
obli
g
ations
by
affecting
the
fi
r
m'
cash
flows and/or
the underlying
assets
that serve
asar colcompanies
lateral. This
maysameresulindustry.
t in
bond-rating
downgrades
and
may
also
affect
si
m
i
l
i
n
the
suchexpenditures
as changestoinmeet
cleannewair requirements,
maymaycausereduce
companies
tocashincuravailarge
cash
regulations.
This
then the
l
abl
e
to
bondholders
and
result
i
n
a
rati
n
gs
downgrade.
A
change
i
regulaoftiosecuri
ns forty,somesuchfinasancial
institutions
prohibiting
them
fromcanholding
certain
types
junk
bonds
(those
rated
bel
o
w
BBB),
l
e
ad
to
a volume
of sales that decreases prices for the whole sector of the market.
Investors
buy bonds
foreignreasons
governments
face sovereign
with credit
risk, we canwhoidentify
threeofseparate
that soverei
gn bond pririsk.cesJustmayasdecline.
The credit spread for a sovereign bond may increase although its rating has not
1. changed.
2. A sovereign bond's credit rating may decline.
A sovereign bond can default.
Pria foreign
ce declines
in sovereign
bonds
dueintoterest
creditandevents
usuallyin result
from This
deterioration
in
government'
s
abil
i
ty
to
pay
principal
the
future.
inability
tohigpayh government
typically is spending,
the result orof both.
poor economic
conditions
that
result
i
n
low
tax
revenues,
cant decline in Greek government debt
prices in 2009-2010 is an example ofThesuchsignifi
a scenario.
With
foreign
bonds
we
must
also
consider
the
fact
that
the
forei
g
n
government
may
refuse
topoorpayfi(repudiate)
the poor
debt ateconomic
some future
date. Historical
ly,theinability
tocause
pay of
due
to
s
cal
policy
and
conditions
has
been
primary
sovereign defaults.
•
Disasters
•
Corporate restructurings
•
Regulatory issues,
3.
Page 38
©2012 Kaplan, Inc.
Study Session 1 5
Cross-Reference to CFA Institute Assigned Reading #53 - Risks Associated With Investing in Bonds
KEY CONCEPTS
LOS
There are many risk-uncertainty
types of risk associated
with
fixprices
ed income
securities:
about
bond
due
to
changes
in
market
interest
rates.risk-the risk that a bond will be called (redeemed) prior to maturity under the
terms
of
the
call
provision
and
that
the
funds
must
then
be
rei
n
vested
at
the
then-currentri(lower)
yiuncertainty
eld. about the amount of bond principal that will be
s
k-the
repaid priorritosk-the
matuririskty. that changes in the shape of the yield curve will reduce
bond values.
the risk
of a decrease
in bond value
amcrease.
ratingsrisk-includes
downgrade, and
the riofskdefault,
that thethecrediriskt spread
for a particular
ratingduewiltol
risk-the
riskprice).
that an immediate sale will result in a price below fair value
(the prevailing
market
risk-the
risk
that
the
domestic
currency
val
u
e
of
bond
payments
i
n
a
foreign currency
wirisk
ll decrease
due toinexchange
rateinterest
changes.rate volatility will affect the
ri
s
k-the
that
changes
expected
values ofrisk-the
bonds witrihskembedded
options.
thatcashinflfloawstionfrom
will abefixhigher
than security.
expected, eroding the
purchasing
power
of
the
ed
income
risk-the
risk
of
decreases
i
n
a
security'
s
value
from
disasters,
corporate
restructurings,
or regulatory
changes that negatively
affect
theorfirnot
m. be able to make
risk-the
ri
s
k
that
governments
may
repudi
a
te
debt
debt payments in the future.
LOS a bond's coupon rate is less than its market yield, the bond will trade at a discount
When
to its par value.
When
a
bond'
s
coupon
rate
i
s
greater
than
its
market
yield,
the
bond
will
trade
at
a
premium to its par value.
LOS
ThePositively
level of a relbond'ateds interest
rate risk (duration) is:
to
its
maturity.
Negativelyy relrelaatedted toto itsits market
coupon YTM.
rate.
Negativel
Less over some ranges for bonds with embedded options.
LOSprice of a callable bond equals the price of an identical option-free bond minus the
The
value of the embedded call.
53.a
•
Interest rate
•
Call
•
Prepayment
•
Yield curve
•
Credit
•
Liquidity
•
Exchange rate
•
Volatility
•
Inflation
•
Event
•
Sovereign
53.b
53.c
•
•
•
•
53.d
©20 12 Kaplan, Inc.
Page 39
Study Session 1 5
Cross-Reference to CFA Institute Assigned Reading #53
-
Risks Associated With Investing in Bonds
LOS
53.e bonds have interest rate risk between reset dates, and their prices can differ
Floating-rate
from
their
par
values,
even
at
reset
dates,
due
t
o
changes
i
n
liquidity
or
i
n
credit
ri
s
k
after they have been issued.
LOS
53.f of a bond is the approximate percentage price change for a change in
The
duration
yield.
The
yield.dollar duration of a bond is the approximate dollar price change for a change in
LOS
53.g
Yiportfolio'
eld curves value
risk ofmaya bond
portfolio
isathenon-paral
risk (inleaddition
totheinyield
terestcurve
rate risk)
thatintheits
decrease
due
to
l
shift
in
(change
shape).
When
yielthed true
curvepriceshiftseffects
are notbecause
parallel,yieldstheonduration
of a bond
portfol
ioportfolio
does notmay
capture
the
various
bonds
in
the
change by different amounts.
LOS
53.h to an investor of a callable or prepayable security:
Disadvantages
Timing
of
cash
fl
o
ws
is
uncertain.
Principal is most
liokw.ely to be returned early when interest rates available for
reinvestment
are
l
Potential price appreciation is less than that of option-free bonds.
53.i has more reinvestment risk when it has a higher coupon, is callable, is an
ALOS
security
amortizing security, or has a prepayment option.
Aofprepayable
security haswhengreater
risk because
of the probability
acceleratedamortizing
principal payments
interestreinvestment
rates, including
reinvestment
rates, fall.
LOS
53.t riskj includes:
CrediDefaul
t
ri
s
k-the
probability
of
default.
Downgrade
risrik-the
probabilityabout
of a reduction
inyield
the bond
rating.
Credi
t
spread
s
k-uncertainty
the
bond'
s
spread
to Treasuries based on
its bond rating.
Credi
t ratings
arewitdesigned
to indicate
to investors
a bond'
serelati
ve probability
of rated
default.
Bonds
h
the
lowest
probability
of
default
recei
v
ratings
of
Bonds
AA,
BBBBBareoralslower.
o considered investment grade bonds. Speculative or high yield
bondsA,areandrated
1%
1%
•
•
•
•
•
•
AAA .
Page 40
©2012 Kaplan, Inc.
Study Session 1 5
Cross-Reference to CFA Institute Assigned Reading #53 - Risks Associated With Investing in Bonds
LOS of liquidity can have adverse effects on calculated portfolio values and, therefore,
Lack
onevenperformance
measures
for
a
portfolio.
Thi
s
makes
liquidity
a
concern
for
a
manager
though sale of the bonds is not anticipated.
LOSinvestor who buys a bond with cash flows denominated in a foreign currency will see
thethe valforeiuegnofcurrency
the bonddecli
decrease
if
the
forei
g
n
currency
depreciates
(the
exchange
val
u
e
of
nes) relative to the investor's home currency.
LOS
If inflationandincreases
decreased
bond valunexpectedl
ues fall. y, the purchasing power of a bond's future cash flows is
LOS
Increasesdecreasi
in yielndgvoltheatility
increase
theablevalue
of(because
put andthecallbondholder
options embedded
in call)
bonds,
val
u
e
of
a
cal
l
bond
i
s
short
the
and increasing the value of putable bonds (because the bondholder is long the put).
LOS
Event
riskdiencompasses
non-fintheancialissuer'events
thatngscanorhurt
the value
ofvalues;
a bond,takeovers or
including
s
asters
that
reduce
s
earni
diminish
asset
restructuri
nregul
gs thatatiocann thathavecannegati
ve effects
on thes earnings
priority ofor bondholders'
claims;foranda
changes
in
decrease
the
issuer'
narrow
the
market
particular class of bonds.
Soverei
gton repay
risk isithe
possibility
that
a economic
foreign government
willandrefuse
to pay deficit
or become
unable
t
s
debts
due
to
poor
conditions
government
spending.
53.k
An
53.1
53.m
53.n
53.o
©20 12 Kaplan, Inc.
Page 4 1
Study Session 1 5
Cross-Reference to CFA Institute Assigned Reading #53
-
Risks Associated With Investing in Bonds
CONCEPT CHECKERS
with
a
7.3%
yield
has
a
duration
of
5.4
and
i
s
tradi
n
g
at
$985.
If
the
1. Ayiebond
decreases
to 7.1 o/o, the new bond price is to:
A.B. ld$974.
4
0.
$995.
6
0.
$1 ,091.40.
2. price
If interest rate volatility
which of the following bonds will experience a
A.B. AA putable
callable bond.
bond.
C. A zero-coupon, option-free bond.
3. A noncallable,
AA-rated, 5-year zero-coupon bond with a yield of 6% is
to
have:
A.B. reinvestment
interest rate risk.risk.
C. default risk.
The current
price ofpricea bond
is 102.50.
IfWhat
interestis rates
change byof the0.5%,bond?the
4. value
of
the
bond
changes
by
2.50.
the
duration
A.B. 2.50.
2.44.
4.88.
of
the
following
bonds
has
the
interest
rate
risk?
5. Which
A.B. 5%5% 11 0-year
0-year callable
bond.
putable
C. 5% 1 0-year option-freebond.bond.
6. AA.flotheating-rate
security
wi
l
have
the
greatest
duration:
theresetresetdate.date.
the day
day before
after
the
B.C. never-fl
oating-rate securities have a duration of zero.
7. The
duration
is 5.4of7, theandbond
its current
price isif$986.
fol2%?lowing
is theof a bondestimate
price change
interest30. Which
rates of theby
A.B. -$107.
-$109.490.0.
$109.40.
8. A$981.
straight
5%calbond
has twothatyearsis theremai
ningin every
to maturity
andas theis priced
at bond,
6
7.
A
l
abl
e
bond
same
respect
straight
except
for
the
call
feature,
is
priced
at
$917.
6
0.
Wi
t
h
the
yield
curve
fl
a
t
at
6%,
is the80.value of the embedded call option?
A.what
$45.
B. $64.
07.
$101.00.
closest
c.
increases,
decrease?
least
likely
c.
greatest
best
increase
c.
c.
Page 42
©2012 Kaplan, Inc.
Study Session 1 5
Cross-Reference to CFA Institute Assigned Reading #53 - Risks Associated With Investing in Bonds
straight
5%000coupon
bond
hasA putable
two yearsbond,remaini
nhgistothematurity
andeveryis priced
at
9. A$981.
6
7
($1,
par
val
u
e).
whi
c
same
in
respect
asparthevalstraight
bond
except
for
the
put
provision,
is
priced
at
101.
7
6
(percent
of
ue). With the yield curve flat at 6%, what is the value of the embedded
put
option?
A.B. $17.60.
$26.
$35.797.3.
10. Which
ofto thefixed-income
following securities?
is
to fall under the heading of event risk with
respect
A.B. AOnechange
inacquisition
rate regulation.
fi
r
m'
s
by another.
C. A Federal Reserve decrease
in money supply.
11. Which
ofoating-rate
the followibond.
ng 5-year bonds has the interest rate risk?
A.B. AA flzero-coupon
bond.bond.
C. A 5% fixed-coupon
12. Anbondsinvestor
is concerned
about
interest
ratety)risk.has Whi
ch ofintheterestfollrate
owingrisk?threeThe
(similar
except
for
yi
e
l
d
and
maturi
the
A.B.bond5%
5%with:yiyieelldd and
10-year maturi
ty.y.
and
20-year
maturi
t
C. 6% yield and 1 0-year maturity.
13. Which of the following statements about the risks of bond investing is
A.B. AA bond
rated callAAAprotection
has no credit
risk.atility risk.
bond
with
has
vol
C. A U.S. Treasury bond has no reinvestment risk.
14. Which
of theinvestor?
following securities will have the reinvestment risk for a
long-term
A.B. AA 6-month
1 0-year, zero-coupon
bond.
T-bill. e amortizing bond.
C. A 30-year, prepayabl
15. AA. 2-year,
zero-coupon
U.S. Treasury note is
to have:
i
n
fl
a
ti
o
n
risk.
currencyity risk.
C.B. volatil
risk.
c.
least likely
highest
least
most
accurate?
least
least likely
©20 12 Kaplan, Inc.
Page 43
Study Session 1 5
Cross-Reference to CFA Institute Assigned Reading #53 - Risks Associated With Investing in Bonds
ANSWERS - CONCEPT CHECKERS
x
1.
B
The percentage price change, based on duration is equal to -5.4
The new price is 1 .0 1 08 x 985 = $995.64.
2.
A
An increase in volatility will increase the value of the call option and decrease the value
of a callable bond. A putable bond will increase in value. The value of option-free bonds
will be unaffected.
3.
B
A zero-coupon bond, as a security, has no reinvestment risk because there are no cash
flows prior to maturity that must be reinvested. A double-A bond has some {small)
default risk. Zero-coupon bonds have the most interest rate risk for a given maturity.
4.
C
The duration is computed as follows:
.
durauon
=
percentage change in price
change in yield as a decimal
2.50
102.5
0.005
=
2. 44o/o
0.5%
=
(-0.2%) = 1 .08%.
4.88
5.
C
Embedded options reduce duration/interest rate risk.
6.
B
The duration of a floating-rate bond is higher the greater the time lag until the next
coupon payment/reset date. The greatest duration/interest rate risk is, therefore,
immediately after the coupon has been reset.
7.
B
The approximate dollar change in price is computed as follows:
dollar price change = -5.47
8.
B
x
0.02
x
986.30 = -$107.90
The option value is the difference between the value of an option-free bond and the
corresponding price of the callable bond. Its value is computed as:
call option value = $981 .67 - $9 17.60 = $64.07
9.
C
The value of the embedded put option is the difference between the price of the putable
bond and the price of the straight bond. So it is computed as:
option value = $ 1 ,0 1 7.60 - $981 .67 = $35.93
Page 44
1 0. C
Event risk refers to events that can impact a firm's ability to pay its debt obligations that
are separate from market risks. The Fed's actions can impact interest rates, but this is a
market risk factor, not event risk.
11. B
The zero-coupon bond will have the greatest duration of any of the three bonds and, as
such, will be subject to the greatest interest rate risk.
12. C
Interest rate risk is inversely related to the yield and directly related to maturity. All else
equal, the lower the yield, the greater the interest rate risk. All else equal, the longer the
maturity, the greater the interest rate risk. This bond has the higher yield and the shorter
maturity, and, thus, has the lowest interest rate risk.
©2012 Kaplan, Inc.
Study Session 1 5
Cross-Reference to CFA Institute Assigned Reading #53 - Risks Associated With Investing i n Bonds
13. B
A Treasury bond pays semiannual coupon interest and, therefore, has reinvestment risk.
A triple-A rated bond can lose its AAA rating, so it has downgrade risk, a component
of credit risk. A bond with a call feature has volatility risk even when the call cannot be
exercised immediately. The call feature still has value (to the issuer), and its value will be
affected by volatility changes.
14. A
A 10-year, zero-coupon bond has no cash Bows prior to maturity to reinvest while the
entire amount invested in 6-month bills must be reinvested twice each year.
15. C
It will have inflation (purchasing power) risk. It will have currency risk to non-U.S.
dollar investors. Volatility risk only applies to bonds with embedded options.
©20 12 Kaplan, Inc.
Page 45
The following is a review of the Analysis of Fixed Income Investments principles designed to address the
learning outcome statements set forth by CFA Institute. This topic is also covered in:
OVERVIEW OF BOND SECTORS AND
INSTRUMENTS
Study Session 15
EXAM FOCUS
This
reviology
ew introduces
thefixedvarious
types
of fixedPayincome
securities
andto thea fairmechanics
amount ofof
termi
n
rel
a
ti
n
g
to
income
securities.
special
attention
these
securities;
that
is,
how
they
pay,
when
they
pay,
and
what
they
pay.
The
additional
information
s nice, butoutcome
likely notstatements
crucial. Tryso that
to gaiyoun enough
understanding
ofwhen
the terms
liarestedusedin thein ailearning
wil
l
understand
them
they
question.
Knowi
n
g
the
basics
about
Treasury
securities,
mortgage-backed
securities,
andtmunicipal
securities
is important
asmore
a foundation
for muchonoffithexedmateri
al
onvaluation
debt securi
i
e
s
that
fol
l
ows,
as
well
as
for
the
detai
l
e
d
material
income
and risk that is contained in the Level II and Level III curriculum.
LOS 54.a: Describe features, credit risk characteristics, and distribution
methods for government securities.
CFA® Program Curriculum, Volume 5, page 357
Bonds gissued
byThea country'
sgcentral
government
are referredconsists
to as sovereign
bonds or
soverei
n
debt.
soverei
n
debt
of
the
U.
S
.
government
of
U.
S
.
Treasury
securities,
whi
c
h
are
considered
to
be
essentially
free
of
default
risk.
The
sovereign
debt
ofbe other
countries
is considered
to havemarket,
varyinganother
degreescountry'
of credits forei
risk.gSoverei
gmarket,
n debt canor
issued
in
a
country'
s
own
domestic
n
bond
in the Eurobond market.
Sovereiingnother
debt currencies
is typicallyasissued
inBond
the currency
of the issui
ngascountry,
butandcanPoor'be s,
issued
well
.
rati
n
g
agencies,
such
Standard
rate
sovereign
debt
based on itsin theperceived
credit risk,(localoftencurrency)
giving different
ratings
to
soverei
g
n
debt
denominated
home
currency
and
to
the
sovereign
debt of the same country denominated in foreign currency.
Professor's Note: Remember that it is often easier for a country to print currency
(expand the money supply) in order to meet obligations denominated in the home
currency than it is to exchange the local currency for a fixed amount offoreign
currency. Thus, local currency sovereign debt often receives a higher rating than the
foreign currency denominated debt ofthe same country.
Page 46
©2012 Kaplan, Inc.
Study Session 1 5
Cross-Reference to CFA Institute Assigned Reading #54 - Overview of Bond Sectors and Instruments
There are four primary methods used by central governments to issue sovereign debt.
this price
method,(lowest
the debt
isatauctioned
1. periodically according to a cycle and theUnderhighest
yield)
whi
chsystem
the
enti
r
e
issue
to
be
auctioned
can
be
sold
i
s
awarded
to
all
bidders.
Thi
s
i
s
the
used by the U.S. Treasury.
2. the bonds at the price(s) that they bid. Under this method, winning bidders receive
refers tomarket
a methodconditions
where thearecentral
government auctions
3. Annew securities when it determines
advantageous.
4. Abonds. Underrefers
to
the
issuance
and
auction
of
bonds
identical
to
previousl
y
issued
this system, bonds are sold periodically, not according to a regular cycle.
Regular cycle auction-single price.
Regular cycle auction-multiple price.
ad hoc auction system
tap system
LOS 54.b: Describe the types of securities issued by the U.S. Department of
the Treasury (e.g., bills, notes, bonds, and inflation protection securities), and
distinguish between on-the-run and off-the-run Treasury securities.
CFA® Program Curriculum, Volume 5, page 358
(Treasuries)
areU.S.issuedgovernment,
by the U.S.theyTreasury.
Because totheybe arefreebacked
byfromthecredit
full fairistkh and
credit
of
the
are
considered
(though
they'
re still subject
to in(2)terestnotesrate/price
risk).andThe(3)Treasury
issues
three
distinct
types
of
securities:
(1)
bills,
and
bonds,
inflation­
protected securities.
(T-bills)
haveonlymaturiti
es of(par)lessvalue
than atonetheyearmaturi
and tdoy date.
not make
explici
t
interest
payments,
paying
the
face
T-bills
are
sold
at(likea discount
to parbonds).
value and
interest
isonreceived
when
thempares calvalueled is paid at maturity
zero-coupon
The
interest
T-bills
is
someti
siinnaceseparate,
the interestexpl(difference
between
theon purchase
pricenotes.andSecurities
the par value)
istype
not made
i
cit
payment,
as
it
is
bonds
and
of
this
are
known as
securities.
There
aredue to holidays. They are28,also91,known
and 182as 4-week,
days, adjustable
byandone6-month
day (up or
down)
3-month,
T-bills,
respecti
v
ely.
Periodical
ly,daysthe Treasury
also issues
bills with
maturities
rangintog
from
a
few
to
si
x
months
to
hel
p
overcome
temporary
cash
shortages
prior
the quarterly receipt of tax payments.
and
pay
semiannual
coupon
interest
at
a
rate
that
is
fi
x
ed
atmaturities
issuance.ofNotes
original maturities of 2, 3, 5, and 10 years. Bonds have original
20 orhave
30 years.
Prior
to 1984,
some Treasury
issuedbonds
that aresincecallable
maturity.
The Treasury
has notbonds
issuedwerecallable
1984. at par five years prior to
Treasury securities
Treasury bills
implicit interest
pure discount
•
three maturity cycles:
•
Treasury notes
cash management
Treasury bonds
©20 12 Kaplan, Inc.
Page 47
Study Session 1 5
Cross-Reference to CFA Institute Assigned Reading #54 - Overview of Bond Sectors and Instruments
Treasury bond and note prices in the secondary market are quoted in percent and 32nds
of 1 o/o of face value. A quote of 102-5 (sometimes 102:5) is 102% plus 1._ % of par,
which for a $100,000 face value T-bond, translates to a price of:
[102 ;2 ] o/o $100,000 1.0215625 X $100,000 $102,1 56.25
32
+
X
=
=
Since 1997,infltheation-protected
U.S. Treasury has
issued1 0-year notes and 20-year bonds are offered(TIPS).
Currently,
5and
by the
Treasury. TIPS work as follows:
TIPS
make
semiannual
coupon
interest
payments
at
a
rate
fi
x
ed
at
issuance,
just
li
k
e
notesparandvalue
bonds.of TIPS begins at $1,000 and is adjusted semiannually for changes
The
in theadjusted
Consumer
PriceisIndex
(CPI).for If thereperiod.
is deflTheationfixed(fallcoupon
ing priceratelevels),
the
par
value
reduced
i
s
paid
semiannually
asn thea percentage
offromthethe inflation adjustment is taxed as income in the
Any
i
n
crease
i
par
value
year of the adjustment:
. . .USted par value stated coupon rate
TIPS coupon payment mflanon-adJ
2
For
example,
considerlater,
a $100,the000 par rate
valueofTIPS
with(CPI)
a 3o/o iscoupon
rate,parsetvalue will be
issuance.
Six
months
infl
a
tion
4%.
The
increased by one-half of the 4% (i.e., 2%) and will be 1.02 100,000 = $102,000.
The
fi
r
st
coupon
wil
l
be
one-half
of
the
3%
coupon
rate
ti
m
es
the
inflation
adjusted
par value:period
1.5% wi102,
0used
00 = to$1,530.
Any
percentage
change
in0the00 toCPIa new
over
theinflation-adjusted
next 6-month
l
l
be
adj
u
st
the
par
value
from
$102,
val
u
e,
whi
c
h
wi
l
l
be
multiplied
by
1.
5
%
to
compute
the
next
coupon
payment.
Ifreceithevesadjusted
par
value
(per
bond)
i
s
greater
than
$1,
0
00
maturity,
the
holder
adj000usted
valuaetion),
as theholders
maturityreceipayment.
adjustedty asparthisvalueis theis
lminimum
ess thanthe$1,repayment
(dueparamount.
to defl
ve $1,000If thematuri
Treasury Inflation-Protected Securities
•
•
that
inflation adjusted par value.
•
x
=
----''----
-
-
at
annual
semiannual
x
x
at
at
On-the-Run and Off-the-Run Treasury Securities
Treasury issues are divided into two categories based on their vintage:
1.
are the most recently auctioned Treasury issues.
2. by a more recently auctioned
are older issues
thatIssueshavereplbeen
replaced
(asmore
the most
traded
issue)
issue.
a
ced
by
several
recent
issues
are
known as
issues.
On-the-run issues
Off-the-run issues
well off-the-run
Page 48
©2012 Kaplan, Inc.
Study Session 1 5
Cross-Reference to CFA Institute Assigned Reading #54 - Overview of Bond Sectors and Instruments
The
distinction
isoff-the-run
that the on-the-run
issues prices
are moreof on-the-run
actively traded
andprovide
thereforebetter
more
liquid
than
issues.
Market
issues
information about current market yields.
LOS 54.c: Describe how stripped Treasury securities are created and
distinguish between coupon strips and principal strips.
CPA® Program Curriculum, Volume 5, page 360
Since
the
U.S.
Treasury
does
not
issue
zero-coupon
notes
and
bonds,
investment
bankers
began
stripping
theinvestor
couponsdemand.
from Treasuries
to createarezero-coupon
securitTreasuries
ies of variousor
maturities
to
meet
These
securities
termed
stripped
Treasury
strips.Principal
In 1985,Securities
the Treasury
introduced
theUnder
SeparatethisTrading
of theRegiTreasury
stered
Interest
and
(STRIPS)
program.
program,
issues coupon-bearing
notes andto buy
bondslargeas iamounts
t normallofy does,
butissues,thenstriitpalthelowscoupons
certain
government
securities
dealers
these
from
the
principal,
repackage
the
cash
fl
o
ws,
and
sell
them
separately
as
zero-coupon
bonds, at discounts to par value.
For
example,
a
10-year
T-note
has
20
coupons
and
one
principal
payment;
these
21
cash
flsecurities
ows can be(Treasury
repackaged
as 21intodifferent
zero-coupon securities. The stripped
strips)andaresolddivided
two groups:
1. stripped
Coupon from
stripsthe(denoted
originalassecurirefers
ty. to strips created from coupon payments
2. Principal
strips
refers
to
bond
and
note
principal
payments
wi
t
h
the
coupons
stripped
stripped off.
notesThose derived from stripped bonds are denoted and those from
ci)
bp
np.
0
Proftssor's Note: While the payments on coupon strips and principal strips with
the same maturity date are identical, certain countries treat them differently for
tax purposes, and they often trade at slightly different prices.
STRIPS
arefulltaxed
by thee investors,
IRS on theiresults
r implicit
interest
(movement
towardpriorpartovalue),
which,
for
y
taxabl
in
negati
v
e
cash
fl
o
ws
i
n
years
maturi
t
y.
The
TreasuryfromSTRIPS
programpieces.
also created a procedure for
Treasury notes
and bonds
the individual
reconstituting
LOS 54.d: Describe the types and characteristics of securities issued by U.S.
federal agencies.
CPA® Program Curriculum, Volume 5, page 363
Agency
bonds are such
debt assecurities
issuedHome
by various
agencies(FHLB).
and organizations
the are
U.S. government,
the Federal
Loan Bank
Most agencyofissues
©20 12 Kaplan, Inc.
Page 49
Study Session 1 5
Cross-Reference to CFA Institute Assigned Reading #54 - Overview of Bond Sectors and Instruments
obligations
of the U.S. Treasury and technically should not be considered the same as
Treasury
securities.
Even so, they are very high quality securities that have almost no risk of default.
There are two types of federal agencies:
1. (Ginnie Mae) and the Tennessee
suchVallas theey Authori
Government
National
Mortgage
Association
t
y
(TVA),
which
are
owned
by
the
U.regiSs. trati
government
and arethese
exemptsecurities
from Securities
andby Exchange
Commission
(SEC)
o
n.
In
general,
are
backed
the
full
fai
t
h
and
credi
t
of
theCorporation.
U.S. government,
except
i
n
the
case
of
the
TVA
and
Pri
v
ate
Export
Funding
Essentially, these securities are free from credit risk.
2. the Federal Home Loan Bank System,
(GSEs)theinclude
theNational
Federal Mortgage
Farm CreditAssociation
System,
Federal
(Fannie
Mae),
the
Federal
Home
Loan
Bank
Corporation
(Freddi
e
Mac),
and
the
Student Loan
Marketi
ng Association
(Sallie
Mae). These
areU.Spri. Congress.
vately owned,
butissue
publicly
chartered
organizations,
and
were
created
by
the
They
their
securities
directly
in
the
marketplace
and
expose
i
n
vestors
to
some
(albeit
very
little) credit risk.
are securities
that are notThesebacked
bymany
collateral
(i.e., structures
they are unsecured).
GSEs
commonly
issue
debentures.
are
of
maturity
coupon interest paying securities or discount securities (referred to as bills).and can be
not
Federally related institutions,
Government sponsored enterprises
Debentures
LOS 54.e: Describe the types and characteristics of mortgage-backed securities
and explain the cash flow and prepayment risk for each type.
CFA® Program Curriculum, Volume 5, page 3 64
(MBSs)butarealsobacked
(secured)tobyservice
poolstheof mortgage
loans,
which
not
only
provide
the
debt.
A
mortgage­
backed
mortgages.security is any security where the collateral for the issued security is a pool of
The
cash flloans
ows from
a mortgageloans
are diinfferent
frommake
the cash
flowsof ofequala coupon
bond.
Mortgage
are
amortizing
that
they
a
series
payments
consisting
of
the
periodic
interest
on
the
outstanding
principal
and
a
partial
repayment
of the principal
amount.
Residential
real Inestatethe early
mortgages
arethetypigreater
callyportion
for 30 years
and
consist
of
360
equal
monthly
payments.
years,
of
the
payment is interest, and the final payment, after 30 years, is almost all principal.
Mortgage-backed securities
collateral
cash flows
� Professor's Note: Amortizing loans and amortization schedules are covered in the
� Study Session on Quantitative Methods.
The
Government
National
Mortgage
Association
(GNMA),
the
Federal
National
Mortgage Association (FNMA), and the Federal Home Loan Mortgage Corporation
Page 50
©2012 Kaplan, Inc.
Study Session 1 5
Cross-Reference to CFA Institute Assigned Reading #54 - Overview of Bond Sectors and Instruments
(FHLMC) allandissuetheymortgage-backed
securities.
All three
areMae,
sponsored
byMae,the and
U.S.
government
are
known
now
by
the
names
Ginnie
Fannie
Freddi
e
Mac.
Each
purchases
mortgages
from
lenders
to
provide
funds
for
mortgage
loans. The agencies
issuecollthree
types
ofmortgage
mortgage-backed
securities:
mortgage
passthrough
securities,
a
teral
i
zed
obligations,
and
stripped
mortgage­
backed
securities.
Thi
s
process
of
combining
many
si
m
i
l
ar
debt
obligations
as
the
collateral for issuing
securitiestheisdebt'callsedattractiveness toTheinvestors
primaryandreason
for mortgage
securitization
i
s
to
increase
to
decrease
required rates of return, increasing the availability of funds for home mortgages.investor
There
are threeof principal,
types of cash
fl(3)owsprincipal
from a mortgage:
(1)inperiodic
interest,
(2)principal
scheduled
repayments
and
repayments
excess
of
scheduled
payments.
Borrowerswithout
(issuerspenalty,
of mortgages)
typical
ly have the principal
right to payamount
additional
principal
amounts
reducing
the
outstanding
and
thereby
reducing
future
interest
cash
fl
o
ws.
If
the
borrower
sells
the
property
backing
thecan mortgage,
the
entire
principal
amount
i
s
repaid
at
one
time.
Because
the
borrower
accelerateriskprincipal
repayment,
theexcept
ownerthatof prepayments
a mortgage hasmay be part of or all
Prepayment
is
similar
to
cal
l
risk
ofcalledthe outstanding principal
amount.
(Partial
prepayment
of
remaining
principal
is
This,when
in turn,yieldsubjects
the mortgageareholder
principal may be repaid
s for reinvestment
low. to reinvestment risk, as
Ginnie Mae,interest
Fanniand
e Mae,principal
and Freddi
e Macfrom
all guarantee
the timely payment
of They
scheduled
payments
thei
r
mortgage-backed
securities.
arecertain
ablestandards
to do thisregarding
because they
only
purchase
or
underwri
t
e
loans
that
conform
to
to the value of the propertyborrower
securing it.credit ratings, loan size, and the ratio of each loan
Athrough proportionally to each security
passesholder.
the payments
made
onmortgage
a pool ofpassthrough
mortgages
A
holder
of
a
security
that
owns
a
o/o
portion
of
the
issue
wil
l
receive
a
1
o/o
share
of
al
l
the
monthly
cash
flows Each
from monthl
all the mortgages,
after a small
percentage
fee forprincipal
administration
is and
deducted.
y
payment
consists
of
interest,
scheduled
payments,
prepayments
ofalprincipal
inws,excess
of the scheduled
amount.
Since
each holder recei
ves
aa sipercentage
of
l
cash
fl
o
a
mortgage
passthrough
security
has
prepayment
ri
s
k
as
ngle mortgage
would,ofbutmortgages.
there is some
diversi
ficationtend
benefitto accelerate
from the pooling
of
hundreds
or
thousands
Since
prepayments
when
interest
rates
fall,
due
to
the
refi
n
anci
n
g
and
early
payoff
of
existing
mortgage
loans,
security
holders cansinceexpectthetomortgages
receive greater
decreased
in the principal
pool werepayments
issued. when mortgage rates have
(CMOs)
are created securities,
from mortgage
passthrough
certifi
c
ates
and
referred
to
as
derivative
mortgage-backed
since
they than
are
derived
from
a
simpler
MBS
structure.
CMOs
have
a
more
complex
structure
mortgage
passthroughs.
AtheCMOcashissue
hasfromdifferent
each of(i.whie., ctheir
h hasclaims
a are
dinot
fferent
type
of
claim
to
fl
o
ws
the
pool
of
mortgages
just a proportional claim on the total cash flows from the pool).
securitization.
prepayment risk.
curtailment.)
mortgage passthrough security
1
Collateralized mortgage obligations
tranches,
©20 12 Kaplan, Inc.
Page 5 1
Study Session 1 5
Cross-Reference to CFA Institute Assigned Reading #54 - Overview of Bond Sectors and Instruments
Professor's Note: Tranche is from the French wordfor "slice. " In finance, when
a security issue consists ofdiffirent classes ofsecurities with diffiring claims
and especially with diffiring risks, the diffirent classes ofsecurities are called
tranches. You will likely run into this term only in reference to the diffirent
classes of securities that make up a CMO.
Anillustrate
exampla eCMO
of a simple
CMO
structure
with arethreecreated
tranchesoutwiloflahelp
to
structure.
Assume
that
three
tranches
passthrough
security.
Let'ng sparcallvalues.
them The
Tranches
I, II, areandtheIII.detail
Theys receive
interest ontotheeachbasiofs theof their
outstandi
foll
o
wing
of
the
payments
three
tranches.
I
(the
segment
of
the
issue)
receives
net
interest
on
outstanding
1. Tranche
principal andpaidall off.of the principal payments from the mortgage pool until it is
completely
2. Tranche
IIall(theof the principal payments
receiafter
ves itsTranche
share ofI hasnet been
interestcomplandetely
startspaid off.
receiving
Prior to that, it only receives interest payments.
IIIrepayments
(the after Tranches
receives monthly
net interest
and startspaid
receivioff.ngPrior
all to
3. Tranche
principal
I
and
II
have
been
completely
that, it only receives interest payments.
Tranche
I
has
the
shortest
expected
maturity
and
may
appeal
to
an
investor
wi
t
h
a preference
forinsecurities
with a shortersecurities
time horizon,
whoOther
previously
couldwith
not
participate
the
mortgage-backed
market.
structures,
prepayments
primarily
affecting
only
some
of
the
tranches,
are
used
to
redistribute
prepayment
risk.Investors
The tranches
with
lessto bear
prepayment
risk riwillsk will
become
more
attractivewittoh
some
investors.
better
able
prepayment
fi
n
d
the
tranches
higher prepayment risk attractive.
are eitheraffect
the principal
orofinterest
portions(IO)of
astrips
mortgage
passthrough
securi
t
y.
Prepayments
the
val
u
es
interest-only
and prepayments
principal-onlybecause
(PO) strips
differently.
The
holder ofis arecei
principal-only
strip
will
gain
from
the
face
val
u
e
of
the
security
v
ed
sooner
rather
than
later. Theratesholarederhigher
of an interest-only
striis only
p wilpaid
l receive
lessoutstanding
total payments
when
prepayment
since
interest
on
the
principal
amount, which is decreased by prepayments.
sequential
short-term
intermediate-term)
long-term)
Stripped mortgage-backed securities
LOS 54.f: Explain the motivation for creating a collateralized mortgage
obligation.
CFA® Program Curriculum, Volume 5, page 369
The passthrough securitiesCMOs
is to
inherent in
mortgage
and/or
The
CMOallstructure
takesprincipal
the cashpayments
flows from(boththeschedul
mortgageed payments
pool and, andin aprepayments)
simple
structure,
o
cates
any
sequentially over time to holders of different CMO tranches, rather than equally to
motivation for creating
Page 52
redistribute the prepayment risk
create securities with various maturity ranges.
©2012 Kaplan, Inc.
Study Session 1 5
Cross-Reference to CFA Institute Assigned Reading #54 - Overview of Bond Sectors and Instruments
all security
Creatirinsgk.a CMO does not alter the risk of prepayment, it
redi
stributesholders.
prepayment
Aspreferences-maki
a general rule, CMOs
arencreated
to satisfy a broader
range
of investor
risk/return
n
g
investi
g
i
n
mortgage-backed
securi
t
ies
more
appeali
n
g
to
a
wi
d
er
audience and decreasing overall borrowing costs.
overall
LOS 54.g: Describe the types of securities issued by municipalities in the
United States and distinguish between tax-backed debt and revenue bonds.
CFA® Program Curriculum, Volume 5, page 371
Debt securities issued(or by stateforandshort).
local governments in theare Uni
tedbyStates
arecounties,
known
ascities,
issued
states,
and
other
political
subdivisions
(e.
g
.
,
school,
water,
or
sewer
districts).
These
bonds
ofteneachissuedwithas its own maturithatty date
is, a and
largercoupon
issue israte.divided into a series of
smallerareissues,
Municipalis exempt
bonds arefromoftenfederal
referred
to astaxes. Note that,
or while interest
bonds, since
themay
coupon
interest
income
income
beat
taxthe free,
real
i
zed
capital
gai
n
s
are
not.
They
are
subject
to
normal
capital
gai
n
s
taxes
federal level. However, not all municipal bonds are tax exempt; some are taxable:
Different states tax(i.municipal
securities
differently;
theas taxvastexempt,
majoritybut
ofconsider
states treat
e
.
,
those
i
s
sued
within
the
state)
the interest
income
earned
on out-of-state
bonds
as fullyoftaxabl
estate
. Thus,is freethe
ifrom
nterest income
earned
on
most
in-state
bonds
held
by
a
resident
that
state
and federal
income
tax.certain
Such bonds
arestandards
referred into order
as to qualify
A
municipal
bond
must
meet
federal
for the tax-exempt status. If they don't, the bonds are considered
taxable
and
the
(they could
stillthanbe the
exempt
from
state
taxes).
rather
rule, as most municipal issues are exempt from federal taxes.
Anfirmopinion
as
to
the
tax-exempt
status
of
the
bonds,
typically
by
a
well-respected
l
a
w
issued.specializing in municipal bond issues, is provided to purchasers when the bonds are
municipal bonds
munis
Municipal bonds
serial bonds,
tax-exempt
•
tax-free
Tax exempt.
their own bonds
•
both
Taxable.
double tax free.
interest income on these bonds is subject to federal income tax
Taxable municipal bonds are the exception
Tax-Backed Debt and Revenue Bonds
Tax-backed
bonds,
also
called
general
obligation
(GO)
bonds,
are
backed
by
the
ful
l
faith,
of thespecial
issuer.districts,
Tax-backed
debt is issued
by school
districts,
towns,credit,
cities, andcounties, states, and
and include
the followi
ng types:
to a statutory limit on taxes that may be raised to pay
off the obligation. is subject
the
most
common
type
of
GO
bond,
is
secured
by
the
full
faiincludes
th andthecrediability
t of theto impose
borrowerindividual
and backedincome
by itstax,unlimited
taxiproperty
ng authority,
which
sal
e
s
tax,
tax,
and
corporate tax. This is the more secure form of GO.
taxingpower
•
•
Limited tax GO debt
Unlimited tax GO debt,
©20 1 2 Kaplan, Inc.
Page 53
Study Session 1 5
Cross-Reference to CFA Institute Assigned Reading #54 - Overview of Bond Sectors and Instruments
a special
clabyss additional
of GOs, areresources
backed not
only
byinclude
the issuing
authority'
s
taxing
power,
but
also
that
could
fees,
grants, and special charges that falarel outside
the
general
fund.
alsofundsknown
as during times of shortfal
Statesl.
someti
m
es
act
as
a
back
up
source
of
for
issuers
However,
the
state'
s
obligation
is
not
legall
y
binding,
but
is
a
"moral
obligation.
"
Thesecurity
state mayof appropriate
funds from its general fund. This
enhances
the
such
bonds.
Debt orsupported
by
programs
possess
a guarantee
by the
state
federal
government,
whi
c
h
i
s
a
l
e
gal
l
y
enforceable
contract
and
i
s
used
normally to assist the state's school system.
Revenue
bondsthearehelpsupported
only through
revenues
generatedrevenue
by projects
thatcanarebe
funded
with
of
the
original
bond
issue.
For
example,
bonds
issued
to
fund
transportation
systems,
housing
projects,
higher
education,
health
care,
sports
harbors, and ports. These bonds fall outside GO debt limits and do not
requirearenas,
voter approval.
The distinctionbecause
between
a generalof aobligation
and ais revenue
bondto payis important
for a
bondholder,
the
issuer
revenue
bond
obligated
principal
and
ithere,
nterestthe issuer does not make payments on the bond.by Inthecontrast,
project. general
If the funds
aren'
t
obligation
bonds
are
required
to
be
servi
c
ed
in
a
timel
y
fashion
irrespective
of
the
level
ofvolve
tax more
income
generated
by
the
municipali
t
y.
At
issuance,
revenue
bonds
typical
l
y
i
n
risk than general obligation bonds and, therefore, provide higher yields.
•
Double-barreled bonds,
•
Appropriation-backed obligations
moral obligation bonds.
moral pledge
•
public credit enhancement
only ifa sufficient level ofrevenue is generated
Insured Bonds and Prerefunded Bonds
Insured bonds
carrymadetheinguarantee
of a thirdThepartythird-party
that all principal
and(insurance)
interest
payments
wil
l
be
a
timely
manner.
guarantee
typi
c
ally
cannot
be
canceled;
i
t
i
s
good
for
the
life
of
the
bond.
There
are
several
fi
r
ms
that specialiresults
ze in iprovi
dingratings,
insurancewhiforch municipal
bond
issues.yieldMunicipal
bond
insurance
n
higher
reduces
the
required
and
improves
the
liquidi
t
y
of
the
bonds.
Insured
bonds
are
especi
a
ll
y
common
i
n
the
revenue
bond
market,
the general
to broadenbuttheir
appeal toobligation
investors.bonds of smaller municipal issuers are often insured
Prerefunded
bondsescrow
are bonds
for which
Treasurysuffi
securities
havemakebeenallpurchased
and
plrequi
acedredinbond
a special
account
in
an
amount
c
ient
to
the
remai
n
ingmust
payments.
The
Treasury
securi
t
i
e
s'
income
and
principal
payments
be suffi
ccall
ient date.
to fundBonds
the municipal
bond's required
payments
until
maturi
ty orarethrough
the
fi
r
st
that
are
prerefunded
have
l
i
t
tle
or
no
credit
risk
and
likely
to receive a rating of
AAA .
Page 54
©2012 Kaplan, Inc.
Study Session 1 5
Cross-Reference to CFA Institute Assigned Reading #54 - Overview of Bond Sectors and Instruments
LOS 54.h: Describe the characteristics and motivation for the various types of
debt issued by corporations (including corporate bonds, medium-term notes,
structured notes, commercial paper, negotiable CDs, and bankers acceptances).
CFA® Program Curriculum, Volume 5, page 375
Rating Agencies and Credit Ratings
Rati
n
g
agencies,
such
as
Moody'
s
and
S&P,
rate
specifi
c
debt
issues
of
corporations.
Some
oftativethe factors
factors can
theybeconsider
are quantitative,
butratimany
are issued
qualitative.
Even the
quanti
somewhat
subjecti
v
e.
The
n
gs
are
to
indicate
reltheatisecurity
ve probability
that all promised
paymentslooking.
on theRati
debtngswionll belong-term
made overbonds
the liwifellof
and,
therefore,
must
be
forward
consider factors that may come into play over at least one full economic cycle.
Some of the firm-specific factors considered are:
Past
repayment
history. ability to adapt to changing conditions.
Quali
t
y
of
management,
The
industry
outlook
andfirm.firm strategy.
Overal
l
debt
level
of
the
Operating
cashoffloliw,quidity
ability(cash,
to service
debt.assets).
Other
sources
sal
a
ble
Competi
position, regulatory
environment, and union contracts/history.
FiSusceptibility
nancialtivemanagement
and
controls.
to event risk and political risk.
Some factors specific to a particular debt issue are:
Priori
t
y
of
the
claim
being
rated.
Value/quality
ofofanythecoldebtlateral
pledged to secure the debt.
The
covenants
issue.
Any guarantees or obligations for parent company support.
•
•
•
•
•
•
•
•
•
•
•
•
•
Professor's Note: It may help to remember the primary factors as all Cs:
•�• Character ofthe issuer, Capacity to repay, the Collateral provided, and the
Covenants of the debt issue.
Secured Debt, Unsecured Debt, and Credit Enhancements for Corporate Bonds
Secured
forms: debt is backed by the pledge of assets/collateral, which can take the following
Personalproperty (e. g . , machinery, vehicles, patents) .
Real property (e. g . , land and buildings) .
Financial assets (e. g . , stocks, bonds, notes). These assets are marked to market from
tiofmmore
e to tiassets
me toifmonitor
theirinsuffiliquidati
oBonds
n values.backed
Covenants
may require
a pledge
values
are
c
ient.
by
fi
n
ancial
assets
are
called
collateral trust bonds.
•
•
•
©20 1 2 Kaplan, Inc.
Page 55
Study Session 1 5
Cross-Reference to CFA Institute Assigned Reading #54 - Overview of Bond Sectors and Instruments
Inof default,
all of thesethe cases,
the bondholder
holds
a lienandon usethe thepledged
property.
In thethecase
l
i
e
n
holder
can
sell
the
property
proceeds
to
satisfy
obligations
of
the
borrower.
In
most
cases
of
default,
some
mutual
agreement
wi
l
l
be reached
a new structure,
but the ibondhol
ders' claim on the pledged assets
signifi
cantlyforstrengthens
their position
n renegotiation.
debt
i
s
not
backed
by
any
pledge
of
specific
col
l
ateral.
Unsecured
bonds
are referred
tobeen
as debentures.
They
represent
a general
claim
onassetsanygenerate
assets offunds
the issuer
that
have
not
pl
e
dged
to
secure
other
debt.
If
pl
e
dged
upon
liquidation
i
n
excess
of
the
obligation,
then
these
excess
funds
are
avai
l
abl
e
for
satisfying
thesatisfied
claimsafterof unsecured
debt
holders.
Subordinated debentures have claims that are
(subordinate to) the claims of senior debt.
Credi
are theTypiguarantees
be paidt enhancements
in a timely manner.
cally, theyof others
take onethatofthethe corporate
following debt
forms:obligation wil
Third-party guarantees that the debt obligations will be met. Often, parent
companies guarantee the loans of their affiliates and subsidiaries.
Letters ofcredit are issued by banks and guarantee that the bank will advance the
funds to service the corporation's debt.
Bond insurance can be obtained from firms that specialize in providing it.
When
analyzi
n
g
credi
t
-enhanced
debt,
analysts
should
focus
on
the
fi
n
anci
a
l
strength
of
both
theenhancement.
corporationThe
issuingprotection
the debttoandthethebondfinancial
strength
of thethanpartytheprovidi
ng
credi
t
hol
d
er
is
no
better
promise
ofguarantor
the entity(enhancer)
offering thecan credit
enhancement.
decrease
in
the
creditworthiness
of
the
A
lead to a rating downgrade of the debt issue.
Unsecured
•
•
•
Medium-Term Notes
Professor's Note: Be careful here. Medium-term notes are not necessarily
medium-term or notes!
issues
typicalanlyunderwriting
(1) are sold alsyndi
l at conce,
(2) are soldtheonsalea fiofrm­the whole
commitment
basis
whereby
ate
guarantees
issue, and (3) consist of bonds with a single coupon rate and maturity.
Medium-term
(MTNs)
differ
from
a
regul
a
r
corporate
bond
offering
i
n
al
l
of
these characteristics.
MTNs
are
regi
s
tered
under
SEC
Rule
415
(shelfregistration) which means that they need
not bein sold
all at once.
Once
registered,
such securities
can MTNs
be "placedare sold
on theovershelf"
and
sold
the
market
over
time
at
the
discretion
of
the
issuer.
time,
wi$1thmieach
sal
e
satisfying
some
minimum
dollar
amount
set
by
the
i
s
suer,
typical
l
y
llion and up.
MTNs
are
issued
i
n
various
maturities,
rangi
n
g
from
nine
months
to
periods
as
long
as 100theyyears.wishIssuers
provide
maturity ranges (e.g., 18 months to two years) for MTNs
that
to
sell
and
provide
quotes forinterested
those ranges,
typicallytheas anotes
spreadmaketo
comparable maturity Treasury issues.yieldInvestors
in purchasing
Corporate bond
notes
Page 56
©2012 Kaplan, Inc.
Study Session 1 5
Cross-Reference to CFA Institute Assigned Reading #54 - Overview of Bond Sectors and Instruments
an offer
to ranges
the issuer'offered.
s agent,Thespecifying
theconfi
facermsvaluetheandissuer'an sexact
maturittoy wisellthinthose
one
of
the
agent
then
will
i
ngness
MTNs and effects the transaction.
The
offering
i
s
done
by
the
issuer'
s
agent
on
a
best-efforts basis. There is no firm
commitment on the agent's part to sell a specific amount of bonds.
MTNs
can
have
fi
x
ed
or
fl
o
ating-rate
coupons,
can
be
denominated
in
any
currency,
and
can have
special
features,cansuch
as calls, caps,
flderioors,vatiandve non-interest
ratecreate
indexed
coupons.
The
notes
issued
be
combined
wi
t
h
i
n
struments
to
the is
special
features
that
an
investor
requires.
The
combination
of
the
deri
v
ati
v
e
and
notes
called a structured security.
Structured Notes
Aor note with a derivative.
is a debtThissecurity
created
whena security
the issuerthatcombines
a typical
bond
is
done
to
create
has
special
appeal
to the
some
institutional
investors.
The
targeted
institutional
i
n
vestors
face
restrictions
on
types of securities
they
caninnovati
purchase.
Structured
securities
allow them
to avoid
these
restrictions.
As
wi
t
h
any
v
e
debt
securi
t
y,
the
motivation
to
i
s
sue
them
is to
lower overall borrowing costs.
Asor deri
an example,
consider
anissuer
institutional
investora structured
that is prohibited
fromtheowning
equity
v
ati
v
e
securi
t
ies.
An
could
create
note
where
periodic
coupon
payments
werenote
basedwoulon dthestillperformance
of an equity
securityproduce
or an equity
index.
This
structured
be
a
debt
security,
bur
would
returns
closer
to
holdi
n
g
the
equity
i
n
dex
i
t
sel
f
.
The
mechani
c
s
of
creati
n
g
this
security
would
bederivative
to issuethata debtrequires
securitytheandpayment
combineof aitfiwith
an equity
swap. An equity swap is a
x
ed
rate
of
interest
(theor equity
couponindex
rate oneachthe
bond
here),
and
pays
i
t
s
owner
the
rate
of
return
on
the
equity
period.
By
combining
the
bond
wi
t
h
the
equity
swap,
a
structured
note
is
created
that
pays
percentage rate of return on the equity semiannually instead of paying a fixed
couponthepayment.
Types of structured medium-term notes include:
Step-up n tes Coupon rate increases over time on a preset schedule.
Inversefl aters Coupon rate increases when the reference rate decreases and
decreases
when
the
reference
rate
increases.
Deleveragedfl aters Coupon rate equals a fraction of the reference rate plus a
constant margin.
Dual-indexedfl aters Coupon rate is based on the difference between two reference
rates.
Range n es Coupon rate equals the reference rate if the reference rate falls within a
speci
f
i
e
d
range,
or
zero
if
the
reference
rate
fall
s
outside
that
range.
Index amortizing n tes Coupon rate is fixed but some principal is repaid before
maturity, with the amount of principal prepaid based on the level of the reference
rate.
structured note
•
•
o
o
•
-
-
o
•
•
•
-
o
ot
-
-
o
-
©20 1 2 Kaplan, Inc.
Page 57
Study Session 1 5
Cross-Reference to CFA Institute Assigned Reading #54 - Overview of Bond Sectors and Instruments
We
wil cover
equitynotes
swaps,in interest
rate swaps,
andsession.
otherForderiourvatipurposes
ves commonly
usedis
tosufficient
create
structured
a
subsequent
study
here,
it
that
you
understand
that
structured
notes
are
created
by
combining
regular
debt withtoderivati
ve securiti
es to maketheyaface"debtandsecuri
ty" thatreduceallowsthecertain
institutional
investors
get
around
restrictions
thereby
borrowing
costs of
the company creating the structured note.
Commercial Paper: Directly-Placed and Dealer-Placed Paper
isrates
a short-term,
unsecured
debtCommercial
instrumentpaper
used isbyissued
corporations
tomaturi
borrow
money
at
lower
than
bank
rates.
witorh less
t
i
e
s
of
270
days
or
less,
si
n
ce
debt
securities
wi
t
h
maturities
of
270
days
aremostexempt
It is issued
issues from
beingSEC
in theregistration.
2-day to 90-day
range.with maturities as short as two days, with
SimilaratosinglT-bills,
commercial
paperthe iface
s typically
issued
as a pure
discount
security
and
makes
e
payment
equal
to
val
u
e
at
maturity.
There
i
s
no
active
secondary
market in commercial paper, and most buyers hold commercial paper until maturity.
Commercial
generall
bycredicorporations
hfirrelativel
y strongorcredit
and
theinventories.
proceedsFipaper
arenance
oftenissubsidiaries
used toy fiissued
nofancemanufacturi
t givenng tofirmsthewitissue
m'scommercial
customers
to
fi
n
ance
paper tobank
fund
customers'
purchases
of
the
parent
company'
s
products.
Issuers
often
keep
unused
lineeded
nes oftocredipayt inoffplace
to
use
in
case
new
paper
cannot
be
issued
to
generate
the
funds
maturing paper.
i
s
commercial
paper
that
i
s
sol
d
to
large
investors
without
going
through an agent
broker-dealer.
Large issuers
willlarge
deal wiamounts.
th a select group of regular
commercial
paperorbuyers
who customarily
buy very
iscommercial
sold to purchasers
throughto serve
a commercial-paper
dealer.
Mostshort­
large
investment
firms
have
paper
desks
thei
r
customers'
needs
for
term cash-management products.
Commercial paper
Directly-placed paper
Dealer-placed paper
Negotiable CDs and Bankers' Acceptances
(CDs)bankaretoissued
bya certain
banks andamount
sold plus
to theirinterest
customers.
They
represent
a
promi
s
e
by
the
repay
and,
i
n
thatissuedway,
arein speci
similfaicr denominations
to other bank deposits.
In
contrast
to
regul
a
r
bank
deposits,
CDs
are
and
for specifibyethed periods
ofDeposit
time thatInsurance
can be ofCorporation
any length.
In(FDIC)
the Uniuptedto States,
CDs
are
insured
Federal
a maximum
valuevalue
in theareevent
the issuing
bank
becomes only
insolvent.
Amounts
above
the
maximum
not
insured
and
are,
therefore,
as
secure
as
the bank that issues the CD.
Typical
bank CDsearliiner thethanUnited
Statestycarry
aofpenalty
to the owner ifhowever,
the funds
arepermit
withdrawn
the
maturi
date
the
CD.
sell thebyCDU.S.in banks
the secondary
at anyCDs,
time.whereas
Negotiable
issued inthetheowner
Unitedto States
are termedmarket
domestic
U. S .CDs
Certificates of deposit
CD
Negotiable COs,
Page 58
©2012 Kaplan, Inc.
Study Session 1 5
Cross-Reference to CFA Institute Assigned Reading #54 - Overview of Bond Sectors and Instruments
dollaUnir denominated
CDs
issuedEurodollar
by foreigCDs.
n banksNegoti
andabranches
of U.S.maturities
banks outside
the
t
ed
States
are
termed
ble
CDs
have
ranging
from
days
up
to
fi
v
e
years.
The
i
n
terest
rate
paid
on
them
is
call
e
d
the
London
Interbank
Offering Rate because they are primarily issued by banks' London branches.
Bankers'are acceptances
areofessential
ly guarantees
by a bank
that ainternational
loan will be trade.
repaid.As
They
created
as
part
commercial
transactions,
especially
an example,45 consider
antheimporter
whoshipped.
agrees The
to payimporter
for goodsgoesshipped
tobankhimandbygets
an
exporter,
days
after
goods
are
to
his
aletter
lettermust
of credi
t statitontheg thatbanktheofbank
will guarantee
thethepayment,
say $1actualmillion.
Thisthe
be
sent
the
exporter
before
exporter
will
l
y
ship
goods.
When
the
exporter
del
i
vers
the
shipping
documents
to
her
bank,
she
wil
l
recei
v
e
forthe 45present
days.value of the $1 million, discounted because the payment will not be made
Theevidence
final stepofinshipment
the creationto theof aissuing
bankers'bankacceptance
is thats bank)
the exporter'
sthen
bankaccepts
presents
the
(the
importer'
which
the
evidence
of
shipment.
It
is
this
accepted
promise
to
pay
$1
million
i
n
45
days
that
is
the
bankers'andacceptance.
Theborrower
importerof wilthelfunds.
sign documents
evidencing
hiss completed,
obligationtheto
hiimsporter
bank
becomes
the
When
thi
s
final
step
i
receives the documents necessary to receive the shipment of goods.
The
exporter'
s bank
canfundeitherinterested
continueintoshort-term
hold the acceptance
oracceptance
sell it to anis aindiscount
vestor,
often
a
money
market
paper.
The
instrument
andthesellsshipping
for thedate.
present
value
of themarket
single $1formillion
payment
to beismade
45limdays
from
The
secondary
bankers'
acceptances
itedtysodates.
their liquidity is limited and most purchasers intend to hold them until their
maturi
The
the riskfailthat
the importer
(the initial
of thecredit
funds)riskandof thea bankers'
acceptiacceptance
ng bank wilils both
to make
the promised
payment.borrower
LOS 54.i: Define an asset-backed security, describe the role of a special purpose
vehicle in an asset-backed security's transaction, state the motivation for a
corporation to issue an asset-backed security, and describe the types of external
credit enhancements for asset-backed securities.
CFA® Program Curriculum, Volume 5, page 386
Credit
card debt,
automortgages
loans, bank
loans,
and corporate
recei
vablfinancial
es are often
securitized
iunderlying
n the same
way
as
are
in
the
MBS
structure.
These
assets
areethethe
collateral
for
bonds
that
are
also
asset-backed
securities
(
A
BSs).
Whil
above
types
of
underl
y
ing
assets
are
the
most
common,
innovati
v
e
ABSs
have
al
s
o
been
created.
David Bowie
millionreleased
dollar ABS
where the
underlyinIng one
assetscase,weresinthegerroyalties
from sold
25 ofa hi$55s albums
priorissue
to 1990.
©20 12 Kaplan, Inc.
Page 59
Study Session 1 5
Cross-Reference to CFA Institute Assigned Reading #54 - Overview of Bond Sectors and Instruments
Role of a Special Purpose Vehicle
Awhich
speciala corporation
purpose vehicle,
or special
purpose corporation, is a separate legal entity to
transfers
the
financial
assets
forto the
an ABS
issue.purpose
The importance
ofshithis
i
s
that
a
legal
transfer
of
the
assets
i
s
made
special
vehiclnge.itThis
e
lds
the
assets
from
the
cl
a
i
m
s
of
the
corporation'
s
general
creditors,
maki
possibleBecause
for the theABSassets
issueareto receive
athehigher
credit
ratingvehicle,
than thetheycorporation
asunlaikely
whole.
sold
to
special
purpose
are
hi
g
hly
tospecibeasubject
to
any
cl
a
ims
ari
s
i
n
g
from
the
bankruptcy
of
the
corporation,
and
the
l purpose vehicle is termed a bankruptcy remote entity.
Motivation for a Corporation to Issue an Asset-Backed Security
The
motivation
fornga thecorporation
to aissue
asset-backed
securi
tiescanis toissuereducethe borrowing
costs.
By
transferri
assets
into
separate
entity,
the
entity
bonds
and
receive
her ratingyiethan
reducesathehigrequired
ld onthetheunsecured
(ABS) debt.debt of the corporation. The higher rating
External Credit Enhancements
Because
asset-backed
securities,
on
their
own,
may
not
receive
the
highest
possible
credit rating,or thesecurity.
issuerCredit
may choose
tocanenhance
the crediteitherratingexternal
by providing
additional
guarantees
quality
be
enhanced
l
y
or
i
n
ternall
y.
External credit enhancement commonly takes the following forms:
Corporate guarantees, which may be provided by the corporation creating the ABS or
itsLetters
parent.ofcredit, which may be obtained from a bank for a fee.
Bond insurance, which may be obtained from an insurance company or a provider
speci
a
lizing
in
underwriting
such
structures.
This
is
also
referred
to
as
an
insurance
wrap.
None
of thesetoenhancements
comea tradeoff
without between
cost. Thethedecision
ofenhancement
how much and the
enhancement
provide
involves
cost
of
resulting decrease in the market yield required on the bonds.
Noteguarantor,
that the qual
itytheofcredit
a credit-enhanced
security canis onlyrefleasctgood
as the qualityinofthe
the
and
rati
n
g
of
the
security
any
deterioration
guarantor's rating.
•
•
•
LOS 54.j: Describe collateralized debt obligations.
CFA® Program Curriculum, Volume 5, page 388
Apromise
collateralized
debt
obligation
(CDO)
is
a
debt
instrument
where
the
col
l
ateral
for
the
to pay is andebtunderlying
poolcanofbeother
debt loans,
obligations
and evendebtother
CDOs.
These
underlying
obligations
business
mortgages,
of
devel
oping
countries,
corporate
bonds
of
various
ratings,
asset-backed
securities,
or
even
problem/
non-performing loans. Tranches of the CDO are created based on the seniority of the
Page 60
©2012 Kaplan, Inc.
Study Session 1 5
Cross-Reference to CFA Institute Assigned Reading #54 - Overview of Bond Sectors and Instruments
clainmgss todependi
the cashng flonowstheofseniority
the underlying
assets, asandwelltheseas thearecreditworthiness
given separate credit
rati
of
the
claim,
of the
underlying pool of debt securities.
CDOs
may
be
created
by
a
sponsor
that
seeks
to
profi
t
on
the
spread
between
the
rate
to be earnedCDO),
on theor underlying
assets
andor insurance
the rate promised
toseekithenCDO
holderits(anloan
arbitrage
created
by
a
bank
company
g
to
reduce
exposure on its balance sheet (a balance sheet CDO).
LOS 54.k: Describe the mechanisms available for placing bonds in the primary
market and distinguish between the primary and secondary markets for bonds.
CPA® Program Curriculum, Volume 5, page 389
The
primary
market
for
debt
(newl
y
created
debt
securities)
functions
in
a
manner
similar
to thetheprimary
marketandforin distributing
equities. Typical
liy,ng)antheinvestment
bankertoisinvestors.
involved
iWhen
n advising
debt
i
s
suer
(sell
debt
securities
thehaveinvestment
banker
actually
purchases
the entireis termed
issue anda firm
resellscommitment
it, they are
said
to
"underwri
t
ten"
the
issue.
Thi
s
arrangement
while the dealwiisll termed
a put
bought deal. In an underwritten offering of debt securities, the
underwriter
typi
c
al
l
y
together
a syndicancatereduce
of othertheiinvestment
bankers asto much
aid in
distributing
the
securities.
The
underwriters
r
risk
by
preselling
ofexposure
the offering
asissuepossible
to period
their institutional
clientsowniandnghedging
the interest
rate
riskve
of
the
for
the
they
anticipate
the
securities.
An
al
t
ernati
istermed
for thedoiinvestment
to sell all of the issue that they can and this is
ng the offeribanker
ng ontoa agree
best efforts basis.
Because
the
price
paid
for
the
issue
and
the
anticipated
sal
e
price
are
determined
between
the (lead) investment bank and the issuing company, the offering is termed
asecurities
negotiated offering. Another approach is an auction process where an issuer of debt
determines
theofsizmultiple
e and termsinvestment
of the issuebanks,andbidseveral
investment
banks,
or
underwri
t
i
n
g
syndicates
on
what
interest
rate
they
require to sell it. The syndicate with the lowest interest rate bid will be awarded the deal.
InthetheSEC.United
States,
securities
to besecurities
offered toispublic
investorsformustsalebeto registered
with
When
a
new
issue
of
debt
not
registered
the
public,
stillRulemay144Abe offering
sold to a(after
smallthenumber
of investors.
Thistransactions).
is called a private
placement
oritregistration
rule
that
al
l
ows
such
Avoidance
of
the
processnumber
is valuable
to the issuer and, because
a pricanvatebe placement
involneeds
ves
aandsalepreferences
to a small
of
investors/institutions,
the
i
s
sue
tailored
to
the
ofregithestered,
buyers.theBecause
thewilissue
cannota slightly
be soldhigher
to theinpublic
unletoss
itcompensate
is subsequently
buyers
l
require
terest
rate
placement. them for the lack of liquidity of securities that are sold though a private
The
secondary
market trading
for debtnetworks.
securitiesTraditionall
includes exchanges,
an over-the-counter
dealer
market,
and
electronic
y
,
most
secondary
tradi
n
g
in
debt
securitiesforwasandtransacted
a dealer market,
ers buyingMoreandrecently,
selling
bonds
from theirininventories
(i.e., actiwintgh asbroker/deal
market makers).
©20 1 2 Kaplan, Inc.
Page 6 1
Study Session 1 5
Cross-Reference to CFA Institute Assigned Reading #54 - Overview of Bond Sectors and Instruments
theoperations
costs andhaverisksincreased
of supplying
the capital
necessary
toBecause
adequatelofythis,fundelectroni
bond trading
and
spreads
have
decreased.
c trading
haselectroni
becomec networks
a more important
part
of
the
secondary
market
for
debt
securities.
These
can be bidscustomer
and offersbidsbyanda single
dealposted
er, bidons and
offers byc multiple
deal
e
rs,
or
simply
anonymous
offers
an
electroni
trading
system with a trade clearing system.
Page 62
©2012 Kaplan, Inc.
Study Session 1 5
Cross-Reference to CFA Institute Assigned Reading #54 - Overview of Bond Sectors and Instruments
KEY CONCEPTS
LOS
54.gna debt refers to the debt obligations of governments. U.S. Treasury securities are
Soverei
sovereign
debt
of
the
U.S.
government
and
are
considered
free
of
credit
ri
s
k.
Soverei
g
n
debt of other countries has varying degrees of credit risk.
SovereiRegulgn adebt
is typicyclcalleywith
issuedtheusing
one
of four
methods:
r
auction
enti
r
e
issue
sold
at a single
price.
Regul
a
r
auction
cycl
e
with
bonds
issued
at
multiple
prices.
AdTaphocsystem,
auctionauctioning
system with
no
regul
a
r
cycle.
new bonds identical to previously issued bonds.
LOS
54.b issued by the U.S. Treasury include:
Securities
Bills-pure-discount
securities
maturing
i
n
four
weeks,
three
months,
or
six
months.
Notes-coupon securi
ties maturi
and ten years.
Bonds-coupon
securities
maturingng inin two,
20 orfiv30e, years.
Treasury
InfliastionfixedProtected
Securities
(TIPS)
areperiodical
U.S. Treasury
issues
in which
theon
coupon
rate
but
the
par
val
u
e
is
adjusted
l
y
for
infl
a
tion,
based
changes in the CPl.
U.Treasuries
S. Treasuries
from
the
most
recent
auction
are
referred
to
as
on-the-run
issues,
whi
l
e
from previous auctions are referred to as off-the-run issues.
LOS
54.
c
Strippedeach
Treasury
securities
are created
byandbondprincipal
dealerspayments,
who buy Treasury
securities,
separate
of
their
scheduled
coupon
and
resel
l
these as
zero-coupon securities.
Treasury
strips
are
traded
i
n
two
forms-coupon
strips
and
principal
strips-and
are
taxed by the IRS on the basis of accrued interest, like other zero-coupon securities.
LOS 54.dof the U.S. government, including federally related institutions and
Agencies
government-sponsored
enterprises,to ibessuealmost
bondsdefault
that arerisknotfree.obligations of the
U.S. Treasury bur are considered
LOS
54.
e
A(themortgage
passthrough
securityy cash
is backed
bythata pool
of amortizing
mortgagescheduled
loans
col
l
ateral)
and
has
monthl
fl
o
ws
include
interest
payments,
principal payments, and prepayments of principal.
Prepayment
riskcontain
is signifiacprepayment
ant for investors
in passthrough
securities
because
mostto
mortgage
loans
option,
which
al
l
ows
the
issuer
(borrower)
make additional principal payments at any time.
•
•
•
•
•
•
•
©20 12 Kaplan, Inc.
Page 63
Study Session 1 5
Cross-Reference to CFA Institute Assigned Reading #54 - Overview of Bond Sectors and Instruments
Collateralinterest
ized mortgage
obliof mortgage
gations (CMOs)
are customized
claimsredistribute
to the principal
payments
passthrough
securities
and
the
and/or
prepayment risk and/or maturity risk of the securities.
LOS
54.
f
CMOsngarethecreated
decrease borrowing
by redistributing
alteri
maturittoy structure
to better suicosts
t investor
preferences.prepayment risk or
LOS
54.gpayments on state and local government securities (municipal securities, or
Interest
munis)
are
usual
l
y
exempt
from
U.
S
.
federal
taxes,
and
from
state
taxes
in
the
state
of
tssuance.
Municipal
bonds(general
include:obligation) bonds backed by the taxing authority of the
Tax-backed
governmental
unitbacked
issuingonlythebysecurities.
Revenue
bonds,
the
revenues
from
the
project
specifi
c
ally
financed
by the bond issue.
LOS
54.h debt securities include bonds, medium-term notes, and commercial paper.
Corporate
Bond
rating
agenci
e
s
rate
corporate
bonds
on
capacity
to
repay
(liquid
assets
and
cash
flcredi
ow),t himanagement
qualidebtty,leindustry
prospects,
corporate
strategy,
financial
policies,
s
tory,
overall
vels,
the
collateral
for
the
issue,
and
the
nature
of the
covenants.
Corporate
may financial
be securedassets,
or unsecured
debentures). Security can be in the
form
of realbonds
property,
or personal(called
property/equipment.
Medium-term
notes
(MTN)
are
issued
periodically
by
corporations
under
a
shelf
regi
stration,to sold
on a best-efforts basis, and have maturities ranging from
morebythanagents30 years.
9 months
combine ainvestors.
bond with a derivative to create a security that fills a need
forStructured
particulnotes
ar institutional
Commercial
a short-term
corporate
finthan
ancing270vehicle
and
does notin require
regisDirectly-placed
tration wipaper
th theispaper
SEC
ifsoldits dimaturi
t
y
is
less
days.
CP
comes
two
forms:
rectly bythrough
the issuer.agents/brokers.
Dealer-placed paper sold to investors
Negotiablaree CDs
arebyissued
inassets,
a wideandrangeare termed
of maturities
by banks,
trade
indenominated
a secondary
market,
backed
bank
Eurodollar
CDs
when
in U.S. dollars and issued outside the United States.
Bankers'
acceptances
are
issued
by
banks
to
guarantee
a
future
payment
for
goods
lishipped,
mited liqsolduidity.at a discount to the future payment they promise, short-term, and have
•
•
•
•
Page 64
©2012 Kaplan, Inc.
Study Session 1 5
Cross-Reference to CFA Institute Assigned Reading #54 - Overview of Bond Sectors and Instruments
LOS 54.i securities (ABS) are debt that is supported by the cash flows from an
Asset-backed
underlying
pool
of
mortgages,
auto
loans,
credit
card
receivables,
commercial
loans,
or
other financial assets.
Atransferred.
special purpose
vehi
cle is an transferring
entity to whithese
ch theassets
assetsgoesthatbankrupt,
back an ABS
are legall
ynot
If
the
corporation
the
assets
are
subject
to
cl
a
ims
from
its
creditors.
As
a
result,
the
ABS
can
recei
v
e
a
higher
credit
rating
than the corporation and reduce the corporation's funding costs.
External
credit
enhancement
for
an
ABS
can
include
corporate
guarantees,
letters
of
credit, or third-party bond insurance.
LOS
54.j ized debt obligations (CDOs) are backed by an underlying pool of debt
Coll
a
teral
securities
whichmortgage-backed
may be any onesecurities,
of a numberor other
of types:CDOs.
corporate bonds, loans, emerging
markets debt,
LOS
54.
k
The
in bonds includes underwritten and best-efforts public offerings, as
well primary
as privatemarket
placements.
The secondary
market
indealer
bondsmarket,
includesandsome
trading
onnexchanges,
awhimuchch arelargeran
volume
of
tradi
n
g
in
a
electroni
c
tradi
g
networks
increasingly important part of the secondary market for bonds.
©20 12 Kaplan, Inc.
Page 65
Study Session 1 5
Cross-Reference to CFA Institute Assigned Reading #54 - Overview of Bond Sectors and Instruments
CONCEPT CHECKERS
security
i
s
quoted
at
97-17
and
has
a
par
val
u
e
of
$100,
0
00.
Whi
c
h
1. AofTreasury
followi0n0.g is its quoted dollar price?
A.B. the$97,170.
$97,531.
$100,000.205.0.
investor(TIPS)
holds that
$100,carry
000 a(par2.5o/ovalue)
worth
of
Treasury
Infl
a
ti
o
n
Protected
2. AnSecurities
coupon.value
If theofannual
iafter
nflatisixonmonths?
rate is 3o/o, what is the inflasemiannual
tion-adjustedpayprincipal
the bond
A.B. $102,500.
$101,500.
$103,000.
holds
$100,
0is00paid(parsemiannual
value) worth
ofTIPS
currentlinflation
y tradingrateat ipar.
3. AnTheinvestor
coupon
rate
of
4o/o
l
y
,
and
the
annual
s
2.months?
5o/o. What coupon payment will the investor receive at the end of the first six
A.B. $2,$2,0000.25.
$2,050.
note li(T-note)
principaltostriap6-month
has six months
remaining
to maturity.
4. AHowTreasury
i
s
i
t
s
price
k
el
y
to
compare
Treasury
bil
l
(T-bill)
that
has
been issued? The T-note price should be:
A.just
lower.
C.B. higher.
the same.
ch of theprincipal
followingstrips
statements
aboutcreated
Treasuryfromsecurities
is bills.
most accurate?
5. A.WhiTreasury
are
usually
Treasury
bonds
maystripsbe make
used tolower
createcoupon
Treasurypayments
couponthanstrips.Treasury principal
B.C. Treasury
Treasury
coupon
strips.
of thehigher
followiyields?
ng municipal bonds typically has the greater risk and is
6. Which
issued
with
Revenue taxbonds.
A.B. Limited
C. Unlimited taxgeneral
generalobligation
obligationbonds.
bonds.
is serviced
withis thecalledearnings
from a pool ofTreasury securities
7. Athatbondhaveissuebeenthatplaced
i
n
escrow
a(n):
A.B. prerefunded
insured bond.bond.
C. credit-enhanced obligation.
c.
c.
c.
Page 66
©2012 Kaplan, Inc.
Study Session 1 5
Cross-Reference to CFA Institute Assigned Reading #54 - Overview of Bond Sectors and Instruments
8.
9.
10.
11.
12.
13.
14.
Ofthe therequirements
following, oftheSECdebtRulsecurities
that registration)
are most oftenare:registered according to
e
415
(shelf
A.B. corporate
bonds.
medium-term notes.securities.
C. mortgage-backed
Aofcorporation
issuing
asset-backed
securities
can oftenbyimtransferring
prove the credit
rating
the
securities
to
above
that
of
the
issuing
company
the
assets
A.toB. a(n):
asset
trust.
bond
insurer.
C. special purpose vehicle.
Which
ofon-the-run
the followinissue:
g is a
between an on-the-run and an off-the-run
issue?
An
A.B. hasis thea shorter
most recentl
y tissued
security
of that type.
maturi
y
than
an
off-the-run
issue.
C. is publicly traded whereas an off-the-run issue is not.
to a public
offering,
aeprild.vate placement of debt securities has:
more
liquidi
t
y
and
a
l
o
wer
yi
A.Compared
B.C. less
liquidity
and
a
l
o
wer
yi
e
ld.
less liquidity and a higher yield.
to liquid.
negotiable CDs, bankers acceptances:
A.Compared
are
more
B.C. have
shorter
maturities
on
average.
are more likely to pay periodic interest.
Adeveldebtopisecurity
that isiscollateralizeda(n):by a pool of the sovereign debt of several
n
g
countries
A.B. CMO.
CDO.
C. ABS.
vities inmaking.
the primary market for debt securities would
include:
A.Acti
market
B.C. aa fibest-efforts
offering.
rm commitment.
difference
Likely
most Likely
Least Likely
©20 1 2 Kaplan, Inc.
Page 67
Study Session 1 5
Cross-Reference to CFA Institute Assigned Reading #54 - Overview of Bond Sectors and Instruments
ANSWERS - CONCEPT CHECKERS
1.
B
This value is computed as follows: dollar price =
97
17
32
o/o X $100,000 = 0.9753125 X $ 1 00,000 = $97,531.25.
2.
A
The annual inflation rate is 3%, which corresponds to 1 .5% semiannually. Therefore,
the principal value has increased by 1 . 5%. So we have: new principal = $ 1 00,000 x
1 .015 = $ 1 0 1 ,500.
3.
B
This coupon payment is computed as follows:
coupon payment = ($100,000 x l .0125)
Page 68
(�)
0 4
·
= $2,025
4.
C
The T-note principal strip has exactly the same cash flows (the principal) as the T-bill.
Therefore, the prices of the two securities should be (about) equal. However, market
imperfections, such as illiquidity, may lead to differences.
5.
B
Treasury coupon and principal strips are created by separating (stripping) the principal
and coupons from Treasury notes and bonds and selling packages of these single­
maturity cash flows as individual zero-coupon securities. Treasury bills cannot be used
because they are already zero-coupon securities.
6.
A
Revenue bond issues are only obligated to pay principal and interest if revenue from
the project that they helped fund is sufficient to service the issue. When issued, revenue
bonds typically are riskier than general obligation bonds and, consequently, have higher
yields.
7.
B
The cash flows generated by an escrow pool of Treasury securities are used to service
prerefunded bonds. Insured bonds carry third-party guarantees. There are no securities
formally known as absolute priority bonds or credit enhanced obligations (yet) .
8.
B
Shelf registration is used with medium-term notes. This permits the issue to be held in
inventory (on the shelf) and sold in parcels at the discretion of the issuer. Corporate
bonds and MBS are usually sold all at once.
9.
C
The assets are sold to a special purpose vehicle to protect them from general claims
against the issuing corporation.
10. A
On-the-run issues are the most recently issued securities.
11. C
Investors require a higher yield to compensate for the fact that privately placed debt is
not registered for public sale and is therefore less liquid than debt registered for public
sale.
12. B
Bankers' acceptances are short-term and pay no periodic interest. Like negotiable COs,
they are as good as the credit of the issuing bank but have a very limited secondary
market.
13. B
A COO or collateralized debt obligation is backed by an underlying pool of debt
securities which may be emerging markets debt. A CMO is backed by a pool of
mortgages, and an ABS is backed by financial assets.
14. A
Market making refers to a dealer that trades in the secondary market for its own account
from inventory.
©2012 Kaplan, Inc.
The following is a review of the Analysis of Fixed Income Investments principles designed to address the
learning outcome statements set forth by CFA Institute. This topic is also covered in:
UNDERSTANDING YIELD SPREADS
Study Session 1 5
EXAM FOCUS
Yiofedebt
ld spreads
are
si
m
pl
y
di
f
ferences
between
the
yiel
d
s
of
any
two
debt
securiti
e
s
or
types
securities.cs that
Try drito vgete yiaeldgoodspreads.
grip You
on theshouldspreadknowtermiallnthree
ologytheori
in thiess ofrevitheewterm
and
thestructure,
characteristi
not
only
thei
r
impli
c
ati
o
ns
for
the
shape
of
the
yi
e
ld
curve
but
also
what
the
yiel
d
curve
can tell yiel
us under
of thetax-free
three andtheories.
taxableshape
and after-tax
ds andeach
between
taxablLearn
e equivthealentrelyiatieldsonships
well. between
LOS 55.a: Identify the interest rate policy tools available to a central bank.
CPA® Program Curriculum, Volume 5, page 408
While theinterest
are determined
by a varito emanage
ty of economic
conditions,
in theitsUnited
States
FederalratesReserve
(Fed)
attempts
short-term
rates
through
The four interest rate tools of the Fed are as follows:
monetary policy tools.
1. The
discount
rate
is
the
rate
at
whi
c
h
banks
can
borrow
reserves
from
the
Fed.
A
l
o
wer
rate tendsdiscount
to increase
lending,
higher
rate hasbankthereserves,
oppositeencourage
effect, raising
rates.and decrease interest rates. A
2. Fed
Openinmarket
operations
referstheto theFedbuying
or sellingcash
ofTreasury
securities
byinthe
the
open
market.
When
buys
securities,
replaces
securities
iSales
nvestorof securities
accounts,bymorethe funds
are
avai
l
able
for
lending,
and
interest
rates
decrease.
opposite effect,
funds available for lendingFedashave
welltheas increasing
rates. reducing cash balances and
reserveBy requirements
arepercentage
the percentage
of deposits
thatrequired
banks must
retainas(not
3. Bank
loan out).
increasi
n
g
the
of
deposits
banks
are
to
retain
thein amounts
Fed effectively
decreases
the funds
that toareinavail
ablinterest
e for lending.
This
decrease
avail
a
ble
for
lending
wil
l
tend
crease
rates.
A
decrease
i
n
the
percentage
reserve
requirement
will
increase
the
funds
available
for
loans and tends to decrease interest rates.
banks
to tighten
orattempts
loosen their
credittheirpolicies.
By asking
banksEncouraging
to alter
4. Persuading
thei
r
lending
policies,
the
Fed
to
affect
will
i
ngness
to
lend.
lending wil tend to decrease rates and vice versa.
The most commonly used policy tool is
reserves,
open market operations.
©20 12 Kaplan, Inc.
Page 69
Study Session 1 5
Cross-Reference to CFA Institute Assigned Reading #55 - Understanding Yield Spreads
LOS 55.b: Describe a yield curve and the various shapes of the yield curve.
CFA® Program Curriculum, Volume 5, page 410
WeFor have
yieldTreasury
curvesyielprevid curve
ously asandjustrelated
a plotinformation,
of yields by years
to maturity.
a.bviloomberg.
ewmentioned
of a current
you
can
l
o
ok
at
com/markets/rates/index.
html.andThebonds)
Treasurywithyieldmaturicurvetiesshows
yimonths
elds fortoU.30S.years.
Treasury
securities (bills, notes,
from thethree
We use four general shapes to describe yield curves:
1. Normal or upward sloping.
2. Inverted or downward sloping.
3. Flat.
4. Humped.
These four shapes are illustrated in Figure 1.
Figure Yield Curve Shapes
www
1:
Yield
Yield
Yield
Yield
Humped
Inverted
Page 70
©2012 Kaplan, Inc.
Study Session 1 5
Cross-Reference to CFA Institute Assigned Reading #55 - Understanding Yield Spreads
Yionlyeldones
curvesobserved.
can takeThese
on justfourabout
any shape, vsoe don'
t thinktypes,
these and
examples
are theto be
are
representati
of
general
you
need
fami
l
i
ar
wi
t
h
what
i
s
meant
by
an
"upward
sloping"
or
"normal"
yi
e
ld
curve
and
by
an
"inverted"
ordescriptive
"downwardnames
sloping"andyield
curve.t present
Humpedanyandproblem.
flat yieldJustcurves
usuallthat
y go a
byflatjustyieldthosecurve
shouldn'
remember
means that yields are all equal at every maturity.
LOS 55.c: Explain the basic theories of the term structure of interest rates and
describe the implications of each theory for the shape of the yield curve.
CPA® Program Curriculum, Volume 5, page 413
The
states
that
the
yield
for
a
particular
maturity
is
an
average
(not arates
simpleare average)
oftotheriseshort-term
ratesinterest
that arerateexpected
in thelongerfuture.maturities
If short­will
term
expected
in
the
future,
yields
on
beIf short-term
higher thanratesthoseareonexpected
shorter tomaturities,
and thelonger
yieldmaturity
curve wibonds
ll be upward
sloping.
fal
l
over
time,
will
be
offered
at
lower yields.
Proponents
ofshort-term
the rates, investors requirebelieve
that, in addition
to expectations
about
future
a
risk
premium
for
holding
longermaturity
term
bonds.
This
i
s
consistent
wi
t
h
the
fact
that
interest
rate
risk
i
s
greater
for
longer
bonds.
Under thiscompensation
theory, the sizeinofvestors
the liquidity
premium
withemll depend
ononhow
much
additional
requi
r
e
to
i
n
duce
to
take
the
greater
risk
of longer ofmaturi
ty bonds
or, alitsernati
vlustration
ely, how strong
their
preference
for thepremium
greateron a
liquidity
shorter
term
debt
.
i
l
of
the
effect
of
a
liquidity
yield curve, where expected future short-term rates are constant, is presented in Figure 2.
pure expectations theory
liquidity preference theory
An
Figure 2: Liquidity Premium
Yield
Yield curve with liquidity preference
I
Liquidicy p«mium
Yield curve without liquidity preference (pure expectations)
u
The
i
s
based
on
the
idea
that
i
n
vestors
and
borrowers
have
preferences
for dithefferent
Undertothilend)s theory,
the supply
of bondsyields(desire
to borrow) and
demand for bonds (desire
determine
equilibrium
,
_
_
_
_
_
_
_
_
_
_
_
_
_
_
_
_
_
L_
Mat rity
market segmentation theory
maturity ranges.
©20 12 Kaplan Inc.
Page 7 1
Study Session 1 5
Cross-Reference to CFA Institute Assigned Reading #55 - Understanding Yield Spreads
forfor thematurivarious
maturithatty ranges.
Institutional
investors Limayfe ihave
strong
preferences
t
y
ranges
cl
o
sel
y
match
thei
r
liabilities.
n
surers
and
pension
funds
may
prefer
long
maturities
due
to
the
l
o
ng-term
nature
of
the
liabilities
they
must
fund.
bank
thatsecurities.
has liabilities
of argument
a relativelyforshortthe maturity
may prefer to
itheory
nvestAiniscommercial
shorter-term
debt
Another
market
segmentation
that
there
are
legal
or
institutional
policy
restrictions
that
prevent
i
n
vestors
from
purchasingofsecuriti
es wivarious
th maturities
outside
aofparticul
aldr maturity
range.
Thein
determination
yiel
d
s
for
maturi
t
y
ranges
the
yi
e
curve
is
ill
u
strated
Figure 3.
3:
Figure
Market Segmentation Theory and the Yield Curve
Yield
Long-term
Short-term
Intermediate-term
0
s
s
0
Maturiry
A somewhat
weaker
versionyields
of thealsomarket
segmentation
theory
is thefor various maturity
Under
thi
s
theory,
depend
on
supply
and
demand
move from theimaturi
r preferred
maturity ranges when
yiranges,
elds arebutsuffiinvestors
ciently canhigherbe induced
in other to(non-preferred)
ty ranges.
preferred habitat
theory.
Term Structure Theories and the Shape of the Yield Curve
The
by
itself
has
no
implications
for
the
shape
of
the
yield
curve. The various expectations and the shapes that are consistent with them are:
Short-term rates
expected
to risefalliinn thethefuture
upward
sloping
yieldyielcurve
Short-term
rates
are
expected
future
downward
sloping
d curve
Short-term
rates
expected
to
rise
then
fal
l
humped
yi
e
ld
curve
Short-term rates expected to remain constant flat yield curve
The
shape ofabout
the yiienldvestor
curve,expectati
under theonspure
theory,rates.
provides us with
information
aboutexpectations
future short-term
theidenti
liquidity
theto falyieldl a great
curvedealmayintaketheonfuture,
any ofeventheaddi
shapesng
weaUnder
have
f
i
e
d.
If
rates
are
expected
liquidity
premi
u
m
to
the
resulting
negati
v
el
y
sl
o
ped
yield
curve
can
resul
t
in
a
sloping yiadded
eld curve.
yieldnote
curvethat,couldunder
still thebe humped
with a
lidownward
quidity premium
to all Athehumped
yields. Also
liquidityeven
preference
pure expectations theory
-+
-+
-+
-+
preference theory,
Page 72
©2012 Kaplan, Inc.
Study Session 1 5
Cross-Reference to CFA Institute Assigned Reading #55 - Understanding Yield Spreads
theory,
yieldThicurve
consistentin Figure
with expectations
of declining
short-terman upward
rates in sloping
the future.
s casecanis beillustrated
4.
4:
Figure
Liquidity Premium Added to Decreasing Expected Rates
Yield
Liquidity Preference Yield Curve
Pure Expectations Yield Curve
(short-term rates expected to decline)
'------ Maturity
The
of theandterm
structure
is consistent
wiatteach
h anymaturi
yield tcurve
shape.
Under
this
theory,
i
t
i
s
supply
demand
for
debt
securities
y
range
thatthe determines
theerentyieldmaturities,
for that maturi
ty range.
There
is no specific linkage
among
yields
at
diff
although,
under
the
higher
at an adjtheiacent
maturityrangerangeof can
induce investors to purchase bonds with
maturitiesratesoutside
r preferred
maturities.
market segmentation theory
preferred habitat theory,
LOS 55.d: Define a spot rate.
CPA® Program Curriculum, Volume 5, page 415
Yield
to
maturi
t
y
is
the
singl
e
di
s
count
rate
that
makes
the
present
value
of
a
bond'
s
promised
flowscome
equalattodifitsferent
marketpointsprice.in Actually,
the appropriate
discount
rates
fordiscount
cash flrate
ocashwsforthat
ti
m
e
are
typical
l
y
not
all
the
same.
The
a
payment
that
comes
one
year
from
now
i
s
not
necessari
l
y
the
same
discount
rate
that
should
be
applied
to
a
payment
that
comes
fi
v
e
or
ten
years
from
now.
That is, the spot-rate yield curve is not (horizontal).
The
appropriate
discount
ratestimeforperiods
individual
future payments
are calleda value equal to
The
spot
rates
for
di
f
ferent
that
correctl
y
value
(produce
marketorprice)
the cash flows from a Treasury bond
arewillcalexami
led ne the methodology
Treasuryforspot
rates,
the
We
these rates
and
why
theyratesare tocaldifferentiate
led "arbitrage-free"
spotcoupon
rates a bitbondlater.yieHere
weestimating
j
u
st
introduce
the
i
d
ea
of
spot
them
from
lds
(YTMs).
Conceptuall
y
,
spot
rates
are
the
discount
rates
for
(yi
e
lds
on)
zero-coupon
bonds,
securities
thatthanhavesemiannual
only a singlepayments)
cash flowwiatll aillustrate
future date.
A simpleasexampl
e to
(wi
t
h
annual
rather
thi
s
concept
applied
coupon bonds.
flat
spot rates.
arbitrage-free
theoretical Treasury spot-rate curve.
,
©20 12 Kaplan Inc.
Page 73
Study Session 1 5
Cross-Reference to CFA Institute Assigned Reading #55 - Understanding Yield Spreads
Consider
anmakeannual-pay
bond wiFor
th a a1 $1,Oo/o0coupon
ratetheseandpayments
three yearswiltol bematuri
ty.inThis
bond
wi
l
l
three
payments.
00
bond,
$100
one
year,
$1
00
at
the
end
of
two
years,
and
$1,100
three
years
from
now.
Suppose
we
are
given the following spot rates:
1 year = 8o/o
2 year = 9o/o
3 year = 1 Oo/o
Discounting
bond
as: each promised payment by its corresponding spot rate, we can value the
100 + __!QQ_2 + 1,1003 1,003.21
1.08 1.09 1.10
=
LOS 55.e: Calculate and compare yield spread measures.
416
Abonds.
yield Three
spreaddiisffsierent
mplyyitheeld difference
betweenaretheas yields
spread measures
follows:on two bonds or two types of
absolute
yield spread
is simplycaltheleddifference
between yiAbsolute
elds on twoyieldbonds.
1. The
This
simple
measure
i
s
sometimes
the
spreads
are usually expressed in basis points (lOOths of 1 o/o).
absolute yield spread = yield on the higher-yield bond-yield on the lower-yield bond
2. The
relati
v
e
yield
spread
is
the
absolute
yield
spread
expressed
as
a
percentage
of
the
yield on the benchmark bond.
yield spread
re attve yt.eld spread = yieldabsolute
on the benchmark bond
3. The
yield
ratio
is
the
rati
o
of
the
yield
on
the
subject
bond
to
the
yiel
d
on
the
benchmark bondsubj. ect bond yield
-yt.eld ratt.o = --"- ---'benchmark
bond-yi-eld
Note that
yieldmeasures
ratio is simply
one plusin thethe folrelalowing
tive yieldexample.
spread. The calculation of
these
yieldthespread
is illustrated
CPA® Program Curriculum, Volume 5, page
nominal spread.
1
Page 74
.
©2012 Kaplan, Inc.
Study Session 1 5
Cross-Reference to CFA Institute Assigned Reading #55 - Understanding Yield Spreads
Example:
yield spreads
Consider
two
bonds,
X
andY.
Thei
r
respective
yields
are
6.50%
and
6.
7
5%.
Using
bond
as thethebenchmark
spread,Xand
yield ratio bond,
for thesecompute
bonds.the absolute yield spread, the relative yield
Answer:
absolute
yieldspread=
spread =0.25%
6.75%-6.50%
=0.0.25%
or 25 basis points
relyieldativratio=
e yield
6.50%
=
0
38
=
3.8%
6.75% 6.50% = 1.038
Computing
I
I
The
mostsimplistic.
commonlyAused
yield spreadof theis theabsolute yieyildeldspread
spread,is thatevenitthough
it isn
theconstant,
most
shortcoming
may
remai
even
though
overall
rates
ri
s
e
or
fall.
In
thi
s
case,
the
effect
of
ri
s
i
n
g
or
fall
i
ng
rates on spreads is captured by the relative yield spread or the yield ratio.
For
example,
consider
two
yields
that
rise
from
6.
5
%
and
7.0%
to
7.
0
%
and
7.
5
%,
respecti
ely. Thefallabsolute
at 50o decreases
basis points,fromwhi1.l0e77theto
rel1.0a71.tive vspread
s from 7.yi6e9%ld spread
to 7.14%remaiandns theconstant
yield rati
absolute
LOS 55.f: Describe credit spreads and relationships between credit spreads and
economic conditions.
418
Ain credit
(or except spread
is therating.difference
in yieldsof abetween
two issues
thatdifference
are similar
all
respects
for
credit
An
example
credit
spread
is
the
in
yiGOeldsmunis
between(an lintramarket
ong AA ratedspread
generalas weloblilgation
(GO) municipal
bondsshowandthelongeffectA rated
).
Obviously,
these
spreads
of
credi
t
qual
i
t
y
on
yi
e
l
d
s
and
reveal
the
ri
s
k-return
tradeoff
the
i
n
vestor
can
expect
(i.e., how
mucht riadded
percei
ved credi
sk). return an investor can earn by investing in issues with higher
Credittspreads
spreadsdecli
are related
to the state ofaretheexpected
economy.to have
Duringstronger
an expanding
economy,
credi
n
e
as
corporations
cash
fl
o
ws.
Onto a
the
other
hand,
during
economic
contractions,
cash
fl
o
ws
are
pressured,
leading
greater
probability
of default
and hithey
gheroften
yieldssellonlow-quality
lower-qualitissues
y issues.andWhen
investors
antici
p
ate
an
economic
downturn,
buy
high-quality
issues,
including
Treasuries.
This
puts
downward
pressure
on
the
prices
of low-quality issues, raising their yields.
CFA® Program Curriculum, Volume 5, page
quality)
flight to quality
©20 12 Kaplan, Inc.
Page 75
Study Session 1 5
Cross-Reference to CFA Institute Assigned Reading #55 - Understanding Yield Spreads
LOS 55.g: Describe how embedded options affect yield spreads.
CFA® Program Curriculum, Volume 5, page 420
call option ontoa bond
is antooption
theFrombondtheissuer
holds ands perspective,
will only bea noncallable
exercised if it
isbondadvantageous
the
i
s
suer
do
so.
bondholder'
that iscompared
otherwisetoidentical
butbondcallable.
Investors
will feature.
l require
higheris preferred
yieldyieldonspreads
atocalla bond
ableto abond,
the
same
without
the
cal
aTherefore,
benchmark
bond,
such
as
a
similar
maturity
Treasury
issue,
are higher forbondholders
the callableforbond.the Byprepayment
the same reasoning,
yield spreads
must bepassthrough
greater to
compensate
option
embedded
in
mortgage
securities.
The
inclusioneffect;
of a puttheprovision
orwhether
a conversion
option
withofathese
bondoptions
will haveis the
thebondholder'
opposite
choice
of
to
exerci
s
e
ei
t
her
s
.
Compared
to
an
identical
option-free
bond,
a
putable
bond
wi
l
l
have
a
lower
bond. yield spread to Treasuries due to the value of the put feature included with the
The
fact
thatforoption
provisions
affect yield
spreads
is important
because forthiscredi
tellstusrisk,
that
spreads
bonds
wi
t
h
embedded
options
are
not
purely
premiums
liquidity differences, and maturity (duration) risk.
A
LOS 55.h: Explain how liquidity and issue-size affects the yield spread of a
bond relative to other similar securities.
CFA® Program Curriculum, Volume 5, page 422
Bonds
that
have
t
o
Treasuries.
Investors
prefer
more
liquidity
to less and
will payinaallpremium
for greater
liitquiisdmore
ity. actihigher
price
for a bond
that
is
identical
to
another
aspects
except
that
v
el
y
traded-and
therefore more liquid-translates into a lower yield compared to the less liquid bond.
Liquidity
is affected
byactivel
the sizey traded
of an issue.
because
they
are
more
i
n
the
secondary
market.
Empirical
evi
d
ence
suggests
that
issueslerwiissues,
th larger-size issues have lower yieldsWhen
compared
with
identical
but
smal
due
to
their
greater
liquidity.
less liquidity have higher spreads
A
Larger issues normally have greater liquidity
greater size have lower yield spreads.
Page 76
©2012 Kaplan, Inc.
Study Session 1 5
Cross-Reference to CFA Institute Assigned Reading #55 - Understanding Yield Spreads
LOS 55.i: Calculate the after-tax yield of a taxable security and the tax­
equivalent yield of a tax-exempt security.
CFA® Program Curriculum, Volume 5, page 423
The
on a taxable security can be calculated as:
after-tax yield = taxable yield (1-marginal tax rate)
after-tax yield
X
Example: Computing after-tax yield
the after-tax
yield on a corporate bond with a yield of 10% for an investor with
aWhat
40%ismargi
nal tax rate?
Answer:
Investors
arebe paid
concerned
wionth after-tax
returns.
Thelar ofmarginal
taxinrate
iscasetheinterest
percentage
that
must
in
taxes
one
additi
o
nal
dol
income,
thi
s
mcome.
For
an
investor
wi
t
h
a
marginal
tax
rate
of
40%,
40
cents
of
every
additional
dollar
of
taxable inyiterest
mustwibethpaida 40%in taxes.
For ataxtaxable
after-tax
eld toincome
an investor
marginal
rate wilbond
l be:that yields 10%, the
10%(1 - 0.4) = 6.0% after tax
Tax-exempt
securities
can
offer
lower
yields
compared
to
taxable
securities
because
the yieldsthethey
offer are after-tax
Theissuehigcompared
her an investor'
s marginal
taxTherate, the
greater
attractiveness
ofis thea taxyieldyields.
exempt
to
a
taxable
issue.
a
particular
investor
must
earn
on
a
taxable
bond
to
have
the sameis justafter-tax
return theyofwould
receive from
particular
calculation
a rearrangement
the after-tax
yieldaformul
a listedtax-exempt
previouslissue.
y. The
tax-fre--'-e yield
. yt.eld = (1-margi
taxable-equivalent
nal tax rate)
taxable-equivalent yield
-
-
-
©20 12 Kaplan, Inc.
Page 77
Study Session 1 5
Cross-Reference to CFA Institute Assigned Reading #55 - Understanding Yield Spreads
Example: Taxable-equivalent yield
Consider
a
municipal
bond
that
offers
a
yiel
d
of
4.5%.
If
an
investor
i
s
considering
buying
fully taxablor thee Treasury
security
a 6.7her5%marginal
yield, should
Treasurya security
municipal
bond,offering
given that
tax ratesheisbuy35%?the
Answer:
We can approach this problem from two perspectives. First, the taxable equivalent yield
4·5 o/o 6.92%, which is higher than the taxable yield, so
on the municipal bond is (1-0.
35)
the municipal bond is preferred.
Alternatively, the after-tax return on the taxable bond is 0.0675 X (1-0.35) 4.39%.
bond (4.5%)bondis greater
than the after-tax
yiThus,
eld onthetheafter-tax
taxablereturn
bond (4.on3the9%),municipal
and the municipal
is preferred.
Either approach gives the same answer; she should buy the municipal bond.
=
=
�
�
Professor's Note: Because investors have different marginal tax rates, investors
will have different tax-equivalent yields. Thus, the Treasury yield curve is not
the appropriate benchmark to use for municipal bond yield spreads. The AAA
rated municipal general obligation yield curve is the benchmark for municipal
yield spreads.
LOS 55.j: Define LIBOR and explain its importance to funded investors who
borrow short term.
CPA® Program Curriculum, Volume 5, page 427
We
mentioned
theable CDs by banks and bank branches(LIBOR)
in London.
reference
toLIBOR
thepreviously
rateshas paibecome
d on negoti
located
in
the most important
benchmark
or reference
ratedayforandfloatipublished
ng-rate
debt
securities
and
short-term
lending.
LIBOR
is
determi
n
ed
each
byandtheAustral
BritishianBankers'
Association
for several
currencies,
including
the U.francs,
S., Canadian,
dollars,
the
Euro,
Japanese
yen,
Bri
t
ish
pounds,
and
Swiss
amongto
others.
Whil
e
the
maturity
of
the
CDs
that
banks
invest
i
n
can
range
from
overnight
five years, LIBOR is most important for short-term rates of one year or less.
London Interbank Offered Rate
Page 78
©2012 Kaplan, Inc.
Study Session 1 5
Cross-Reference to CFA Institute Assigned Reading #55 - Understanding Yield Spreads
funded investor
is onein who
borrowsistoasfianmeasure
ance an iofnvestment
position.
The
of
LIBOR
thi
s
context
the
funding
costs
becauseloansthe
importance
loans
to
fi
n
ance
the
i
n
vestment
are
most
often
fl
o
ati
n
g-rate
loans
or
short-term
where
the reference
rate
is published
LIBOR.
Recalwilththata borrowing
floating-raterateloans
are based on
a(60-day)
reference
rate
plus
a
margin.
funded
investor
of
2-month
LIBOR
40
basis
points
would
have
a
borrowing
cost
(annualized)
of
2.
6
%
when
2-month
LIBOR
is quoted
at greater
2.2%. Thethanprofi
t6s%ofannual
such a rate
fundedon theinvestor
would
depend
on
his
or
her
ability
to
earn
a
2.
investments
funded in such a manner.
A
+
A
©20 12 Kaplan, Inc.
Page 79
Study Session 1 5
Cross-Reference to CFA Institute Assigned Reading #55 - Understanding Yield Spreads
'
KEY CONCEPTS
55.a Reserve Board's tools for affecting short-term interest rates are the discount
The
Federal
rate,
operations, the reserve requirement, and persuasion to influence
banks'open-market
lending policies.
55.b
Yield curves represent the plot of yield against maturity.
The general yield curve shapes are upward or downward sloping, flat, or humped.
55.cof the yield curve and their implications for the shape of the yield curve are:
Theories
The
arguesrates
thatandratesisatconsistent
longer maturities
depend
onlyshape.
on
expectati
o
ns
of
future
short-term
with
any
yiel
d
curve
The
of thefuture
term structure
statesratesthatandlonger-term
rates
refl
e
ct
i
n
vestors'
expectations
about
short-term
an
increasing
liinqterest
uidityratepremium
to
compensate
i
n
vestors
for
exposure
to
greater
amounts
of
risk
atdownward
longer maturities.
The liquidity
preference
theoryin short-term
can be rates
consistent
wi
t
h
a
sloping
curve
i
f
an
expected
decrease
outweighs the liquidity premium.argues that lenders and borrowers have preferred
The
maturi
ty rangesfor and
that thewithin
shapeeachof thematurity
yield curve
isindependent
determined byof thethe supply
and
demand
securities
range,
yield in
other
maturity
ranges.
It
i
s
consistent
wi
t
h
any
yi
e
ld
curve
shape
and
in
a
somewhat
weaker form is known as the preferred habitat theory.
55.d
Treasury spot
rates arefromtheaappropriate
discount
ratesgivforen thesingletimecashuntilflowsthe(coupon
oris to
principal
payments)
U.S.
Treasury
security,
payment
be received.
55.e
TypesTheof yield spreads: is the difference between the yield on a particular security
oron-the-run
sector andTreasury
the yieldsecurities
of a reference
(benchmark)
security or sector, which is often
of
l
i
k
e
maturi
t
y.
The
isarguably
the absolute
yield spread
expressed
as a percentage
of the
benchmark
yield.
This
i
s
a
superior
measure
to
the
absolute
spread,
since
iremai
t willnrefls constant.
ect changes in the level of interest rates even when the absolute spread
The
is theorratiosector;of theit isyieldsimplyon aonesecurity
benchmark security
plus theor sector
relativetoyitheeldyield
spread.on a
LOS
LOS
LOS
•
pure expectations theory
•
liquidity preference theory
•
market segmentation theory
LOS
LOS
•
absolute yield spread
•
relative yield spread
•
Page 80
yield ratio
©2012 Kaplan, Inc.
Study Session 1 5
Cross-Reference to CFA Institute Assigned Reading #55 - Understanding Yield Spreads
LOS 55.f
Acredicredit
spread is the yield difference between two bond issues due to differences in their
t ratings.
Credi
t
spreads
narrow
when
the
economy
is
healthy
and
expanding,
while
they
increase
during contractions/recessions reflecting a flight to (higher) quality by investors.
LOS 55.g
Call optionsbonds.
and prepayment options increase yields and yield spreads compared to
option-free
Put options and
conversion
comparable
option-free
bonds.options decrease yields and yield spreads compared to
Bonds
h lessliquid
liquidityand,areother
less desirabl
e and wilmustl haveofferlower
a higyield
her yield.
issues arewitmore
things equal,
spreads.Larger bond
LOS 55.h
LOS 55.i
To compare
ayield
tax-exempt
bond
with(1a taxable
issue,
userate),eitherandofcompare
the following:
Mter-tax
=
taxabl
e
yield
-margi
n
al
tax
it
to
tax-exempt yield.
tax-free yield , and compare .tt to a taxable yteld.
Taxable-equivalent yield (1-margi
nal tax rate)
LIBORmoney
for various
currencies
isis determi
nedimportant
from ratesreference
at whichratelargeglobally
Londonforbanks
loan
to
each
other
and
the
most
floating-rate debt and short-term loans of various maturities.
•
•
x
___:_
_
_
_
_
_
_
_
.
LOS 55.j
©20 12 Kaplan, Inc.
Page 8 1
Study Session 1 5
Cross-Reference to CFA Institute Assigned Reading #55 - Understanding Yield Spreads
CONCEPT CHECKERS
1.
2.
3.
4.
5.
Under
theory, an inverted yield curve is interpreted as
eviA. ddemand
encethethat:purefor expectations
long-term
bonds tois falling.
B.C. ishort-term
rates
are
expected
the future.
nvestors have very little demandfallforinliquidity.
According
the liquidity preference theory, which of the following statements
iA.s All elsetoequal,
invvestors
preferdifferenti
short-term
securitiesshort-term
over long-term
securities.
B. Investors
percei
e
littl
e
risk
a
l
between
and
long-term
securities.
C. over
Borrowers
will paydebt.a premium for long-term funds to avoid having to roll
short-term
Witheory
th respect
to the term structure of interest rates, the market segmentation
holds
that:
an increase
in demand for long-term borrowings could lead to an inverted
A. yield
curve.
expectations
about
theshapefutureof theof short-term
interest rates are the major
B. determi
n
ants
of
the
yield
curve.
C. ithenvestors.
yield curve reflects the maturity demands of financial institutions and
mostdiscount
commonly
used tool of the Fed to control interest rates is:
A.The
the
rate.
the bank
reserveoperations.
requirement.
B.C. open
market
For twoisbonds
thatTheareyialeldikeratio
in alils respectsto:except maturity, the relative yield
spread
7.14%.
A.B. 0.714.
1.0714.
107.14.
Assume
the
fol
l
owi
n
g
yields
for
di
f
ferent
bonds
issued
by
a
corporation:
1-year bond:
5.50%.
2-year
bond:
3-year bond: 6.00%.
7.00%.
Ifthea 3-year
3-year corporate
U.S. Treasury
is yielding 5%, then what is the yield spread on
issue?
A.B. 0.10040.bp.
200 bp.
least accurate?
closest
c.
6.
•
•
•
absolute
c.
Page 82
©2012 Kaplan, Inc.
Study Session 1 5
Cross-Reference to CFA Institute Assigned Reading #55 - Understanding Yield Spreads
thebond:
following
corporate yield curve:
7. Assume
1-year
5.00%.
2-year
bond:
6.00%.
3-year bond: 7.00%.
If a 3-yearon theU.S.3-year
Treasury
yieldingis: 6% is the benchmark bond, the yield
spread
corporate
A.B. 1.167.
16.67%.
14.28%.
8. bonds
If a U.Sand. investor
is forecasting
thatis going
the yield
spreadwhibetween
U.S.followi
Treasuryng
U.
S
.
corporate
bonds
to
widen,
c
h
of
the
woul
d he beisalsogoing to expand.to hold?
A.beliefs
The
economy
The economy
C.B. There
will be nois going
changetoincontract.
the economy.
a Treasury
bond
and
aiscorporate
bond
that areon altheikecorporate
in all respects
except
9. For
credit
risk,
the
yi
e
ld
ratio
1.0833.
If
the
yield
bond
is 6. 5 %,
the
Treasury
(benchmark)
bond
yield
is
to:
A.B. 6.5.50%.
0%.
8.033%.
venntwo
bonds
that wiarel equi
valanentinvestor
in all respects
exceptbetween
tax status,
the2% taxable
10. Gimargi
al
tax
rate
that
make
indi
f
ferent
an
8.
bond
and39%.a 6.2% tax-exempt bond is to:
A.B. 24.
43.37.404%.
7%.
11. Which
ofthetheeconomic
followinghealstatements
describes
the relationship
between
t
h
of
a
nation
and
credit
spreads?
A.B. Credit
spreads
and economic
well-being
are noteconomy
correlated.
Credit
spreads
decrease
during
an
expanding
because
corporate
cash Rowsspreads
are expected
to rise. an expanding economy because corporations
C. invest
Credit
increase
during
in more speculative projects.
12. Which
of
the
foll
o
wing
describes
the
relationship
between
liquidity and yield spreads relative to Treasury issues? All else being equal, bonds
with:
A.B. less
liquidity
havehavelowerhigher
yieldyispreads
to Treasuries.
greater
liquidity
e
ld
spreads
to
Treasuries.
C. less liquidity have higher yield spreads to Treasuries.
•
•
•
relative
c.
most likely
closest
c.
closest
c.
most accurately
most accurately
©20 12 Kaplan, Inc.
Page 83
Study Session 1 5
Cross-Reference to CFA Institute Assigned Reading #55 - Understanding Yield Spreads
13. Aofnarrowi
ng ofngcredi
t spreads would have the impact on the value of which
the
followi
investments?
A.B. AAA
corporate
bond.
30-yearratedTreasury
C. BB+
corporatebond.bond.
anofinvestor
is7.in5 %thecorporate
31% margi
nalthattax isbracket.
She
is considering
the
14. Assume
purchase
either
a
bond
sell
i
ng
at
par
or
a
5.25%
municipal
bond thatexcept
is alstheir
o selling
at par.theGivinvestor
en that theshould
two buy
bondsthe:
areA.tax-exempt
comparable
i
n
all
respects
tax
status,
corporate bond,
because
i
t
has
the
higher
yield
of7.
5
0%.
B.C. municipal
bond, because
becauseiitsts after-tax
taxable-equi
corporate bond,
yieldvalent
is higyield
her. is 7.6 1 %.
least
Page 84
©2012 Kaplan, Inc.
Study Session 1 5
Cross-Reference to CFA Institute Assigned Reading #55 - Understanding Yield Spreads
ANSWERS - CONCEPT CHECKERS
1.
B
An inverted or downward-sloping yield curve, under the pure expectations theory,
indicates that short-term rates are expected to decline in the future.
2.
B
Rational investors feel that long-term bonds have more risk exposure than short-term
securities (i.e., long-term securities are less liquid and subject to more price volatility) .
The other statements are correct.
3.
C
The market segmentation theory holds that certain types of financial institutions and
investors prefer to confine (most of) their investment activity to certain maturity ranges
of the fixed-income market and that supply and demand forces within each segment
ultimately determine the shape of the yield curve.
4.
C
Open market operations are carried on frequently. The Fed's selling ofTreasuries in the
open market takes money out of the economy, reducing the amount of loanable funds
and increasing interest rates. The opposite occurs when the Fed buys Treasuries in the
open market.
5.
B
The yield ratio is 1 + relative yield spread, or 1 + 0.0714 = 1 .0714.
6.
C
Absolute yield spread = yield on the 3-year corporate issue - yield on the on-the-run
3-year Treasury issue = 7.00o/o - 5.00% = 2.00o/o or 200 bp.
7.
A
8.
B . A contracting economy means lower corporate earnings which increases the probability
of default on debt and increases yield spreads between corporate issues and Treasuries at
a particular maturity.
9.
B
o
· 7o
1.
· yte
· ld spread IS
7
0 , so the reIauve
The y1e
· ld on the corporate IS
· 7o/ - 6o/o , wh1.ch 1·s 1/6
6 o/o
or 16.67% of the 3-year Treasury yield.
. ld rano
. = corporate bond yield = 1.0833. Given that the corporate bond yield is 6.5%,
pe
Treasury bond yield
the Treasury bond yield can be calculated as:
10. A
6 5o/o
·
= 6.0 o/o .
1.0833
The tax rate that makes investors indifferent between two otherwise equivalent bonds is
determined by solving for the tax rate in the equation: tax-exempt yield = (1 - tax rate) x
taxable yield . Rearranging this relationship, we have:
6.2
tax-exempt rate
.
= 1 - - = 24.39%.
margmal tax rate = 1 8.2
taxable rate
11. B
As an economy expands, credit spreads decline as expected corporate earnings rise. This
is because, with stronger earnings, corporations are less likely to default on their debt.
12. C
The less liquidity a bond has, the higher its yield spread relative to Treasuries. This is
because investors require a higher yield to compensate them for giving up liquidity,
which results in a greater spread over Treasury issues, which are very liquid.
13. B
Because we usually speak of credit spreads as yield spreads to Treasuries, a change in the
yield spread does not imply any change in the values ofTreasuries.
©20 12 Kaplan, Inc.
Page 85
Study Session 1 5
Cross-Reference to CFA Institute Assigned Reading #55 - Understanding Yield Spreads
14. B
The taxable-equivalent yield on this municipal bond is
5 25
·
(1 - 0.31)
=
5 25
·
0.69
=
7.61 %.
Because this is higher than the yield on the (taxable) corporate bond, the municipal
bond is preferred. Alternatively, the after-tax yield on the corporate is 7.5% ( 1 - 0.3 1)
5.175%, which is less than the tax-exempt yield, leading to the same decision.
Page 86
©2012 Kaplan, Inc.
=
The following is a review of the Analysis of Fixed Income Investments principles designed to address the
learning outcome statements set forth by CFA Institute. This topic is also covered in:
INTRODUCTION TO THE VALUATION
OF DEBT SECURITIES
Study Session 16
EXAM FOCUS
Bond
valuation
i
s
all
about
calculating
the
present
val
u
e
of
the
promised
cash
fl
o
ws.
If
your
time-value-of-money
(TVM)
skilconcepts.
ls are notThe
up tomaterial
speed, take
thes topitimce revi
nowewtoirevi
sit
theimportant.
Study
Session
2
review
of
TVM
in
thi
s
very
Calculating
the
val
u
e
of
a
bond
by
discounting
expected
cash
fl
o
ws
should
become
anrates
easyand
exercise.
The
fin"arbi
al material,
onbond
discounting
a bond'
s expected
cashasflwell.
ows
using
spot
the
i
d
ea
of
t
rage-free"
valuation,
is
quite
important
A good understanding here will just make what follows easier to understand.
LOS 56.a: Explain steps in the bond valuation process.
CPA® Program Curriculum, Volume 5, page 447
The
generalvalues
procedure
forthevaluing
fixed-income
securities
(or anyup tosecurity)
isvaltouetakeof the
thesecuripresent
of
al
l
expected
cash
fl
o
ws
and
add
them
get
the
ty.
There are three steps in the bond valuation process:
over
the
l
i
f
e
of
the
security.
For
a
bond,
there
are
two
types of cash flows: (1) the coupon paymentsbasedandon(2)thetheriskreturn
of principal.
of
(uncertainty
about) the receipt of the estimated cash flows.
by multiplying the
bond's expected cash flows by the appropriate discount factors.
Step 1: Estimate the cash flows
Step 2: Determine the appropriate discount rate
Step 3: Calculate the present value of the estimated cash flows
LOS 56.b: Describe types of bonds for which estimating the expected cash
Bows is difficult.
CPA® Program Curriculum, Volume 5, page 448
Certainly,
one problem
inproblems
estimatingthatfuture
cash
flows forofbonds
icash
s predicting
defaults
and
any
potential
credit
make
the
receipt
future
flows
uncertain.
Aside
from
credit
risk,
however,
we
can
identify
three
situations
where
estimating
future cash flows poses additional difficulties.
1. bonds with embedded options (puts, calls, prepayment options,This
category
includes
and accelpayments
erated is
sinking fund provisions). For these bonds, the future stream of principal
The principal repayment stream is not known with certainty.
©20 12 Kaplan, Inc.
Page 87
Study Session 1 6
Cross-Reference to CFA Institute Assigned Reading #56 - Introduction to the Valuation of Debt Securities
uncertain
andwerwirates
l depend
to a largeprepayments
extent on theof mortgage
future pathpassthrough
of interest securities,
rates. For
example,
l
o
will
increase
and principal will be repaid earlier.
2. future coupon payments depend on the path of interestWirates.
th flWioating-rate
securities,
t
h
some
floroating-rate
securities,
the
coupon
payments
may
depend
on
the
price
of
a
commodity
the rate
of inflation over some future period.
information
3. about future stock prices and interest rates, we don't know when Without
the cash flows will
come or how large they will be.
The coupon payments are not known with certainty.
The bond is convertible or exchangeable into another security.
LOS 56.c: Calculate the value of a bond (coupon and zero-coupon).
CPA® Program Curriculum, Volume 5, page 449
For a Treasury
bond,maythebeappropriate
rateusedusedtotodiscount
value theallpromised
cashflows,
flowsorisa the
risk-free
rate.
This
a
single
rate,
of
the
cash
series of discount rates that correspond to the times until each cash flow arrives.
For
non-Treasury
securities,
we
must
add
a
risk
premium
to
the
risk-free
(Treasury)
rate to measures
determinecovered
the appropriate
discountrevirate.
Thisisriskthe premium
is one
of the yield
spread
in
the
previous
e
w
and
added
yield
to
compensate
forusinggreater
riskdiscount
(credit risk,
liquidity
risk, calltherisk,riskprepayment
risk,
andtosotheon).risk-free
When
a
single
rate
to
value
bonds,
premium
is
added
rate to get the appropriate discount rate for all of the expected cash flows.
yield on a risky bond = yield on a default-free bond risk premium
Other
thi
n
gs
being
equal,
the
riskier
the
securi
t
y,
the
higher
the
yield
di
f
ferential
(or risk premium) we need to add to the on-the-run Treasury yields.
+
Calculating the Value of a Coupon Bond
Recall
that we valued
an annuity
using
the
tipayments
me valuecanof money
keys
on
the
calculator.
For
an
option-free
coupon
bond,
the
coupon
be valued
aswilanl enter
annuithis
ty. Infinorder
to takeasintotheaccount
the payment
of the
par
value
at
maturi
t
y,
we
al
payment
future
value.
Thi
s
is
the
basic difference between valuing a coupon bond and valuing an annuity.
For simplicity,
considerata securi
ty that(in wiltenl years).
pay $100If theperappropriate
year for tendiscount
years andratemakeis 8%a
single
$1,
0
00
payment
maturity
for all the cash flows, the value is:
100 + 1002 + 1003 + 1004 + . . +--+-10010 1,00010
1.08 1.08 1.08 1.08 1.08 1.08
= $1,134.20 = present value of expected cash flows
Valuation with a single yield (discount rate).
-
Page 88
--
--
--
©2012 Kaplan, Inc.
Study Session 16
Cross-Reference to CFA Institute Assigned Reading #56 - Introduction to the Valuation o f Debt Securities
This
is simandply$1,000
the sum(theof theprincipal
presentrepayment)
values of theto befuture
cash atflothews, end
$100ofpertheyeartenthfor
ten
years
received
year, at the same time as the final coupon payment.
The calculator solution is:
N = 10; PMT = 100; FV = 1,000; 1/Y = 8; CPT PV = -$1,134.20
where:
NPMT == number
of
years
the discount
coupon payment
1/Y
=
the
FV = the par value or sellingrateprice at the end of an assumed holding period
-t
annual
annual
�
�
Professor's Note: Take note ofa couple ofpoints here. The discount rate is entered
as a whole number in percent, 8, not 0.08. The ten coupon payments of$100
each are taken care ofin the N 10 entry, the principal repayment is in the FV
1,000 entry. Lastly, note that the PV is negative; it will be the opposite sign to
the sign ofPMT and FV. The calculator is just "thinking" that ifyou receive the
payments andfuture value (you own the bond), you must pay the present value of
the bond today (you must buy the bond). That's why the PV amount is negative; it
is a cash outflow to a bond buyer. just make sure that you give the payments and
future value the same sign, and then you can ignore the sign on the answer (PV).
=
=
Valuation
with
a
single
yield
and
semiannual
cash
flows.
Let'
s
cal
c
ulate
the
val
u
e
of
the
same bond with semiannual payments.
Rather
than
$100
per
year,
the
security
wi
l
l
pay
$50
every
six
months.
Adjust
the
discount rate of 8% per year to 4% per six months. The par value remains $1,000.
The calculator solution is:
N = 20; PMT = 50; FV = 1,000; 1/Y = 4; CPT PV = -1,135.9 0
where:
NPMT == thenumber
of semiannual
periods
semiannual
coupon
payment
1/Y
=
the
semiannual
discount
rate
FV = the par value
Calculating the Value of a Zero-Coupon Bond
Because
a
zero-coupon
bond
has
only
a
si
n
gle
payment
at
maturity,
the
val
u
e
of
a
zero
is simply theonpresent
value ofbasis
the paris: or face value. Given the yield to maturity, the
calculation
a semiannual
t
y
val
u
e
bond va ue (1 i)maturi
number ofyears 2
1
=
+
x
©20 12 Kaplan, Inc.
Page 89
Study Session 1 6
Cross-Reference to CFA Institute Assigned Reading #56 - Introduction to the Valuation of Debt Securities
Note that this valuation model requires just three pieces of information:
The
s maturidiscount
ty value,rate,assumed to be $1,000.
The lbond'
semiannual
2.3.1. The
ife of the bond, years.
Alternatively, using the TVM keys, we can enter:
PMT-=-+0;PVFV = par; N = years 2; 1/Y = YTM/2 = semiannual discount rate;
CPT
Although
zero-coupon
bonds
do notrates.payNote
coupons,
it isis now
customary
to valtheuenumber
zero-coupon
bonds
using
semiannual
discount
that
two
times
of
years
to
maturi
t
y
and
that
the
semiannual
di
s
count
rate
i
s
one-half
the
yield
to
maturity
expressed as a BEY.
Valuing zero-coupon bond
Computeofthe8%.value of a 10-year, $1,000 face value zero-coupon bond with a yield to
maturity
Answer:
findcalculate:
the value of this bond given its yield to maturity of 8% (a 4% semiannual rate),
weTo can
1,000 = $456.39
bond value= ( 0.1,00800) = (1.04
)
1+ 2
Or, use the following inputs:
N = 10 2 = 20; FV = 1,000; 1/Y = _% = 4; PMT = 0; CPT --+ PV = -$456.39
The
di00)fference
between
thecompound
current priceinterest
of thethatbondwill($456.
39) andoveritsthepar1 0-year
value life of
($1
,
0
i
s
the
amount
of
be
earned
the issue.
i.
N
#
x
N
Example:
a
l OxZ
20
x
� Professor's Note: Exam questions will likely specifY whether annual or semiannual
� discounting should be used. just be prepared to value a zero-coupon bond either
way.
Page 90
©2012 Kaplan, Inc.
Study Session 16
Cross-Reference to CFA Institute Assigned Reading #56 - Introduction to the Valuation o f Debt Securities
LOS 56.d: Explain how the price of a bond changes if the discount rate changes
and as the bond approaches its maturity date.
CFA® Program Curriculum, Volume 5, page 450
Prior
to
maturity,
a
bond
can
be
selling
at
a
significant
discount
or
premium
to
par
value.
However,
regardless
of itsarequired
yield,$1,000
the price
will converge
to parlifevalue
as
maturity
approaches.
Consider
bond
with
par
value
and
a
3-year
paying
6o/6%,o semiannual
coupons.
The
bond
values
corresponding
to
required
yields
of
3%,
and 12% as the bond approaches maturity are presented in Figure 1.
Figure
1:
Bond Values and the Passage of Time
Time to Maturity
YTM = 3%
YTM = 6%
YTM = 12%
3.0 years
$ 1 ,085.46
$1,000.00
$852.48
2.5
1,071 .74
1,000.00
873.63
2.0
1,057.82
1,000.00
896.05
1 .5
1 ,043.68
1,000.00
919.81
1 .0
1,029.34
1,000.00
945.00
0.5
1,014.78
1,000.00
971 .69
0.0
1,000.00
1,000.00
1 ,000.00
Tobondcompute
the
change
in
bond
value
due
to
the
passage
of
time,
just
revalue
the
withwith
the number
of periods
(remaining
until
maturity)
reduced.
Theis FVval=ue1 of,000;a
6o/PMT
o bond
three
years
until
maturity
and
a
yield
to
maturity
of
3o/o
= 30; N = 6; 1/Y = 1.5; CPT � PV = $1,085. 4 6. To see the effect of the passage
ofthetime
(wi
t
h
the
yield
to
maturity
held
constant)
just
enter
N
= 5 CPT � PV to get
one period
x months)
fromnownowofof$1,057.82.
$1,071.74, or N = 4 CPT � PV to get
the value
value two
periods(si(one
year) from
The
change inin value
with graphically
the passage inofFigure
time for2. the three bonds
represented
Figureassociated
1 is presented
©20 12 Kaplan, Inc.
Page 9 1
Study Session 1 6
Cross-Reference to CFA Institute Assigned Reading #56 - Introduction to the Valuation of Debt Securities
Figure
2:
Premium, Par, and Discount Bonds
Bond
Value ($)
1,0 8 5. 4 5 S
A premium bond (e.g. , a 6% bond trading at
IT
M of3%) �
r---�
�
.:_
A par value bond (e.g., a 6% bond trading at
1,000.00
ITM of6%) �
M
A discount bond (e.g., a 6% bond trading at
ITM of l2%) �
'-----
Time
LOS 56.e: Calculate the change in value of a bond given a change in its
discount rate.
CFA® Program Curriculum, Volume 5, page 450
Anflows; a decrease
in theindiscount
rate wilratel
the
present
value
of
a
bond'
s
expected
cash
the
discount
wiin lresponse
l increasetothea change
presentivalue
of a bond'rates expected
cash flows.asThethechange
in bond
value
n
the
discount
can
be
calculated
di
f
ference
between
the present values of the cash flows at the two different discount rates.
Bond values and bond yields are inversely related.
decrease
Page 92
©2012 Kaplan, Inc.
increase
Study Session 16
Cross-Reference to CFA Institute Assigned Reading #56 - Introduction to the Valuation o f Debt Securities
Example: Changes in required yield
ACompute
bond hasthea parbondvalvalues
ue of $1,when000,thea 6o/oyieldsemiannual
coupon,
and
three
years
to
maturi
t
y.
to maturity is 3o/o, 6o/o, and 12o/o.
Answer:
60 CPT PV = -1,085.458
At II Y = -;32 N = 3x2; FV = 1,000; PMT =-;
2
At I I Y = .§_2 ; N = 3 x 2; FV = 1,000; PMT = 602 ; CPT PV = -1,000.000
12 N = 3 x 2; FV = 1,000; PMT = -;
60 CPT PV = -852.480
At I I Y = -;
2
2
We haverate,
illustrated
herevalaupoint
covered
earlier;
ifyitheeldyielto dmaturity
to maturiisthigher
y equals{lothewer) than
coupon
the
bond
e
is
equal
to
par.
If
the
the coupon rate, the bond is trading at a discount (premium) to par.
We
now calculate
changeof thein price
changesby:in yield. If the required
yieldcandecreases
from 6o/othetopercentage
3o/o, the value
bondforincreases
1,085.46 = 8.546%.
1,000.00
Ifthe yield increases from 6o/o to 12o/o, the bond value decreases by:
852.48 -1 -14.752%.
1,000.00
---t
---t
---t
-1
=
�
�
Professor's Note: Notice that in these calculations, you only need to change the
interest rate (flY) and then compute PV once the values ofN, PMT, and FV have
been entered. The TVM keys remember the values for these inputs even after the
calculator has been turned off!
If you iplot
a bond'3. sHere
yieldwetoseeits that
corresponding
value,are you'
ll get awith
graph
li
k
e
the
one
shown
n
Figure
higher
prices
associated
lbutoweris yields.
ThisFor graph
is callebonds,
d the the price-yield curve
Noteisthatconvex
it is toward
not a straitheghtorigin,
line
curved.
option-free
meaning it looks like half of a smile.
Price-yield profile.
price-yield curve.
©20 12 Kaplan, Inc.
Page 93
Study Session 1 6
Cross-Reference to CFA Institute Assigned Reading #56 - Introduction to the Valuation of Debt Securities
Figure
3:
The Price-Yield Profile
Bond
Value (o/o of Par)
108.5
100.0
85.2
'
'
'
'
------- �-------� -------------'
'
'--'
�
.:...
._
_
_
_
_
_
3o/o
6%
12%
Marker
Yield
LOS 56.f: Explain and demonstrate the use of the arbitrage-free valuation
approach and describe how a dealer can generate an arbitrage profit if a bond is
mispriced.
CPA® Program Curriculum, Volume 5, page 462
Yield
tono maturity
is
a
summary
measure
and
is
essentially
an
internal
rate
of
return
based
awebond'getsthecashyieldflowsto and
its market
price.withIn thematurity
traditional
valuation
approach,
maturity
of
bonds
and
risk
characteristics
similar
to
those
of
the
bond
we
wish
to
value.
Then
we
use
this
rate
to
discount
the
cash flows of the bond to be valued.
With the
we Again, these discount rates are called
ratesatandvarious
can betimthought
as the required rates of return on zero-coupon bonds
maturing
es in theoffuture.
The
arbitrage-free
valuati
on approach
simply
saysthethatvaluetheofvalue
of a Treasury
bond
based
on
(Treasury)
spot
rates
must
be
equal
to
the
parts
(i.
e
.
,
the
sum
of
thean arbipresent
values
of allty.ofIfthea bond
expected
cash flforows).less Ifthanthistheis notsumtheof case,
there must
be
t
rage
opportuni
is
selling
the
present
val
u
es
ofbondits expected
cash
flows,thanan arbi
tsum
rageurof will
buy theofbond
and sell(indithevidpieces.
If theflows),
i
s
selling
for
more
the
the
values
the
pieces
ual
cash
tooneearncouldan buy
arbittheragepieces,
profit.package them to make a bond, and then sell the bond package
Theappropriate
first step inspot
checkirates.ng forThearbisecond
trage-free
valuation
is tothisvaluevaluea coupon
bond
using
the
step
is
to
compare
to
the
market
price
ofprofithet tobond.
If
the
computed
value
i
s
not
equal
to
the
market
price,
there
i
s
an
arbi
t
rage
becashearnedflows)by buying
theng ltheower-priced
alternati
ve (eivte.herOfthecourse,
bond thior stheassumes
indi
v
idual
and
sell
i
higher-priced
alternati
that
there
are
zero-coupon
bonds
available
that
correspond
to
the
coupon
bond'
s
cash
flows.
arbitrage-free valuation approach,
discount each cash flow using a discount
rate that is specific to the maturity ofeach cash flow.
spot
Page 94
©2012 Kaplan, Inc.
Study Session 16
Cross-Reference to CFA Institute Assigned Reading #56 - Introduction to the Valuation o f Debt Securities
Example: Arbitrage-free valuation
ay)6o/oare:Treasury
note= 5%,
with1 1.5year=years6%,to maturi
ty.years
Spot=rates
(expressed
asis yields
toforConsider
maturi
t
6
months
and
1.5
7o/o.
If
the
note
selling
$992, compute the arbitrage profit, and explain how a dealer would perform the
arbitrage.
Answer:
To$1,value
the
note,
note
that
the
cash
fl
o
ws
(per
$1,
0
00
par
value)
wi
l
l
be
$30,
$30,
and
030 and that the semiannual discount rates are half the stated yield to maturity.
Using the semiannual spot rates, the present value of the expected cash flows is:
1,030 = $986.55
present value usmg. spot rates= 1.30025 + 1.3003 1.035
Thi
s value
is less thanbonds),
the market
pricthem
e of theintonote,
so we winotell buypackage,
the indiandvidual
cash
flows
(zero-coupon
combine
a
1.5-year
sell
the
package
for
the
market
pri
c
e
of
the
note.
This
wil
l
result
in
an
immediate
and
riskl
e
ss
profit of992.00 - 986.55 = $5.45 per bond.
Determining
whetherof thea bond
isusing
over- either
or undervalued
is a two-step
process.
First,
compute
the
value
bond
the
spot
rates
or
yield
to
maturi
ty,rate(s).
rememberi
n
g
that
both
are
often
gi
v
en
as
two
ti
m
es
the
semiannual
discount
Second,
compare
this
value
to
the
market
price
gi
v
en
in
the
problem
to
see
whi
c
h
is
higher.
--
2
--
+
3
---
How a Dealer Can Generate an Arbitrage Profit
Recal
l
that
the
Treasury
STRIPS
program
all
o
ws
dealers
to
divide
Treasury
bonds
into
their
coupon
payments
(by date)alsoandaltheilowsr maturity
payments
in orderbonds/notes
to create zero­by
coupon
securities.
The
program
reconstitution
ofTreasury
putting
theofindividual
cashtheseflotransformations,
ws back together theto create
Treasury
securities.
Ignoring
any
costs
performing
ability
to
separate
and
reconstitute
Treasury securities will insure that the arbitrage-free valuation condition is met.
The
program
allowsitsforarbijusttrage-free
the arbitrage
wea dealoutlined
previously.
If the price
ofcashtheSTRIPS
bond
i
s
greater
than
value,
e
r
could
buy
the
individual
andits arbitrage-free
sell the packagevalue,for thean arbitrageur
market pricecanofmake
the bond.
If the priceandofrithesklessbond
isprofilesstflows
than
an
immediate
by purchasing the bond and selling the parts for more than the cost of the bond.
Such
arbi
t
rage
opportunities
and
the
related
buying
of
bonds
priced
too
low
and
sal
e
s
of
bonds
too highfurther
will force
prices toward equality with their arbitrage-free
values,priced
eliminating
arbitragethe bond
opportunities.
©20 12 Kaplan, Inc.
Page 95
Study Session 1 6
Cross-Reference to CFA Institute Assigned Reading #56 - Introduction to the Valuation of Debt Securities
'
KEY CONCEPTS
LOS 56.a
To value
a bond,
one must:and timing of the bond's future payments of interest and
Estimate
the
amount
principal.
Determi
discountvaluesrate(s).
Calculatenethethesumappropriate
of the present
of the bond's cash flows.
•
•
•
LOS 56.b
Certain
bond
features,
including
embedded
options,
convertibil
i
ty,
or
fl
o
ating
rates,
can
makeontheof bond
estimation
estimati
values.of future cash flows uncertain, which adds complexity to the
Toannuity
compute
the
value
of
an
option-free
coupon
bond,
value
the
coupon
payments
as
an
and add the present value of the principal repayment at maturity.
The
val
u
e
of
a
zero-coupon
bond
cal
c
ul
a
ted
using
a
semiannual
discount
rate,
(one-half its annual yield to maturity), is:
tyofvalue
------=---'---=bond value = -(!--i)maturi
number
years X 2
LOS 56.c
i
+
LOS 56.d
When
interest
rates
(yiel
d
s)
do
not
change,
a
bond'
s
price
wi
l
l
move
toward
its
par
value
as time passes and the maturity date approaches.
Tobondcompute
the
change
in
value
that
i
s
attributabl
e
to
the
passage
of
time,
revalue
the
with a smaller number of periods to maturity.
LOS 56.e
The change
inthevalchange
ue thatinis theattributable
to a change
in the ondiscount
ratediscount
can be rate
calcul
a
ted
as
bond'
s
present
val
u
e
based
the
new
(yield).
Asecuri
Treasury
spotayield
curvethese
is considered
"arbitrage-free"
if themarket
presentprices.
values of Treasury
ties calcul
ted using
rates are equal
to equilibrium
If bondts byprices
areg thenotlower-pri
equal to ctheied alternative
r arbitrage-free
values,
dealersor canthe generate
arbicashtrage
profi
buyi
n
(ei
t
her
the
bond
i
n
divi
d
ual
flows) andof selltheingindividual
the higher-priced
ternative (either
the individual cash flows or a
package
cash flowsalequivalent
to the bond).
LOS 56.f
Page 96
©2012 Kaplan, Inc.
Study Session 16
Cross-Reference to CFA Institute Assigned Reading #56 - Introduction to the Valuation o f Debt Securities
CONCEPT CHECKERS
observes
aHow
5-year,much1Oo/ois coupon
bond payment?
with semiannual payments. The
1. Anfaceanalyst
val
u
e
i
s
£1,
0
00.
each
coupon
A.B. £50.
£25.
£100.
2. Abond20-year,
10o/o
annual-pay
bond
has
a
par
val
u
e
of
$1,
0
00.
What
would
this
be trading for if it were being priced to yield 15% as an annual rate?
A.B. $685.14.
$687.
0
3.
$828.39.
observes
abelieves
5-year, that
1Oo/othesemiannual-pay
bond.
Thethisfacebondamount
isbe
3. An£1,0analyst
00.
The
analyst
yield
to
maturi
t
y
for
should
15%.
Based
on
thi
s
yield
estimate,
the
price
of
thi
s
bond
would
be:
A.B. £1,189.
£828.40.5 3.
£1 ' 193.04.
4. priced
Two bonds
haved 8o/oparasvalues
of $1,rate;
000.theBondotherA is(Bond
a 5o/oB)annual
-pay,
15-year bond
to
yiel
an
annual
is
a
7.
5
%
annual-pay,
20-yearwould
bond be:priced to yield 6o/o as an annual rate. The values of these two
bonds
Bond
A
Bond
B
A.B. $740.
611 $847.
0804
$740.
6
$1,172.
$743.22 $1,172.04
Atyisofa 8o/o,
15-year,
10.Bond
5 % semiannual-pay
bondsemiannual-pay
priced with a bond
yield topriced
5. Bond
maturi
whil
e
B
i
s
a
15-year,
7%
wi$1,th000,thethesameprices
yieldoftothese
maturitwoty.bonds
Givenwould
that both
bonds have par values of
be:
Bond
A
Bond
B
A.B. $1,216.15
$913.54
$1,216.15
$944.5441
$746.61 $913.
the
8.
analystsemiannual-pay
observes a 20-year,
8o/oto maturi
option-free
bonds bond
withwassemiannual
coupons. itThedrops to
required
yiel
d
t
y
on
thi
8o/o,
but
suddenly
7.25%.
of the drop, the price of this bond:
6. AsA. awiresult
l
l
increase.
decrease.
C.B. will
will stay
the same.
c.
c.
c.
c.
c.
Use
following data to answer Questions 6 through
An
©20 12 Kaplan, Inc.
Page 97
Study Session 1 6
Cross-Reference to CFA Institute Assigned Reading #56 - Introduction to the Valuation of Debt Securities
7. A.Prio92.r to6the4. change in the required yield, what was the price of the bond?
B. 107.85.
100.00.
change in the price of this bond when the rate decreased is
8. The
to:A. 7.percentage
8
6%.
B. 8.7.070%.
9%.
spotmonths
rates=(expressed
as=semiannual-pay
yields to maturity) are as
9. Treasury
follows:
6
4o/o
,
1
year
5o/o,
1.5
years
= 6o/o. A 1.5-year, 4o/o Treasury
is trading
at $965.
Thepieces,
arbitrage
trade
andperarbitrage
profit are:
A.B.notebuy
the
bond,
sell
the
earn
$7.
0
9
bond.
bond.
C. sell
sell thethe bond,
bond, buy
buy thethe pieces,
pieces, earn
earn $7.$7.9109 per
per bond.
10. Aremains
$1,000,unchanged,
5o/o, 20-yearhowannual-pay
bond
has avalyieulde iofncrease
6.5%.overIf thetheyield
much
wi
l
l
the
bond
next three
years?
A.B. $13.62.
$13.
$13.976.8.
valsemiannual-pay
ue of a 17-year,yield
zero-coupon
bond
withto:a maturity value of $100,000
11. The
and
a
of
8.
2
2%
is
A.B. $24,618.
$25,
425.
$26,108.
c.
closest
c.
c.
closest
c.
Page 98
©2012 Kaplan, Inc.
Study Session 1 6
Cross-Reference to CFA Institute Assigned Reading #56 - Introduction to the Valuation o f Debt Securities
ANSWERS - CONCEPT CHECKERS
1.
2.
B
CPN = 1,000x
B
bond value
=
0.10
-
2
20
L
t=l
= £50
100
(1+ 0.15)'
+
1,000
20
(1 + 0.15)
=
$687.03
N = 20; IIY = 15 ; FV = 1 ,000; PMT = 100; CPT --+ PV = -$687.03
3.
A
N = 10; IIY = 7.5; FV = 1 ,000; PMT = 50; CPT --+ PV = -$828.40
4.
C
Bond A: N = 1 5 ; I/Y = 8; FV = 1 ,000; PMT = 50; CPT --+ PV = -$743.22
Bond B: N = 20; I/Y = 6; FV = 1 ,000; PMT = 75; CPT --+ PV = -$ 1 , 1 72.04
Because the coupon on Bond A is less than its required yield, the bond will sell at a
discount; conversely, because the coupon on Bond B is greater than its required yield,
the bond will sell at a premium.
5.
A
8
105
Bond A: N = 15 x 2 = 30; I/Y = - = 4; FV = 1,000; PMT = - = 52.50;
2
2
CPT --+ PV = - $ 1 ,216. 1 5
Bond B: N = 15
x
8
2 = 30; I/Y = - = 4;
2
FV =
70
1,000; PMT = - = 35;
2
CPT --+ PV = - $9 1 3.54
6.
A
The price-yield relationship is inverse. If the required yield falls, the bond's price will
rise, and vice versa.
7.
B
IfYTM = stated coupon rate =? bond price = 100 or par value.
8.
A
The new value is 40
=
N,
7 25
·
2
=
I I Y, 40
=
PMT, 1,000 = FV
CPT � PV = -1,078.55, an increase of7.855%
9.
A
.
20
20
arbitrage-free value =
+
2
1.02 1 .025
-
--
+ -3
1020
1.03
=
$972.09
Since the bond price ($965) is less, buy the bond and sell the pieces for an arbitrage
profit of $7.09 per bond.
10. A
With 20 years to maturity, the value of the bond with an annual-pay yield of 6.5% is 20
= N, 50 = PMT, 1 ,000 = FV, 6.5 = I/Y, CPT - PV = -834.72. With 17 = N, CPT --+ PV
= -848.34, so the value will increase $ 1 3 .62.
©20 12 Kaplan, Inc.
Page 99
Study Session 1 6
Cross-Reference to CFA Institute Assigned Reading #56 - Introduction to the Valuation of Debt Securities
11.
B
22
PMT = O, N = 2 x 17 = 34, I I Y = 8 · = 4. 1 1 , FV = 100,000
2
CPT � PV = -25,424.75,
or
100,000
= $25 ,424.76
(l .o4ur
Page
100
©2012 Kaplan, Inc.
The following is a review of the Analysis of Fixed Income Investments principles designed to address the
learning outcome statements set forth by CFA Institute. This topic is also covered in:
YIELD MEASURES , SPOT RATES, AND
FORWARD RATES
Study Session 1 6
EXAM FOCUS
This
topic
revi
ew gets aandlittlyield
e moreto specific
aboutpayyield
measuresattention
and introduces
currentof
yield,
yield
to
maturity,
cal
l
.
Please
particular
to
the
concept
aother
bondimportant
equivalentthiyinegldabout
and how
to
convert
vari
o
us
yi
e
l
d
s
to
a
bond
equival
e
nt
basis.
The
the yiellimitations.
d measures here is to understand what they are telling
you so that you understand their
The
final
sectionratesofisthians revi
ew introduces
forward
rates.youTheshould
relationshi
p betweento solve
forwardfor
rates
and
spot
important
one.
At
a
minimum,
be
prepared
spot
rates givalenso forward
ratesgripandontothesolveconcept
for anofunknown
forward
ratespread,
givenwhen
two spotit isrates.
You
should
get
a
firm
an
opti
o
n-adj
u
sted
and how to interpret it, as well as how and when it differs from a zero-volatility spread.used
LOS 57.a: Describe the sources of return from investing in a bond.
CFA® Program Curriculum, Volume 5, page 492
Debt securities that make explicit interest payments have three sources of return:
1. The periodic
made by the issuer.
2. The
that
occurs
when
the
bond matures, is called, or is sold.
3. payments (i.e., the compound
or the income
earned
from
reinvesti
n
g
the
periodic
coupon
interest on reinvested coupon payments).
The
interestTheearned
on reinabout
vestedhow
income
important income
source ofa bondholder
return to bondwill
investors.
uncertainty
muchis anreinvestment
realize is what we have previously addressed as
coupon interest payments
recovery ofprincipal, along with any capital gain or loss
Reinvestment income,
reinvestment risk.
LOS 57.b: Calculate and interpret traditional yield measures for fixed-rate
bonds and explain their limitations and assumptions.
CFA® Program Curriculum, Volume 5, page 493
Current
yield
is
the
simplest
of
al
l
return
measures,
but
it
offers
limited
information.
This measure looks at just one source of return:
does
a bond's annual interest income-it
©20 12 Kaplan, Inc.
Page 1 0 1
Study Session 1 6
Cross-Reference to CFA Institute Assigned Reading #57 - Yield Measures, Spot Rates, and Forward Rates
yinoteldconsider
is: capital gains/losses or reinvestment income. The formula for the current
payment
current yield = annual cashbondcoupon
price
--'._
---"
.o...
_
_
_
_
_
_
Example: Computing current yield
Consider
par value,
at $802.07.a 20-year,
Calculate$1,the000current
yield.6%
semiannual-pay
bond that is currently trading
Answer:
The cash coupon payments total:
annual cash coupon payment = par value stated coupon rate = $1,000 X 0.06 = $60
Because the bond is trading at $802.07, the current yield is:
current yield = 802.6007 = 0.0748, or 7.48%.
Note
that current
is based onbond withcoupon
thatandit isprice.
the same for a
semiannual
-pay andyieldannual-pay
the sameinterest
couponsorate
annual
x
annual
(YTM)cashisflanows.annualized
internal
rate of return,coupon
basedpayments,
on a bond'thes
priyieclde toandmaturity
its promised
For
a
bond
wi
t
h
semiannual
i
s
stated
as
two
ti
m
es
the
semiannual
internal
rate
of
return
implied
by
the bond'
The formula
YTM
for sa price.
semiannual
couponthatbondrelis:ates the bond price (including accrued interest) to
1 + CPN2 + . . . + CPN2N + Par
bond price = (1 +CPN�)
�t
(
1
+
(
�t
1
+
where:
bond
price == fulthel (semiannual)
price includingcoupon
accruedpayment
interestreceived after semiannual periods
CPN
NYTM == yinumber
of
years
to
maturity
eld to maturity
YTM
the sameyou information.
is, given the YTM, you can calculate
the priceandandpricegivencontain
the price,
can calculateThat
the YTM.
We
cannotpayment
easily solve
for weYTMcouldfromsoltheve ibond
price.andGiven
a tryibondng price
and valtheues of
coupon
amount,
t
by
trial
error,
di
f
ferent
YTM until the present value of the expected cash flows is equal to price. Fortunately,
Yield to maturity
...,.
....- ....!.
--:-;...
YT
--=.,...
-
YT
r
Page 102
N
YT
t
©2012 Kaplan, Inc.
Study Session 16
Cross-Reference to CFA Institute Assigned Reading #57 - Yield Measures, Spot Rates, and Forward Rates
your
calculator
wid thell dodiscount
exactly theratesame
thing, only
faster.sidesIt ofusesthea pritrialcinandg formula
error
algorithm
to
fi
n
that
makes
the
two
equal.
YTM
Consider
a
20-year,
$1,
0
00
par
value
bond,
with
a
6o/o
coupon
rate
(semiannual
payments) with a full price of $802.07. Calculate the YTM.
Example: Computing
Answer:
Using a financial calculator, you'd find the YTM on this bond as follows:
PV = -802.07; N = 20 x 2 = 40; FV = 1,000; PMT = 60/2 = 30; CPT ---+ 1/Y = 4.00
4o/o is the semiannual discount rate, YTM
2 in the formula, so the YTM = 2 x 4o/o = 8o/o.
Note dothatthisthetosignsavoidofPMT
and FV"Error
are positive,
andonthethesignTIofPV
is negative;
youget the
must
the
dreaded
5"
message
calculator.
If
you
"Error
can assume
negativedve from
valuetheto thebond.price
(PV) of5"themessage,
bond andyoua positi
ve signyouto thehavecashnotflassigned
ows to bea recei
There area certain
relationships
thatat exia discount,
st betweenordiatfferent
yield measures,
dependingareon
whether
bond
is
trading
at
par,
a
premium.
These
relationships
shown in Figure 1.
Figure 1 : Par, Discount, and Premium Bond
Bond Selling at:
Relationship
Par
coupon rate
=
current yield
Discount
coupon rate
<
current yield < yield to maturity
Premium
coupon rate
>
current yield
=
>
yield to maturity
yield to maturity
These
conditions
wiislllessholthan
d in allits cases;
every
discount
bond wiyielll dhavethataisnominal
yielitsd
(coupon
rate)
that
current
yi
e
l
d
and
a
current
less
than
YTM.
The
yield
to maturi
tyacalculated in the previous(BEY),
examplande (2wexwillthealsosemireferannualto itdiscount
rate)
i
s
referred
to
as
as
a
semiannual
YTM
or that
semiannual
-paydivide
YTM.byIftwoyoutoaregetgiven
yields that arediscount
identifirate.ed as
BEY,
you
wi
l
l
know
you
must
the
semiannual
With bonds that
make
annual
coupon
payments,
we
can
calculate
an
flows. which is simply the internal rate of return for the expected annual cash
bond equivalent yield
annual-pay yield
to maturity,
©20 1 2 Kaplan Inc.
,
Page 103
Study Session 1 6
Cross-Reference to CFA Institute Assigned Reading #57 - Yield Measures, Spot Rates, and Forward Rates
Example: Calculating for annual coupon bonds
Consider
an annual-pay
price of $802.
07. Calculate20-year,
the $1,000 par value, with a 6o/o coupon rate and a full
Answer:
The relation between the price and the annual-pay YTM on this bond is:
60 r 1,000 YTM = 8.0 19%.
802.07 = I: (1 + YTM)
YTM)
Here we have separated the coupon cash flows and the principal repayment.
The calculator solution is:
PV8.0 19%
= -802. 0 7; N = 20; FV = 1,000; PMT = 60; CPT ---7 IIY = 8.019;
is the annual-pay YTM.
Use
a
discount
rate
of
8.
0
19o/o,
and
you'
l
l
fi
n
d
the
present
value
of
the
bond'
s
future
cash flowspric(annual
market
e of thecoupon
bond. payments and the recovery of principal) will equal the current
For
zero-coupon Treasury
(semiannual-pay
YTMs). bonds, the convention is to quote the yields as BEYs
Example: Calculating for zero-coupon bonds
Aannual-pay
5-year Treasury
YTM.STRIP is priced at $768. Calculate the semiannual-pay YTM and
Answer:
The
directis:calculation method, based on the geometric mean covered in Quantitative
Methods,
1,000 ) 10 - 1 2 = 5.35o/o.
the sem1annu
. -pay YTM or BEY= (-768
1,000 )5 -1 = 5.42%.
the annual-pay YTM = (-768
YTM
annual-pay YTM.
20
+
t=1
(I+
20
=>
The discount rate is the bond's YTM.
YTM
1
al
1
Page 104
©2012 Kaplan, Inc.
X
Study Session 16
Cross-Reference to CFA Institute Assigned Reading #57 - Yield Measures, Spot Rates, and Forward Rates
Using the TVM calculator functions:
--+ 1/Y 2.675% 2 5.35% for
PV
-768;
FV
1,000;
PMT
0;
N
10;
CPT
the semiannual-pay
PV -768;YTM.
FV 1,000; PMT 0; N 5;
CPT
---+ 1/Y 5.42%YTM,
for theandannual-pay
The
YTM ofgrow5.4to2%$1,means
5.42%annual-pay
per year would
000 inthatfive$768
years.earning compound interest of
=
=
=
=
=
x
=
=
=
=
=
=
The
yield
topar.
call Foris usedbondsto calculate
thea premium
yield on callable
bonds that are may
sellingbeatlessa
premi
u
m
to
tradi
n
g
at
to
par,
the
than
the
yi
e
ld
to
maturi
t
y.
This
can
be
the
case
when
the
call
pri
c
e
i
s
below
the
current
market price.
The
culation
the calculation
oftheyield to maturity,
exceptcalthat
the of the yield to call is thefor same
the paras value
i
n
FV
and
for periods
tofirmaturi
tover
y, theWhen
a
bond
has
a
peri
o
d
of
cal
l
protection,
we
cal
c
ul
a
te
the
yield
to
st
call
period
until
may fiwerst canbe called,
andtheuseyielthed first
callsubsequent
price in thecallcalculation
astheFV.
Inappropriate
a simithelbond
ar manner,
calculate
to
any
date
using
call price.
If the abond
contains a provision forusinga calltheatnumberat some
timeuntiinl thethe future,
wedatecanand
calcul
te
the
of
years
par
call
parmeasure,
for thethematurity
payment.
If youcalculation;
have a goodjustunderstanding
ofabout
the yieldthe tonumber
maturityof
YTC
i
s
not
a
difficult
be
very
careful
years
to
the
call
and
the
call
price
for
that
date.
An
example
wi
l
l
il
l
ustrate
the
calculation
of these yield measures.
yield to call
callprice is substituted
semiannual periods until the call date is substituted
number of
N.
par
yield to first par call
Example: Computing the YTM, YTC, and yield to first par call
Consider
av20-year,
10%
semiannual-pay
bond
withyears.
a fullCalculate
price of 112the that
canYTC,
be and
call
e
d
in
fi
e
years
at
102
and
call
e
d
at
par
in
seven
YTM,
yield to first par call.
Professor's Note: Bondprices are often expressed as a percent ofpar
(e.g., 100 = par).
©20 1 2 Kaplan, Inc.
Page 105
Study Session 1 6
Cross-Reference to CFA Institute Assigned Reading #57 - Yield Measures, Spot Rates, and Forward Rates
Answer:
The
YTM1/Ycan= 4.be361%
calculated
PV = -112; PMT = 5; FV = 100;
CPT---+
2 = as:8.7N2%= =40;YTM.
Toperiods
compute
thetheyield
to firstdatecall(10)(YTFC),
we substi
tstutecalthel pricenumber
offorsemiannual
until
fi
r
st
call
for
N,
and
the
fi
r
(102)
FV, as
follows:
N = PV = -112; PMT = 5; FV =
CPT ---+ 1/Y = 3.71% and 2 3.71 = 7.42% = YTFC
To calculateperiods
the yielduntilto first
par
call
(YTFPC),
we forwillNsubstitute
the number
ofas
semiannual
the
fi
r
st
par
call
date
(14)
and
par
(100)
for
FV
follows:
N = PV = -112; PMT = 5; FV =
CPT ---+ 1/Y = 3.873% 2 = 7.746% = YTFPC
thatIf thethe yield
towerecall,tradi7.4n2%,g atias significantly
lowervalue,thanthere
the yiel
d tobematuri
ty, to
8.Note
72%.
bond
discount
to
par
would
no
reason
calcul
a
te
the
yi
e
l
d
to
cal
l
.
For
a
discount
bond,
the
YTC
wi
l
l
be
hi
g
her
than
the
YTM
since
the bondcalwill price.
l appreciate
morearerapidly
witonh thea yicaleldl toto atcallleastbasisparwhen
and,theperhaps,
an
even
greater
Bond
yields
quoted
YTC
i
s
less
than
the
YTM,
whi
c
h
can
only
be
the
case
for
bonds
trading
at
a
premium
to
the
call price.
The
yield toofworst
is theInworst
yield example,
outcome oftheanyyielthat
arefirstpossible
gissventhanthethecallYTM
provisions
the
bond.
the
above
d
to
cal
l
is
l
e
and
less
than
the
yield
to
first
par
cal
l
.
So,
the
worst
possible
outcome
i
s
a
yi
e
ld
of
7.42%; the yield to first call is the
The
yield
to
refunding
refers
to
a
specific
situation
where
a
bond
i
s
currently
callable
and
currentcontain
rates make
callinggithevingissueprotection
attractivefromto therefunding
issuer, but
where
thefuturebonddate.
covenants
provisions
until
some
The
calculation
of
the
yiel
d
to
refunding
i
s
just
l
i
k
e
that
ofYTM
or
YTC.
The
di
ff
erence
here
is that theof periods
yield toused
refunding
would
use theis calthel price,
but therefundi
daten(and
therefore
theends.number
in
the
calculation)
date
when
g
protection
Recal
l
that
bonds
that
are
callable,
but
not
currently
refundable,
can
be
called
using funds from sources other than the issuance of a lower coupon bond.
The
yield
to
put
(YTP)
is
used
if
a
bond
has
a
put
feature
and
is
selling
at
a
discount.
The
yield toisputjustwilikllelithekelyyield
be higher
than thewityihetheld tonumber
maturity.of semiannual
The yield toperiods
put until
calculation
to
maturity
the put date as N, and the put price as FV
X
10;
102;
x
14;
100;
X
yield to worst.
Page 106
©2012 Kaplan, Inc.
Study Session 16
Cross-Reference to CFA Institute Assigned Reading #57 - Yield Measures, Spot Rates, and Forward Rates
YTM YTP
Consider
000 is at par ibond.
is sellingtheforYTMa fullandpricethe
ofYTP.$925.40.a 3-year,
The fir6%,
st put$1,opportunity
n two The
years.bond
Calculate
Example: Computing
and
semiannual-pay
Answer:
Yield to maturity is calculated as:
= 6; FV = 1,000; PMT = 30; PV = -925.40; CPT � 1/Y = 4.44 2 = 8.88%
=NYTM
x
Yield to put is calculated as:
= 4; FV = 1,000; PMT = 30; PV = -925.40; CPT � 1/Y = 5.11 2 = 10.22%
= YTP
x
N
In this example,
gher than the YTM and, therefore, would be the
appropri
ate yieldtheto lyielookdattoforputthisis hibond.
The
cash
(CFY)
is
used
for
mortgage-backed
securities
and
other
amortizing
asset-backedrepayment
securitiescanthatbe have
monthl
ythecashamount
flows. requi
In many
cases,amortithezeamount
ofover
the
principal
greater
than
r
ed
to
the
loan
its original
life. Cash
flow yielodns(CFY)
incorporates
an assumed
schedule
of Once
monthlywe
cash
flows
based
on
assumpti
as
to
how
prepayments
are
likely
to
occur.
have
projected
can calcul
of return
basedtheon monthly
the marketcashpriflceows,of thewe securi
ty. ate CFY as a internal rate
flow yield
monthly
Professor's Note: I believe you are more likely to be required to interpret a CFY
� than to calculate one. Ifyou need to calculate a CFY, just use the cash flow keys,
� put the price ofthe security as a negative value as CF0 , enter the monthly cash
flows sequentially as CFn's, and solve for IRR, which will be a monthly rate.
The following formula is used to convert a (monthly) CFY into bond equivalent form:
bond equivalent yield [(1 +monthly CFY)6 -1] 2
Here,
we
have
converted
the
monthly
yi
e
ld
into
a
semiannual
yield
and
then
doubled
it
to make it equivalent to a semiannual-pay YTM or bond equivalent yield.
Aassumed
limitation
of
the
CFY
measure
is
that
actual
prepayment
rates
may
di
f
fer
from
those
in the calculation of CFY.
=
X
©20 1 2 Kaplan, Inc.
Page 107
Study Session 1 6
Cross-Reference to CFA Institute Assigned Reading #57 - Yield Measures, Spot Rates, and Forward Rates
The Assumptions and Limitations of Traditional Yield Measures
The
primaryrate of return that we will realize on a fixed-income
is that it idoes
not telover
l us theits life.
compound
n
vestment
This
is
because
we
do
not
know
the
rate
of
interest
we
wi
l
l
real
i
z
e
on
the
rei
n
vested
payments
(theonreia bond.
nvestment
rate).earlReiiner,vestment
income can
be thea signifi
cantonpart
ofcoupon
the
overal
l
return
As
noted
the
uncertainty
about
return
reinvestedrates,cashother
flowsthiisnreferred
gher forbonds
bondsaswiwellth .higher
coupon
gs equalto, andas potentially higherItforis hicallable
The
yield onIt ias bond
is computed
the actual atcompound
return
that was earned
on For
the a
ibond
nitiarealized
ltoinvestment.
usually
the
end
of
the
investment
horizon.
have aat the YTM, andequalthe tobondits YTM,
allhelcashd until
flowsmaturity.
prior to maturity
must
bereinvestment
reinvested
must
be
If
the
average
rate
is
below
the
YTM,
the
realized
yield
wi
l
l
be
below
the
YTM.
For
this
reason, it is often stated that:
limitation of the yield to maturity measure
reinvestment risk.
realized yield
The yield to maturity assumes cash flows will be reinvested at
the YTM and assumes that the bond will be held until maturity.
The other internal
ratetheyofarereturn
measures,
YTC andandYTP,
sufferaccount
from forthe reinvestment
same
shortcomings
since
calcul
a
ted
li
k
e
YTMs
do
not
income.
The
CFY
measure
i
s
also
an
i
n
ternal
rate
of
return
measure
and
can
differ
greatl
y fromandtheprepayments
realized yieldmustif reinvestment
scheduled
principal
payments
be reinvestedrates
alongarewithlow,thesinceinterest
payments.
LOS 57.c: Explain the reinvestment assumption implicit in calculating yield to
maturity and describe the factors that affect reinvestment risk.
CPA® Program Curriculum, Volume 5, page 495
is onimportant
because
iflethess thanreinvestment
rateTheisreallessizedthanyieldthe will
YTM,
the
realized
yi
e
l
d
the
bond
wi
l
l
be
the
YTM.
always be between the YTM and the assumed reinvestment rate.
bondholder
a bondbyuntil
maturity
interest payments,
theIf a total
amountholds
generated
the bond
overandits lifereinvests
has threeall coupon
components:
1. Bond principal.
2. Coupon interest.
3. Interest on reinvested coupons.
Once
we
calculate
the
total
amount
needed
for
a
particular
level
of
compound
return
over
a bond'
s life, we canincome
subtractnecessary
the principal
andevecoupon
payments
to example
determinewithell
amount
of
reinvestment
to
achi
the
target
yi
e
ld.
An
illustrate this calculation.
Reinvestment income
Page 108
©2012 Kaplan, Inc.
Study Session 16
Cross-Reference to CFA Institute Assigned Reading #57 - Yield Measures, Spot Rates, and Forward Rates
Example: Required reinvestment income for
a
bond
Ifmustyoubepurchase
a 6%,over1 0-year
Treasury
bond
at par, howwithmuch
reinvestment
income
generated
i
t
s
l
i
fe
to
provide
the
investor
a
compound
return
of 6o/o on
a semiannual basis?
Answer:
Assumi
ng thetenbondyearshas(20a parsemiannual
value of $100,
first calculate
be generated
periods)we from
now as: the total value that must
100(1.03) 20 = $180.61
There
bond tcoupons
principalare at20maturi
y. of$3 each, totaling $60, and a payment of$100 of
Therefore, the required reinvestment income over the life of the bond is:
180.61 - 100-60 = $20.61
Professor's Note: Ifwe hadpurchased the bond at a premium or discount, we would
still use the purchase price (which would not equal I 00) and the required compound
return to calculate the totalfuture dollars required, and then subtract the maturity
value and the total coupon payments to get the required reinvestment income.
Factors That Affect Reinvestment Risk
Other things being equal, a coupon bond's
will with:
because there'
s
more
cash
fl
o
w
to
reinvest.
moreonofcoupon
the totalcashvalueflows).
of the investment is in the
coupon cash flows (and interest
In both
cases,
thereturn
amountand,oftherefore,
reinvestedintroduce
income wimore
ll playreinvestment
a bigger rolrisk.
e in Adetermining
the
bond'
s
total
noncallable
zero-coupon
bond
has
no
reinvestment
risk
over
its
l
i
f
e
because
there
are
no
cash
fl
o
ws
to reinvest prior to maturity.
reinvestment risk
•
•
increase
Higher coupons
Longer maturities-because
-
©20 1 2 Kaplan, Inc.
Page 109
Study Session 1 6
Cross-Reference to CFA Institute Assigned Reading #57 - Yield Measures, Spot Rates, and Forward Rates
LOS 57.d: Calculate and interpret the bond equivalent yield of an annual-pay
bond and the annual-pay yield of a semiannual-pay bond.
CFA® Program Curriculum, Volume 5, page 494
Thi
s
LOS
requires
that
you
be
able
t
o
turn
a
semiannual
return
into
an
annual
return,
and an annual return into a semiannual return.
bonds with
thatofa corporati
on hasan annual
a semiannual
coupon
bond trading
in thewithUnia YTM
ted States
wi6.Suppose
t3h0%.a YTM
6.
2
5%,
and
coupon
bond
trading
i
n
Europe
of
Which bond has the greater yield?
Answer:
To(semiannual
determine-pay)
the answer,
the yield
to a
bond equiwevcanalentconvert
yield. That
is: on
BEY of an annual-pay bond = [(1 +annual YTM - 1] 2
Thus, the BEY of the 6.30% annual-pay bond is:
[(1 0.0630)0·5 -1] 2 [1.031-1] 2 0.031 2 0.062 6.2%
The 6.25% semiannual-pay bond provides the better (bond equivalent) yield.
Alternati
velyield)
y, we tocouldan equi
convert
theannual-pay
YTM of thebasis.semiannual-pay
bondannual
(whiyield
ch is a bond
equival
e
nt
v
alent
The
equi
v
alent
(EAY is:
to the 6.25% semiannual-pay
YTM
equivalent annual yield (1 0'0�25 r -1 0.0635 � 6.35%
Example: Comparing
different coupon frequencies
the annual-pay bond
1
X
)2
+
X
X
=
X
=
=
=
-sometimes known as the effective annualyield)
=
+
=
The
EAY ofbond.
the semiannual-pay
bond
is 6.35%, which
is greater
thanyietheld as6.3%longforas thewe
annual-pay
Therefore,
the
semiannual-pay
bond
has
a
greater
put theas bond
yields equi
on anvalent
equivalent
basis, calculating
both
yields (semiannual
yieldsboth2).as annual yields or calculating
x
Page 1 1 0
©2012 Kaplan, Inc.
Study Session 16
Cross-Reference to CFA Institute Assigned Reading #57 - Yield Measures, Spot Rates, and Forward Rates
LOS 57 .e: Describe the calculation of the theoretical Treasury spot rate curve
and calculate the value of a bond using spot rates.
CFA® Program Curriculum, Volume 5, page 508
The
par
yi
e
ld
curve
gi
v
es
the
YTMs
of
bonds
currentl
y
trading
near
their
par
values
(YTM calcoupon
need to use these yields to get the
theoreti
Treasuryrate)spotforratevarious
curvematurities.
by a processHere,callewed bootstrapping.
The
method
of bootstrapping
canc andbe detailed
a little confusing,
so legeneral
t's first getideatheis that
mainweideawilland
then
go
through
a
more
realisti
example.
The
solve
for
spot
rates
by
knowi
n
g
the
prices
of
coupon
bonds.
We
always
know
one
spot
rate totwobeginspotwithrates,andwethencancalculate
therdspot
rateonforthethemarket
next longer
period.
When
we
know
get
the
thi
based
pri
c
e
of
a
bond
wi
t
h
three
cash flows by using the spot rates to get the present values of the first two cash flows.
Asannual
an exampl
e of thisas shown
method,in Ficonsider
we know
-pay bonds
gure 2. that
All three
bondstheareprices
tradingandatyields
par orof$1,three000.
�
r s and
Figure 2: P ice
Yield for Three
An
a Bonds
nual P y
Maturity
Coupon
Yield
Price
1 year
3%
3%
$ 1 ,000
2 years
4%
4%
$ 1 ,000
3 years
5%
5%
$ 1 ,000
-
Because
thethe1-year
bond
makes
only
oneyipayment
(its'ssingle
an annual-pay
bond)
of $1,030
at
maturi
t
y,
1-year
spot
rate
is
3%,
the
e
ld
on
thi
payment.
The
2-year
bond
makes
two
payments,
a
$40
coupon
in
one
year
and
a
$1,
0
40
payment
at
maturity
i
n
two years.weBecause
thethespotsumrateoftothediscount
theval2-year
bond'bond'
s firsstcash
cashflfloowsw imust
s 3%,equal
and
because
know
that
present
u
es
of
the
its (no-arbitrage) price of $1,000, we can write:
40
1,040 2 $1,000
1.03 (1 2-year spot rate)
Based on this, we can solve for the 2-year spot rate as follows:
1,-0---40----=-2 = 1,000- 40 = 1,000-38.83 = 961.17
1. --'
1.03
(1 2-year spot)
1,040 = (1 2-year spot)2 = 1.082
2. 961.17
+
+
=
-
+
---
+
1
3. 2-year spot= (1.082)2 -1 = 0.04019 = 4.019%
©20 1 2 Kaplan, Inc.
Page 1 1 1
Study Session 1 6
Cross-Reference to CFA Institute Assigned Reading #57 - Yield Measures, Spot Rates, and Forward Rates
Now
have both
price that
of thewe3-year
bondtheto wri1-year
te: and 2-year spot rates, we can use the cash flows and
_2Q_ + 50 2 1,050 3 = 1,000
1. 03 (1.04019) (1 3-year spot)
And solve for the 3-year spot rate:
50
1,050
1,000- _2Q_
2
1.03 (1.04019) (1 3-year spod
1' 050 3
1,000-48.54-46.21 = (1 3-year
spot)
1' 050 3
905.25 = (1 + 3-year
spot)
( 1,o5o )X - 1 = 3-year spot = 0.05069 = 5. 069%
905.25
+
+
+
+
So, we can state that:
_2Q_
50 2 1,050 3 = $1,000
1.03 (1.040 19) (1.05069)
We have just solved for the 2-year and 3-year spot rates by the method of bootstrapping.
In practice,
Treasury
bondsillustrates
pay semiannuall
y, andofthei
r YTMs arewhen
semiannual-pay
YTMs.
The
next
example
the
method
bootstrapping
coupons
are
paid
semiannually.
Consider
the
yi
e
l
d
s
on
coupon
Treasury
bonds
tradi
n
g
at
par
gi
v
en
in
Figure
3.
YTM
for
the bonds is expressed as a bond equivalent yield (semiannual-pay YTM).
+
Figure
Page 1 1 2
3:
+
Par Yields for Three Semiannual-Pay
Maturity
YTM
Coupon
Price
6 months
5%
5%
1 00
1 year
6%
6%
1 00
1 8 months
7%
7%
1 00
Bonds
©2012 Kaplan, Inc.
Study Session 1 6
Cross-Reference to CFA Institute Assigned Reading #57 - Yield Measures, Spot Rates, and Forward Rates
The
wi0.0th25si=x 2.5%
monthsorle5o/oft toonmaturity
hasBEYa semiannual
discount
rate ofwill only
0.make
05 bond
2one= payment
an
annual
basis.
Because
this
bond
5 in six months, the YTM is the spot rate for cash flows to be
received six monthsoffrom102.now.
The bootstrapping
process
proceedswifromth thethisprice/YTM
point usinginformation
the fact thatonthethe6-month
annualized
spot
rate
is
5o/
o
together
1-year
bond.
We
wil
l
use
the
formula
for
valui
n
g
a
bond
using
spot
rates
that
we
covered
earlier.
Noti
n
g
that
the
1-year
bond
wi
l
l
make
two
payments,
one
in
six
months
of
3.
0
and
one
i(whi
n onechyear
0, and from
that thenow),appropriate
spot rate to discount the coupon payment
comesof si1 03.x months
we can write:
-1.o3-25 103 100, where is the annualized 1-year spot rate,
(1 � )
3
927=97.073
and solve for 1 ·n�l2 as: ( 103 =100---=100-2.
1.
o
25
1 �)
1 0_3_ (1 121)2 ' so 'J97.073
_
{103 1 12I
97.073
0.030076 and 2 0.030076 0.060152 6.0152%
Now
thatce ofwethehave18-month
the 6-month
andto set1-year
spot rates,
weequalcantousethethisvalueinformation
ands
thecashpriflows
bond
the
bond
price
of
the
bond'
as:
3.5 3.5 2 103.5 00
1.025 (1.030076) (1 ?{r
where is the annualized 1.5-year spot rate, and solve for ?{
103· 5 =100-_22_ - 3· 5 2 = 100-3.4 15-3.30=93.285
(1 ?{r 1.025 (1.030076)
I
+
2
+ 51.
51 0
=
·
5
+ 51.
=
+ 5Lo
51 .0
=
--
-
=
+
+
2
X
=
5Lo
=
=1
+ 5l.
=
)
51.
51 .5
+ 5l .
103.5 (1 121) 3 , so ( 103.5 )3 _ 1 12I
93.285
93.285
=
51. 5
=
+ 51. 5
1
=
51. 5
0.0705 7.05%
=
©20 12 Kaplan, Inc.
Page 1 13
Study Session 1 6
Cross-Reference to CFA Institute Assigned Reading #57 - Yield Measures, Spot Rates, and Forward Rates
To summarize the method of bootstrapping spot rates from the par yield curve:
1. Begin with the 6-month spot rate.
2. Set1-yearthespot
valuerateof thedivid1-year
present value of the cash flows with the
ed bybond
two asequal
the onlto ytheunknown.
3. Solve for the 1-year spot rate.
the
6-month
and
1-year
spot
rates
and
equate
the
present
value
of
the
cash
4. Use
flunknown.
ows of the 1.5-year bond equal to its price, with the 1.5-year spot rate as the only
5. Solve for the 1.5-year spot rate.
Professor's Note: You are responsible for "describing" this calculation, not for
computing theoretical spot rates.
Example: Valuing a bond using spot rates
Given the following spot rates (in BEY form):
0.1.05 years
years == 4%
5%
1.5 years = 6%
Calculate the value of a 1.5-year, 8% Treasury bond.
Answer:
Simply
ay outsincethethey
cashareflowsquoted
and discount
by the spot rates, which are one-halfthe
quoted lrates
in BEY form.
4
4
104 102.9
(1 0.�4 ) (1 0.�5 ) (1 0.�6 )
or, with the TVM function:
NN == 2;1; PMT
=
0;
1/Y
=
2;
FV
=
4;
CPT
PV
=
-3.
9
2
PMT == 0;0; 1/Y
N = 3; PMT
1/Y == 2.5;
3; FVFV= =104;4; CPT
CPT PVPV==-3.81
-95.17
Add these values together to get 1 02.9.
-:1
+
-
+
+
2
+
+
3
=
--t
--t
--t
Page 1 14
©2012 Kaplan, Inc.
Study Session 1 6
Cross-Reference to CFA Institute Assigned Reading #57 - Yield Measures, Spot Rates, and Forward Rates
LOS 57.f: Explain nominal, zero-volatility, and option-adjusted spreads and the
relations among these spreads and option cost.
CFA® Program Curriculum, Volume 5, page 513
The
nominal
spread
is
the
simplest
of
the
spread
measures
to
use
and
to
understand.
It is simplythean iusessue'ofs YTM
minus spread
the YTMsuffers
of a from
Treasury
security
of similarasmaturity.
Therefore,
the
nominal
the
same
limitations
the YTM.
YTM uses aInsinfact,
gle discount
rate
to
val
u
e
the
cash
fl
o
ws,
so
it
YTMis forflat.a coupon bond is theoretically correct only to the extent
that the spot rate curve
ignores the shape ofthe spot
yield curve.
The Zero-Volatility Spread
One
way
to
get
a
bond'
s
nominal
spread
to
Treasuries
i
s
to
add
different
amounts
to
the
yield oftoathecomparable
Treasury
bond,
and value
thevaluebondequal
withtothose
YTMs. price
The amount
added
Treasury
yield
that
produces
a
bond
the
market
of the
bond must be the nominal yield spread.
This themayzero-volatility
seem like an odd
wayorto static
get thespread,
spread,is but
it makesThesensezero-volatil
when youityseespread
how
spread,
calculated.
iins theorderequalto make
amountthethatpresent
we must
addof theto each
ratebond'ons thecashTreasury
spotto
yiits(Z-spread)
eldmarket
curveprice.
value
ri
s
ky
fl
o
ws
equal
Instead
of
measuri
n
g
the
spread
to
YTM,
the
zero-vol
a
ti
l
i
t
y
spread
measures prithecesspread
Treasury(i.e.spot
rates necessary
produce a spot rate curve that
correctly
a riskyto bond
, produces
its markettoprice).
For a riskyspotbond,ratesthewilvall beuetooobtained
from discounting
thespotexpected
cashlower
flowsthanat those
Treasury
hi
g
h
because
the
Treasury
rates
are
appropri
a
te
for
a
ri
s
ky
bond.
In
order
to
val
u
e
i
t
correctl
y
,
we
have
to
i
n
crease
each
of thesTreasury
spotdiscounted
rates by some
equal
amountspotso that
theequals
presentthe market
value ofvalue
the riofskythe
bond'
cash
fl
o
ws
at
the
(increased)
rates
bond. The following example wil illustrate the process for calculating the Z-spread.
©20 12 Kaplan, Inc.
Page 1 1 5
Study Session 1 6
Cross-Reference to CFA Institute Assigned Reading #57 - Yield Measures, Spot Rates, and Forward Rates
Example: Zero-volatility spread
1-,Consider
2-, anda 3-year
spot
rates
on
Treasuries
are
4%,
8.167%,
and
12.
3
77%,
respecti
v
ely.
3-year,
9o/o annual
coupon
corporate
bondCompute
tradingtheat 89.nominal
464. Thespread
YTMandis
13.50%,
and
the
YTM
of
a
3-year
Treasury
is
12%.
the zero-volatility spread of the corporate bond.
Answer:
The
is:
= 13.50- 12.00 = 1.50%.
nominal spread = YTM BondTomarket
compute
the
Z-spread,
set
the
present
value
of
the
bond'
s
cash
fl
o
ws
equal
to
today'
s
price.
Discount
eachZS.cash
floforw atZSthein appropriate
zero-coupon
bondyouspot
ratethe
a
fi
x
ed
spread
equals
Solve
the
fol
l
owing
equation
and
have
Z-spread:
89.464 = (Lo4 9 zsY ( 1. 0 81679 zs)2 (1.12377109 zs)3
ZS 1.67% or 167 basis points
Noteitthatintothithes spread
is foundsidebyoftrial-and-error.
In other
words,
pickequals
a number
"ZS,If"
plug
right-hand
the
equation,
and
see
if
the
result
89.
4
64.
theanother
right-hand
"ZS" andsidestartequalover.s the left, then you have found the Z-spread. If not, pick
nominal spread
YTMTreasury
plus
+
+
+
+
+
=>
=
Professor's Note: This is not a calculation you are expected to make; this example
is to help you understand how a Z-spread differsfrom a nominal spread.
There
two primary
factors that influence the difference between the nominal spread
and theareZ-spread
for a security.
The
steepermeasures.
the benchmark
spot
ratedifference
curve, thebetween
greaterthethenominal
differenceandbetween
thewhen
two
spread
There
i
s
no
Z-spread
thelargerspotthanyieldthecurve
is flaspread.
t. If theThespotZ-spread
yield curveis leisss upward
sloping,
thespread
Z-spread
is
nominal
than
the
nominal
when
theThespot
yi
e
ld
curve
i
s
negatively
sloped.
earlmeasures.
ier the bondFor principal
is paid, theslopedgreateryieldthecurve,
difference
between security,
the two
spread
a
gi
v
en
positively
an
amortizing
such
an MBS,
will have
greater difference between its Z-spread and nominal
spreadasthan
a coupon
bondawill.
•
•
Page 1 1 6
©2012 Kaplan, Inc.
Study Session 1 6
Cross-Reference to CFA Institute Assigned Reading #57 - Yield Measures, Spot Rates, and Forward Rates
The Option-Adjusted Spread
Thecallable bond, for example,
s r (OAS)
measure
is usedyieldwhenthana bond
has embedded
options.
Abond,
must
have
a
greater
an
identical
option-free
and a greater
nominalmeasures
spreadwiorllZ-spread.
Without
accounting
forwhen,
the value
of
thethe additional
options,
these
spread
suggest
the
bond
is
a
great
value
in
fact,
yield
is compensation
for caloutl risk.
Loosely
speaking,
thethe option­
takes
the
option
yield
component
of
the
Z-spread
measure;
adjusted
spread
is
the
spread
to
the
Treasury
spot
rate
curve
that
the
bond
would
have
if
itliqwere
The OASrateisrisk.
the spread for non-option characteristics like credit risk,
uidityoption-free.
risk, and interest
option-adjusted p ead
option-adjusted
spread
Proftssor's Note: The actual method ofcalculation is reservedfor Level II; for our
purposes, however, an understanding ofwhat the OAS is will be sufficient.
Embedded Option Cost
If we scalculate
anTheoption-adjusted
spread
foryiaeldcallrequired
able bond,to compensate
it will be lessforthanthe thecall
bond'
Z-spread.
di
f
ference
is
the
extra
option. Calling that extra yield the option cost, we can write:
Z-spread - OAS = option cost in percent
Example: Cost of an embedded option
Supposebonds
you learn
that
a bondofis call167ablebasiand
has anCompute
OAS of the135bp.costYouof thealsoembedded
know that
similar
have
a
Z-spread
s
points.
option.
Answer:
The option cost= Z-spread-OAS = 167- 135 = 32 basis points.
For
embedded
short
cal
l
s
(e.
g
.
,
cal
l
abl
e
bonds):
option
cost>
0
(you
receive
compensation for writing the option to thethanissuer)for an option-free
OAS < Z-spread.
you
bond.In other words,
For
embedded
puts
(e.
g
.
,
putable
bonds),
option
cost
<
0
(i.
e
.
,
you
must
pay
for
the
option)
> Z-spread.
than for anOAS
option-free
bond.In other words, you
�
require more yield on the callable bond
�
require lessyield on theputable bond
©20 12 Kaplan, Inc.
Page 1 17
Study Session 1 6
Cross-Reference to CFA Institute Assigned Reading #57 - Yield Measures, Spot Rates, and Forward Rates
LOS 57.g: Explain a forward rate and calculate spot rates from forward rates,
forward rates from spot rates, and the value of a bond using forward rates.
CPA® Program Curriculum, Volume 5, page 520
is
a
borrowing/lending
rate
for
a
loan
to
be
made
at
some
future
date.
The
notation
used must
identifywilboth
the length of the lending/borrowi
ng period and
when
in
the
future
the
money
l
be
loaned/borrowed.
Thus,
/1 is the rate for a 1-year
loan
one
year
from
now
and
f
i
s
the
rate
for
a
1-year
loan
to
be
made
two
years
from
1
2
now,
andratesoason./o·Rather
than
introducevaluesa separate
notation,
we cancashrepresent
theneedcurrent
1-year
To
get
the
present
of
a
bond'
s
expected
fl
o
ws,
we
to
discount
each
cash
fl
o
w
by
the
forward
rates
for
each
of
the
periods
until
it
i
s
received.
(The
present
value
of
$1
to
be
recei
v
ed
in
peri
o
d
di
s
counted
by
the
forward
rates
for
periods 1 to is called the
for period
A forward rate
n,
forward discount factor
n,
n.)
The Relationship Between Short-Term Forward Rates and Spot Rates
The idea here is that
Thi
s
relation
i
s
il
l
ustrated
as
(1
5 3)3 = (1 /0)(1 1f )(1 /2) and the reverse as
3
53 = [(1 /0)(1 /1)(1 /2)] 1 1 - 1, which is the geometric mean we covered in
Quantitative Methods.
borrowingfor three years at the 3-year rate or borrowingfor 1-year
periods, three years in succession, should have the same cost.
+
+
+
+
+
+
1
+
Example: Computing spot rates from forward rates
Ifforward
the current
1-year
rate
is
2o/o,
the
1-year
forward
rate
(
f1)
i
s
3o/o
and
the
2-year
1
rate (1f2) is 4o/o, what is the 3-year spot rate?
Answer:
[(1.02)(1.03)(1.04)] 1 13 - 1 = 2.997%
This
canproduce
be interpreted
toending
mean valthatueaasdolaldollar
ar compounded
atcompound
2.997% forinterest
threeofyears2o/o
would
the
same
that
earns
the first year, 3o/o the next year, and 4o/o for the third year.
53 =
Proftssor's Note: You can get a very good approximation ofthe 3-year spot
rate with the simple average oftheforward rates. In the previous example,
we calculated 2.997% and the simple average of the three annual rates is
2 3 4 3o/o.
3
+ +
Page 1 1 8
=
©2012 Kaplan, Inc.
Study Session 1 6
Cross-Reference to CFA Institute Assigned Reading #57 - Yield Measures, Spot Rates, and Forward Rates
Forward Rates Given Spot Rates
Wecalculcanateuseforward
the sameratesrelationship
we used to calculate spot rates from forward rates to
from spot rates.
Our basic relation between forward rates and spot rates (for two periods) is:
Which,
again,
tells
us
that
an
investment
has
the
same
expected
yi
e
ld
(borrowi
n
g
has
therate,same
expected cost) whether we invest (borrow) for two periods at the 2-period spot
52, or for one period at the current rate, 5 1 , and for the next period at the expected
forward rate, 1f1 • Clearly, given two of these rates, we can solve for the other.
Example: Computing a forward rate from spot rates
The
2-period
spot
rate,
52, is 8% and the current 1-period (spot) rate is 4% (this is both
5 1 and /0). Calculate the forward rate for one period, one period from now, /1 •
Answer:
The following figure illustrates the problem.
Finding a Forward Rate
2-year bond (52 8.0%)
=
1-year bond (today)
(SI 4.000%)
=
1-year bond
(one year from roday)(J1
=
?)
2
0
©20 12 Kapl
an ,
In c
.
Page 1 19
Study Session 1 6
Cross-Reference to CFA Institute Assigned Reading #57 - Yield Measures, Spot Rates, and Forward Rates
From our original equality, (1 + S2)2 = (1 S1)(1 1f1), we can get (1(1+SS2t))2 -1 = ft
or, because we know that both choices have the same payoff in two years:
(1.08) 2 = (1.04)(1 /))
(1 f ) = (1.(1.008)4)2
f = (l.(1.008)4)2 -1= 1.1664
1.04 -1=12.154%
Intheyother
words,
investors
are
wi
l
l
i
ng
to
accept
4.
0
%
on
the
1-year
bond
today
(when
2-yearThis
bondfuture
today)rateonlythatbecause
12.154%
1-yearcould
bondgetone8.0%
yearonfromthetoday.
can bethey
lockedcaningettoday
is a on a
+
+
+
l
+
+ 1 1
l 1
forward rate.
Similarly, we can back other forward rates out of the spot rates. We know that:
And that:
This
last theequation
says thatvaliunevesting
for threeforyears
at theat3-year
spot spot
rate should
produce
same
ending
as
i
n
vesting
two
years
the
2-year
then for a third year at f2, the 1-year forward rate, two years from now. rate and
Solving for the forward rate, 1 f2, we get:
1
Page 120
©2012 Kaplan, Inc.
Study Session 1 6
Cross-Reference to CFA Institute Assigned Reading #57 - Yield Measures, Spot Rates, and Forward Rates
Example: Forward rates from spot rates
Let'
s
extend
the
previ
o
us
example
to
three
periods.
The
current
1-year
spot
rate
i
s
4.0%, the current 2-year spot rate is 8.0%, and the current 3-year spot rate is 12.0%.
Calculate the 1-year forward rates one and two years from now.
Answer:
We know the following relation must hold:
We can use it to solve for the 1-year forward rate one year from now:
We also know that the relations:
(1 + S 3) 3 = (1 + S I )(1 + /I ) (1 + /z)
+ S 3) 3 = + S2)2 (1 + /2)
and, equivalently (1 (1
must hold.
Substituting values for S3 and 52, we have:
so that the 1-year forward rate two years from now is:
f2 (1 .12)2 -1 20.45%
1
=
(1.08)
3
=
To verify these results, we can check our relations by calculating:
s3 = [1(I.04)(1.121 54)(1 .2045)l 1 13 - 1= 12.ooo/o
Thi
s may alperil seem
a bi1-period
t complirates
cated,should
but thehavebasictherelation,
thatas borrowi
ng forat
successive
o
ds
at
same
cost
borrowing
multiperiod spot rates, can be summed up as:
2 = (1 + S 1 )(1 + f1) for two periods, and (1 + S ) 3 = (1 + 52) 2 (1 + /2) for
(1three+ 52)periods.
3
1
©20 12 Kaplan, Inc.
Page 121
Study Session 1 6
Cross-Reference to CFA Institute Assigned Reading #57 - Yield Measures, Spot Rates, and Forward Rates
Professor's Note: Simple averages also give decent approximations for calculating
forward rates from spot rates. In the above example, we had spot rates of4% for
one year and 8% for two years. Two years at 8% is 16%, so if the first-year rate
is 4%, the second-year rate is close to 16- 4 12% (actual is 12. 154). Given
a 2-year spot rate of8% and a 3-year spot rate of 12%, we could approximate
the 1-year forward rate from time two to time three as (3 x 12) - (2 x 8) 20.
That may be close enough (actual is 20. 45) to answer a multiple-choice question
and, in any case, serves as a good check to make sure the exact rate you calculate is
reasonable.
=
=
We
can
al
s
o
calculate
implied
forward
rates
for
loans
for
more
than
one
period.
Gi
v
en
spot rates of: 1-year = 5%, 2-year = 6%, 3-year = 7%, and 4-year = 8%, we can calculate
l2 '
The implied forward rate on a 2-year loan two years from now is:
Professor's Note: The approximation works for multi-periodforward rates as well.
��� Here, we have (4 8 -2 6 2)
X
X
=
10 .
.
The difference between two years at 6% and
four years at 8% is approximately 20%. Since that is for two years, we divide by
two to get an annual rate ofapproximately 10%.
Valuing a Bond Using Forward Rates
Example: Computing a bond value using forward rates
The
current
1-year rate (1 f0) is 4%, the 1-year forward rate for lending from time = 1 to
time
=
2
is
/1 = 5%, and the 1-year forward rate for lending from time= 2 to time = 3 is
1 f2 = 6%. Value a 3-year annual-pay bond with a 5% coupon and a par value of $1,000.
Answer:
_2Q_ +
50 +
1,050
$1 000. 98
1.04 (1.04)(1.05) (1.04)(1.05)(1 .06) '
=
Professor's Note: Ifyou think this looks a little like valuing a bond using spot rates,
as we didfor arbitrage-free valuation, you are right. The discountfactors are
equivalent to spot rate discountfactors.
Page 122
©2012 Kaplan, Inc.
Study Session 1 6
Cross-Reference to CFA Institute Assigned Reading #57 - Yield Measures, Spot Rates, and Forward Rates
KEY CONCEPTS
LOS 57.a
ThreeCoupon
sourcesinterest
of returnpayments.
to a coupon bond:
Reinvestment
couponvalue.
cash flows.
Capi
tal gain orincome
loss ononthetheprincipal
Yield
to amaturi
tdiscount
y (YTM)ratefor athatsemiannual-pay
couponvaluebondof theis calculated
as two times
the
semi
nnual
makes
the
present
bond'
s
promised
cash
fltheowsYTM
equalis tosimply
its market
price plus
accrued
interest.
Forthean present
annual-pay
coupon
bond,
the
annual
discount
rate
that
makes
val
u
e
of
the
bond's
promised cash flows equal to its market price plus accrued interest.
The current yield for a bond is its annual interest payment divided by its market price.
Yi(put)eld and
to callthe(put)
is calculated
as a YTMforbutthewithnumber
the number
of periods
until theandcallthe
call
(put)
pri
c
e
substituted
of
periods
to
maturity
maturity value.
The
cashtheflowcurrent
yield ismarket
a monthly
rate of return based
on a presumed
rate and
priceinofternal
a mortgage-backed
or asset-backed
securiprepayment
ty.
Thesebeyidiscounted
eld measuresat theare same
limitedrate;by theirthecommon
assumptions
that:
(1) all cash flows
can
bond
wi
l
l
be
hel
d
to
maturi
tsy,YTM;
with alandl
coupons
reinvested
to
maturi
t
y
at
a
rate
of
return
that
equals
the
bond'
(3) all coupon payments will be made as scheduled.
YTM
is not the realized yield on an investment unless the reinvestment rate is equal to
the YTM.
The
amount
of
rei
n
vestment
income
requi
r
ed
to
generate
the
YTM
over
a
bond'
s
l
i
f
e
i
s
thematuridifference
price of and
the bond,
ty, and thebetween
sum ofthethepurchase
bond's interest
principalcompounded
cash flows.at the YTM until
Reinvestment
whentthey (coupon
couponraterateheld
is greater
(maturity held constant) and
when
the bondriskhasislohigher
nger maturi
constant).
The bond-equivalent yield of an annual-pay bond is:
BEY= [�(1 + annual-pay YTM) - 1]
•
•
•
LOS 57.b
(2 )
LOS 57.c
LOS 57.d
x
2
©20 12 Kaplan, Inc.
Page 123
Study Session 1 6
Cross-Reference to CFA Institute Assigned Reading #57 - Yield Measures, Spot Rates, and Forward Rates
The annual-pay yield can be calculated from the YTM of a semiannual-pay bond as:
YTM )2 -1
EAY = (1 semiannual-pay
2
+
LOS
The
theoretical
Treasury
spoton theratespot
curverateis derived
by Ncalculating
themarket
spot ratepricefor ofeacha
successive
period
based
for
period
1
and
the
bond with coupon payments.
Tousingcompute
theratevalcorresponding
ue of a bond using
spotnumber
rates, ofdiscount
each
separate
cashflowfloiswto be
the
spot
to
the
periods
until
the
cash
received.
LOS commonly used yield spread measures:
Three
bond(Z-spread
YTM -Treasury
YTM.
or
static
spread):
the
equal
amount
of
additional
yield
addedforto aeachbondTreasury
spotits market
rate to getprice.spot rates that will
producethata must
presentbe value
equal
to
(OAS):
spread
to
the
spot
yield
curve
after
adj
u
sting
for
the
effects ofly.embedded options. OAS reflects the spread for credit risk and liquidity risk
primari
Theresteeper
is no dithefference
berween
theandnominal
andbond
Z-spread
whenisthepaidyield(amorti
curvezinisgflat.
The
spot
yiel
d
curve
the
earlier
principal
securities), the greater the difference in the rwo spread measures.
The option cost for a bond with an embedded option is Z-spread OAS.
For callable bonds, Z-spread > OAS and option cost > 0.
For putable bonds, Z-spread < OAS and option cost < 0.
LOS
Forward
rates
are
current
lending/borrowi
n
g
rates
for
short-term
loans
to
be
made
in
future periods.
A spot
rateThe
for asame
maturity
ofon canperiods
is theto solve
geometric
mean ofrateforward
rates
over
thefor
periods.
relati
be
used
for
a
forward
gi
v
en
spot
rates
rwo different periods.
Toproduct
valueofa bond
one plususingeachforward
forwardrates,ratediscount
for periodsthe 1cashto flowsandatsumtimesthem.1 through by the
57.e
N
N
57.f
•
•
Nominal spread:
Zero-volatility spread
•
Option-adjusted spread
-
57.g
N
N
N
N,
Page 124
©2012 Kaplan, Inc.
Study Session 1 6
Cross-Reference to CFA Institute Assigned Reading #57 - Yield Measures, Spot Rates, and Forward Rates
CONCEPT CHECKERS
4.
An102.analyst
observes
a Widget
&$1Co.,000).7.125%,
4-year,is callable
semiannual-pay
bond
tradingandat
3
47%
of
par
(where
par
=
The
bond
at
101
i
n
two
years
putable at 100 in two years.
1. What
i
s
the
bond'
s
current
yield?
A.B. 6.7.9362%.
28%.
7.426%.
i
s
the
bond'
s
yi
e
ld
to
maturity?
2. What
A.B. 3.5.8264%.
25%.
6.450%.
i
s
the
bond'
s
yield
to
call?
3. What
A.B. 3.167%.
64%.
6.5.6334%.
the bond's yield to put?
4. What
A.B. 4.5.82is64%.
25%.
6.450%.
Based on semiannual
compounding,
what
would
the tradi
YTMngbeaton$331.
a 15-year,
5. zero-coupon,
$1,
0
00
par
val
u
e
bond
that'
s
currently
4
0?
A.B. 3.5.151%.
750%.
7.500%.
analystWhat
observes
a
bond
wi
t
h
an
coupon
that'
s
being
priced
to
yield
6. An6.350%.
is this issue's bond equivalent yield?
A.B. 3.175%.
3.126%.
6.252%.
determines
that
theequicashvalent
flowyield?
yield of GNMA Pool 3856 is 0.382%
7. An analyst What
is
the
bond
A.B. 4.9.3663%.
28%.
9.582%.
Use the following data to answer Questions 1 through
c.
c.
c.
c.
c.
annual
c.
per month.
c.
©20 12 Kaplan, Inc.
Page 125
Study Session 1 6
Cross-Reference to CFA Institute Assigned Reading #57 - Yield Measures, Spot Rates, and Forward Rates
Ifnvestment
the YTM iequals
the actual
an investor
ithat:
n a coupon
bondcompound
purchased atreturn
a premium
to par,realiit ziess on an
A.B. cash
flowswilwilllnotbe paid
as promised.
the
bond
be
sold
C. cash flows will be reinvestedat aatcapital
the YTMloss.rate.
4-year
spot
rate
is
9.
4
5%,
and
the
3-year
spot
rate
is
9.85%.
What
i
s
the
9. The
forward rate three years from today?
A.B.1-year8.258%.
9.850%.
11.059%.
10. Anoptioninvestor
purchases
a bond
that istheputable
at theas option
ofs thepoints.holder.TheThe
has
val
u
e.
He
has
calculated
Z-spread
223
basi
spread
will be:
A.option-adjusted
equal
to
223
basis
points.
C.B. less
greaterthanthan223223basisbasispoints.
points.
Use the following data to answer Questions 11 and 12.
Given:
Current
1-year
rate
=
5.5%.
One-year
forward
rate
one
year
from
today
==7.12.18%.
63%.
One-year
forward
rate
two
years
from
today
One-year forward rate three years from today= 15.5 %.
11. The
val
u
e
of
a
4-year,
10%
annual-pay,
$1,
0
00
par
value
bond
would
be
A.to:B. $995.
89.
$1,009.16.
$1,085.62.
12. value
Usingbond
annualwould
compounding,
the value of a 3-year, zero-coupon, $1,000 par
be:
A.B. $785.
$852.
$948.
s nominal
spread,bond
zero-volif: atility spread, and option-adjusted spread will
13. Aallbond'
be
equal
for
a
coupon
curve
i
s
flat.
A.B. thethe yield
bond curve
is optionis flatfree.and the bond has no embedded options.
C. the yield
8.
least likely
c.
•
•
•
•
closest
c.
c.
Page 126
©2012 Kaplan, Inc.
Study Session 1 6
Cross-Reference to CFA Institute Assigned Reading #57 - Yield Measures, Spot Rates, and Forward Rates
14. A.Theifzero-vol
atilcurve
ity spread
will be zero:
the
yield
i
s
fl
a
t.
B.C. forfor ana zero-coupon
bond.
on-the-run Treasury bond.
theyielTreasury
spot-rate
yield
curvebond
is upward
sloping.
Compared
to the
15. Assume
nominal
d
spread
between
a
Treasury
and
an
option-free
corporate
bond
of
similar
maturity,
the
Z-spread
will
be:
A.B. less
greaterthanthanthethenominal
nominspread.
al spread.
C. equal to the nominal spread.
CHALLENGE PROBLEMS
1. Ansellsinvestor
buys
a
10-year,
7%
coupon,
semiannual-pay
bond
for
92.
8
0.
He
yearsisla6.ter,9%.justCoupon
after receiving
thehassixth
coupon
payment,
whenthatits
yiyieeldldsitto5%three
maturity
interest
been
placed
i
n
an
account
bond and calculate the
dollar return(BEY).
fromState
each thesourcesources
basedofonreturn
a $100,on 0thi00s bond.
2. What
pricediats thepar?yield on a bond equivalent basis of an annual-pay 7% coupon bond
3. What
bond? is the annual-pay yield to maturity of a 7% coupon semi-annual pay
yield
to
maturi
t
y
on
a
bond
equival
e
nt
basis
on
6-month
and
1-year
T-bills
4. The
andis the3.218-month
%, respectivel
y. A 1.5-year,
4% Treasury note is selling at par.
A.B.are 2.8%
What
Treasury
spot
rate?
Iffora 102.
1.5-year
semiannual-pay
corporate
bond
wisthbond?
a 7%Iscoupon
is sellingity
3
95,
what
is
the
nominal
spread
for
thi
the
zero-volatil
spread (in basis points) 127, 130, or 133?
5. Assume the following spot rates (as BEYs).
Years to Maturity
Spot Rates
0.5
4.0o/o
1 .0
4.4o/o
1.5
5.0 o/o
2.0
5.4o/o
A.B. What
iiss thethe 6-month
forwardraterateoneoneyearyearfromfromnow?now?
What
1-year
forward
C. What is the value of a 2-year, 4.5% coupon Treasury note?
©20 12 Kaplan, Inc.
Page 127
Study Session 16
Cross-Reference to CFA Institute Assigned Reading #57 - Yield Measures, Spot Rates, and Forward Rates
6. Assume
currentin the6-month
is 3.5% and the 6-month forward rates (all as
BEYs) arethethose
followingratetable.
Periods From Now
Forward Rates
3.8%
2
4.0%
3
4.4%
4
4.8%
A.B. What
Calculisatethethevalue
corresponding
of a 1.5-year,spot4%rates.Treasury note?
7. Consider
the follzero
owingcoupon
three bond
bondspriced
that allathave
par0. values of $100,000.
I.II. AA 5-year
1 0-year
48.
2
8% semiannual-pay
semiannual-pay bond
bond priced
priced with
with aa YTM
YTM ofof 8%.
III. A 5-year 9%
8%.
Rank
the
three
bonds
in
terms
of
how
important
reinvestment
income
is
to
an investorit towhomaturi
wishesty. to realize the stated YTM of the bond at purchase by
holding
Page 128
©2012 Kaplan, Inc.
Study Session 1 6
Cross-Reference to CFA Institute Assigned Reading #57 - Yield Measures, Spot Rates, and Forward Rates
ANSWERS - CONCEPT CHECKERS
1.
A
2.
c
3.
4.
5.
c
B
c
71.25
current yield =
8
1 ,023.47
=
0.06962, or 6.962%
� YTM
6.450%
8
c=l (1 + YTM/2)' ( 1 + YTM/2)
N = 8; FV = 1 ,000; PMT = 35.625; PV = - 1 ,023.47 ___. CPT IIY = 3.225
1 ,023.47 =
35.625
I:
1,000
+
=
1 ' 010
35 · 625
+
� YTC
6.334%
+
+
•= I (1 YTC I 2)'
(1 YTC/2)4
N = 4; FV = 1 ,0 10; PMT = 35.625; PV = - 1 ,023.47; CPT ___. IIY = 3 . 1 67
6.334%
1 ,02 3.47 =
t
(
1 000
'
331.40
t
)30
2 = 6.45%
=
1'000
35 625
+
·
� YTP
5.864%
(1+ YTP/2)4
•=I (1+ YTP/2)'
N = 4; FV = 1 ,000; PMT = 35.625; PV = - 1 ,023.47; CPT ___. 1/Y = 2.932
5.864%
1 ,023.47 =
x
x
2 =
x
2 =
=
I
X
-1
2
=
7.5%
or,
Solving with a financial calculator:
N = 30; FV = 1 ,000; PMT = 0; PV = -331 .40; CPT ___. IIY = 3.750
2 = 7.500%
6.
C
bond equivalent yield = [ ( 1 + EAY) 112 - 1 ]
7.
A
bond equivalent yield = [(1 + CFY)6 - 1 ]
8.
B
For a bond purchased at a premium to par value, a decrease in the premium over time
(a capital loss) is already factored into the calculation ofYTM.
9.
A
3
( 1 . 0945)4 = (1 .0985)
(1.0945)
4
-'----=-::-
(1 .0985)3
10. C
-1
=
1
f3
=
X
x
x
2 = [(1 .0635) 112
x
-
= [(1 .00382) 6 - 1 ]
1]
x
x
2 = 6.252%
2 = 4.628%
(1 + /3)
8.258%
For embedded puts (e.g., putable bonds): option cost < 0,
©20 1 2 Kaplan, Inc.
�
OAS
>
Z-spread.
Page 129
Study Session 1 6
Cross-Reference to CFA Institute Assigned Reading #57 - Yield Measures, Spot Rates, and Forward Rates
11. B
Spot rates: 5 = 5.5%.
1
52 = [(1 .055)(1 .0763)]112 - 1 = 6.56%
53 = [(1 .055)(1 .0763) ( 1 . 1 2 1 8)] 113 - 1 = 8.39%
54 = [(1 .055)(1 .0763) ( 1 . 12 1 8 ) ( 1 . 155)] 114 - 1 = 1 0 . 1 3%
Bond value:
N = 1 ; FV =
N = 2; FV =
N = 3; FV =
N = 4; FV =
12. A
100; I/Y = 5.5; CPT --+ PV=
-94.79
100; I/Y = 6.56; CPT --+ PV=
-88.07
100; I/Y = 8.39; CPT --+ PV=
-78.53
1 , 100; 1/Y = 1 0 . 1 3 ; CPT --+ PV= -747.77
Total: $ 1 ,009 . 1 6
Find the spot rate for 3-year lending:
53 = [(1 .055)(1 .0763) ( 1 . 1 2 1 8)] 113 - 1 = 8.39%
Value of the bond: N = 3 ; FV = 1 ,000; 1/Y = 8.39; CPT--+PV = -785.29
or
$ 1 000
'
= $785.05
(1.055)(1.0763)(1 . 1 2 1 8)
13. C
If the yield curve is flat, the nominal spread and the Z-spread are equal. If the bond is
option-free, the Z-spread and OAS are equal.
14. C
A Treasury bond is the best answer. The Treasury spot yield curve will correctly price an
on-the-run Treasury bond at its arbitrage-free price, so the Z-spread is zero.
15. A
The Z-spread will be greater than the nominal spread when the spot yield curve is
upward sloping.
ANSWERS - CHALLENGE PROBLEMS
1.
The three sources of return are coupon interest payments, recovery of principal/capital
gain or loss, and reinvestment income.
Coupon interest payments: 0.07 I 2
x
$ 100,000
x
6 = $ 2 1 ,000
Recovery ofprincipal/capital gain or loss: Calculate the sale price of the bond:
N = (10 - 3) X 2 = 14; 1/Y = 6.9 I 2 = 3.45; PMT = 0.07 I 2 X 100,000 = 3,500;
FV = 100,000; CPT --+ PV = - 1 00,548
Capital gain = 100,548 - 92,800 = $7,748
Reinvestment income: We can solve this by treating the coupon payments as a 6-period
annuity, calculating the future value based on the semiannual interest rate, and
subtracting the coupon payments. The difference must be the interest earned by
reinvesting the coupon payments.
N=3
x
2 = 6; IIY = 5 I 2 = 2.5; PV = 0; PMT = -3,500; CPT --+ FV = $22,357
Reinvestment income = 22,357 - (6
Page 130
x
3,500) = $ 1 ,357
©2012 Kaplan, Inc.
Study Session 1 6
Cross-Reference to CFA Institute Assigned Reading #57 - Yield Measures, Spot Rates, and Forward Rates
2.
x
BEY = 2
semiannual discount rate
semiannual discount rate = ( 1 .07)112 - 1 = 0.344 = 3.44%
X
BEY = 2
3.44% = 6.88%
(
3.
0.07
annual-pay YTM = 1 + -2
4.
A.
2
- 1 = 0.0712 = 7. 1 2%
Because the T-bills are zero-coupon instruments, their YTMs are the 6-month and
1-year spot rates. To solve for the 1 .5-year spot rate, we set the bond's market price
equal to the present value of its (discounted) cash Rows:
100
=
100
(
1+
1+
2
+
0.028
--
2
(
2
1+
0.032
--
1 .9724 + 1.9375 +
=
sl
.5
2
1 +�
2
)3
=
=
2
(
) (
2
+
102
1+
s
�5
)3
100 - 1.9724 - 1 .9375
x
=
)3
102
---:s
--.!.:2..
1+
2
-
102
1 . o6 1 s x
s � 5 = o.o2 o 1
.
B.
)
=
1.0615
1 .0201
2 = o.o4o2 = 4.02%
Compute the YTM on the corporate bond:
N = 1.5
2.6588
x
X
2 = 3; PV = -102.395; PMT = 7 I 2 = 3.5; FV = 100; CPT -+ 1/Y =
2 = 5.32o/o
nominal spread = YTMBond - YTMTreasury = 5.32% - 4.0% = 1 .32%, or 132 bp
Solve for the zero-volatility spread by setting the present value of the bond's cash
Rows equal to the bond's price, discounting each cash Row by the Treasury spot rate
plus a fixed Z-spread.
Substituting each of the choices into this equation gives the following bond values:
Z-spread
Bond value
127 bp
102.4821
130 bp
102.4387
133 bp
102.3953
©20 1 2 Kaplan, Inc.
Page 1 3 1
Study Session 1 6
Cross-Reference to CFA Institute Assigned Reading #57 - Yield Measures, Spot Rates, and Forward Rates
Since the price of the bond is 102.395, a Z-spread of 133 bp is the correct one.
Note that, assuming one of the three zero-volatility spreads given is correct, you
could calculate the bond value using the middle spread ( 1 30) basis points, get a
bond value ( 1 02.4387) that is too high, and know that the higher zero-volatility
spread is the only one that could generate a present value equal to the bond's market
pnce.
Also note that according to the LOS, you are not responsible for this calculation.
Working through this example, however, should ensure that you understand the
concept of a zero-volatility spread well.
5.
A.
(
( )
)
( s�0)
0.5 fJ.o
1+
=
2
s
1 + -.-!.:.2.
2
1+
3
2
=
:
1.025
1 .022
= 1.031 03
0 .5 f1.o = 0.03 103 x 2 = 0.0621 = 6.2 1%
B.
/1 here refers to the 1-year rate, one year from today, expressed as a BEY.
( �r
( ;r
1+
1+
£
2
0.054
1 + -2
£
2
1
f.
( )
( �)
1+
=
2
X
0. 44
4
2
- 1 = 0.0320
0.0320 = 6.40o/o
Note that the approximation 2
bit less work.
Page 132
x
5.4 - 4.4
=
©2012 Kaplan, Inc.
6.4 works very well here and is quite a
Study Session 1 6
Cross-Reference to CFA Institute Assigned Reading #57 - Yield Measures, Spot Rates, and Forward Rates
C.
Discount each of the bond's cash flows (as a percent of par) by the appropriate spot
rate:
2.25
2.25
+
0. 40
0. 44
1+
1+
bond value =
A.
102.25
+ -----:0. 54
1+
( �r ( �r ( �r
�
1+
o. so
102.25
2.25
2.25
= 98.36
+� +
+
1 .02 1.0445 1 .0769 1 . 1 125
=
6_
2.25
+
( � r ( � )( � ) ( � )( � )
1+
S o
S s
= 1+
1 + o.5 o. 5 = 1 +
0. 35
1+
0. 38
= l .0368
� = 1 .0368112 - 1 = 0.0182
2
S .
IO
=
X
0.0 1 82
2
=
0.0364
3.64%
=
( � J ( � )( � )( � )
1+
S
5
1+
=
S
5
1 + o.5 0.5
1 + o.5 1 .o
� = 1 .0576113 - 1 = 0.0188
2
s�.5
=
x
o.o 1 8 8
2
=
o.0376
3.76%
=
( � )( � )( � )( � )
= 1+
0. 35
1+
0. 38
1+
0. 40
1+
0. 44
= 1 .0809
s2·
0 = 1 .08091 14 - 1 = o.o 196
2
S2_0
=
B.
1+
7.
o.o 1 9 6
2
+
0. 35
�
x
2
=
o. o392
2
=
3.92%
102
( �r ( �r
1+
o.o 64
+
1+
0.0 76
= 1 00.35
Reinvestment income is most important to the investor with the 9o/o coupon
bond, followed by the 8o/o coupon bond and the zero-coupon bond. In general,
reinvestment risk increases with the coupon rate on a bond.
©20 12 Kaplan, Inc.
Page 133
The following is a review of the Analysis of Fixed Income Investments principles designed to address the
learning outcome statements set forth by CFA Institute. This topic is also covered in:
INTRODUCTION TO THE
MEASUREMENT OF INTEREST RATE
RISK
Study Session 1 6
EXAM FOCUS
This
topic
reviconcepts
ew is aboutof theduration
relationandofconvexi
yield changes
andisbond
pricenothing
changes,in thisprimarily
based
on
the
t
y.
There
really
study
session
that canofbeduration
safely ignored;
the calculation
of duration,
theimportant.
use of duration,
and
the
limitations
as
a
measure
of
bond
price
risk
are
all
You
should
work
to
understand
what
convexi
t
y
i
s
and
i
t
s
relation
to
the
interest
rate
risk
of
fi
x
ed­
incomethe securities.
There
are twotheimportant
formulas:
thed change
formulabased
for effecti
ve duration
and
formula
for
estimating
price
effect
of
a
yiel
on
both
duration
and
convexi
t
y.
Fi
n
al
l
y,
you
should
get
comfortable
wi
t
h
how
and
why
the
convexity
of a
bond is affected by the presence of embedded options.
LOS 58.a: Distinguish between the full valuation approach (the scenario
analysis approach) and the duration/convexity approach for measuring interest
rate risk, and explain the advantage of using the full valuation approach.
CPA® Program Curriculum, Volume 5, page 556
Theapplying
full valuation
or scenario
analysisweapproach
to measuring
interest
ratein theriskyield
is based
oncurve
the
valuation
techniques
have
learned
for
a
given
change
e., "ifforthea giYTM
ven increases by 50 bp orFor100a sibp,nglewhatoption-free
bond,onthisthecould
beof thesim(i.ply,
i
s
the
impact
value
bond?"
More
compl
i
cated
scenarios
can
be
used
as
well,
such
as
the
effect
on
theshort-term
bond value
of
a
steepeni
n
g
of
the
yield
curve
(long-term
rates
i
n
crease
more
than
If ourin valuation
model
is good, theandexerciseesewhat
is straightforward:
plvalues
ug
inof thethe bonds.
rates rates).
described
the
interest
rate
scenario(s),
happens
to
the
For
more
complex
bonds,
such
as
cal
l
a
bl
e
bonds,
a
prici
n
g
model
that
incorporates
yil valelduvolatil
ity as well Ifasthespecifivaluation
c yield models
curve change
scenarios
is requigood,red
tothis
useis thethe fultheoreticall
atioynpreferred
approach.
used
are
suffi
c
i
e
ntly
approach.
Appli
e
d
to
a
portfolio
of
bonds,
one
bond
at
aaffect
time,thewevalcanuegetof thea veryportfolio.
good idUsing
ea of how
diapproach
fferent interest
rate change
scenarios
will
this
wi
t
h
extreme
changes
i
n
interest
rates is called stress testing a bond portfolio.
The
duration/convexity
approach
proviItsdesmaian napproximation
ofsimplicity
the actual compared
interest rateto
sensi
t
ivity
of
a
bond
or
bond
portfolio.
advantage
is
its
the full valuforationa portfolio
approach.ofThemorefullthanvaluation
approachespecially
can getifquisomete complex
and time
consuming
a
few
bonds,
of
the
bonds
have
more complex
structures,
such shias fcallts andprovisions.
ll see shortly,
our scenarios
to parallel
yield curve
settling Asforwean wiestimate
of interestlimiting
rate risk
interest rate scenario).
Page 134
©2012 Kaplan, Inc.
Study Session 1 6
Cross-Reference to CFA Institute Assigned Reading #58 - Introduction to the Measurement of Interest Rate Risk
allowsprocess
us toofuseestithematisummary
convexiinty.yield.
This greatly simplifies
the
ng the valmeasures,
ue impactduration,
of overalandl changes
Comparedandtocanthebeduration/convexi
tthey approach,
the fulof lmore
valuation
approach
is rate
more
precise
used
to
eval
u
ate
price
effects
complex
interest
scenarios. Strictly
g, the duration-convexi
estimating
the effectsspeakiofnparallel
yield curve shifts.ty approach is appropriate only for
Example: The full valuation approach
Considerty, two
option-free
bonds.
Bond
X (Nis an= 8%5; PMT
annual-pay
bond with five years to
maturi
priced
at
108.
4
247
to
yiel
d
6%
= 8. 0 0; FV = 100; 1/Y = 6. 0 0%;
CPT� PV = -108.4247).
BondY
is
a
5%
annual-pay
bond
wi
t
h
15
years
to
maturi
t
y,
priced
at
81.
7
842
to
yield
7%.
Assume
a
$10
million
face-val
u
e
position
i
n
each
bond
and
two
scenarios.
The
fi
r
st
ieslashiparalft of+lel shift
in thes points.
yield curve
of+
50thebasibonds points,
and
the4second
scenario
isperscenario
a parall
100
basi
Note
that
price
of
108.
24
7
i
s
the
price
$100
of
par
value.
Wi
t
h
$10
mi
l
l
i
on
of
par
value
bonds,
the
market
value
wi
l
l
be
$10.84247 million.
Answer:
fiThegure.full valuation approach for the two simple scenarios is illustrated in the following
The Full
Valuation Approach
Market Value of
Scenario
Yield �
Bond X
(in miiiions}
Bond Y
(in miiiions}
Portfolio
Current
+0 bp
$ 1 0.84247
$8. 17842
$ 1 9.02089
1
+50 bp
$ 1 0.62335
$7.79322
$ 1 8.41657
-3. 1 8%
2
+ 1 00 bp
$ 1 0.4 1 002
$7.43216
$ 1 7.84218
-6.20%
Portfolio
Value � %
N = 5; PMT = 8; FV = 100; 1/Y = 6% + 0.5%; CPT � PV = -106.2335
N = 5; PMT = 8; FV = 100; 1/Y = 6% + 1%; CPT � PV = -104.1002
N = 15; PMT = 5; FV = 100; 1/Y = 7% + 0.5%; CPT � PV = -77.9322
N = 15; PMT = 5; FV = 100; 1/Y = 7% + 1 %; CPT � PV = -74.3216
Portfolio value change 50 bp: (18.41657- 19.02089) 19.02089 = -0.03177 =
-3.18%
I
©20 1 2 Kaplan, Inc.
Page 135
Study Session 1 6
Cross-Reference to CFA Institute Assigned Reading #58
-
Introduction to the Measurement o f Interest Rate Risk
-6.Portfolio
20% value change 100 bp: (17. 84218 - 19.02089) 19.02089 = -0.06197 =
It's worth
noti
nesg that,
onforanBond
individual
bond
basis, the(i.eeffect
ofaan50 increase
in yielin d on
theyields,
bonds'
val
u
is
l
e
ss
X
than
for
BondY
.
,
wi
t
h
bp
increase
theh aval100uebpofincrease,
Bond X falls
byls by2.03.2%,99%,whiwhile thele Yvaldrops
ue ofbyBondY
fallThis,
s by 4.of7course,
1 %;
and
wi
t
X
fal
9.12%).
iofs total
l
y
predictable
since
Bond
Y
is
a
longer-term
bond
and
has
a
lower
coupon-both
which mean more interest rate risk.
I
Professor's Note: Let's review the effects of bond characteristics on duration (price
sensitivity). Holding other characteristics the same, we can state the following:
•
Higher (Lower) coupon means Lower (higher) duration.
Longer (shorter) maturity means higher (Lower) duration.
Higher (lower) market yield means Lower (higher) duration.
Finance professors Love to test these relations.
LOS 58.b: Describe the price volatility characteristics for option-free, callable,
prepayable, and putable bonds when interest rates change.
LOS 58.c: Describe positive convexity and negative convexity, and their
relation to bond price and yield.
CFA® Program Curriculum, Volume 5, page 560
We
established
earliAnerincrease
that theinrelati
on(discount
between rate)
price leads
and yield
for a straight
coupon
bond
is
negati
v
e.
yield
to
a
decrease
in
the
value
ofis
aillbond.
The
precise
nature
of
this
relationship
for
an
option-free,
8%,
20-year
bond
ustrated in Figure 1.
8%,
Figure 1: Price-Yield Curve for an Option-Free,
Price (% of Par)
For an option-free bond
the price-yield curve is
co nvex toward the origin.
1 1 0.67
100.00
90.79
�----�--- YTM
7%
Page 136
8%
9%
©2012 Kaplan, Inc.
20-Year Bond
Study Session 16
Cross-Reference to CFA Institute Assigned Reading #58 - Introduction to the Measurement of Interest Rate Risk
First,
note that
the price-yi
eldtherelationship
isonegativel
y sloped,
so the price
fallBecause
s as the
yithe
eldcurve
rises.
Second,
note
that
relation
foll
ws
a
curve,
not
a
straight
line.
is
convex
(toward
the
origin),
we
say
that
an
option-free
bond
has
positi
v
e
convexity. Because of its positive convexity, the priceInofFigure
an option-free
bondillustrated
1,
we
have
that,
for
an
8%,
20-year
option-free
bond,
a
1%
decrease
i
n
the
YTM
wi
l
l
increase
the
price toto decrease
110.67, ato 90.79, a in price. Ain1%value.increase in YTM will cause the bond
value
relation
were
adeclstraight
line,response
there towoulequald bedecreases
no difference
between
theIfin theyields.
priceprice-yield
increase
and
the
price
i
ne
in
and
increases
Convexity
i
s
a
good
thing
for
a
bond
owner;
for
a
given
volatility
of
yields,
price
are lsarger
than
price
decreases. The
convexity
property
is often
expressed
byrelationship
sayiincreases
ng, "atobond'
pri
c
e
falls
at
a
decreasing
rate
as
yi
e
lds
rise.
"
For
the
price-yiel
d as
be
convex,
the
slope
(rate
of
decrease)
of
the
curve
must
be
decreasing
we move from left to right (i.e., towards higher yields).
Note
that
the
duration
(interest
rate
sensitivity)
of
a
bond
at
any
yield
i
s
(absolute
value
of) the slope
ofoption-free
the price-yield
function
atyouthatremember
yield. Thea convexi
ty of the price-yield
relation
for
an
bond
can
help
result
presented
earlier, that
the duration of a bond is less at higher market yields.
increases
more when yields fall than it decreases when yields rise.
10.67% increase
9.22% decrease
Callable Bonds, Prepayable Securities, and Negative Convexity
Widecreasing
th a callable
or
prepayable
debt,
the
upsi
d
e
price
appreciation
in
response
to
yiiseldcurrently
s is limitedcall(sometimes
calTheledfactpricthat
e compression).
Consider
the caseat any
of
atimbond
that
a
bl
e
at
102.
the
issuer
can
cal
l
the
bond
e
for
$1,
0
20
per
$1,
0
00
of
face
val
u
e
puts
an
effecti
v
e
upper
limit
on
the
value
of
the
bond.curve
As Figriureses more
2 illustrates,
as yields
faloflanandidentical
the pricebutapproaches
$1,020,
theWhenprice­the
yield
slowly
than
that
noncallable
bond.
beginsbends
to over to the left and exhibits
in response
to further
decreases in yield, the price­
yiprieclde curve
negative
convexity.
Thus, in Figure 2, however,
so long asatyiyieldseldsremain those same
callablcale lbonds
will
exhibit
ablcalle options
bonds wibecomes
ll exhibit
In
other
words,
at
higher
yi
e
lds
the
val
u
e
of
the
very
small
so
that
a
callable
bond
will
act
very
much
l
i
k
e
a
noncallable
bond.
It
i
s
only
at
lower yields that the callable bond will exhibit negative convexity.
rise at a decreasing rate
negative convexity;
positive convexity.
below level y',
above level y',
©20 1 2 Kaplan, Inc.
Page 137
Study Session 1 6
Cross-Reference to CFA Institute Assigned Reading #58
-
Introduction to the Measurement o f Interest Rate Risk
Figure Price-Yield Function of a Callable vs. an Option-Free Bond
2:
Price (% of Par)
call option
value
102
�r
- --- -- -- -
- ---.r�.. - .. ..
- - ..
.. ...
- - -_
.. - -
.. ..
r
callable bond
'-------'-- Yield
Negative Convexity
Positive Convexity
y'
In any
termsparticular
of price yisensitivi
tsytheto interest
rate that
changes,
thelds slope
of slope
the price-yield
curve
atcurve
e
ld
tel
l
story.
Note
as
yi
e
fall,
the
of
the
price-yield
for
the
call
a
ble
bond
decreases,
becoming
almost
zero
(fl
a
t)
at
very
low
yields.
This
sinusterest
howrate
a calriskl feature
affects price
sensi
tivitycloseto orchanges
in yield.
Atofhigher
yields,
thetelloption-free
of
a
callable
bond
i
s
very
identical
to
that
a
similar
bond.
At
lower
yields,
the
price
volatility
of
the
call
a
bl
e
bond
wi
l
l
be
much
lower than that of an identical but noncallable bond.
The
effect
of
a
prepayment
option
is
quite
similar
to
that
of
a
call;
at
low
yi
e
lds
i
t
wisecuri
ll leadty. Note
to negati
vewhen
convexiyieldsty andare low
reduceandthecalprilablcee volatility
(interestsecurities
rate risk)exhibit
of theless
that
and
prepayable
interest
rate
risk,
rei
n
vestment
risk
rises.
At
l
o
wer
yields,
the
probability
of
a
cal
l
and
the
prepayment
at the lower rate
rates.both rise, increasing the risk of having to reinvest principal repayments
The Price Volatility Characteristics of Putable Bonds
The
value
of
a
put
increases
at
higher
yields
and
decreases
at
l
o
wer
yields
opposite
to
the privaluece volatil
of a callity option.
an option-freeis ilbond,
at higherCompared
yields. Thitos comparison
lustrateda putable
in Figurebond3. will have
less
Page 138
©2012 Kaplan, Inc.
Study Session 16
Cross-Reference to CFA Institute Assigned Reading #58 - Introduction to the Measurement of Interest Rate Risk
Figure 3: Comparing the Price-Yield Curves for Option-Free and Putable Bonds
Price
putable bond
/
- - - - - .. .. ... _ _ _ _ _ _ _
option-free bond
Yield
y'
In Figure
3,y'thebecause
price ofthethevalueputablof the
e bondembedded
falls moreputslrises
owlyatinhigher
responseyields.to increases
inof
yield
above
The
slope
theduration)
price-yield
relation
is
fl
a
tter,
indicating
less
price
sensi
t
i
v
ity
to
yi
e
ld
changes
(l
o
wer
forandtheaputable
bond
ats prihigchere actsyields.
Atthatyielofdans beloption-free
ow y', thebond
valueinofresponse
the put is
qui
t
e
small,
putabl
e
bond'
li
k
e
to yield changes.
LOS 58.d: Calculate and interpret the effective duration of a bond, given
information about how the bond's price will increase and decrease for given
changes in interest rates.
CPA® Program Curriculum, Volume 5, page 569
Inpercentage
our introduction
to
the
concept
of
duration,
we
described
i
t
as
the
ratio
of
the
change
in pricechange
to change
in yield.to rising
Now that
weis smaller
understand
convexi
ty,
wechange
knowinthat
the
price
i
n
response
rates
than
the
price
response
to fallingduration
rates forofoption-free
bonds.
The formula
we willchanges
use
forin response
calculating
the
effective
a
bond
uses
the
average
of
the
price
to equal
increases
and
decreases
inegati
n yieldvetoconvexity,
account forthethispricefact.increase
Ifwe ishave
asmalcalllerablthan
e bond
that
i
s
trading
in
the
area
of
the price decrease, but using the average still makes sense.
©20 12 Kaplan, Inc.
Page 139
Study Session 1 6
Cross-Reference to CFA Institute Assigned Reading #58
The formula for calculating the effective duration of a bond is:
yields fal -bond price when yields rise)
effecti.ve duranon. (bond2 pri(inciteiawhen
l price) (change in yield in decimal form)
. wnte. as duranon. V_2V -V+
wh1c. h we w1 somenmes
0 (b..y)
where:
bond value
iff the
the yield
yield increases
decreases byby b..yy
value
i
VVV bond
initial bond
0y = change
in yieprice
ld used to get V and V
Consider the following example of this calculation.
=
Introduction to the Measurement o f Interest Rate Risk
--"--='--'-----'
--=-'--
X
X
·11
=
-'-
b.
+
b.
_
+'
expressed in decimal form
Example: Calculating effective duration
Consider
20-year,
semiannual-pay
bondineswithby 50an 8%
coupon
that
is currently
pricedwill
atincrease
$908.0to0a $952.
to yield30,9%.
If
the
yield
decl
basis
points
(to
8.5%),
the
price
and
i
f
the
yiel
d
i
n
creases
by
50
basis
points
(to
9.5%),
the
pri
c
e
widuration
ll declinofe this
to $866.
bond.80. Based on these price and yield changes, calculate the effective
Answer:
Let'
s approachng thethisaverage
intuitivofelytheto percentage
gain a betterchange
understanding
of sthepriceformula.
Weyieldbegin
byincrease
computi
in
the
bond'
for
the
and
the
percentage
change
in
price
for
a
yi
e
ld
decrease.
We
can
calcul
a
te
this
as:
30-$866.80) = 0.0471%, or 4.71%
average
pnce. change = ($952.2x$908.
00
The
2 in the denominator
obtainchange
the average
price change,of theandcurrent
the $908price.in the
denominator
is to obtain thiis stoaverage
as a percentage
Todivideget this
the duration
(to
scal
e
our
result
for
a
1%
change
in
yield),
the
fi
n
al
step
i
s
to
averagee, thepercentage
pricewas
change0.5%,by the
change
in interest
ratesin decimal
that caused
it.as 0.In0the05. exampl
yi
e
l
d
change
whi
c
h
we
need
to
write
form
Our estimate of the duration is:
0·0471 = 4·7 1% = 9.42 =duration
0.005 0.50%
Using the formula previously given, we have:
8) = 9.4 16
effective duration = (2$952.$9083 -$866.
0.005
percentage
X
Page 140
X
©2012 Kaplan, Inc.
Study Session 16
Cross-Reference to CFA Institute Assigned Reading #58 - Introduction to the Measurement of Interest Rate Risk
The interpretati
on of thisanresult,
as youmateshould
beinconvinced
byof this
now,bond
is thatof9.a 14o/o2o/o.
change
i
n
yi
e
ld
produces
approxi
change
the
price
Note,wilhowever,
thatbestthisforestiyielmdatechanges
of duration
wasthisbased
ontude.
a change
inweyiused
eld of0.5o/
o
and
l
perform
cl
o
se
to
magni
Had
a
yield
change
of0.
2
5o/o
or
1
o/o,
we
would
have
obtained
a
slightl
y
di
ff
erent
estimate
of
effective duration.
This
is an important
concept,
andunderstand
you are required
to learn
theremember
formula forit, consider
the the
calculation.
To
further
help
you
thi
s
formul
a
and
following.
The price increase in response to a 0.5% decrease in rates was $4430
$908 4.879%.
The price decrease in response to a 0.5% increase in rates was $41.$90820 4.537%.
The average
of thea 0.percentage
price
inelcrease
andthethepricepercentage
price
decrease
is 4.7thi1 o/o.s
Because
we
used
5
%
change
in
yi
d
to
get
changes,
we
need
to
double
and get a 9.42% change in price for a 1 o/o change in yield. The duration is 9.42.
=
=
For
bonds
witnearl
h noyembedded
options,to calculate
modifiedeffecti
duration
and effectiforvea duration
wianll be
equal
or
very
equal.
In
order
v
e
duration
bond
wi
t
h
embedded
option,
we
need
a
pricing
model
that
takes
account
of
how
the
cash
fl
o
ws
change when interest rates change.
LOS 58.e: Calculate the approximate percentage price change for a bond, given
the bond's effective duration and a specified change in yield.
CFA® Program Curriculum, Volume 5, page 570
Multiplyandeffecti
vechange
durationthebysigthen tochange
indirection
yield to getof thetheprice
magnichange
tude ofrigtheht (yield
price up,
change
then
get
the
price down).
change in bond price = -effective duration change in yield in percent
x
percentage
©20 12
Kaplan, Inc.
Page
141
Study Session 1 6
Cross-Reference to CFA Institute Assigned Reading #58
-
Introduction to the Measurement o f Interest Rate Risk
Example: Using effective duration
What
the expected
for apoints?
bond with an effective duration of
nine inisresponse
to anpercentage
increase inprice
yieldchange
of 30 basis
Answer:
-9 0.3% = -2.7%
We
expect
the
bond'
s
pri
c
e
to
decrease
by
2.
7%
in
response
to
the
yi
e
ld
change.
If
the
bond were priced at $980, the new price is 980 (1 - 0.027) = $953.54.
X
x
LOS 58.f: Distinguish among the alternative definitions of duration and
explain why effective duration is the most appropriate measure of interest rate
risk for bonds with embedded options.
CPA® Program Curriculum, Volume 5, page 576
The formula we used to calculate duration based
on
pri
c
e
changes
i
n
response
to
equal
V- - V , is the formula for effective
increases and decreases in YTM,
2V0(.measure
6.y) because it gives a good
(option-adjusted)
duration.
This
i
s
the
preferred
approximation of interest rate sensitivity for both option-free bonds and
duration =
+
bonds with
embedded options.
Macaulay
duration
is ancash
estimate
ofwilla bond'
s interest
rate
sensitivi
ty basedbond
on thehastime,
ionen years,
until
promised
fl
o
ws
arrive.
Since
a
5-year
zero-coupon
only
cash fltoowa 1%fivechange
years from
today,foritsa 5-year
Macaulay
duration ibond
s five.isTheapproxi
changematelinyvalue
in
response
in
yield
zero-coupon
5%.
A(the5-year
coupon
bond
has
some
cash
fl
o
ws
that
arri
v
e
earl
i
e
r
than
fi
v
e
years
from
today
s Macaulay
durationtheis llessess than
five. sensitivity
This is consistent
learnedcoupons),
earlier: sotheithigher
the coupon,
the price
(duration)withofwhat
a bond.we
Macaulay
durationisisoften
the earliest
measure
ofBecause
duration,Macaul
andabecause
it wasis based
basedononthe
theexpected
time, cash
duration
stated
as
years.
y
duration
fl
o
ws
for
an
option-free
bond,
i
t
i
s
not
an
appropriate
esti
m
ate
of
the
pri
c
e
sensitivity of bonds with embedded options.
Modified
duration
is
deri
v
ed
from
Macaulay
duration
and
offers
a
slight
improvement
over
Macaulandayforduration
in that
it takesmodified
the current
YTMis notintoanaccount.
Like measure
Macaulay
duration,
the
same
reasons,
duration
appropriate
ofhowever,
interesteffecti
rate sensi
t
ivity
for
bonds
wi
t
h
embedded
options.
For
option-free
bonds,
be very similar. ve duration (based on small changes in YTM) and modified duration will
Page 142
©2012 Kaplan, Inc.
Study Session 16
Cross-Reference to CFA Institute Assigned Reading #58 - Introduction to the Measurement of Interest Rate Risk
Professor's Note: The LOS here do not require that you calculate either Macaulay
duration or modified duration, only effective duration. For your own
understanding, however, note that the relation is
Macaulay duration
.
.
modified duratton =
This accounts for thefact we
+ periodic market yield
1
.
Learned earlier that duration decreases as YTM increases. Graphically, the slope of
the price-yield curve is Less steep at higher yields.
Effective Duration for Bonds With Embedded Options
noted earlier,
inarecomparing
thedivarious
duration
measures,cashbothfloMacaulay
and with
modified
duration
calculated
r
ectly
from
the
promised
ws
for
a
bond
nois calculated
adjustmentfromfor expected
the effectprice
of anychanges
embedded
optionstoonchanges
cash floiws.n yield
Effectithatveexpl
duration
in
response
icitly
take
i
n
to
account
a
bond'
s
option
provisions
(i.
e
.
,
they
are
i
n
the
price-yield
function
used).
As
Interpreting Duration
We can interpret duration in three different ways.
First,
durationly,isthetheslslope
ofthetheprice-yield
price-yieldcurve
curveisatthethefibond'
s current
YTM.
Mathematical
o
pe
of
r
st
derivati
v
e
of
the price-yield
curve with respect to yield.
A secondofinterpretation
of duration,
as original
lwy devel
opedreceibyved.Macaulay,
isghtsa weiareghted
average
the
time
(in
years)
until
each
cash
fl
o
wil
l
be
The
wei
the
proportions
comes years.of the total bond value that each cash flow represents. The answer, again,
Aa 1%thirchange
d interpretati
on This
of duration
is the approximate
percentage
changetoina change
price forin
i
n
yield.
interpretation,
price
sensi
t
i
v
ity
i
n
response
yield, is the preferred, and most intuitive, interpretation of duration.
m
�
�
Professor's Note: The fact that duration was originally calculated and expressed
in years has been a source of confusion for many candidates andfinance students.
Practitioners regularly speak of "longer duration securities. " This confusion is
the reason for this part ofthe LOS. The most straightforward interpretation of
duration is the one that we have used up to this point: '1t is the approximate
percentage change in a bond's price for a I % change in YTM. Ifyou see duration
expressed in years, just ignore the years and use the number. Questions might ask
whether duration becomes longer or shorter in response to a change; longer means
higher or more interest rate sensitivity. A duration of 6 82 years means that for a
I % change in YTM, a bond's value will change approximately 6 82%. This is the
best way to interpret duration.
"
©20 1 2 Kaplan, Inc.
Page 143
Study Session 1 6
Cross-Reference to CFA Institute Assigned Reading #58
-
Introduction to the Measurement o f Interest Rate Risk
LOS 58.g: Calculate the duration of a portfolio, given the duration of the
bonds comprising the portfolio, and explain the limitations of portfolio
duration.
CPA® Program Curriculum, Volume 5, page 580
The
concept
ofmeasure
durationof can
alsorate
be applied
to portfolios.
In fact, one of theisbenefi
ts of
durati
o
n
as
a
interest
ri
s
k
i
s
that
the
simply
theMathemati
weightedcallaverage
of
the
durations
of
the
i
n
di
v
idual
securities
i
n
the
portfolio.
y, the duration of a portfolio is:
duration of a portfolio
where:
wD.i == market
value ofofbond
bond ii divided by the market value of the portfolio
the
duration
N = the number of bonds in the portfolio
I
Example: Calculating portfolio duration
youis $6,have000,a two-security
portfolvalueio containing
Bonds
A andTheB.duration
The market
value
ofASuppose
Bond
A
and
the
market
of
Bond
B
is
$4,
0
00.
of
Bond
is 8.5, and the duration of Bond B is 4.0. Calculate the duration of the portfolio.
Answer:
First,0fi00nd=the$6,wei
market ivalue
$10,
000g+hts$4,of0each
00, thebond.weightBecause
of eachthesecurity
s as follofothews:portfolio is
$6' 000 = 60%
weight in Bond A= $10,
000
$4,000 = 40%
weight in Bond B = $10,000
Using the formula for the duration of a portfolio, we get:
portfolio duration = (0.6 8.5) + (0.4 4.0) = 6.7
x
x
Limitations of Portfolio Duration
The
l
i
mitations
of
portfolio
durati
o
n
as
a
measure
of
interest
rate
sensi
t
ivity
stem
from
the fact thatthatyiincludes
elds maybonds
not change
equally
onmaturities,
the bonds
inrisks,
the portfoli
o. With a
portfolio
wi
t
h
di
f
ferent
credit
and
embedded
there
is nowhen
reasonthetoyield
suspect
thatchanges.
the yieldsAs anonexample,
individuala steepening
bonds will change
byyioptions,
equal
amounts
curve
of
the
eld curve can increase yields on long-term bonds and leave the yield on short-term
all
Page 144
©2012 Kaplan, Inc.
Study Session 1 6
Cross-Reference to CFA Institute Assigned Reading #58 - Introduction to the Measurement of Interest Rate Risk
bonds
for thisto reason thatchanges
we sayin that
duration
sensitivunchanged.
ity of portfolItioisvalue
the yield
curve.is a good measure of the
parallel
LOS 58.h: Describe the convexity measure of a bond and estimate a bond's
percentage price change, given the bond's duration and convexity and a
specified change in interest rates.
CPA® Program Curriculum, Volume 5, page 581
is
a
measure
of
the
curvature
of
the
price-yield
curve.
The
more
curved
the
price-yield
relation
is, thewere,greater
the aconvexi
ty.line,A straitheghtconvexity
line haswould
a convexi
ty ofThe
zero.
Ifreason
the price-yi
e
l
d
curve
i
n
fact,
strai
g
ht
be
zero.
we care
about convexity
is thatof thebondmorepriccurved
theinprice-yield
relachanges
tion is, intheyield
worse
our
duration-based
esti
m
ates
e
changes
response
to
are.
Ashasana yield
example,
consider
again
an 8%,
20-year
Treasury bond
pricedve atduration
$908 soofthatthisit
to
maturi
t
y
of
9%.
We
previ
o
usly
calculated
the
effecti
bond as 9.42. Fiestiguremates
4 illustrates
differences
betweenyieldactual
duration-based
of price thechanges
at different
levels.bond price changes and
Bond
Convexity
Figure 4: Duration-Based Price Estimates vs. Actual
Prices
Price
$ 1 ,000.00
$993.53
f------+ Prices based on duration
are underestimates of actual prices.
$908.00
$828.41
$822.47
'
'
--------------- - - - - - - -------,
,
'
'
Actual price-yield curve
'
Price estimates based
on a duration of9.42
�---�--�---- YTM
8%
9%
1 0%
Based onina yiel
valued (toof 9.8%42andfor duration,
we1.would
estimate
the new prices after 1%
changes
to
10%)
as
0
942
908
= $993. 5 3 and (1 - 0.0942) 908
= $822. 4 7, respectively. These price estimates are shown in Figure 4 along the straight
line tangent to the actual price-yield curve.
The
actual
price
ofofthe10%,8%thebondactualat aprice
YTMofofthe8%bond
is, ofiscourse,
par1, about
value $6($1higher
,000). than
Based
on
a
YTM
$828.
4
our
duration
based estimate
Note thatandpricea 1%estidecrease
mates based
on duration are
less than
the actual
prices forofboth$822.a 41%7. increase
in yield.
Figure
4
illustrates
why
convexity
i
s
important
and
why
estimates
of
price
changes
based
solely on duration are inaccurate. If the price-yield relation were a straight line
x
©20 1 2 Kaplan, Inc.
x
Page 145
Study Session 1 6
Cross-Reference to CFA Institute Assigned Reading #58
(i.e., if convexity
werein zero),
duration
alone wouldTheprovide
good
estimates
of bond
pricethe
changes
for
changes
yiel
d
of
any
magnitude.
greater
the
convexi
t
y,
the
greater
error in price estimates based solely on duration.
Introduction to the Measurement o f Interest Rate Risk
A Bond's Approximate Percentage Price Change Based on Duration and
Convexity
Bypercentage
combiningchange
duration
and
convexity,
we
can
obtain
a
more
accurate
estimate
of
the
inmpriatingce ofa bond'
a bond,s percentage
especially price
for relchange
atively based
large changes
in yield. and
The
formula
for
esti
on
its
convexity
duration is:
percentage change in price duration effect+ convexity effect
= {[-duration (�y)J + [convexity (�y)2]}
With 6.y entered as a decimal, the 100" is necessary to get an answer in percent.
and
Consider
an
8%
Treasury
bond
wi
t
h
a
current
price
of
$908
and
a
YTM
of
9%.
Calculate
of bothtya of1%68.increase
YTM
basedtheonpercentage
a durationchange
of9.42inandpricea convexi
33. and a 1% decrease in
=
X
x
x 100
"x
Example: Estimating price changes with duration
convexity
Answer:
The
durati
o
n
effect,
as
we
calculated
earlier,
i
s
9.
4
2
0.01
= 0. 0 942 = 9. 4 2%. The
2
convexity effect is f68.33(from0.019% to1008%)= 0.is09.0683
1000.683%
= 0. 6 83%. The total effect for
aestimate
4
2%
+
= + 10.103%, and the
of
the
new
price
of
the
bond
is
1.10103
908
= 999. 74. This is much closer to
the actual price of $1,000 than our estimate using only duration.
decrease in yield o I %
x
x
x
x
x
The
total
effect
for
an
f (from 9% to 1 0%) is -9.42% + 0. 6 83% =
-8.this7is37%,
andclotheser estimate
of thepricebond($828.
price4i0)s (1than-0.the08737)(908)
= $828. 6 7. Again,
much
to
the
actual
esti
m
ate
based
solely on
duration.
There
are
a
few
points
worth
noting
here.
First,
the
convexi
t
y
adjustment
i
s
al
w
ays
2
convexity
isgurepositi4, vwhie because
(6.y)thatisthealwduration-only
ays positive. This
goesestimate
along of
wiapositive
tbond'
h thes when
illustration
i
n
Fi
c
h
shows
based
pri
c
e
change
suffered
from
being
an
underestimate
of
the
percentage
i
n
crease
in theprice
bondwhen
price yiwhen
yieldsRecall,
fell, andthatanforoveresti
mbleatebond,
of theconvexi
percentage
decrease
in vthee
bond
e
lds
rose.
a
call
a
t
y
can
be
negati
at low yields. When convexity is negative, the convexity adjustment to the duration-only
increase in yield o I %
Page 146
©2012 Kaplan, Inc.
Study Session 16
Cross-Reference to CFA Institute Assigned Reading #58 - Introduction to the Measurement of Interest Rate Risk
basedyieestild mdecreases.
ate of the percentage price change will be negative for both yield increases
and
Professor's Note: Different dealers may calculate the convexity measure differently.
Often the measure is calculated in a way that requires an analyst to divide the
measure by two to get the correct convexity adjustment.
LOS 58.i: Distinguish between modified convexity and effective convexity.
CPA® Program Curriculum, Volume 5, page 584
Eff
elctie modified
ve convexiconvexi
ty takesty idoes
nto account
changes
in cash
flowsmodifi
due toedembedded
options,
whi
not.
The
di
f
ference
between
convexi
t
y
and
effecti
v
e
convexi
t
y
mi
r
rors
the
di
f
ference
between
modifi
e
d
duration
and
effecti
vae bond's
duration.
Recal
l
that
modi
f
i
e
d
duration
is
calculated
wi
t
hout
any
adjustment
to
cash
flowiwsthforembedded
embeddedoptioptions.
Also recall
that effecti
ve were
duration
was appropriate
for
bonds
o
ns
because
the
inputs
(prices)
calculated
under
the
assumptionin thethatsecurities.
the cash Clearl
flows ycould
varyve convexi
at different
yitheeldappropri
s becauseateofmeasure
the embedded
options
,
effecti
t
y
is
to
use
foreffectbonds
with embedded
since sitcash
is based
of embedded
optionsoptions,
on the bond'
flows.on bond values that incorporate the
LOS 58.j: Calculate the price value of a basis point (PVBP), and explain its
relationship to duration.
CPA® Program Curriculum, Volume 5, page 584
The
value
of a basis
point
(PVBP)
is thebydollar
change
in theor 0.01
price/value
of
acalcul
bondprice
or
a
portfolio
when
the
yield
changes
one
basis
point,
%.
We
can
ate thethePVBP
directly
for aAsbond
by changi
ng theweYTM
by duration
one basis topointcalculate
and
computing
change
in
value.
a
practi
c
al
matter,
can
use
the price value of a basis point as:
price value of a basis point = duration 0.0001 bond value
x
x
©20 1 2 Kaplan, Inc.
Page 147
Study Session 1 6
Cross-Reference to CFA Institute Assigned Reading #58
-
Introduction to the Measurement o f Interest Rate Risk
The following example demonstrates this calculation.
Example: Calculating the price value of a basis point
Aofbond
a market value of$100,000 and a duration of9.42. What is the price value
a basishaspoint?
Answer:
the duration
formula,
the2 =percentage
change
incalculate
the bond'0.0s 942%
price forof athechange
in
yiUsing
e$100,ld of0.01
o/o
i
s
0.01
o/o
9.
4
0.
0
942%.
We
can
original
000 portfolio
valuepoint,
as 0.0the00942
100,000
= $94. 2 0. If the bond's yield increases
(decreases)
by
one
basis
portfolio
val
u
e
l (rise) by $94.20. $94.20 is
the (duration-based) price value of a basis point forwillthifals bond.
We
could altheso directl
y calculate
the0001)
priceandvaluecalofculating
a basis thepointchange
for thisin bond
bond value.
by This
increasing
YTM
by
0.01
o/o
(0.
would
give us theestiPVBP
for an induration
crease in yield.
Thisgoodwoulestidmbeateveryof interest
close to rate
our risk for
duration-based
m
ate
because
is
a
very
small
changes
in
yiel
d
.
We
can
ignore
the
convexity
adjustment
here
because
it
i
s
of
2
2
very small magnitude: (�y) = (0.0001) = 0.00000001, which is very small indeed!
x
x
LOS 58.k: Describe the impact of yield volatility on the interest rate risk of a
bond.
CPA® Program Curriculum, Volume 5, page 585
Earlier
in thia lsotopic
review, weis lessintroduced
duration
aschange
a measurein yiofeldinthan
terestaratebondriswith
k. A
bond
with
wer
duration
affected
by
a
gi
v
en
greater
its interestduratirateon.risHere
k. we combine a bond's duration with its yield volatility in assessing
Consider
a aTreasury
bond
wiBased
th a durati
on of 7alone,
and a wesimilar
singlsaye-Bthatratedthe Treasury
corporate
bond
with
durati
o
n
of
5.
on
duration
would
bond has more
interest
rate
risk.greater
If, however,
thevolatil
volaitytiliofty theof themarket
marketyieldyielond onthethe
corporate
bond
i
s
suffici
e
ntly
than
the
Treasury
bond,
the
corporate
bond
can
have
greater
price
volatility
due
to
yield
(interest
rate)
changes
thanvaltheuesTreasury
bond.
Investors
mustwhenconsider
both theinterest
effectsrateofrisk.
yield
changes
on
bond
and
how
volatile
yields
are
estimating
One measure of price risk that considers both these components is value-at-risk (VaR).
Page 148
©2012 Kaplan, Inc.
Study Session 16
Cross-Reference to CFA Institute Assigned Reading #58 - Introduction to the Measurement of Interest Rate Risk
KEY CONCEPTS
LOS 58 .a
The
fultol valuation
approachbonds
to measuring
interest
ratefinrisk
involves
using aofpricing
model
value
individual
and
can
be
used
to
d
the
price
impact
any
scenario
of interest rate/yield curve changes. Its advantages are its flexibility and precision.
The duration/convexi
tusey approach
is based
onbonds
summary
measures
of interest
rate riskis
and,
while
simpler
to
for
a
portfol
i
o
of
than
the
ful
l
valuati
o
n
approach,
theoretically correct only for parallel shifts in the yield curve.
LOS 58.b
Cal
l
abl
e
bonds
and
prepayable
securities
wi
l
l
have
less
price
vol
a
ti
l
i
t
y
(l
o
wer
duration)
at
low yields, compared to option-free bonds.
Putable
bonds. bonds will have less price volatility at high yields, compared to option-free
LOS 58.c
Option-free
bondssaidhave
a price-yield
relationship
thatthiiss case,
curvedbond(convex
toward
thein
origin)
and
are
to
exhi
b
i
t
posi
t
i
v
e
convexi
t
y.
In
prices
fal
l
l
e
ss
response to an increase in yield than they rise in response to an equal-sized decrease in
yield.
exhibitto anegati
ve convexity
at lowtheyyieldfalllevels.
In thistocase,an equal-sized
bond prices
riCal
sincrease
ellablesseinibonds
response
decrease
i
n
yield
than
i
n
response
n yield.
LOS 58.d
Eff
ective duration
ulated asithen yield,
ratiotoofthethechange
averageinpercentage
equal-sized
increaseisandcalcdecrease
yield. price change for an
enecuve. durauon. = 2Vv-0 -(.6.yv+)
a:
LOS 58 .e
Approximate percentage change in bond price = -duration change in yield in percent.
The
tive interpretation
of duration is as the percentage change in a bond's
pricemost
for aintui
1% change
in yield to maturity.
Macaulay duration and modified duration are based on a bond's promised cash flows.
Effecti
v
e
duration
is
appropriate
for
estimating
price
changes
in
bonds
wi
t
h
embedded
options
flows. because it takes into account the effect of embedded options on a bond's cash
x
LOS 58.f
©20 1 2 Kaplan, Inc.
Page 149
Study Session 1 6
Cross-Reference to CFA Institute Assigned Reading #58
58.g of a bond portfolio is equal to a weighted average of the individual bond
The
duration
durations,
where
the
wei
g
hts
are
the
proportions
of
total
portfolio
value
i
n
each
bond
position.
Portfolio
duration
it givines thetheportfolio,
sensitivityanofunlikely
portfolioscenario
value onlyfor tomost
yiportfolios.
eld changes
that areis limited
equal forbecause
all bonds
58.hof convexity, the duration measure is a poor approximation of price sensitivity
Because
eld changesof thethatpriarece-yield
not absolutely
small. The convexity adjustment accounts for
thefor yicurvature
relationship.
Incorporating
convexi
ty, weas:can estimate the percentage change in
price
in responsebothto duration
a change and
in yield
of (.6.y)
{[(-duration)(�y )J + [( convexity)( �y )2 ]}
Introduction to the Measurement o f Interest Rate Risk
LOS
LOS
x
100
58.iconvexity considers expected changes in cash flows that may occur for bonds
Effective
with embedded options, while modified convexity does not.
58.
j
Price value
of a basis
(PVBP)
an estiminateyield.
of the change in a bond's or a bond
portfoli
o's value
for apoint
one basis
pointis change
PVBP = duration
bond (or portfolio) value
YiUncertai
eld 58.k
volatil
iabout
ty is thea bond'
standard
deviprice
ation due
of theto changes
inin theyieldyieldresultsof afrom
bond.both a
n
ty
s
future
changes
sensitivity to yield changes (its duration) and also from the volatility of its
yibond'
eld ins prithecemarket.
LOS
LOS
x
0.0001
x
LOS
Page 150
©2012 Kaplan, Inc.
Study Session 16
Cross-Reference to CFA Institute Assigned Reading #58 - Introduction to the Measurement of Interest Rate Risk
CONCEPT CHECKERS
1. Why
i
s
the
price/yield
profi
l
e
of
a
call
a
bl
e
bond
less
convex
than
that
of
an
idecreases.
ncreaseidentical
is cappedoption-free
from above,bond?at orThenearprice:the call price as the required yield
A.otherwise
ncrease is capped from above, at or near the call price as the required yield
B. imcreases.
C. decrease
mcreases.is limited from below, at or near the call price as the required yield
2. The
4.
6
5%
semiannual-pay
Portage
Health
Authority
bonds
have
exactl
y
17 years toapproach,
maturitytheandinterest
are currently
priced to(inyipercent
eld 4.39%.of value)
Usingforthethese
full
valuation
rate
exposure
given a 75 basis point increase in required yield, is to:
A.bonds,
-9.104%.
B. -8.-9.3044%.
31%.
14% semiannual-pay
coupon
bond
hass point
six yearschange
to maturity.
The
bondectivise
3. Acurrentl
y
tradi
n
g
at
par.
Using
a
25
basi
i
n
yield,
the
eff
0.3.8389.89.of the bond is to:
A.B.duration
3.970.
Supposechange
that thein yibond
in Question
3 isvcallable
at parassuming
today. Usithatngitsa price
25 basis
4. point
e
l
d
,
the
bond'
s
effecti
e
duration
exceed 100 is to:
A.B.cannot1.972.
19.1.998.
72.
modififoreda duration
of a bond
is 7.basis87. points
The percentage
change in price using
5. The
duration
yield
decrease
of
110
i
s
to:
A.B. -8.+7.155%.
657%.
+8.657%.
a convexi
t
y
of
57.
3
.
The
convexity
effect
if
the
yiel
d
decreases
by
6. A110bondbasishaspoints
is to:
A.B. -1.+0.6673%.
93%.
+1.673%.
a bondmeasures,
has an effecti
ve durationpercentage
of 10.5 andchangea convexity
of97.3.
Using
7. Assume
both
of
these
the
estimated
in
price
for
thi
s
bond,
to a decline in yield of 200 basis points, is to:
A.iB.n response
19.05%.
22.989%.
5%.
24.
closest
c.
closest
c.
closest
c.
closest
c.
closest
c.
closest
c.
©20 1 2 Kaplan, Inc.
Page 1 5 1
Study Session 1 6
Cross-Reference to CFA Institute Assigned Reading #58
-
Introduction to the Measurement o f Interest Rate Risk
has determi
ned thatbondif market
yieladconvexity
s rise by 100effectbasisof points,
a
8. Ancertaianalyst
n
hi
g
h-grade
corporate
will
have
1.
7
5%.
Further,
she'
s
found
that
the
total
esti
m
ated
percentage
change
in
price
for
thi
s
bond shouldchange
be -13.35%.
Given
thisduration
information,
it follows that the bond's
percentage
in
price
due
to
is:
A.B. -15.10%.
+16.11.60%.
85%.
9. A.Theaddi
totalngprithece bond'
volatislitconvexity
y of a typieffect
cal noncallable
bond
can be found by:
to
i
t
s
effecti
v
e
duration.
B.C. addi
n
g
the
bond'
s
negati
v
e
convexi
t
y
to
i
t
s
modified
duration.
subtracting the bond's negative convexity from its positive convexity.
10. The
current
pricbond'
e of as$1,PVBP
000,is7-year, 5.5%
semiannual coupon bond is
$1,
0
29.
2
3.
The
to:
A.B. $0.05.
$5.$0.764.0.
11. The effectestionma ated
bondbyportfol
io's value of a decrease in yield would be
using:
approach.
A.B. thethe prifullcevaluation
value
of
C. both the portfolio'as basis
duratipoint.
on and convexity.
12. when
An analyst
has
noticed
latel
y
that
the
pri
c
e
of
a
particular
bond
has
ri
s
en
l
e
ss
the yiconclude
eld falls bythat0.1theo/o bond:
than the price falls when rates increase by 0.1 o/o.
She
could
is ananoption-free
bond.
A.B. has
embedded
put
option.
C. has negative convexity.
ch of the follduration.
owing measures is for a currently callable bond?
13. A.WhiMacaulay
B.C. Effecti
v
e
duration.
Modified duration.
-
c.
closest
c.
most
accurately
lowest
Page 152
©2012 Kaplan, Inc.
Study Session 16
Cross-Reference to CFA Institute Assigned Reading #58 - Introduction to the Measurement of Interest Rate Risk
CHALLENGE PROBLEMS
6.
A bond dealer provides the following selected information on a portfolio offixed-income
securities.
Use the following information to answer Questions 1 through
Market Price
Coupon
Modified
Duration
Effective
Duration
Effective
Convexity
$2 million
1 00
6.5%
8
8
1 54
$3 million
93
5.5%
6
$ 1 million
95
7%
8.5
8.5
130
$4 million
1 03
8o/o
9
5
-70
Par Value
1.
2.
3.
4.
5.
6.
7.
8.
50
What is the effective duration for the portfolio?
Calculate the price value of a basis point for this portfolio.
Which
coupon)bond(s) likely has (have) no embedded options? (identify bonds by
Which bond(s) is (are) likely callable?
Which bond(s) is (are) likely putable?
What
is
the
approxi
m
ate
pri
c
e
change
for
the
7%
bond
if
i
t
s
yi
e
ld
to
maturity
increases by 25 basis points?
Why
might two bond dealers differ in their estimates of a portfolio's effective
duration?
Why
migforht portfolio
effectiveeven
duration
beassume
an inadequate
measure
ofdurati
interest
rate
risk
a
bond
portfolio
i
f
we
the
bond
effecti
v
e
o
ns
are
correct?
©20 1 2 Kaplan, Inc.
Page 153
Study Session 1 6
Cross-Reference to CFA Institute Assigned Reading #58 - Introduction t o the Measurement o f Interest Rate Risk
ANSWERS - CONCEPT CHECKERS
1.
A
As the required yield decreases on a callable bond, the rate of increase in the price of
the bond begins to slow down and eventually level off as it approaches the call price, a
characteristic known as "negative convexity."
2.
C
We need to compare the value of the bond today to the value if the YTM increases by
0. 75%.
Price today = 103.092
4.65
N = 34 ; PMT = - = 2.325; FV = 1 00;
2
4.39
I I Y = -- = 2.195%; CPT ---. PV = - 1 03.092
2
Price after a 75 basis point increase in the YTM is 94.490
4.65
N = 34 ; PMT = - = 2.325; FV = 100;
2
5 14
1/Y = ·
= 2.57%; CPT --+ PV = -94.490
2
Interest rate exposure =
3.
c
v_
94.490 - 103 092
·
= -8 .344%
103.092
= 100.999
14.00
N = 12; PMT = -- = 7.00; FV = 100;
2
13.75
1 / Y = -- = 6.875%; CPT --+ PV = - 1 00.999
2
v+
= 99.014
14.00
N = 12; PMT = -- = 7.00; FV = 100;
2
14.25
1 / Y = -- = 7.125%; CPT --+ PV = -99.014
2
V0 = 100.000
b.y = 0.0025
duration =
Page 154
V_ - V+
2V0 (b.y)
=
100.9 99 - 99 .014
2(100)0.0025
= 3.970
©2012 Kaplan, Inc.
Study Session 1 6
Cross-Reference to CFA Institute Assigned Reading #58 - Introduction to the Measurement of Interest Rate Risk
4.
A
1 00
v
=
V+=
99.014
V0=
100
6.y=
0.0025
v_ - v+
.
=
duranon =
2V0 (6.y)
100-99.014
= 1 . 972
2(1 00)0.0025
5.
c
Est.[6. V_ o/o] = -7.87 x(-1.10%) = 8.657%
6.
B
convexity effect = convexity x ( 6.y )2 =
7.
c
Total estimated price change = (duration effect + convexity effect)
{[- 10.5
8.
A
X
[
(-0.02)] + 97.3 (-0.02)2
X
[57.3(0.01 1? ]
]}
x 100 = 0.693%
x 100 = 21.0o/o + 3. 8 9o/o = 24.89o/o
Total percentage change in price = duration effect + convexity effect. Thus:
- 13.35 = duration effect + 1.75 =? duration effect = -15. 10%·
(Note: the duration effect must be negative because yields are rising.)
9.
A
Total percentage change in price = duration effect + convexity effect. Thus:
Total percentage change in price = effective duration + convexity effect.
(Note: since this is a noncallable bond, you can use either effective or modified duration
in the above equation.)
10.
B
PVBP = initial price - price if yield is changed by 1 basis point. First, we need to
calculate the yield so that we can calculate the price of the bond with a 1 basis point
change in yield. Using a financial calculator: PV = -1,029.23; FV = 1 ,000; PMT = 27.5
= (0.055 x 1,000) I 2; N =14 = 2 x 7 years; CPT � IIY = 2.4999 8 , multiplied by 2 =
4.99995, or 5.00%. Next, compute the price of the bond at a yield of 5.00% + 0.01 o/o,
or 5.01 o/o . Using the calculator: FV = 1 ,000; PMT = 27.5; N = 14; IIY = 2.505 (5.01 I
2); CPT � PV = $1,028.63. Finally, PVBP = $ 1 ,029.23 - $1,028.63 = $0.60.
11.
A
The full valuation approach is the most complex method, but also the most accurate.
12.
C
A bond with negative convexity will rise less in price in response to a decrease in yield
than it will fall in response to an equal-sized increase in rates.
13.
B
The interest rate sensitivity of a bond with an embedded call option will be less than
that of an option-free bond. Effective duration takes the effect of the call option into
account and will, therefore, be less than Macaulay or modified duration.
©20 12 Kaplan, Inc.
Page
155
Study Session 1 6
Cross-Reference to CFA Institute Assigned Reading #58 - Introduction t o the Measurement o f Interest Rate Risk
ANSWERS - CHALLENGE PROBLEMS
1.
Portfolio effective duration is the weighted average of the effective durations of the
portfolio bonds.
Numerators in weights are market values (par value
Denominator is tOtal market value of the portfolio.
2
0.95
4.12
2.79
-- ( 8) +
( 1) +
( 8.5 ) + -- ( 5)
9.86
9.86
9.86
9.86
--
2.
=
price as percent of par).
.
.
4 . 8 1 (we1ghts are m m1'll'wns)
Price value of a basis point can be calculated using effective duration for the portfolio
and the portfolio's market value, rogether with a yield change of 0.01 o/o. Convexity can
be ignored for such a small change in yield.
4.81
X
0.0001
X
9,860,000
=
$4,742.66
3.
The 6 . 5 % and 7o/o coupon bonds likely have n o embedded options. For both of these
bonds, modified duration and effective duration are identical, which would be the case
if they had no embedded options. (It is possible that these bonds have options that are
so far out of the money that the bond prices act as if there is no embedded option. One
example might be a conversion option tO common stock at $40 per share when the
market value of the shares is $2.)
4.
The 8o/o bond is likely callable. It is trading at a premium, its effective duration is less
than modified duration, and it exhibits negative convexity. Remember, call price can be
above par.
5.
The 5.5% bond is likely putable. It is trading at a significant discount, its effective
duration is much lower than its modified duration (close to zero in fact), and its
convexity is positive but low. Note that a putable bond may trade below par when the
put price is below par (also if there is risk that the issuer cannot honor the put). If it
were callable, we would expect its modified and effective durations tO be closer in value
because the market price is significantly below likely call prices.
6.
Based on the effective duration and effective convexity of the 7o/o bond, the approximate
price change is:
[-8.5
Page 156
--
x
X
0.0025]
+
[ 1 30
X
0.0025 2]
X
950,000
=
-$ 19,4 1 5 .63
7.
In order to estimate effective duration, the dealers must use a pricing model for the
bonds and choose a specific yield change. Differences in models or the yield change used
can lead tO differences in their estimates of effective duration.
8.
Effective duration is based on small changes in yield and is appropriate for parallel
changes in the yield curve (or equal changes in the yields to maturity for all portfolio
bonds). Other types of yield changes will make portfolio duration an inadequate
measure of portfolio interest rate risk.
©2012 Kaplan, Inc.
The following is a review of the Fixed Income Analysis and Valuation principles designed to address the
learning outcome statements set forth by CFA Institute. This topic is also covered in:
FUNDAMENTALS OF CREDIT
ANALYSIS
Study Session 1 6
EXAM FOCUS
This
topic
revi
e
w
introduces
credit
analysis,
primarily
for
corporate
bonds,
but
considerations
foron credi
t analysis
ofcredithighspreads,
yield, sovereign,
and municipal
bonds
areratings
also
covered.
Focus
credit
ratings,
and
the
impact
on
return
when
and spreads change.
LOS 59.a: Describe credit risk and credit-related risks affecting corporate
bonds.
CPA® Program Curriculum, Volume 5, page 606
isandthe fulriskl payments
associatedofwiitnhterest
lossesorstemming
ure two
of a components:
borrower to
make timelyand
principal.from
Credittherifailsk has
i
s
the
probabi
l
i
t
y
that
a
borrower
(bond
issuer)
fai
l
s
to
pay
i
n
terest
or
repay principalorwhen due. refers to the value a bond investor will lose if the
issuer
defaults.
Loss
severi
t
y
can
be
stated
as
a
monetary
amount
or
as
a
percentage
of a bond's value (principal and unpaid interest).
The
equal astoathemonetary
default value
risk multiplied
by the lossof severi
loss can likewise beisstated
or as a percentage
a bond'ty.s Expected
value.
The Loss severity
is theas percentage
will receiverate.if the issuer
defaults.
a percentageofias bond'
equal stovalue
one anminusinvestor
the recovery
Bondsdifwith
crediintyiriskeldtrade
at hiagcredit-ri
her yieldsskythanbondbonds
thought
to be freebond
of credit
risk.
The
ference
between
and
a
credit-risk-free
of
similar
maturity
i
s
called
i
t
s
For
example,
i
f
a
5-year
corporate
bond
i
s
trading
at
a
s pointsbond
to Treasuries
6.5%.on 5-year Treasury notes is 4.0%,
thespreadyieldofon+250thebasicorporate
is 4.0% and2.5%the=yield
Bond andpricesa narrower
are inverselspread
y relaimplies
ted to spreads;
widerThespreadsizeimplies
a lowerreflbond
price
a higheraprice.
of the spread
ects the
Credit risk
default risk
loss severity.
•
Default risk
•
Loss severity,
loss given default,
expected loss
recovery rate
yield spread.
+
©20 1 2 Kaplan, Inc.
Page 157
Study Session 1 6
Cross-Reference to CFA Institute Assigned Reading #59
-
Fundamentals o f Credit Analysis
tworthinessthatofathebond'issuers spread
and thewilliquidity
for itsofbonds.
thecredipossibility
l widen dueof theto onemarket
or both
these factors. is
or
i
s
the
possibil
i
ty
that
spreads
will
increase
because
the issuer
hasg agencies
becomeassign
less credi
tworthy.
As weandwiissuers,
ll see laterandinmaythisupgrade
topic or
revi
e
w,
credit
rati
n
ratings
to
bonds
downgrade these ratingsis theoverrisktime.of receiving less than market value when selling
a bond forandtheis reflbonds
ectedofinlessthecredi
sizetworthy
of the biissuers
d-ask spreads.
Market
liquidity
risker issuers
is
greater
and
for
the
bonds
of
small
with relatively little publicly traded debt.
Spread risk
•
Credit migration risk
•
Market liquidity risk
downgrade risk
LOS 59.b: Describe seniority rankings of corporate debt and explain the
potential violation of the priority of claims in a bankruptcy proceeding.
CFA® Program Curriculum, Volume 5, page 609
Each
category
of debt Afrombond'thes same
issuerof claims
is rankedto theaccordi
ngs assets
to a and cash flows isin
thereferred
event
of
a
default.
priority
issuer'
to as its
Debt canunsecured
be eitherdebt or or represent a generalSecured
debttheisissuer'
backeds assets
by collateral,
while
claim
to
cash flows. Secured debt has higher priority of claims than unsecured debt. and
Secured
debt can be further distinguished
as debt.orUnsecured debt(where
a specific
asset
i
s
pledged),
or
i
s
further
divided
into
and
rank ofdebt.
unsecured debt is
senior unsecured. Subordinated
debtgradations.
ranks belowTheotherhighest
unsecured
The general seniority rankings for debt repayment priority are the following:
FiSenior
rst liensecured
or firstdebt.
mortgage.
Junior
secured
debt.
Senior
unsecured
debt.debt.
Senior
subordinated
Subordinated
debt.
Junior subordinated debt.
Allclaims.
debtAllwitsenior
hin thesecured
same category
is saidfortoexampl
rank e, are treatedor have
same
priority of
debt
holders,
al
i
k
e
in
a
corporate
bankruptcy.
Recovery
ratesrankareofhighest
fory. Thedebtlower
withthetheseni
highest
priority
ofofclaims
andthedecrease
with
each
lower
seniori
t
o
rity
ranki
n
g
a
bond,
higher
its
credit risk. Investors require a higher yield to accept a lower seniority ranking.
Inbefore
the junior
event oflenders
a defaultandorequireorganizati
o
n,
seni
o
r
lenders
have
claims
on
the
assets
ty holdiers.n theory
A strictthepriority
always applied in practice. Although
priorityofofclaims,
claimshowever,
is absolute,is notin many
priority of claims
seniority ranking.
secured debt
unsecured debt.
debentures
first lien
senior secured, junior secured
senior, junior,
subordinated
first mortgage
•
•
•
•
•
•
•
pari passu,
Page 158
©2012 Kaplan, Inc.
Study Session 1 6
Cross-Reference to CFA Institute Assigned Reading #59 - Fundamentals o f Credit Analysis
cases
lower-priori
debt holders
are notty debt
paidholders
in full. (and even equity investors) may get paid even if senior
Bankruptciesthecanvalue
be costly
and
take as long
time
todeteri
settleo. rate
Duringduebankruptcy
proceedings,
of
a
company'
assets
could
to
loss
of
customers
and
keyrmedemployees,
whiamong
le legalall clexpenses
mount.
Awibankruptcy
reorgani
zrecovery
ation planrate.is
confi
by
a
vote
a
sses
of
i
n
vestors
t
h
less
than
100%
Tomayavoid
unnecessary
delzation
ays, negoti
athattiondoesandnotcompromise
among tovarious
clgaiimholders
result
in
a
reorgani
plan
strictly
conform
the
ori
n
al
pri
o
rity
of claims.
By such
from
absolute
prioriatvote
y. or by order of the bankruptcy court, the final plan may differ
LOS 59.c: Distinguish between corporate issuer credit ratings and issue credit
ratings and describe the rating agency practice of "notching".
CPA® Program Curriculum, Volume 5, page 616
Credit
rating
agenci
eboth
s assigntheratings
toecategori
es of bonds
withthesimilar
crediandt risk.
Rating
agenci
e
s
rate
issuer
(i.
.
,
the
company
issuing
bonds)
theratings
debt
issues,
or
the
bonds
themselves.
Issuer
credit
ratings
are
called
corporate
family
(CFR), arewhibased
le issue-speci
foverall
ic ratingscrediaretworthi
calledncorporate
credit ratings
(CCR).
Issuerrated on
ratings
on
the
ess
of
the
company.
The
issuers
are
their senior unsecured debt.
Figure
1 shows
ratinagenci
gs scalees.s used by Standard & Poor's, Moody's, and Fitch, three of the
major credi
t rating
Figure Credit Rating Categories
1:
(a) Investment grade ratings
Moody's
Aaa
Aal
Aa2
Standard &Poor's,
Fitch
AAA
AA+
AA
(b) Non-investment grade ratings
Moody's
Standard &Poor's,
Fitch
Ba l
BB+
Ba2
BB
Ba3
B8-
81
8+
Aa3
AA-
Al
A+
82
8
A
83
8-
A3
A-
Caal
CCC+
Baal
8BB+
Caa2
CCC
Baa2
B8B
Caa3
CCC-
Baa3
88B-
Ca
cc
A2
c
c
©20 12 Kaplan, Inc.
c
D
Page 159
Study Session 1 6
Cross-Reference to CFA Institute Assigned Reading #59
-
Fundamentals o f Credit Analysis
Triarepconsidered
le A or Aaa) is the highestBondsrating.ratedBonds
with orratings
ofareBaa3/BBBor higher
Bal/BB+
lower
considered
and are often called
or
Bonds
i
n
default
are
rated
by
Standard
&
Poor'
s
and
Fitch
and
are
i
n
cluded
i
n
Moody'
s lowestbonds,ratinprovisions
g category,inC.bond
Whenindentures
a companymaydefaults
ondefault
one ofonitstheseveral
outstanding
tri
g
ger
remaining
issues as well. Such a provision is called a
Abutborrower
can haverating.
multipl
e debt
issues
thatdepend
vary notononly
by maturities
and coupons
also
by
credit
Issue
credit
ratings
the
seniori
t
y
of
a
bond
issuengsandto
itsbondscovenants.
is
the
practice
by
rating
agencies
of
assigning
di
f
ferent
rati
of theitssame
Notchingloisss based
bonds and
impactissuer.on potential
severionty. several factors, including seniority of the
Anratinexampl
e of a factor that rating agenci
es consider
when structure,
notching anbothissuethecredit
g
is
In
a
holding
company
parent
company
andthethetransfer
subsidiariof cash
es mayor have
outstanding
debt.theAparent
subsidcompany
iary's debtbefore
covenants
may
restrict
assets
"upstream"
to
theare
subsidiary'
s
debt
i
s
serviced.
In
such
a
case,
even
though
the
parent
company'
s
bonds
not
junior
to
the
subsidi
a
ry'
s
bonds,
the
subsidiary'
s
bonds
have
a
priority
claim
to
the
subsidiary'
flows. Thus the parent company's bonds are effectively subordinated to
the subsidisary'cashs bonds.
Notching
is lesshigcommon
forrihighl
y rated
issuerscantthandifferences
for lower-rated
issuers.
Forrates
lower­of
rated
issuers,
her
default
s
k
leads
to
signifi
between
recovery
debt with different seniority, leading to more notching.
(AAA
investment grade.
investment grade
non­
high yield bonds
junk bonds.
0
cross default provision.
Notching
structural subordination.
LOS 59.d: Explain risks in relying on ratings from credit rating agencies.
CFA® Program Curriculum, Volume 5, page 618
Relying on ratings from credit rating agencies has some risks. Four specific risks are:
1. update their default risk assessments
Credit ratings
change
overof atime.
RatiHigher
ng agenci
etsratings
may
during
the
l
i
f
e
bond.
credi
tend to be more stable than lower credit ratings.
Ratingsweremistakes
occurmuchfromhigher
time ratings
to time.thanFor they
example,
subprime
mortgage
securities
assigned
deserved.
3. difficultriskto ispredict and incorporateRisksintothatcredit
are specific
to
a
company
or
industry
are
ratings.
Litigation such
risk toas tobacco
companies
i
s
one
example.
Events
that
are
di
f
fi
c
ult
to
anticipate,
naturalin
disasters,
acquisitions,
and
equity
buybacks
using
debt,
are
not
easily
captured
credit ratings.
Credit ratings are dynamic.
2. Rating agencies are not perfect.
Event
Page 160
difficult to assess.
©2012 Kaplan, Inc.
Study Session 1 6
Cross-Reference to CFA Institute Assigned Reading #59 - Fundamentals o f Credit Analysis
4. faster
Creditthan
ratingscredilagt ratings.
marketAdditional
pricing. Market
prices
andwithcredit
spreads
changetrademuch
l
y
,
two
bonds
same
rating
can
at
didefault
fferentrisyik.elds. Market prices reflect expected losses, while credit ratings only assess
LOS 59.e: Explain the components of traditional credit analysis.
CPA® Program Curriculum, Volume 5, page 623
Acredit
common
waycapacity,
to categoricollateral,
ze the keycovenants,
componentsand ofcharacter.
credit analysis is by the four Cs of
analysis:
Capacity
Capacityofrefers
to a corporate
borrower'
s abilused
ity repay
its debtanalysi
obligations
on tianalysi
me. s
Analysis
capacity
i
s
simi
l
ar
to
the
process
in
equity
s
.
Capacity
entai
l
s
three
l
e
vel
s
of
assessment:
(1)
i
n
dustry
structure,
(2)
industry
fundamentals,
and
(3) company fundamentals.
Industry Structure
The
firstdescribed
level of abycredit
analyst'
sforces:
assessment
isamong
industryexististructure.
Industry threat
structureof
can
be
Porter'
s
fi
v
e
rival
r
y
n
g
competitors,
new
entrants,
threat
of
substitute
products,
bargai
n
ing
power
of
buyers,
and
bargaining
power of suppliers.
� Professor's Note: We describe industry analysis based on Porter'sjiveforces in the
� Study Session on equity valuation.
Industry Fundamentals
The
level
of a credit analfactors
yst's assessment
is industry
fundamentals,
including
the
iIndustry
nflunext
ence fundamentals
of macroeconomic
on
an
industry'
s
growth
prospects
and
profitability.
evaluation focuses on:
Industry
cyclicality.
Cycl
i
cal
industries
are
sensitive
to
economic
performance.
Cyclcihcalmake
industries
tend toriskyhavethanmorenoncycl
volatilicale earnings,
revenues, and cash flows,
whi
them
more
industries.
Industry
growth
prospects. Creditworthiness
is most questionable for the weaker
companies
i
n
a
slow-growing
or
declining
industry.
Industry published
statistics.
Industry statisti
cs providedagencies
by ratincan
g agencies,
investment
banks,
i
n
dustry
periodicals,
and
government
be a source for
industry performance and fundamentals.
•
•
•
©20 1 2 Kaplan, Inc.
Page 1 6 1
Study Session 1 6
Cross-Reference to CFA Institute Assigned Reading #59
-
Fundamentals o f Credit Analysis
Company Fundamentals
The
last
level
of
credit
analysts'
assessment
is
company
fundamentals.
A
corporate
borrower should be assessed on:
Markettoshare
changes over time and cost structure relative to
peers are some of theThefactors
analyze.
performance
of
the
company
over
different
phases
of
business cycle, trends in margins and revenues,
and current
management'
s tenure.
This
includes
the
soundness
of
the
thebondholders.
ability to execute the strategy, and the effects of management's decisionsstrategy,
on
coverage ratios are importantAs wetoolswilforl discuss
creditlater
analyinsis.this topic review, leverage and
•
Competitive position.
•
Operating history.
•
Management's strategy and execution.
•
Ratios and ratio analysis.
Collateral
Collateral
analysis iss more
important
for lessto creditworthy
companies.
Theconsider
marketwhen
value
of
a
company'
assets
can
be
difficult
observe
di
r
ectly.
Issues
to
assessing collateral values include:
Patents
are
considered
high-quality
intangible
assets
because
they
can beconsimorederedeasilya high-quality
sold to generate
cash flasset
ows and
thanisother
intangibles.
Goodwil
l is
not
intangible
usually
written
down
when
company performance
is poor. expense relative to capital expenditures may signal
High
depreciation
that
management
is notbe ipoor,
nvestingwhichsuffimay
cientlyleadintothereduced
company.
The quali
tyflofowtheand
company'
s
assets
may
operating
cash
potentially
high
loss
severi
t
y.
Equitycompany assets are of lowAqualistockty. that trades below book value may indicate
that
are difficult
to value, but a company may
have intellectual property that canThese
function
as collateral.
•
Intangible assets.
•
Depreciation.
•
•
market capitalization.
Human and intellectual capital.
Covenants
Covenants
are theissue.termsCovenants
and conditions
the borrowers
and lenders
have
agreedfletoxibility
as
part
of
a
bond
protect
lenders
whi
l
e
leaving
some
operating
to the borrowers
and (2) to run the company. There are two types of covenants: (1)
require
the borrower
to takeon certain
actions,
suchmaintaining
as paying
icertain
nterest,fiprincipal,
and
taxes;
carrying
insurance
pledged
assets;
and
nancial ratios within prescribed limits.
restrict
the
borrower
from
taki
n
g
certain
actions,
such
as
incurring
additional
debt or directing cash flows to shareholders in the form of dividends and
stock
repurchases.
of anhand,
issuer'covenants
s operatingcreate
activaitieslegally
maybinding
reduce
theCovenants
issuer's that
abilityaretooverl
repay.y restri
On cthetiveother
affirmative
covenants
negative covenants.
Affirmative covenants
Negative covenants
Page 162
©2012 Kaplan, Inc.
Study Session 1 6
Cross-Reference to CFA Institute Assigned Reading #59 - Fundamentals o f Credit Analysis
framework
forcareful
repayment
of the debt
obligation,
whiassessment
ch reducesofuncertainty
forcontractual
the
debt
holders.
A
credi
t
analysis
should
include
an
whetherthe
the
covenants
protect
the
interests
of
the
bondholders
without
unduly
constraining
borrower's operating activities.
Character
Charactersuchrefersas management'
to management'
s integriqualifications
ty and its commitment
to repay
theareloan.
Factors
s
business
and
operating
record
important
for evaluating character. Character analysis includes an assessment of:
Management'
s ability toindevelop
a sound
strategy.and operating
Management'
s
past
performance
executing
i
t
s
strategy
theled tocompany
wi
t
hout
bankruptcies,
resrructurings,
or
other
distress
situations
that
additional borrowing.
Use
ofasaccounting
policies andissues,
tax frequent
strategies
that
may
be
hidi
n
g
problems,
such
revenue
recognition
restatements, and frequently changi
nrecord
g auditors.
Any
of fraud or other legal and regulatory
problems.
Benefi
t
s
to
equity
holders
at
the
expense
of
debt
holders,
such rating
as debt-financed
especiallythrough
if they ledactiotonscredit
downgrades.acquisitions and special dividends,
•
•
Soundness of strategy.
Track record.
•
Accounting policies and tax strategies.
•
Fraud and malfeasance record.
•
Prior treatment of bondholders.
LOS 59.f: Calculate and interpret financial ratios used in credit analysis.
CPA® Program Curriculum, Volume 5, page 628
Ratio analysis
is part of capacity
analysis. TwoCredit
primaryanalysts
categoricalculate
es of ratios
for credit
analysi
s
are
and
company
rati
o
s
to
assess
viabilityandof apeers.
company, to find trends over time, and to compare companies to
industrytheaverages
leverage ratios
coverage ratios.
Profits and Cash Flows
Profi
t
s
and
cash
fl
o
ws
are
needed
to
servi
c
e
debt.
Here
we
examine
four
profit
and
cash
flow merrics commonly used in ratio analysis by credit analysts.
1. EBITDA is a commonly used measure that is calculated as operating income plus
depreciation
and
amortization.
A
drawback
to
using
this
measure
for
credit
anal
y
sis
is that areit doesnecessary
not adjusesust forof funds
capitalforexpenditures
and changes
in workiforngthesecapital,
which
a
going
concern.
Cash
needed
uses is
not available to debt holders.
fromoperations plus(FFO).
Funds
from
operations
are
net
income
from
2. continuing
depreciation,
amortization,
deferred
taxes,
and noncash
items.
FFO
i
s
similar
to
cash
fl
o
w
from
operations
(CFO)
except
that
FFO
excludes
changes in working capital.
Earnings before interest, taxes, depreciation, and amortization (EBITDA).
Funds
operations
©20 1 2 Kaplan, Inc.
Page 163
Study Session 1 6
Cross-Reference to CFA Institute Assigned Reading #59
-
Fundamentals o f Credit Analysis
3. depreciation and amortization miFree
cashtalfloexpendi
w beforeturesdividends
ins crease
net income
plus
n
us
capi
minus
i
i
n
working
capital. Free cash flow before dividends excludes non-recurring items.
i
s
free
cash
flow
before
dividends
minus
the
4. dividends. If free cash flow afterThis
diviondendstheibalance
s greatersheet.
than zero,
it outcome
representsis cash
that
could
pay
down
debt
or
accumulate
Ei
t
her
a
form
of deleveraging, a positive indicator for creditworthiness.
Free cash flow before dividends.
Free cash flow after dividends.
Leverage Ratios
Analysts
should
adjas uunderfunded
st debt reported
on theplansfinancial
statements
by includi
noff-balance­
g the firm's
obligations
such
pension
(net
pension
liabilities)
and
sheet liabilities such as operating leases.
The threeratio,mostthecommon
measures ofratio,leverage
by credit analysts
capital
debt-to-EBITDA
and theusedFFO-to-debt
ratio. are the debt-to­
1. capital ratio is Capital
is the sumof theof total
debtstructure
and shareholders'
equity.
Thelowerdebt-to­
the
percentage
capital
fi
n
anced
by
debt.
ratio
indicatessuchlessas credit
risk.anIfanalyst
the financial
statements
listsecond
high values
for intangible
assets
goodwill,
should
cal
c
ul
a
te
a
debt-to-capital
ratio
adjusted for a writedown of these assets' after-tax value.
indicates
higher
leverage
and
higher
credit
risk.
This
2. ratio is more volatilhie gforherfirratio
ms inofcyclEBITDA.
ical industries or with high operating leverage
because of their high variability
s ratiocredit
dividrisk.
es a cash flow measure by the value of debt, a
3. higher ratioBecause
indicatesthilower
Debt/capital.
A
Debt/EBITDA. A
FFO/debt.
Coverage Ratios
Coverage
borrower'used
s ability
to generate cash flowsandto£BIT-to-interest.
meet interest
payments.ratiTheostwomeasure
mostthecommonly
are EBITDA-to-interest
higher ratio indicates
lower
credit
risk.
Thi
s
rati
o
i
s
1. used more often than the £BIT-to-interest
expense
ratiw measure,
o. Becausethisdepreciation
and
amortization
are
sti
l
l
included
as
part
of
the
cash
fl
o
ratio
will
be
higher than the EBIT version.
rati
o
indicates
l
o
wer
credi
t
ri
s
k.
This
rati
o
i
s
the
2. more conservative measurehigher
because depreciation and amortization are subtracted
from earnings.
EBITDA/interest expense. A
£BIT/interest expense. A
Page 164
©2012 Kaplan, Inc.
Study Session 1 6
Cross-Reference to CFA Institute Assigned Reading #59 - Fundamentals o f Credit Analysis
1)
Aselcredit
anal
y
st
is
assessing
Saxor,
a
U.
S
.
multimedia
company
wi
t
h
the
followi
n
g
ected financial information:
Example: Credit analysis with financial ratios (Part
20X2
In $ millions
20Xl
Operating income
5,205
6,456
7,726
36,149
38,063
40,893
Depreciation and amortization
1,631
1 ,7 1 3
1 ,841
Capital expenditures
1,753
2, 1 1 0
3,559
Cash Row from operations
5,319
6,578
6,99 4
Total debt
12,701
12,480
1 3 ,977
Total equity
33,734
37,5 1 9
37,385
Dividends paid
648
653
756
Interest expense
300
33 0
360
Revenue
20X3
the cash flows and ratios listed below. Free cash flow (FCF) is after dividends
forCalculate
all calculations.
20Xl
20X2
20X3
EBITDA
FCF after dividends
Operating margin
Debt/EBITDA
EBITDNinterest
FCF/debt
Debt/capital
©20 1 2 Kaplan, Inc.
Page 165
Study Session 1 6
Cross-Reference to CFA Institute Assigned Reading #59
-
Fundamentals o f Credit Analysis
Answer:
EBITDA
=
operating
i
n
come
depreciation
and
amortization:
20Xl:
5,6,240556 1,1,76 3113 == $8,169
$6,836 million
20X2:
million
20X3: 7,726 1,841 = $9,567 million
FCF
=
cash
fl
o
w
from
operations
capital
expenditures
dividends:
20Xl:
5,319
- 2,110
1,753 -- 648
== $2,$3,815
9 18 million
20X2:
6,578653
20X3: 6,994- 3,559 - 756 = $2,679 million
million
Operati5,n2g05margin
= operating
income revenue:
20Xl:
36,149
=
14.
4
%
20X2:
893 == 18.17 .O9o/o%
20X3: 6,7,742656 40,38,063
Debt/EBITDA:
20Xl:
12,701
6,836
=
1.9x
20X2: 12,13,497780 9,567
8,169 == 1.5x
1.5x
20X3:
EBITDNinterest:
300
=
22.
8
x
20Xl:
6,
8
36
20X2:
360 == 24.26.68xx
20X3: 8,169
9,567 330
FCF/debt:
20Xl:
6,
8
36
12,701
=
23.
0
%
20X2:
20X3: 8,169
9,567 13,12,497780 == 30.19.26%%
Debt/capital:
20Xl:
12,701
(12,701
+ 33, 7 34) = 27.4%
20X2:
12,
4
80
(12,
4
80
+ 37,519) = 25. 0 %
20X3: 13,977 (13,977 + 37,385) = 27.2%
+
+
+
+
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
20Xl
20X2
20X3
EBITDA
6,836
8 , 1 69
9,5 67
FCF after djvidends
2,9 1 8
3,8 15
2,679
Operating margin
14.4%
17.0%
18 .9%
1.9x
1 .5x
1.5x
EBITDA/interest
22.8x
24.8x
26.6x
FCF/debt
23.0%
30.6%
19.2%
Debt/capital
27.4%
25.0%
27.2%
Debt/EBITDA
Page 166
©2012 Kaplan, Inc.
Study Session 1 6
Cross-Reference to CFA Institute Assigned Reading #59 - Fundamentals o f Credit Analysis
2)
2.follCoyote
Media
is
al
s
o
a
multimedia
company
and
is
a
ri
v
al
of
Saxor.
Gi
v
en
the
owing
ratios
forandCoyote
over theon which
same period,
calculate
the 3-year
averagesto forhavebotha
Saxor
and
Coyote
comment
mul
t
imedia
company
i
s
expected
better credit rating.
Example: Credit analysis with financial ratios (Part
Coyote Media
20Xl
20X2
20X3
Operating margin
18.0%
7.0%
9.5%
1 .9x
3.0x
2.0x
EBITDA/interest
27.5x
12.7x
18.3x
FCF/debt
15.0%
28.0%
26.6%
Debt/capital
28.7%
4 1 .2%
42.6%
Debt/EBITDA
Answer:
3-Year Averages
Saxor
Coyote
Operating margin
16.8%
1 1 .5%
1 .6x
2.3x
EBITDA/interest
24.7x
19.5x
FCF/debt
24.2%
23.2%
Debt/capital
26.5%
37. 5%
Debt/EBITDA
Allandratios
support
a higher
credit(EBITDA/interest)
rating for Saxor. Saxor
hasdebt
a better(FCF/debt).
operatingLower
margin
better
coverage
for
interest
and
for
leverage as measured by debt-to-capital and debt-to-EBITDA also favor Saxor.
LOS 59.g: Evaluate the credit quality of a corporate bond issuer and a bond of
that issuer, given key financial ratios for the issuer and the industry.
CPA® Program Curriculum, Volume 5, page 631
Ratings
agenciclassifi
es publish
benchmark
valystsuescanforevaluate
financialtheratios
that areforassociated
with
each
ratings
c
ation.
Credit
anal
potential
upgrades
and
downgrades based on subject company ratios relative to these benchmarks.
©20 12 Kaplan, Inc.
Page 167
Study Session 1 6
Cross-Reference to CFA Institute Assigned Reading #59
-
Fundamentals o f Credit Analysis
Example: Credit ratings based on ratios (Part 1 )
credit
rati
n
g
agency
publishes
the
fol
l
o
wing
benchmark
rati
o
s
for
bond
issues
ofaverages
multimedia
in eachto 20X3:
of the investment grade ratings, based on 3-year
over thecompanies
period 20Xl
A
AAA
AA
A
BBB
24.5%
16.5%
1 O.Oo/o
7.5%
1 .3x
1 .8x
2.2x
2.5x
EBITDA/interest
25.0x
20.0x
17.5x
1 5 .0x
FCF/debt
30.0%
24.0%
20.0%
17.0%
Debt/capital
25.0%
30.0%
35.0%
40.0%
Credit Ratings
Operating margin
Debt/EBITDA
Based
the ratioswhatcalculated
in the previous
exampl
e andfortheCoyote
industryandstandards
the tableon above,
are the expected
issuer credi
t ratings
Saxor? in
Answer:
3-Year Averages
Saxor
Coyote
Operating margin
16.8%
1 1 .5%
1.6x
2.3x
EBITDA/interest
24.7x
1 9.5x
BBB
FCF/debt
24.3%
23.2%
BBB
Debt/capital
26.6%
37.5%
BBB
Debt/EBITDA
BBB
A
Coyote
BBB
A
A
Coyote
A
A
Saxor
AA
AA
Coyote
AA
Coyote Saxor
AA
AA
Saxor
AAA
AAA
Saxor
AAA
AAA
Saxor
AAA
Based
on
the
rati
o
averages,
it
is
most
li
k
el
y
that
Saxor'
s
issuer
rati
n
g
is
AA
and
Coyote's issuer rating is
2)
Coyote
Medi
decidesandtowillspinnotoffbeitsa televi
sion division.
Theof Coyote
new company,
Coy
TV,
wiis more
l issueprofi
newtaabldebt
restricted
subsidiary
Media.
Coy
e
and
generates
higher
and
less
vol
a
tile
cash
fl
o
ws.
Describe
possible
notching
Media. for the new CoyTV issue and the potential credit rating change to Coyote
A.
Example: Credit ratings based on ratios (Part
TV
Answer:
Because
CoyTV
may
be
a
better
credit
ri
s
k
due
to
a
better
profit
potential,
the
new
issue may have a credit rating one notch above Coyote Media.
Coyote
Medi
a
may
now
be
less
profitable
and
could
have
more
volatil
e
cash
fl
o
ws.
This
suggests an increase in credit risk that could lead to a credit rating downgrade.
Page 168
©2012 Kaplan, Inc.
Study Session 1 6
Cross-Reference to CFA Institute Assigned Reading #59 - Fundamentals o f Credit Analysis
LOS 59.h: Describe factors that influence the level and volatility of yield
spreads.
CFA ® Program Curriculum, Volume 5, page 642
We
caninterest
thinkrate,of thetheyield
on aninoption-free
corporate
bond
as the asumliquidity
of thepremium,
real risk­
free
expected
fl
a
tion
rate,
a
maturi
t
y
premium,
and
a
credit
spread.
All
bond
prices
and
yields
are
affected
by
changes
in
the
fi
r
st
three
of these components. The last two components are the yield spread:
yield spread = liquidity premium credit spread
Yield spreads on corporate bonds are affected primarily by five interrelated factors:
1. the credit cycle,Thethemarket'
s
perception
of
overall
credit
risk
i
s
cyclical.
At
the
top
of
bondas themarket
perceives
low creditCredit
risk and
is generall
yasbullish.
Credi
t
spreads
narrow
credit
cycle
improves.
spreads
wi
d
en
the
credit cycle deteriorates.
Creditmetrics
spreadstonarrow
as
the
economy
strengthens
and
2. investors expect firms' credit
improve. Conversely, credit spreads widen as
the economy weakens.
CreditCredi
spreads
narrow
in
strong-performing
markets
3. overall, including the equity market.
t spreads
widenity ofin returns,
weak-performing
markets.
In
steady-performing
markets
with
low
volatil
credit spreads
also tend to narrow as investors reach for yield.
4. broker-dealers to providBecause
most bondscapitradetal foroverbond
the counter,
investors
needYield
e
market-making
markets
to
function.
spreadsmarket-maki
are narrowerngwhen
when
capitalbroker-dealers
becomes scarce.provide sufficient capital but can widen
5. demand for bonds. Credit spreads
supply.widenCrediin ttimes
spreadsof low
narrowdemand
in timesfor bonds.
of highExcess
wisupply
deninconditions,
g spreads. such as large issuance in a short period of time, can lead to
Yield
spreads
on
l
o
wer-qual
i
t
y
issues
tend
to
be
more
volatile
than
spreads
on
higher­
quality issues.
+
Credit cycle.
Economic conditions.
Financial market performance.
Broker-dealer capital.
General market demand and
LOS 59.i: Calculate the return impact of spread changes.
CFA ® Program Curriculum, Volume 5, page 646
The
imchange
pact of(�spread)
spread changes
is athecombination
of twooffactors:
(1)totheinterest
magnirate
tude
ofchanges
thereturn
spread
and
(2)
price
sensitivity
the
bond
(i.e., the bond's modified duration).
©20 12 Kaplan, Inc.
Page 169
Study Session 1 6
Cross-Reference to CFA Institute Assigned Reading #59
-
Fundamentals o f Credit Analysis
For small spreadby:changes, the return impact (percent change in bond price) can be
approximated
return impact modified duration �spread
The
negati
ve sign widen
in the (the
equation
reflienctsspread
the inverse
relationship
betweendecrease
pricesandandthe
yields.
As
spreads
change
i
s
positive),
bond
prices
impact
on
return
i
s
negati
v
e.
As
spreads
narrow
(
t
he
change
in
spread
is
negative),
bond
prices increase and the impact on return is positive.
For
spread changes, incorporating convexity improves the accuracy of return
impactlargermeasurement.
return impact modified duration �spread+ _!_2 convexity (�spread)2
�
�
-
-
x
x
x
Professor's Note: Make sure the value ofconvexity is scaled correctly. For option-free
bonds, convexity should be on the same order ofmagnitude as modified duration
squared. For example, ifyou are given that duration is 6 0 and convexity is 0.562,
duration squared is 36 0 and the correctly scaled convexity is 562.
0 Also notice that convexity is divided in halfhere, but was not divided in half
when we adjustedfor convexity in an earlier topic review. This is because different
authors calculate convexity differently. For the exam, use one-halftimes convexity
ifa question asks for the return impact ofa change in spread.
Longer
maturity
bonds
have
higher
duration
and
consequently
higher
spread
sensitivity;
theirhigher
pricestheanduncertainty
returns areofmore
sensitive
to tchanges
inessspread.
The longer
theimplmaturi
ty,
the
the
future
credi
worthi
n
of
the
debt
issuer,
y
i
n
g
higherlarger
credibid-ask
t spreadsspreads
for longer
maturity
bonds. Longer
maturi
tyinbonds
also tend
to
have
(i.
e
.
,
hi
g
her
transaction
costs),
i
m
pl
y
g
investors
in
longer
maturity bonds would require higher spreads.
ormaturity bondsshow
theto have
relationship
betweencredispread
and maturi
ty.cally
Because
l
o
nger
tend
wi
d
er
spreads,
t
curves
are
typi
upward sloping.
Bond performance
is credit
positivelspreads.
y affected
by narrowing
credit
spreads
and negativel
y
affected
by
widening
To
enhance
bond
portfolio
performance,
active
bond managers
forecastbondspreadportfoli
changeso. and expected credit losses for individual
issues
held and forneedthetooverall
Credit curves
Page 170
spread curves
©2012 Kaplan, Inc.
Study Session 1 6
Cross-Reference to CFA Institute Assigned Reading #59 - Fundamentals o f Credit Analysis
Example: Impact on return
AnThis8-year
semiannual-pay
corporate
bond
wi
t
h
a
5.
7
5%
coupon
i
s
pri
c
ed
at
$108.
3
2.
bond'bys75duration
and reported
convexi
ty are 6.upgrade.
4 and 0.Estimate
5. The bond'
s creditimpact
spread
narrows
basis
points
due
to
a
credit
rating
the
return
with and without the convexity adjustment.
Answer:
return impact (without convexity adjustment) -- 6.modifi
ed0duration
D.spread
4
-0.
075
0.0.00480
48 or 4.80%
return impact with convexity adjustment
- modified duration D.spread + _!_2 convexity (D.spread)2
-6.4 -0.0075 _!_2 (50.0) (-0.0075)2
0.0480 + 0.0014
0.0494 or 4.94%
Notice that convexity needed to be corrected to match the scale of duration.
We
can calculate
change inadjustment.
the bond's price from the information given to
illustrate
the needtheforactual
the convexity
Beginning yield to maturity:
NCPT= 16; PMT
= 5.75 I 2 = 2. 8 75; FV = 100; PV = -108. 3 2;
1/Y = 2.25
2 = 4.50
Yield to maturity after upgrade: 4. 5 0 -0.75 = 3.75%
Price after upgrade:
1/Y = 3.75 I 2 = 1.875; CPT PV = -113.71
The
bondisprice
is an intcrease
of (113.71 I 108.32) - 1 = 4.98%.
The calculated
approximation
closerofwi$113.71
th the convexi
y adjustment.
�
�
X
�
x
�
X
�
X
�
+
X
X
�
�
--t
X
--t
©20 12 Kaplan, Inc.
Page 1 7 1
Study Session 1 6
Cross-Reference to CFA Institute Assigned Reading #59
-
Fundamentals o f Credit Analysis
LOS 59.j: Explain special considerations when evaluating the credit of high
yield, sovereign, and municipal debt issuers and issues.
CFA ® Program Curriculum, Volume 5, page 650
High Yield Debt
Hignhgyield
ores. These bonds are alsocorporate
bonds arebecause
rated below
Baa3/BBB
by credivedt
rati
agenci
cal
l
ed
of
their
higher
percei
credit risk.
Reasons for non-investment grade ratings may include:
. history.
HiUnproven
gh leverageoperating
Lowghorsensinegati
ve tofreebusiness
cash flocycles
w. .
HiLow
t
ivity
conficompetitive
dence in management
.
Unclear
advantages
.
Large off-balance-sheet
Industry
in decline . liabilities .
Because
hi
g
h
yield
bonds
have
higher
default
risk
than
investment
grade
bonds,
credi
t
anal
ystsinclude
must paytheimore
attention
to lossprojections,
severity. Special
considerations
for high
yield
bonds
r
liqui
d
i
t
y,
fi
n
ancial
debt
structure,
corporate
structure,
and covenants.
Liquidity
or avaitolability
of cashborrowings,
is critical forandhiavaigh lyield
issuers.tendHighto yield
issuers
have
limited
access
additional
able
funds
be
more
expensi
ve forcanhighquickly
yield issuers.
Bad
company-specifi
cmarkets.
news andMany
diffichiultghfinancial
market
conditions
dry
up
the
liquidity
of
debt
yield
issuers are privately owned and cannot access public equity markets for needed funds.
Analysts focus on six sources of liquidity (in order of reliability):
1. Balance sheet cash.
2. Working capital.
3. Operating cash flow (CFO).
4. Bank credit.
5. Equity issued.
6. Sales of assets.
For
yielddueissuerwithin
with afewshortor unreliable
sources
of liquidity,
signifidefault.
cant amounts
ofoutdebtaofhigh
coming
ti
m
e
frame
may
indicate
potential
Running
cash with
accesshighto external
financing
anceyielor dservice
existing
the primary
reasonnowhy
yield issuers
default.to Forrefinhigh
financial
firmsdebt
thatis
non-investment grade
junk bonds
•
•
•
•
•
•
•
•
Liquidity.
Page 172
©2012 Kaplan, Inc.
Study Session 1 6
Cross-Reference to CFA Institute Assigned Reading #59 - Fundamentals o f Credit Analysis
are highlyislevered
liquidity
critical.and depend on funding long-term assets with short-term liabilities,
Projforecting
futurein earnings
and cash flows,andincluding
stress are
scenari
o
s
and
accounting
changes
capital
expenditures
working
capital,
important for revealing potential vulnerabilities to the inability to meet debt payments.
High
yield
i
s
suers'
capital
structures
often
include
different
types
of
debt
with
severaltypical
levelslyofinclseniority
and hence
varying
levelslienof potential
loss unsecured
severity. Capital
structures
u
de
secured
bank
debt,
second
debt,
senior
debt,may
subordinated
debt,
and
preferred
stock.
Some
of
these,
especially
subordi
n
ated
debt,
be convertible to common shares.
Aancredit
anal
y
st
wil
l
need
to
calculate
l
e
verage
for
each
level
of
the
debt
structure
when
issuer has multiple layers of debt with a variety of expected recovery rates.
High yieldarecompanies
for which secured
bank
debt
is a tohighborrow
proportion
of theincapital
structure
said
to
be
and
have
less
capacity
from
banks
filiknelancially
stressfulandperiods.
top-heavy debt
capitalissues.
structures are more
y to default
have lowerCompanies
recoverythat
rateshavefor unsecured
and
Two
European high yield companies in the same industry have the following financial
information:
Financial projections.
Debt structure.
top heavy
Example: Debt structure
In € million
leverage
A
B
100.0
50.0
Interest expense
40.0
20.0
EBITDA
85.0
42.5
Secured bank debt
500.0
125.0
Senior unsecured debt
200.0
50.0
50.0
200.0
Cash
Convertible bonds
1. Calculate total leverage through each level of debt for both companies.
2. Calculate net leverage for both companies.
3. Comment on which company is more attractive to an unsecured debt investor.
©20 12 Kaplan, Inc.
Page 173
Study Session 1 6
Cross-Reference to CFA Institute Assigned Reading #59 - Fundamentals o f Credit Analysis
Answer:
Secured debt leverage:
secured debt/EBITDA
Senior unsecured leverage:
(secured + senior
unsecured debt)/EBITDA
Total debt leverage:
total debt/EBITDA
Net leverage:
(total debt - cash)/
EBITDA
A
B
500.0 I 85.0 = 5.9x
125.0 I 42.5 = 2.9x
(500.0
+
(500.0
200.0) I 85.0 = 8.2x
+ 200.0 + 50.0) I
85.0 = 8.8x
(750.0 - 1 00.0) I 85.0 = 7.6x
( 1 25.0
+
(125.0
50.0) I 42.5 = 4 . lx
+ 50.0 + 200.0) I
42.5= 8.8x
(375.0 - 50.0) I 42.5 = 7.6x
Company
B
has
a
l
o
wer
secured
debt
leverage
rati
o
than
Company
A,
whi
l
e
total
and
net leverage
ratiosit iares lessabout
theheavysame.andCompany
Bsomeis more
attractito vborrow
e to unsecured
debt
holders
because
top
may
have
capacity
from
banks,
which
suggests
a
lower
probability
of
default.
If
i
t
does
default,
Company
B
may
have
a higherallypercentage
availablebondsto unsecured
holders
than Company A,
especi
if holders ofof assets
convertible
have exercidebt
sed thei
r options.
Many
high-yield
companies
use aofholding
company
structure.
A
parent
company
recei
v
es
di
v
idends
from
the
earnings
subsidiaries
as
its
primary
source
of operatingto aincome.
Because ofarestructural
subordination,
subsidiaries'These
dividdiviendsdends
paidcan
upstream
parent
company
subordinate
to
interest
payments.
beforidebt
nsuffiholders
cient toofpaythetheparent
debt company.
obligations of the parent, thus reducing the recovery rate
Despite
structural
subordination,
a
parent
company'
s
credit
rating
may
be
superi
o
r
to
subsidifrom
aries'diratings
because the parent can benefit from having access to multiple cash
Hows
verse subsidiaries.
Someown
complex
corporate
structures
haveofintermedi
ate holdingstock.companies
that carryare
their
debt
and
do
not
own
100%
their
subsidiaries'
These
companies
typically a result of mergers, acquisitions, or leveraged buyouts.
Default
of
one
subsidiary
may
not
necessarily
result
in
cross
default.
Analysts
need
to
scrutinize
bonds'
indentures
and Tootheranallegal
documents
to fullanal
y understand
thecalculate
impact
ofleverage
complexratios
corporate
structures.
y
ze
these
companies,
y
sts
should
at each level of debt issuance and on a consolidated basis.
Important covenants for high yield debt include:
Changeto ofbuycontrol
put. (typical
This covenant
givesvaluedebtor hola value
ders sltheightly
rightabove
to requipar)reinthe
issuer
back
debt
l
y
for
par
the evently applies
of an acquisition.
For investment
grade
bonds,results
a change
of control
pur
typical
only
i
f
an
acquisition
of
the
borrower
i
n
a
rating
downgrade
to below investment grade.
Corporate structure.
Covenants.
•
Page 174
©2012 Kaplan, Inc.
Study Session 1 6
Cross-Reference to CFA Institute Assigned Reading #59 - Fundamentals o f Credit Analysis
Restricted
payments.
The covenant
protects lenders by limiting the amount of cash
that
may
be
pai
d
to
equity
holders.
Limitations
on
liens.
The
covenant
limits
the
amount
of
secured
debt
that
a
borrower
canincreases
carry. Unsecured
debtamount
holdersavailable
prefer theto issuer
toin have
less secured
debt,
which
the
recovery
them
the
event
ofasdefault.
Restricted
versus
unrestricted
subsidiaries.
Issuers
can
classifY
subsidiaries
restricted
unrestricted.
Restricted
subsidiaries'
cashThisflobenefi
ws andts assets
canofbeholding
used
tocompanies
service orthebecause
debt oftheirthedebt
parent
holding
company.
creditors
is pari passu
with thesubsidiaries
debt of restri
ctypically
ted subsidiaries,
rather
than
structurally
subordinated.
Restricted
are
the
holding
company'
s larger
subsidiaries
thatof subsidi
have signifi
cant assets.status.
Tax andA subsidiary'
regulatorys
issues
can
factor
into
the
classifi
c
ation
a
ry'
s
restriction
restriction status is found in the bond indenture.
Bank
covenants
are
often
more
restri
c
ti
v
e
than
bond
covenants,
and
when
covenants
are
violated,
banks canbanksblockcanadditional
loans until
the eviolation
If a violation
is not remedied,
trigger a default
by accel
rating theis fullcorrected.
repayment
of a loan.
In terms
ofinvestment
the factorsgrade
that affect
their
return,ty. Compared
high yield bonds
may be grade
viewedbonds,
as a
hybri
d
of
bonds
and
equi
to
investment
high
yi
e
ld
bonds
show
greater
price
and
spread
volatil
i
ty
and
are
more
highly
correlated
with the equity market.
Hisuchghasyielenterprise
d analysisvalcanue.inEnterprise
clude somevalue
of the(EV)sameis equity
techniques
as
equity
market
analysi
s
,
market
capitali
zationtraded,
plus
total
debt
minus
excess
cash.
For
high
yi
e
ld
companies
that
are
not
publicly
comparable
public
company
equity
data
can
be
used
to
estimate
EV.
Enterprise
val
u
e
analysis that
can imight
ndicateresula firtm'from
s potential
for additional
leverage,
orcanthecompare
potentialfirmscredibased
t
damage
a
leveraged
buyout.
An
anal
y
st
ona wider
the didifffference
erences between
their
EV/EBITDA
and
debt/EBITDA
ratios.
Firms
wi
t
h
therefore have less between
credit risthese
k. ratios have greater equity relative to their debt and
•
•
•
Sovereign Debt
Sovereign
debt
is
issued
by
national
governments.
Sovereign
credi
t
analysis
must
assess
both
government'
s abilitbecause
y to service
debt andusuall
its willingness
tolegaldo recourse
so. The assessment
ofnational
wilthelingness
i
s
important
bondholders
y
have
no
if a
government refuses to pay its debts.
Afivbasic
areas: for evaluating and assigning a credit rating to sovereign debt includes
e keyframework
1. and
Institutional
effectiveness
includes
successful
policymaking,
absence
of
corruption,
commitment to honor debts.
2. size
Economic
prospectsrelative
includetogrowth
demographics, income per capita, and
of government
the privtrends,
ate economy.
©20 1 2 Kaplan, Inc.
Page 175
Study Session 1 6
Cross-Reference to CFA Institute Assigned Reading #59
-
Fundamentals o f Credit Analysis
International
includes ithen international
country's foreign
external
debt, investment
and the statusposition
of its currency
markets.reserves, its
Fiscal flexibility
includesturesthetogovernment'
s servi
willicne,gnessas wellandasability
toinindebt
creaseas a
revenue
or
cut
expendi
ensure
debt
trends
percentage of GDP.
Monetaryobjflexibility
includes
thebeabillacking
ity to with
use monetary
policy
for domestic
5. economic
e
ctives
(thi
s
mi
g
ht
exchange
rate
targeting
or
membership in a monetary union) and the credibility and effectiveness of monetary
policy.
Credirating
t ratingandagencies
assigngn currency
each national
government
twongsratings:
(1) a localseparatel
currency
debt
(2)
a
forei
debt
rati
n
g.
The
rati
are
assigned
y
because
defaults
on
forei
g
n
currency
denominated
debt
have
historically
exceeded
those
currencyratingdebt.because
Foreigthen currency
debtmust
typicpurchase
ally has aforeign
higher default
ratein and
aonopen
lolocal
wermarket
credit
government
currency
theof
to
make
i
n
terest
and
principal
payments,
whi
c
h
exposes
it
to
the
risk
signifi
currencydomestic
depreciation.
In contrast,
localprinting
currencymore
debtmoney.
can be Rati
repaindgsby
raicansingdifcferanttaxes,aslocalmuch
controlling
spending,
or
simply
as two notches for local and foreign currency bonds.
Sovereign defaults
can
be caused
by events
suchin theas war,pricespolitical
icountry'
nstability,s export
severe
devaluation
of
the
currency,
or
large
declines
of
the
commodities. Access to debt markets can be difficult for sovereigns in bad economic
times.
3.
4.
Municipal Debt
Municipal
bonds
are
issued
by
state
and
local
governments
or
their
agencies.
Municipal
bonds usually have lower default rates than corporate bonds with same credit ratings.
Most
muni
c
ipal
bonds
can
be
classified
as
or
(GO) entity,
bonds whi
are cunsecured
by thebyfullitsfaitaxing
th credit
theGeneral
issuingobligation
governmental
h is to saybonds
they arebacked
supported
power.of
Unlikey soverei
gns, municipalities
cannot
use monetary
policy
to serviceability
their debt
and
usuall
must
balance
their
operating
budgets.
Municipal
governments'
to
service
their
general
obligation
debt
depends
ultimatel
y
on
the
local
economy
(i.
e
.
,
the
tax
base).
Economic
factors
todimensions
assess include
employment,
trends
in perdemographics,
capita income andand
perabilitycapita
debt,
tax
base
(depth,
breadth
and
stability),
to
attract
new
jobs
(location,
i
n
frastructure).
Credit
anal
y
sts
must
also
observe
revenuetovariability
through
economic
cycles.
Relns yandingsaloneshitaxes,
ghly vari
asignal
ble taxeshigthat
are
subject
economic
cycles,
such
as
capi
t
al
gai
can
her
credit
risk. Municipalitiesbenefits.
may have
long-termreporting
obligations
such as underfunded
pensionsareandalso
post-retirement
Inconsistent
requirements
for
municipalities
an ISSUe.
Revenue
c projects.
often tohaveservice
higherthecredit
than
GO bonds
bonds finance
becausespecifi
the project
is theRevenue
sole sourcebondsof funds
debt.risk
general obligation bonds
Page 176
©2012 Kaplan, Inc.
revenue bonds.
Study Session 1 6
Cross-Reference to CFA Institute Assigned Reading #59 - Fundamentals o f Credit Analysis
Analysis
revenueng corporate
bonds combines
using techniques
similar to
those forofanalyzi
bonds, analysis
with analofysistheofproject,
the financing
of the project.
Athekeyratiometric
forprojrevenue
bondsrevenue
is thetodebt
service coverage
ratio
(DSCR),payments
which is
of
the
e
ct'
s
net
the
required
interest
and
principal
onservithece bonds.
Many
revenue
bonds
incl
u
de
a
covenant
requiri
n
g
a
minimum
debt
protect thelowerlenders'
Lenderscreditworthiness).
prefer higher debt service
coveragecoverage
ratios, asratithiso torepresents
defaultinterests.
risk (better
©20 12 Kaplan, Inc.
Page 177
Study Session 1 6
Cross-Reference to CFA Institute Assigned Reading #59 - Fundamentals o f Credit Analysis
'
KEY CONCEPTS
LOS
Credit riskorrefers
to oftheprincipal.
possibilityCredit
that ariskborrower
fails toofmake
therisk,
scheduled
interest
payments
return
i
s
composed
default
which
is
the
probability
of default,
and losswillseveri
ty,thewhiborrower
ch is thedefaults.
portion ofThetheexpected
value oflossa bond
orprobability
loan a lender
or
i
n
vestor
lose
if
is the
of default multiplied by the loss severity.
Spread
the possibilitySpread
that aribond
loses valcredit
ue because
itson credit
spread wiridskensand
relmarket
ative riliquidity
toskitsis benchmark.
s
k
includes
migrati
or
downgrade
risk.
LOS
Corporate
debt
isassets
rankedandbyhasseniority
oroverpriority
of claims.
Secured
debt
is a directdebt
claim
onmay
specifi
c
fi
r
m
priority
unsecured
debt.
Secured
or
unsecured
be further ranked as senior or subordinated. Priority of claims may be summarized
as follows:
FiSecond
rst mortgage
or first lien.
or
subsequent
lien.
Senior
secured
debt. debt.
Senior
subordinated
Senior
unsecured
debt.
Subordinated
debt. debt.
Junior
subordinated
LOS
Issuer
credit nratings,
corporateapplfamily
reflectunsecured
a debt issuer'
creditworthi
ess andortypically
y to a ratings,
firm's senior
debt.s overall
Issue
credi
t
ratings,
or
corporate
credit
ratings,
refl
e
ct
the
credit
risk
of
a
specifi
c
debt
issue.
Notching
refers
to thecredit
practirating
ce oftoadjusting
an issue
creditandrating
upward
or of a
downward
from
the
issuer
reflect
the
seniority
other
provisions
debt issue.
LOS
Lenders
and
bond
investors
should
not
rely
exclusivel
y
on
credit
ratings
from
rating
agencies
forratithengsfolcanlowingchange
reasons:
Credit
during
the credit
life ofriska debtaccurately.
issue.
Rati
n
g
agencies
cannot
al
w
ays
judge
Firms areprices
subjectof bonds
to riskoften
of unforeseen
creditcrediratitnratings.
gs do not reflect.
Market
adjust moreeventsrapithat
dly than
59 .a
59.b
•
•
•
•
•
•
•
59.c
59 .d
•
•
•
•
Page 178
©2012 Kaplan, Inc.
Study Session 1 6
Cross-Reference to CFA Institute Assigned Reading #59 - Fundamentals o f Credit Analysis
59.e of traditional credit analysis are known as the four Cs:
Components
Capaci
t
y:
The
borrower'
s
ability
to
make
timel
y
payments
on
its
debt.
The value of assets pledged against a debt issue or available to creditors if
theCollateral:
issuer
defaults.
Covenants:
Provisi
o
ns
of
a
bond
i
s
sue
that
protect
credi
t
ors
by
requi
r
ing
or
prohibiting
actions by anof anissuer'issuer's management.
Character:
Assessment
past treatment of bondholders. s management, strategy, quality of earnings, and
59.f
Credi
t
analysts
use
profi
t
abi
l
i
t
y,
cash
fl
o
w,
and
leverage
and
coverage
ratios
to
assess
debt
issuers'Proficapacity.
tabitypi
litycrefers
to noperating
incomebefore
and interest
operatingandprofitaxest margin,
with operating
income
all
y
defi
ed
as
earnings
(EBIT).
Cash
fl
o
w
may
be
measured
as
earni
n
gs
before
interest,
taxes,
depreciation,
and
amortizati
oorn (EBITDA);
funds
from
operations (FFO); free cash flow before
divi
d
ends;
free
cash
fl
o
w
after
dividends.
Leverage
ratios
include
debt-to-capital,
debt-to-EBITDA,
and
FFO-to-debt.
Coverage ratios include EBIT-to-interest expense and EBITDA-to-interest expense.
59.gleverage, higher interest coverage, and greater free cash flow imply lower credit
Lower
risk
andinclude
a higherincredit
ratis totalng fordebta fiitsrm.obligations
When calculating
leverage ratios,pensions
analystsand
should
a
fi
r
m'
such
as
underfunded
off-balance-sheet financing.
For
a specifdebt,
ic debtandissue,highersecured
collaimplies
teral implies
risk compared
unsecured
seniority
lowerlower
creditcredit
risk compared
to lowerto
seniority.
59.h bond yields comprise the real risk-free rate, expected inflation rate, credit
Corporate
spread, maturity
liquidity
An issue's yield spread to its
benchmark
includespremium,
its crediandt spread
and premium.
liquidity premium.
The
l
e
vel
and
volatil
i
ty
of
yield
spreads
are
affected
by
the
credit
and
business
cycles,
the
performance
of and
financial
markets
as a iwhole,
availability
oftend
capitalto narrow
from broker­
dealers,
and
supply
demand
for
debt
s
sues.
Yield
spreads
when
theinvestor
creditdemand
cycle isforimprovi
n
g,
the
economy
i
s
expanding,
and
fi
n
ancial
markets
andthe
new
debt
issues
are
strong.
Yiel
d
spreads
tend
to
widen
when
credit
cycle,oftheneweconomy,
nanciaorl markets
are weakening,
the supply
debt issuesandisfiheavy
broker-dealer
capital is andinsuffiin cperiods
ient forwhen
market
making.
LOS
•
•
•
•
LOS
•
•
•
•
LOS
LOS
©20 12 Kaplan, Inc.
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Study Session 1 6
Cross-Reference to CFA Institute Assigned Reading #59
-
Fundamentals o f Credit Analysis
59.ican use duration and convexity to estimate the impact on return (the
Analysts
percentage change in bond price) of a change in credit spread.
For small spread changes:
return impact -duration �spread
For larger spread changes:
return impact -duration �spread 2_2 convexity (�spread)2
Hiincreases
gh 59.yieldjthebonds
are
more
likely
to
default
than
investment
grade
bonds,
which
importance
of estimati
ngperformance,
loss severity. Analysis
ofs corporate
high yieldanddebtdebtshould
focus
on
l
i
qui
d
i
t
y,
projected
fi
n
ancial
the
i
s
suer'
structures, and debt covenants.
Credit
riskityoftosovereign
debtforincludes
the issuing
country'
s sability
and willingness
todebt
pay.
Abil
pay
i
s
greater
debt
issued
i
n
the
country'
own
currency
than
for
issued
a foreign currency. Willingness refers to the possibility that a country refuses to
repay iints debts.
Analysis
ofongeneral
obligation
municipal
debt isandsimilar
to analonytaxsis ofrevenues.
sovereigAnalysis
n debt, of
focusing
the
strength
of
the
local
economy
its
effect
municipal
revenue
bonds
is
si
m
i
l
ar
to
anal
y
si
s
of
corporate
debt,
focusing
on
the
ability
of a project to generate sufficient revenue to service the bonds.
LOS
:=:;j
:=:;j
x
x
+
LOS
Page 180
©2012 Kaplan, Inc.
x
Study Session 1 6
Cross-Reference to CFA Institute Assigned Reading #59 - Fundamentals o f Credit Analysis
CONCEPT CHECKERS
1. A.Expected
lossrisk.can decrease with an increase in a bond's:
default
B.C. loss
severirate.
ty.
recovery
2. A.Absolofuthete priority of clprinciple.
aims in a bankruptcy might be violated because:
negotiatemusta dibefferent
outcome.
B.C. creditors
available funds
distributed
equally among creditors.
is ratidescribed
as issue
a difference
between a(n):
3. A."Notching"
issuer
credit
n
g
and
an
credi
t
rating.
B.C. company
average credit grade
rating.credit rating.
investmentcredit
graderating
creditandratianngindustry
and a non-investment
of thet ratifollngoagencies?
wing statements is
a limitation of relying on ratings
4. Which
from
credi
A.B. Credit
ratingsc riaresksdynami
cc. ult to rate.
Firm-specifi
are
diffi
C. Credit ratings adjust quickly to changes in bond prices.
o analtyy.sis is
used to assess a borrower's:
5. A.Raticapaci
C.B. character.
collateral.
6. A.HigherFFO/debt
credit riratio.
sk is indicated by a higher:
B.C. debt/EBITDA
EBITDNinterestratio.expense ratio.
Compared
tohave
othera lower:
firms in the same industry, an issuer with a credit rating of
7. AAA
should
A.B. FFO/debt
ratio.
operating
margin.
C. debt/capital ratio.
8. A.Creditthespreads
tend
to
wi
d
en
as:
credit cycle
improves.
B.C. economic
conditions
broker-dealers becomeworsen.
more willing to provide capital.
9. A.Compared
to
shorter
duration
bonds,
longer
duration
bonds:
lertbid-ask
spreads.spreads.
arehavelesmal
sslesssensicertainty
ive toregarding
credit
B.C. have
future creditworthiness.
pari passu
best
least likely
most likely
©20 12 Kaplan, Inc.
Page 1 8 1
Study Session 1 6
Cross-Reference to CFA Institute Assigned Reading #59
-
Fundamentals o f Credit Analysis
10. sovereign
One key difference
between sovereign bonds and municipal bonds is that
Issuers:
A.B. have
can print
money.
governmental
taxingconditions.
power.
C. are affected
by economic
Page 182
©2012 Kaplan, Inc.
Study Session 1 6
Cross-Reference to CFA Institute Assigned Reading #59 - Fundamentals o f Credit Analysis
CHALLENGE PROBLEM
Woden,
Inc., ibalance
s a highsheet
yield forbondtheissuer
th a credi
ng ofBa2/BB.
Woden presents
the following
mostwirecent
year t(irati
n millions
of dollars):
Cash
10
Accounts payable
10
Accounts receivable
15
Short-term debt
5
Inventories
...5.2
Current portion of long-term debt
_.2
18
80
Current liabilities
Land
10
Long-term bank loans
30
Property, plant, and equipment, net
85
Secured bonds
10
Current assetS
Goodwill
..22
Unsecured bonds
Non-current assets
120
Total long-term debt
Total assetS
200
Net pension liability
Total liabilities
Paid-in capital
Retained earnings
Total shareholders' equity
Total liabilities and equity
_.1.Q
60
_n
100
10
_..2.Q
100
200
For
the year,were
Woden'
earnings before interest, taxes, depreciation, and amortization
(EBITDA)
$45smillion.
For
fi
r
ms
i
n
Woden'
s
i
n
dustry,
credit
rating
standards
for
an
investment
grade
(Baa3/
BBB-)(based
creditonrating
includeofafinanci
debt-to-EBITDA
ratio
lessOnthan
1.8x and cala debt-to-capital
ratio
all
sources
n
g)
less
than
40%.
a
conference
l wiinvestment
th analysts,
Woden'
s
management
states
that
they
believe
Woden
shoul
d
be
upgraded
to
grade, based on its debt-to-EBITDA ratio of l.Sx and its debt-to-capital ratio of 34%.
Why might a credit analyst disagree with management's assessment?
©20 12 Kaplan, Inc.
Page 183
Study Session 1 6
Cross-Reference to CFA Institute Assigned Reading #59
-
Fundamentals o f Credit Analysis
ANSWERS - CONCEPT CHECKERS
Page 184
1.
C
An increase in the recovery rate means that the loss severity has decreased, which
decreases expected loss.
2.
B
A negotiated bankruptcy settlement does not always follow the absolute priority of
claims.
3.
A
Notching refers to the credit rating agency practice of distinguishing between the credit
rating of an issuer (generally for its senior unsecured debt) and the credit rating of
particular debt issues from that issuer, which may differ from the issuer rating because of
provisions such as seniority.
4.
c
Bond prices and credit spreads change much faster than credit ratings.
5.
A
Ratio analysis is used to assess a corporate borrower's capacity to repay its debt
obligations on time.
6.
B
A higher debt/EBITDA ratio is sign of higher leverage and higher credit risk. Higher
FFO/debt and EBITDA/interest expense ratios indicate lower credit risk.
7.
c
A low debt/capital ratio is an indicator of low leverage. An issuer rated AAA is likely to
have a high operating margin and a high FFO/debt ratio compared to its industry group.
8.
B
Credit spreads widen as economic conditions worsen. Spreads narrow as the credit cycle
improves and as broker-dealers provide more capital to bond markets.
9.
c
Longer duration bonds usually have longer maturities and carry more uncertainty of
future creditworthiness.
10. A
Sovereign entities can print money to repay debt, while municipal borrowers cannot.
Both sovereign and municipal entities have taxing powers, and both are affected by
economic conditions.
©2012 Kaplan, Inc.
Study Session 1 6
Cross-Reference to CFA Institute Assigned Reading #59 - Fundamentals o f Credit Analysis
ANSWERS - CHALLENGE PROBLEM
The debt ratios calculated by management are based on the firm's short-term and long-term debt:
Total debt
=
5
+
Debt/EBITDA
Debt/capital
=
3
=
+
30
+
68 I 45
6 8 I 200
10
=
=
+
20
68
=
1.5x
34o/o
A credit analyst, however, should add Woden's net pension liability to its total debt:
Debt + net pension liability
Adjusted debt/EBITDA
Adjusted debt/capital
=
=
=
68
+
90 I 45
90 I 200
22
=
=
=
90
2.0x
45o/o
Additionally, a credit analyst may calculate what the debt-to-capital ratio would be ifWoden
wrote down the value of its balance sheet goodwill and reduced retained earnings by the same
amount:
Adjusted capital
=
200 - 25
=
175
Adjusted debt I adjusted capital
=
9 0 I 175
=
5 1 o/o
These adjustments suggest Woden does not meet the requirements for an investment grade credit
rating.
©20 12 Kaplan, Inc.
Page 185
SELF-TEST : FIXED INCOME INVESTMENTS
14 questions, 21 minutes
1. Anin itestimate
of
the
price
change
for
an
option-free
bond
caused
by
a
1%
decline
s yieldthat:to maturity based only on its modified duration will result in an
answer
A.B. iiss too
small.
C. maytoobelarge.
too small or too large.
2. Three
companies
the same industry have exhibited the following average
ratios over
a 5-yearinperiod:
5-Year Averages
Alden
Barrow
Collison
Operating margin
1 3 .3%
1 5.0%
20.7%
Debt!EBITDA
4.6x
0.9x
2.8x
EBIT/Interest
3.6x
8.9x
5.7 x
FFO/Debt
12.5%
14.6%
1 1 .5 %
Debt/Capital
60.8%
23.6%
29.6%
Based onlycrediont ratitheninformation
given, the company that is expected to have the
highest
g
is:
A.B. Alden.
Barrow.
C. Collison.
3. Which statement about the theories of the term structure of interest rates is
A. sloped.
Under the liquidity preference theory, the yield curve will be positively
B. Amarket
yield segmentation
curve that slopestheoryup and
then
down
(humped)
is consistenttheory.
with the
but
not
wi
t
h
the
pure
expectations
C. bonds
Evidencesupports
that lifthee insurance
companies havetheory.
a strong preference for 30-year
market segmentation
4. Which
of the following is
a common form of external credit
enhancement?
A.B. APortfolio
insurance.
corporate
guarantee.
C. A letter of credit
from a bank.
bond wiofth6anandembedded
put
option
has
a
modifi
e
d
duration
of
7,
an
effecti
v
e
5. Aduration
a convexity
of 62. 5 . If interest rates rise 25 basis points, the
bond'
s
price
wi
l
change
by
A.B. 1.1.50%.
46%.
1.54%.
most
accurate?
least likely
approximately:
c.
Page 186
©2012 Kaplan, Inc.
Self-Test: Fixed Income Investments
of thebyfoll50obasis
wing points
bonds would
be the best one to own if the yield curve
6. Which
shifts
down
at
all
maturities?
A.B. 4-year
8%,
8%
YTM.
C. 5-year
5-year 8%,
8.5%,7.58%% YTM.
YTM.
ofy onthea folldebtowisecurity?
ng provisions would
decrease the yield to
7. Which
maturi
t
A.B. Conversion
Call option. option.
C. Cap on a floating-rate security.
8. theOtherbondthingsis rated:
equal, a corporate bond's yield spread is likely to be volatile if
A.B. AAA
AA withwith5 3years
totomaturity.
years
C. BBB with 15 years tomaturity.
maturity.
9. The
effects
ofwith
a decrease
in interestoption
rate (yiandeld)onvolatility
on thewith
marketa putyieoption
ld of a
debt
security
a
prepayment
a
debt
security
are Prepaymenta(n):option Put option
Decrease
A.B. Decrease
Increase
Increase
Decrease
C. Decrease
A
has
an
embedded
option,
a
nominal
yi
e
ld
spread
to
Treasuries
of
1.6%,
10. Bond
aB zero-volatil
ityto spread
ofexcept
1.4%,that
anditandoesoption-adjusted
spread
of 1.2%.
Bondhas a
is
identical
Bond
A
not
have
the
embedded
option,
nomioption-adjusted
nal yield spreadspread
to Treasuries
ofThe1.4%, a zero-volatility
spread ofin1.3Bond
%, andA,
anand
of
1.
3
%.
option
embedded
the bond thatoption
is the better valBetter
ue, are:value
Embedded
A.B. Put
Bond
A
Bond
Call
C. Call
Bond AB
most likely
most
most likely
most likely
©20 12 Kaplan, Inc.
Page 187
Self-Test: Fixed Income Investments
11. Atobank
loantwodepartment
is tryi
ngIftocurrent
determiimplied
ne the Treasury
correct rateeffectiforvae2-year
loan
be
made
years
from
now.
annual
spot
rates
are:
1-year
= 2%, 2-year = 3%, 3-year = 3.5%, 4-year = 4. 5 %, the base
forward rate for the loan before adding a risk premium is to:
A.B.(risk-free)
4.5%.
6.9.00%.%.
to mortgage passthrough securities, CMOs created from them
12. Compared
have:
A.B. greater
less prepayment
ri
s
k.
C. a differentaverage
claimyields.
to the mortgage cash flows.
13. A.Thecanarbitrage-free
approach
to bondsecurities.
valuation
only
be
applied
to
Treasury
B.C. requires
each
cash
fl
o
w
to
be
discounted
at
a
rate
specifi
c
to
its
time
period.
that value
discounting
each cash flow at the yield to maturity must result in
theshowscorrect
for a bond.
14. Which
of thewithfollinvesting
owing statements
describes a form of risk
associated
in
fi
x
ed
income
securities?
A.B. Credit
risk hasequal,
only atwobondcomponents,
defaulttoriansk and
downgrade
risk.
Other
things
is
more
valuable
i
n
vestor
when
it
has less
liquidi
t
y
risk.
C. riBonds
are callable,
amortizing
more reinvestment
sk thanthatotherwise
equivprepayabl
alent bondse, orwithout
thesehave
features.
closest
c.
most
likely
most likely:
least accurately
Page 1 8 8
©2012 Kaplan, Inc.
Self-Test: Fixed Income Investments
SELF-TEST ANSWERS: FIXED INCOME INVESTMENTS
1.
A
Duration is a linear measure, but the relationship between bond price and yield for an
option-free bond is convex. For a given decrease in yield, the estimated price increase
using duration alone will be smaller than the actual price increase.
2.
B
Four of the five credit metrics given indicate that Barrow should have the highest credit
rating of these three companies. Barrow has higher interest coverage and lower leverage
than Alden or Collison.
3.
C
The market segmentation theory is based on the idea that different market participants
(both borrowers and lenders) have strong preferences for different segments of the yield
curve. If expectations are that future short-term interest rates will be falling enough,
then the yield curve could be downward sloping even given rhar there is an increasing
premium for lack of liquidity at longer maturities. A humped yield curve is consistent
with expectations that short-term rates will rise over the near term and then decline.
4.
A
External credit enhancements are financial guarantees from third parties that generally
support the performance of the bond. Portfolio insurance is not a third party guarantee.
5.
A
Effective duration must be used with bonds that have embedded options.
�p
=
(-) (ED)(�y)
+
.6.P (-) (6)(0.0025)
-1.461%
=
(C)(�y) 2
+
(62.5)(0.0025) 2
=
-0 . 0 1 5
+
0.00039
=
-0.014610% or
6.
B
The bond with the highest duration will benefit the most from a decrease in rates. The
lower the coupon, lower the yield to maturity, and longer the time to maturity, the
higher will be the duration.
7.
B
A conversion provision is an embedded option that favors the buyer, not the issuer, so
buyers will accept a lower YTM with a conversion option. Call options and caps favor
the issuer and increase the YTM that buyers will require.
8.
C
Spread volatility is typically greatest for lower quality and longer maturities. The BBB
rated 15 -year corporate bond has the lowest credit quality and longest maturity of the
three choices.
9.
B
A decrease in yield volatility will decrease the values of embedded options. The security
holder is short the prepayment option. The decrease in the value of the prepayment
option increases the value of the security, and the required yield will decrease. The
security holder is long the pur option so the value of a putable bond will decrease with a
decrease in yield volatility and the required yield will increase.
10. C
Since the OAS is less than the Z-spread for Bond A, the effect of the embedded option is
to increase the required yield, so it must be a call option and not a put option. The OAS
is the spread after taking out the effect of the embedded option. Since the OAS is higher
for Bond B, it represents the better value after adjusting for the value of the call in Bond A.
©20 1 2 Kaplan, Inc.
Page 189
Self-Test: Fixed Income Investments
11. B
The forward rate is [ 1 .045 4 I 1 .03 2] 112 - 1
[4.5(4) - 3(2)]/2 6.
=
6.02%, or use the approximation
=
Page 190
12. C
CMOs are created to have different claims to the cash flows (principal, scheduled
repayments, prepayments) than those of the underlying mortgage passthrough
securities. On average, the yield will likely be lower on the CMO, since the reason to
create them is to lower overall funding costs. They can have more or less prepayment
risk, but on average will have the same prepayment risk as the underlying MBS.
13. B
The arbitrage-free valuation approach discounts each cash flow at a discount rate specific
to its maturity. For Treasury securities these discount rates are theoretical Treasury spot
rates. For non-Treasury securities, these discount rates are Treasury spot rates plus a
spread to account for liquidity risk, credit risk, and any other relevant risks that differ
from those of a Treasury bond of similar maturity.
14. A
Even if a bond does not default and is not downgraded, it still faces credit spread risk as
the premium in the market for the bond's credit risk may increase. Lower liquidity risk
(i.e., higher liquidity) is preferred by investors, reduces a bond's required rate of return,
and increases its value, other things equal. Reinvestment risk is higher for callable,
prepayable, or amortizing bonds as all these features lead to a greater probability of
receiving principal repayment earlier, which means there are more funds to be reinvested
over the life of the bond.
©2012 Kaplan, Inc.
The following is a review of the Derivatives principles designed to address the learning outcome
statements set forth by CFA Institute. This topic is also covered in:
DERIVATIVE MARKETS AND
INSTRUMENTS
Study Session 1 7
EXAM FOCUS
This
topic revieDerivatives-specifi
w contains introductory
material
forterminology
the upcomingarerevipresented
ews ofspecifi
c types
ofinformation
derivatives.
c
defi
n
itions
and
al
o
ng
wi
t
h
vativesconcepts
markets.thatUponunderlie
completion
ofvthies sandreviethew, candidates
should
beframework.
familiar There
wiabout
th theideri
basic
derivati
general
arbi
tragethe
s
li
t
tle
contained
i
n
thi
s
revi
e
w
that
wil
l
not
be
elaborated
upon
i
n
five reviews that follow.
LOS 60.a: Define a derivative and distinguish between exchange-traded and
over-the-counter derivatives.
CFA® Program Curriculum, Volume 6, page 5
derivative is a security that its value from the value or return of another asset or
security.
physical exchangederivatives
exists foraremanystandardi
optionszedcontracts
contracts.
Exchange-traded
and backedandbyfutures
a clearinghouse.
and
are
custom
instruments
and
are
traded/created
by
deal
e
rs
in
a
market
with no central location.
dealeraremarket
with
no centralmarkets
locationandiseach
referred
to as isanwith
over-the-counter
market.
They
l
a
rgel
y
unregulated
contract
acounterparty
counterparty,doeswhinotch may
owner of a derivative to default risk (when the
honorexpose
their thecommitment).
Some trade in the over-the-counter market, notably bond options.
A
derives
A
Forwards
swaps
A
options
LOS 60.b: Contrast forward commitments and contingent claims.
CFA® Program Curriculum, Volume 6, page 6
forwardForward
commitment
is a legallinclude
y binding
promise
to perform
some
actionandin theswaps.
future.
commitments
forward
contracts,
futures
contracts,
Forward
contracts
and
futures
contracts
can
be
wri
t
ten
on
equities,
indexes,
bonds,
physical assets, or interest rates.
contingent
claim
i
s
a
clai
m
(to
a
payoff)
that
depends
on
a
particular
event.
Options
arefutures,
contingent
claimshavethatpayments
depend that
on aarestockmadepricebasedat some
le forwards,
and swaps
on a future
price ordate.rateWhi
outcome
A
A
©20 12 Kaplan, Inc.
Page 1 9 1
Study Session 17
Cross-Reference to CFA Institute Assigned Reading #60
-
Derivative Markets and Instruments
whether
the movement
isbroken
up or down,
contingent
claims
onlyorrequi
rratee a payment
if a It
certain
threshol
d
pri
c
e
is
(e.
g
.
,
i
f
the
price
is
above
the
i
s
below
takes two options to replicate a future or forward.
Y).
X
LOS 60.c: Define forward contracts, futures contracts, options {calls and puts),
and swaps and compare their basic characteristics.
CFA® Program Curriculum, Volume 6, page 6
Inasseta or a security at a specifi
one party
agrees
to
buy,
and
the
counterparty
to
sell,
a
physical
date inhastheafuture.
the asset increases, the buyerc(atpricetheonolder,a specilowerfic price)
gain, andIf thethefuture
seller aprice
loss.of
Amain differences wiisthaforwards
forward contract
that is standardized
and
exchange-traded.
The
are
that
futures
are
traded
i
n
an
active
secondary
market,
arelosses.regulated, backed by the clearinghouse, and require a daily settlement of gains and
Ashort-termis a (flseries
of
forward
contracts.
In
the
simplest
swap,
one
party
agrees
to
pay
the
oating)
rate(fixofed)interest
oninterest
some iprincipal
amount,
and
the counterparty
agrees
to
pay
a
certain
rate
of
n
return.
Swaps
of
different
currencies and
equity returns are also common.
Anthe option
tohasbuyan an asset attoa particular
priceat isthetermed
a call price, iThe
sellcallerbuyer
of
option
sell
the
asset
agreed-upon
f
the
chooses to exercise the right to buy the asset.
Anoptionoptionhas toansell an assettoatpurchase
a particularthe price
is termed
a price,Theif thesellerputofbuyer
the
asset
at
the
agreed-upon
chooses to exercise the right to sell the asset.
forward contract,
futures contract
swap
option.
obligation
put option.
obligation
Professor's Note: To remember these terms, note that the owner ofa call can "call
the asset in" (i. e., buy it); the owner of a put has the right to "put the asset to"
the writer of the put.
LOS 60.d: Describe purposes of and controversies related to derivative markets.
CFA® Program Curriculum, Volume 6, page 17
The
is that they
are "too riBecause
sky," especially
to investors
winvolth vlimied inted
knowl
e
dge
of
someti
m
es
complex
instruments.
of
the
high
l
e
verage
i
derivatives payoffs, they are sometimes likened to gambling.
The
markets are that they:
Provide
price
information.
AlReduce
low ritransactions
sk to be managed
costs.and shifted among market participants.
criticism ofderivatives
benefits ofderivatives
•
•
•
Page 192
©2012 Kaplan, Inc.
Study Session 1 7
Cross-Reference to CFA Institute Assigned Reading #60 - Derivative Markets and Instruments
LOS 60.e: Explain arbitrage and the role it plays in determining prices and
promoting market efficiency.
CFA® Program Curriculum, Volume 6, page 20
Arbitrage
is
an
important
concept
i
n
val
u
ing
(pricing)
deri
v
ati
v
e
securities.
In
its
purest
sense, arbia portfolio
trage is riskless.
Ifthat
a return
greatera certain
than the(riskl
risk-free
rate canthenbe anearned
byrage
holding
of
assets
produces
e
ss)
return,
arbi
t
opportunity exists.
Arbitrage
opportunities
arisesupply
whenandassetsdemand
are mispriced.
Tradi
ngasset
by arbitrageurs
willcient
continue
until
they
affect
enough
to
bring
prices
to
effi
(no-arbitrage) levels.
There
are
two
arbitrage
arguments
that
are
particularly
useful
i
n
the
study
and
use
of
derivatives.
The
fiflrostwsisinbased
on the regardless
law of futureTwoevents,
securishould
ties orhave
portfolios
thatprice.
have identical
cash
the
future,
the
same
IfB.AYouand
Bhavehaveantheimmediate
identicalprofit,
futureandpayoffs,
and
A
is
priced
l
o
wer
than
B,
buy
A
and
sel
l
the payoff on A will satisfy the (future) liability of being
short on B.
The secondintypea portfolio
of arbitrage
is lused
where
two securities
wia portfolio
th uncertainconsisting
returnsofcanA beand
combined
that
wi
l
have
a
certain
payoff.
If
Bcondition
has a certain
payoff,inthethatportfol
io shouldreturnyieldoftheA andrisk-free
rate. Ifis this
no-arbitrage
is
violated
the
certain
B
together
higher
than
the
ririssk-free
rate,
anbuyarbithetrage
opportunity
exists.earnAnarbiarbitrageur
couldwhenborrow
at the payoff
k-free
rate,
A
B
portfolio,
and
t
rage
profits
the
certain
occurs.
The
payoff
wi
l
l
be
more
than
i
s
requi
r
ed
to
pay
back
the
l
o
an
at
the
risk-free
rate.
of one price.
+
Professor's Note: We will discuss arbitrage further in our review of options.
©20 1 2 Kaplan, Inc.
Page 193
Study Session 17
Cross-Reference to CFA Institute Assigned Reading #60
-
Derivative Markets and Instruments
KEY CONCEPTS
LOS
60.a
A derivative has a value that is derived from the value of another asset or interest rate.
Exchange-traded
derivatives,
notably
futures
and
some
options,
are
traded
i
n
centralized
locations and are standardized, regulated, and default risk free.
Forwards
and
swaps
are
customized
contracts
(over-the-counter
deri
v
ati
v
es)
created
by
dealers andmarkets
by financial
institutions.
There is very
of these contracts in
secondary
and default
(counterparty)
risk limited
must betrading
considered.
LOSforward
60.b commitment is a binding promise to buy or sell an asset or make a
Apayment
i
n
the
future.
Forward
contracts,
futures
contracts,
and
swaps
are
al
l
forward
commitments.
A(e.contingent
claim
is
an
asset
that
has
value
only
i
f
some
future
event
takes
pl
a
ce
g., asset price is greater than a specified price). Options are contingent claims.
LOS
60.ccontracts obligate one party to buy, and another to sell, a specific asset at a
Forward
predetermined price at a specific time in the future.
Swaps
contracts
are equivalent
currencies,
or equity
returns. to a series of forward contracts on interest rates,
Futuresrequire
contracts
are much likeof anyforward
and
daily settlement
gainscontracts,
or losses. but are exchange-traded, quite liquid,
Apredetermined
call option giprice
ves theatholder
not the obligation, to buy an asset at a
some titheme right,
in thebutfuture.
Apredetermined
put option giprice
ves theatholder
not the obligation, to sell an asset at a
some titheme right,
in thebutfuture.
LOS
60.d markets are criticized for their risky nature. However, many market
Derivative
participants use derivatives to manage and reduce existing risk exposures.
Derivative
securities
play
an
important
role
i
n
promoting
effi
c
ient
market
prices
and
reducing transaction costs.
LOS
60.ss arbi
e trage refers to earning more than the risk-free rate of return with no risk, or
Riskl
e
earning an immediate gain with no possible future liability.
Arbi
be expected
forcefuture
the prices
securitiesoforfuture
portfolios
to betrage
equalcanif they
have thetosame
cash flofowstworegardless
events.of securities
Page 194
©2012 Kaplan, Inc.
Study Session 1 7
Cross-Reference to CFA Institute Assigned Reading #60 - Derivative Markets and Instruments
CoNCEPT CHECKERS
1. AWhich
of
the
foll
o
wi
n
g
describes
a
deri
v
ati
v
e
security?
A.B.derihasalwvatiaysnove:increases
risdate.
k.
expi
r
ati
o
n
C. has a payoff based on another asset.
2. Which of the following statements about exchange-traded derivatives is
A.B. They
are
liquid.
They arecarrystandardi
contracts.risk.
C. They
significzanted default
3. A customized agreement to purchase a certain T-bond next Thursday for $1,000
A.B. ana futures
option.contract.
C. a forward commitment.
is: regulated.
4. AA.swap
highly
of forward
B.C. thea series
exchange
of onecontracts.
asset for another.
givselles theat aholder:
5. A.A calltheoption
right
to
speci
f
i
c
price.
right to buyto atsella atspecific
C.B. antheobligation
a certaiprice.
n price.
6. Arbitrage
prevents:
A.B. market
effi
c
iency.
higherwitthan
the risk-free
return. at different prices.
C. profit
two assets
h identical
payoffsratefromof selling
are
to provide or improve:
7. A.Derivatives
liquidi
t
y.
B.C. price
information.
inflation reduction.
most accurately
least
accurate?
lS:
least likely
©20 12 Kaplan, Inc.
Page 195
Study Session 17
Cross-Reference to CFA Institute Assigned Reading #60
-
Derivative Markets and Instruments
ANSWERS - CoNCEPT CHECKERS
Page 196
1.
C
A derivative's value is derived from another asset.
2.
C
Exchange-traded derivatives have relatively low default risk because the clearinghouse
stands between the counterparties involved in most contracts.
3.
C
This non-standardized type of contract is a forward commitment.
4.
B
A swap is an agreement to buy or sell an underlying asset periodically over the life of the
swap contract. It is equivalent to a series of forward contracts.
5.
B
A call gives the owner the right to call an asset away (buy it) from the seller.
6.
C
Arbitrage forces two assets with the same expected future value to sell for the same
current price. If this were not the case, you could simultaneously buy the cheaper asset
and sell the more expensive one for a guaranteed riskless profit.
7.
C
Inflation is a monetary phenomenon, unaffected by derivatives.
©2012 Kaplan, Inc.
The following is a review of the Derivatives principles designed to address the learning outcome
statements set forth by CFA Institute. This topic is also covered in:
FORWARD MARKETS AND CONTRACTS
Study Session 1 7
EXAM FOCUS
This
topic
revi
e
w
introduces
forward
contracts
in
general
and
covers
the
characteristi
c
s
ofmaterial
forward, andcontracts
ondvarious
fintime
ancialto securities,
as This
well asmaterial
interestonrates.
It iscontracts
not easy
you
shoul
take
the
l
e
arn
i
t
well.
forward
provides
a
good
basis
for
futures
contracts
and
many
of
the
characteristics
of
both
types
the same. Take the time to understand the intuition behind the valuation
ofof contracts
forward rateare agreements.
FO RWARD CONTRACTS
Ato forward
contract
i
s
a
bil
a
teral
contract
that
obl
i
gates
one
party
to
buy
and
the
other
sell aly,specifi
c quantity
oftheancontract
asset, at pays
a set anything
price, on toa specific
datethe contract.
in the future.
Typical
neither
party
to
get
into
If theto buy
expected
future
price
of
the
asset
i
n
creases
over
the
life
of
the
contract,
the
ri
g
ht
atnegati
thevcontract
price
will
have
positi
v
e
value,
and
the
obli
g
ation
to
sel
l
wil
l
have
an
equal
e value.
Ifthetherigfuture
price(atofantheabove-market
asset falls below
thewillcontract
price,positive
the result
iThe
s opposite
and
ht
to
sell
pri
c
e)
have
the
value.
parties
may
enter
i
n
to
the
contract
as
a
speculation
on
the
future
price.
More
often,
a party seeks
to enter
into a forward
contract
tothehedgefuturea riprice
sk it already
has. itTheplansforward
contract
i
s
used
to
el
i
minate
uncertainty
about
of
an
asset
to buy
orhavesellexisted
at a laterfor date.
Forward
contracts
on
physical
assets,
such
as
agricultural
products,
The Level
however,andfocuses
their (more
recent) use for ficenturies.
nancial assets,
such asI CPA
T-bills,curriculum,
bonds, equities,
foreignoncurrencies.
LOS 61 .a: Explain delivery/settlement and default risk for both long and short
positions in a forward contract.
CFA® Program Curriculum, Volume 6, page 28
The
to theposition
forwardandcontract
that
agrees toThebuyparty
the financial
or physical
assetthathas
aagrees
longparty
forward
i
s
cal
l
e
d
the
to
the
forward
contract
to sell or deliver the asset has a short forward position and is called the
We
illustrateandthesalemechani
cs of the bill.
basicNote
forward
contract
throughandanfutures
examplecontracts
based
onon T-bi
thewillpurchase
of
a
Treasury
that
whi
l
e
forward
usuallto make
y quotedthe inexampl
termse ofeasya discount
percentage
fromconventions
face value, weandwill
usecalculations
dollarlls areprices
to
fol
l
ow.
Actual
pricing
are among the contract characteristics covered later in this review.
long.
short.
©20 1 2 Kaplan, Inc.
Page 197
Study Session 17
Cross-Reference to CFA Institute Assigned Reading #61 - Forward Markets and Contracts
Considerbilla contract
underB 30whichdaysParty
Anowagreesat atoprice
buy ofa $1,$990.
000 Party
face value,
90-day
Treasury
from
Party
from
A
is
the
longwiland
Party
B
is
the
short.
Both
parties
have
removed
uncertainty
about
the
price
they
l
pay/recei
veshort
for themustT-bidelllivaterthethefuture
date.
Iflong
30 daysin exchange
from nowforT-bills
arepayment.
trading atIf
$992,
the
T-bill
to
the
a
$990
T-bills
are
trading
at
$988
on
the
future
date,
the
long
must
purchase
the
T-bill
from
the
short for $990, the contract price.
Each
party
to
a
forward
contract
i
s
exposed
to
default
risk
(or
counterparty
risk),
the
probabil
iforty that
the
other
party (the
counterparty)
wiinception
l not perform
as promised.
It is
unusual
any
cash
to
actually
be
exchanged
at
the
of
a
forward
contract,
unl
i
ke
futures
contracts
i
n
which
each
party
posts
an
initial
deposit
(margin)
as
a
guarantee of performance.
Atcontract
any point
in
time,
including
the
settl
e
ment
date,
only
one
party
to
the
forward
wiofll theowecontract
money, meani
ng that
side ofvaltheuecontract
has amount.
a negativFole value.
Thethe
other
si
d
e
wi
l
l
have
a
positive
of
an
equal
l
o
wing
example,
i
f
the
T-bill
price
i
s
$992
at
the
(future)
settlement
date
and
the
short
does
not
deliver the T-bill for $990 as promised, the short has defaulted.
LOS 61.b: Describe the procedures for settling a forward contract at
expiration, and how termination prior to expiration can affect credit risk.
CPA® Program Curriculum, Volume 6, page 29
The
previous
example
was
for
a
deliverable
forward
contract.
The
short
contracted
to
deliver the actual instrument, in this case a $1,000 face value, 90-day T-bill.
Thi
is one eprocedure
for settling a forward contract at the
or expiration
dates specifi
d in the contract.
Anhas alternati
ve wisettlement
method
iiss cash
settlement.
Underamount
this method,
the party
that
a
position
t
h
negati
v
e
value
obligated
to
pay
that
to
the
other
party.
Inshortthewould
previoussatisfyexampl
e
,
i
f
the
pri
c
e
of
the
T-hill
were
$992
on
the
expi
r
ation
date,
the
thesame
contractresultbyaspaying
$2 tovery.theIflotheng. short
Ignoring
transactions
costs,
this
method
yi
e
lds
the
asset
deli
had
the
T-hill,
i
t
could
besubtracting
sold in thethemarket
for
$992.
The
short'
s
net
proceeds,
however,
woul
d
be
$990
after
$2
payment
to
the
long.
If
the
T-hi
l
l
price
at
the
settlement
date
were
$988,ce ofthe$988,
longtogether
would make
athi$2s payment
to thewould
short.makePurchasing
aT-bill
at thejustmarket
priwould
with
$2
payment,
the
total
cost
$990,
as it
be if it were a deliverable contract.
Onpricetheofexpiration
(orabovesettlement)
date of the(forward)
contract,price;
the long
receivesreceiavpayment
if the
the
asset
is
the
agreed-upon
the
short
es
a
payment
if the price of the asset is below the contract price.
settlement date
Page 198
©2012 Kaplan, Inc.
Study Session 1 7
Cross-Reference to CFA Institute Assigned Reading #61 - Forward Markets and Contracts
Terminating a Position Prior to Expiration
Aintopartyan opposite
to a forward
contract
can with an expiration dateprior
totoexpithertime
ationremai
by entering
forward
contract
equal
ning
on the original contract.
Recall
our theexample
andforward
assumeprice
thatoftena days
afterfaceinception
(it wasT-hil
originally
a 30-day
contract),
20-day
$1,
0
00
value,
90-day
l
i
s
$992.
The
short,contract.
expectinSigncethethepriceshortto beis obli
evengated
higherto sellby thethedeliT-hillvery20date,
wishes
tofuture,
termihenatecan
the
days
i
n
the
effecti
exit the(a long
contract
by enteri
into a new
(20-day)
identicalvelyT-hill
position)
at thengcurrent
forward
priceforward
of $992.contract to buy an
The
position
of
the
original
short
now
is
two-fold,
an
obligation
to
sell
a
T-hill
in
20
days
forin $990
(under
the original
contract)
anda $2anloss,obligati
on toeffecti
purchase
antedidentical
T-hill
20
days
for
$992.
He
has
locked
i
n
but
has
v
ely
exi
theof the
contract
since
the
amount
owed
at
settlement
i
s
$2,
regardless
of
the
market
price
T-hill
at
the
settlement
date.
No
matter
what
the
pri
c
e
of
a
90-day
T-hill
is
20
days
from
now,
$990.he has the contractual right and obligation to buy one at $992 and to sell one at
However,contract,
if the short'
s new forwardremains.
contractIfisthewitprice
h a different
partyl atthanthe theexpiration
first
forward
some
of
the
T-hil
date
i
s
above
$992,
and
the
counterparty
to
the
second
forward
contract
fai
l
s
to
perform, the short's losses could exceed $2.
alternative
is toThisenterwould
into avoi
the dsecond
(offsetti
ng)thecontract
with themakesamea $2partypayment
as the
original
contract.
credit
ri
s
k
since
short
could
to theorigcounterparty
at contract
expiration,
thetheamount
ofposition
his netinexposure.
In fact,
if
the
i
n
al
counterparty
were
wil
l
i
n
g
to
take
short
the
second
(20-day)
at theunti$992
price,
a payment
of the present
valuevalentof thetransaction.
$2 (discounted
fornal
thecontract
20
days
l
the
settlement
date)
would
be
an
equi
The
origi
counterparty
would
be
wi
l
l
i
ng
to
allow
termi
n
ati
o
n
of
the
ori
g
i
n
al
contract
for
an
immediate payment of that amount.
Ifto theexitoriginal
counterparty
requi
r
es
a
payment
larger
than
the
present
value
of
$2
thethecontract,
thesk heshortbearsmustby enteri
weightngthisintoadditional
cost tocontract
exit thewithcontract
agai
n
st
defaul
t
ri
the
off
s
etting
a different
counterparty at a forward price of $992.
terminate the position
credit risk
An
LOS 61 .c: Distinguish between a dealer and an end user of a forward contract.
CPA® Program Curriculum, Volume 6, page 30
The
is ritypical
ly wish
a corporation,
government
unit,
or
nonprofit
institution
that
has
existing
s
k
they
to
avoid
by
l
o
cking
i
n
the
future
price
of
an
asset.
A
U.S.
corporation
that
has
an
obligation
to
make
a
payment
i
n
Euros 60 days from now can eliminate its exchange rate risk by entering into a forward
end user of a forward contract
©20 1 2 Kaplan, Inc.
Page 199
Study Session 17
Cross-Reference to CFA Institute Assigned Reading #61 - Forward Markets and Contracts
contract towithpurchase
the required
payment
a settlement
date 60amount
days inoftheEuros
future.for a certain dollar-denominated
Dealers
areIdealoften
banks,wilbutl balance
can alsotheibe rnonbank
financial
institutions
suchoverall
as securities
brokers.
l
y
,
dealers
overall
long
positions
with
their
short
positions
by entering
forward
contracts
with
enda buying
users whopricehave(atopposite
exiswiltingl
risk
exposures.
A
deal
e
r'
s
quote
desk
wi
l
l
quote
which
they
assume
a long position)
and a slspread
ightlybetween
higher selthelingtwopriceis the(atdeal
whiecr'hs they
will assume
aforshort
position).
The
bid/ask
compensation
administrative
costs aspositions.
well as bearing
default
risenter
k andinto
any contracts
asset pricewiriskth other
from
unbalanced
(unhedged)
Dealers
wil
l
also
dealers to hedge a net long or net short position.
LOS 61 .d: Describe the characteristics of equity forward contracts and forward
contracts on zero-coupon and coupon bonds.
CPA® Program Curriculum, Volume 6, page 32
Equity
forward
contracts
wherein themuchunderlying
asset
is a assingle
stock,
a portfolio
of An
stocks,
or
a
stock
index,
work
the
same
manner
other
forward
contracts.
itonvestor
who
wishes to sellabout10,0the00 stock
sharesprice
of IBMon that
stockdate,
90 days
fromdo sonowbyandtakiwishes
avoid
the
uncertainty
could
ngthea
short
position
i
n
a
forward
contract
coveri
n
g
10,
0
00
IBM
shares.
(
W
e
wil
l
leave
motivation for this and the pricing of such a contract aside for now.)
A10,deal000ershares
might90quote
a
price
of
$100
per
share,
agreei
n
g
to
pay
$1
mil
l
i
o
n
for
the
daysstock
fromselnow.ler hasThelocked
contractin themayselling
be deliprice
verablofe orthesettled
inandcashwilas
described
above.
The
shares
getactualnolymore
i
f
the
pri
c
e
(i
n
90
days)
i
s
actually
hi
g
her,
and
wi
l
l
get
no
l
e
ss
if
the
price
lower.
Acanportfoli
o
manager
who
wi
s
hes
to
sel
l
a
portfolio
of
several
stocks
60
days
from
now
similofaeach
rly request
a quote,
giviniog. The
the dealer
the companybetween
namesthiands typetheofnumber
of
shares
stock
in
the
portfol
only
difference
forward
contract
and
several
forward
contracts
each
covering
a
si
n
gle
stock,
i
s
that
the
pricing
would
be better
higherbetotal
the portfoli
o because
origination
costs(awould
less forprice)theforportfol
io forward
contract.overall administration/
Anotiforward
contractandonwila stock
except that thecontract.
contract will be based on a
onal amount
l veryindex
likelyibes similar
a cash-settlement
Page 200
©2012 Kaplan, Inc.
Study Session 1 7
Cross-Reference to CFA Institute Assigned Reading #61 - Forward Markets and Contracts
Example: index forward contracts
Aportfolio
portfolithat
o manager
desires
to
generate
$10
million
100
days
from
now
from
a
is quite
similarin ain1 00-day
composition
to contract
the S&Pbased
100 index.
Sheindexrequests
a
quote
on
a
short
position
forward
on
the
wi
t
h
a
notional
amount
of
$10
mi
l
lion
and
gets
a
quote
of
525.
2
.
If
the
index
level
at
the
settlement
the contract.date is 535.7 , calculate the amount the manager will pay or receive to settle
Answer:
The actual index level is 2% the contract price, or:
535.7 I 525.2 1 = 0.02 = 2%
the
short
party,
the
portfoli
o
manager
must
pay
2%
of
the
$10
million
notional
amount, $200,000, to the long.
Alternati
velvye, ifa payment
the indexfwere
1 o/olong
belowofthe$100,contract
level,ch would
the portfoli
o manageroffset
woul
d
recei
r
om
the
0
00,
whi
approximately
any decrease in the portfolio value.
Equity
above
-
As
Divi
d
ends
are
usual
l
y
not
included
i
n
equity
forward
contracts,
as
the
uncertai
n
ty
about
divi
dendprices.
amounts
andforward
paymentcontracts
dates isaresmalcustom
l compared
to the theuncertainty
aboutspecify
future
equity
Since
instruments,
parties
could
aeffecti
totalvreturn
valuedi(including
dividends)asrather
ely remove
vidend uncertainty
well. than simply the index value. This would
Forward Contracts on Zero-Coupon and Coupon Bonds
Forward
contracts
onngshort-term,
zero-coupon
bonds
(T-bills
in the However,
United States)
and
coupon
i
n
terest-payi
bonds
are
quite
similar
to
those
on
equities.
whil
e
equities
do
not
have
a
maturity
date,
bonds
do,
and
the
forward
contract
must
settle
before the bond matures.
we The
notedpercentage
earlier, T-bidiscount
ll pricesforT-bills
are often iquoted
as a percentage
discountT-bill
fromquoted
face at
value.
s
annualized
so
that
a
90-day
a 4% discount
pricedofat(1a-(900.0 1)360)$1,04%00 == $990
1 o/o discount
face value.
equival
ent to a wiprillcebequote
per $1,0from
00 offace
value.This is
As
I
x
x
©20 12 Kaplan, Inc.
Page 201
Study Session 17
Cross-Reference to CFA Institute Assigned Reading #61 - Forward Markets and Contracts
Example: Bond forwards
Ato forward
contract
covering
a
$10
mill
i
on
face
val
u
e
ofT-bi
l
ls
that
wi
l
l
have
100
days
at contract
settlement
at 1.96 foron athediscount
thematurity
dollar amount
the long
must payis priced
at settlement
T-bills. yield basis. Compute
Answer
The
1.96%
annualized
discount
must
be
"unannualized"
based
on
the
100
days
to
maturity.
0. 0 196 (1 00 I 360) = 0.005444 is the actual discount.
The dollar settlement price is (1 - 0.005444) $10 million = $9,945,560.
Please fall.
noteAthatlong,whenwhomarket
interest
rates
increase,
discountswillincrease,
andonT-hill
prices
i
s
obli
g
ated
to
purchase
the
bonds,
have
losses
the
forward
and gains on the contract when interest rates
fall. Thecontract
outcomeswhen
for theinterest
shortrates
wil rise,
be opposite.
x
x
The
specifieasd inofforward
contractsdate,onexclusive
coupon-bearing
bondsinterest.
is typical
ly stated
as a
yiis eonldprice
tobonds
maturity
the
settlement
of
accrued
If
the
contract
with
the
possibility
of
default,
there
must
be
provisions
in
the
contract
to
defi
ne defaultmustandalsospecify
the obliigfations
of thehaveparties
in the event
ofsuch
default.as callSpecial
provisions
be
included
the
bonds
embedded
options
features
conversion
features. Forward contracts can be constructed covering individual
bonds ororportfoli
os of bonds.
LOS 61 .e: Describe the characteristics of the Eurodollar time deposit market,
and define LIBOR and Euribor.
CFA® Program Curriculum, Volume 6, page 36
Eurodollar
deposit
is
the
term
for
deposits
in
large
banks
outside
the
United
States
denominated
intheU.London
S. dollars.Interbank
The lending
rateRate
on dollar-denominated
loansas between
banks
is
called
Offered
(LIBOR).
It
is
quoted
anLIBOR is
annualized
rate
based
on
a
360-day
year.
In
contrast
to
T-hill
discount
yields,
anas aadd-on
certificate loans
of deposit.
LIBOR is used
referencerate,ratelikefora flyield
oatingquoterateonU.S.a short-term
dollar-denominated
worldwide.
Page 202
©2012 Kaplan, Inc.
Study Session 1 7
Cross-Reference to CFA Institute Assigned Reading #61 - Forward Markets and Contracts
Example: LIBOR-based loans
Compute
the
amount
that
must
be
repaid
on
a
$1
million
loan
for
30
days
i
f
30-day
LIBOR is quoted at 6%.
Answer:
The add-onwould
interestrepayis $1,calc0ul00,ated000as $1$5,000
million= $1,0.0005,6 000(30at the360)end= $5,of30000.days.The
borrower
+
x
x
I
isompublia number
shed dailofylabyrgethebanks;
BritishsomeBanker'
sargeAssociation
and isbanks
compiled
from
quotes
f
r
are
l
multinational
based
in
other
countries that have London offices.
There
i
s
also
an
equivalent
Euro
lending
rate
called
Euribor,
or
Europe
Interbank
Offered Rate. Euribor, established in Frankfurt, is published by the European Central
Bank.
The
floating
rates
are forLIBOR
various(orperiods
and90-day
are quoted
as such.
For
example,
the
termi
n
ol
o
gy
i
s
30-day
Euribor),
LIBOR,
and
180-day
LIBOR,
depending
on
the
term
of
the
loan.
For
l
o
nger-term
fl
o
ating-rate
loans,
the
interest
rate
is reset periodically based on the then-current LIBOR for the relevant period.
LIBOR
LOS 61.f: Describe forward rate agreements (FRAs) and calculate the gain/loss
on a FRA.
LOS 61 .g: Calculate and interpret the payoff of a FRA and explain each of the
component terms of the payoff formula.
CFA® Program Curriculum, Volume 6, page 35
Amoney at a certain rate at some
(FRA)future
can bedate.viewed
as
a
forward
contract
to
borrow/lend
Indate.practice,
these contracts
settle in cash,
but
no
actual
loan
i
s
made
at
the
settlement
This
means
that
the
creditworthiness
ofessentially
the partiesriskless
to therate,contract
need
not
be
considered
in
the
forward
interest
rate,
so
an
as LIBOR,
in the contract.
(The parties) to
the contract may still besuchexposed
to defaulcant ribeskspecifi
on theedamount
owed at settlement.
The ltheongcontract
positionprice
in anbeing
FRA theis theinterest
party rate
that onwould
borrowIfthethemoney
(long
theat contract
loan
with
the
loan).
fl
o
ating
rate
expiration
Euribor)canisbeabove
the asratethespecifi
etod inborrow
the forward
agreement,
the
landongthepositilongo(LIBOR
nwiinllthereceiorcontract
vi
e
wed
right
at
below
market
rates
ve a payment.
Ife thea cashreference
ratefromat thetheexpiration
daterightis below
the
contract
rate,
the
short
wil
l
recei
v
payment
long.
(The
to lend
at rates
market rates would have a positive value.)
forward rate agreement
higher than
©20 12 Kaplan, Inc.
Page 203
Study Session 17
Cross-Reference to CFA Institute Assigned Reading #61 - Forward Markets and Contracts
Tocalculcalculate
thevaluecashas payment
at settlement
formaki
a forward
rateatagreement,
weis eineed
toabove
a
te
the
of
the
settlement
date
of
n
g
a
loan
a
rate
that
t
her
orperiod,
belowthethecashmarket
rate.
Since
the
i
n
terest
savings
would
come
at
the
end
of
the
loan
payment
atatesettlement
of thevalue
forwardat theis thesettlement
present date
valueofofthetheinterest
interest
savings.
We
need
to
cal
c
ul
the
discounted
savings
or
excess
i
n
terest
at
the
end
of
the
loan
period.
An
example
wi
l
l
il
l
ustrate
the
calculation of the payment at expiration and some terminology of FRAs.
FRAs
Consider an FRA that:
res/settl
esnotional
in 30 days.principal amount of $1 million.
IsExpi
based
on
a
IsSpecifi
basedesona forward
90-day rate
LIBOR.
of 5o/o.
Assume
thatthethecashactual
90-daypayment
LIBOR 30-days
from now
(at expiration)
is 6o/omakes
.
Compute
settlement
at
expiration,
and
identify
which
party
the payment.
Example:
•
•
•
•
Answer:
If6o/othe, thelonginterest
couldsaved
borrowonata 90-day
the contract
rate ofloan5o/o,woul
ratherd be:than the market rate of
$1 million
(0.06 - 0.05)(90 360) 1 million = 0.0025 1 million = $2,500
The
$2,500
in interest
savings would
not
comevaluntil
thetheseendsavings.
of the 90-day
loan
period.
The
value
at
settlement
is
the
present
u
e
of
The
correct
discount rate to use is the actual rate at settlement, 6o/o, not the contract rate of 5o/o.
The payment at settlement from the short to the long is:
2' 500
1 [(0.06) (90 360)] $2,463.05
Inanddoing
the calculation
of the settlement
payment,
remember
thatarethe term
of the FRA
the
term
of
the
underlying
"loan"
need
not
be
the
same
and
interchangeable.
Whil
the settlement
date
can berateanyonfuture
date,
in practicetheitvalue
is usually
some
multiple
oftypi30caledays.
The
specifi
c
market
which
we
calculate
of
the
contract
will
l
y
be
similar,
30-day,
60-day,
90-day,
or
180-day
LIBOR.
If
we
describe
an
FRA
asthea payment
60-day FRA
on
90-day
LIBOR,
settlement
or
expi
r
ati
o
n
i
s
60
days
from
now
and
at settlin (30-day)
ement is months,
based onand90-daywoulLIBOR
60 days asfroma 2-by-5
now. Such
an(orFRA
could
be
quoted
d
be
described
FRA
2 5to
FRA).
The
2
refers
to
the
number
of
months
until
contract
expiration
and
the
5
refers
the total time until the end of the interest rate period (2 3 = 5).
I
+
X
I
x
x
=
not
x
+
Page 204
©2012 Kaplan, Inc.
Study Session 1 7
Cross-Reference to CFA Institute Assigned Reading #61 - Forward Markets and Contracts
The general formula for the payment to the long at settlement is:
days )
(floating -forward ) (
{ notional principal)
[ ( days
1 (floating) 360
where:
days number of days in the loan term
The
factor.numerator is the interest savings in percent, and the denominator is the discount
Notespecified
that if thein the contract,
rate underl
ying the agreement
turnsisoutnegati
to beve below
theshort
rate
the
numerator
in
the
formula
and
the
receives a payment from the long.
FRAs
for non-standard
off-the-run
FRAs. periods (e.g., a 45-day FRA on 132-day LIBOR) are termed
+
T
=
floating
forward
LOS 61 .h: Describe the characteristics of currency forward contracts.
CFA® Program Curriculum, Volume 6, page 38
Under
theofterms
of a for a certain amount of another
one partycurrency
agrees toat aexchange
a certain
amount
one
currency
future
date.
This
type
of
forward
contract
in
practice
wi
l
l
specify
an
exchange
rate
at
whi
c
h
one
party
can10 millbuyiona fiEuros
xed amount
of. dolthelarscurrency
underlying
the contract.
Ifrecei
we vneed
to exchange
for
U.
S
60
days
in
the
future,
we
mi
g
ht
e
a
quote
of5
USD0.
9
5.
The
forward
contract
specifi
e
s
that
we
(the
l
o
ng)
wi
l
l
purchase
USD9.
million
for
EURI
0
mi
l
lion
at
settlement.
Currency
forward
contracts
can
be
del
i
v
erable
oramount
settlednecessary
in cash. Asto compensate
with other forward
contracts,
the becashdisadvantaged
settlement amount
is the
the
party
who
would
by
the
actual
change in market rates as of the settlement date. An example will illustrate this.
currency forward contract,
©20 12 Kaplan, Inc.
Page 205
Study Session 17
Cross-Reference to CFA Institute Assigned Reading #61 - Forward Markets and Contracts
Example: Currency forwards
Gemco
expects
to
recei
v
e
EUR50
million
three
months
from
now
and
enters
i
n
to
a
casheuro.
settlement
currencyexchange
forwardrateto exchange
thesepereuroseuroforat U.S.
dollarswhat
at USD1.
23
per
If
the
market
is
USD
1.25
settlement,
is
the
amount of the payment to be received or paid by Gemco?
Answer:
Under the terms of the contract Gemco would receive:
USD 1.23 = USD61.5 million
EUR50 million EUR
Without the forward contract, Gemco would receive:
USD 1.25 = USD62.5 million
EUR50 million EUR
The
counterparty
would
beamount
disadvantaged
bythetheadvantage
differencethatbetween
thehavecontract
rateto
and
the
market
rate
i
n
an
equal
to
would
accrued
Gemco had they not entered into the currency forward.
Gemco must make a payment of USD 1.0 million to the counterparty.
A direct calculation of the value of the long (USD) position at settlement is:
( USD 1.23- USD 1.25) EUR50 million= -USDI.O million
EUR EUR
x
x
x
Page 206
©2012 Kaplan, Inc.
Study Session 1 7
Cross-Reference to CFA Institute Assigned Reading #61 - Forward Markets and Contracts
KEY CONCEPTS
LOS 6 l .a
Aa certai
deliverable
forward
contractdateontoantheassetshort,specifiwhoes that
the longa certain
(the buyer)
will ofpayan
n
amount
at
a
future
wil
l
deliver
amount
asset.
Default riatsksettlin aement,
forwardbecause
contracttypical
is thely risk
that thechanges
other party
toatthethecontract
willofnotthe
perform
no
money
hands
initiation
contract.
LOS 6 l .b
Aasset,forward
contract
with
cash
settlement
does
not
require
del
i
v
ery
of
the
underlying
paymentpricate andthe thesettlement
based buton thea cashcontract
market date
pricefrom
of theoneassetcounterparty
at settlement.to the other,
Early
termination
oftha theforward
contract
can beat accomplished
by entering
into
a newprice.
forward
contract
wi
opposite
position,
the
then-current
expected
forward
This
early
termination
wi
l
l
fi
x
the
amount
of
the
gain
or
loss
at
the
settlement
date.
s newriforward
is withsiandiceffoneerentofcounterparty
than the original,
there
is creditits
orIfoblithidefault
s
k
to
consider
the
two
counterparties
may
fai
l
to
honor
gation under the forward contract.
LOS 6 l .c
end user of a forward contract is most often a corporation hedging an existing risk.
Forward
deal
ers, large
banks,andor thebrokerages
origi
nothers,
ate forward
contracts
andpricing
take theto
long
side
i
n
some
contracts
short
si
d
e
i
n
wi
t
h
a
spread
i
n
compensate
must bear. them for actual costs, bearing default risk, and any unhedged price risk they
ty forward
contract
may
betheon riassiknofgleequity
stock,prices
a customized
portfolio,
or an
equityequi
index,
and
is
used
to
hedge
at
some
future
date.
Equity
forward
contracts
cany based
be wrisolel
ttenyonon aantotalindexreturn
basis (including
divi
d
ends),
but
are
typi
c
all
value.
Index
forwards
notionalcontract
amountandandthetheactual
percentage
diatffsettlement.
erence
betweensettletheinincash
dex based
value ionn thetheforward
index level
Forward
contracts
i
n
whi
c
h
bonds
are
the
underlying
asset
may
be
quoted
in
terms
of
the
discountbonds.
on zero-coupon
bonds
(e.g., T-bi
lls)must
or incontain
terms ofspecial
the yieldprovisi
to maturi
tdeal
y
onwithcoupon
Forwards
on
corporate
bonds
o
ns
to
the possibility
or conversion
Forward
contracts
may also beofwridefault
tten onas well
portfolias wiostofh anyfixedcallincome
securitiesfeatures.
or on bond
indexes.
An
LOS 6l.d
An
•
•
©20 12 Kaplan, Inc.
Page 207
Study Session 17
Cross-Reference to CFA Institute Assigned Reading #61 - Forward Markets and Contracts
LOS
6l.lear time deposits are USD-denominated short-term unsecured loans to large
Eurodol
money-center banks outside the United States.
The
London
Interbank
Offered
Rate
(LIBOR)
is
an
international
reference
rate
for
Eurodol
ar deposits and is quoted for 30-day, 60-day, 90-day, 180-day, or 360-day
(1-year) lterms.
Euribor is the equivalent for short-term Euro-denominated bank deposits (loans to
banks).
For
rates are ofexpressed
basedbothon LIBOR
the loanandtermEuribor,
as a proportion
a 360-dayas annual
year. rates and actual interest is
LOS
6Lf
Forward
agreements
(FRAs)thatserve
to hedgein thethe uncertainty
aboutrise,short-term
rates
(e.a payment
g., 30-rateorat90-day
LIBOR)
wil
l
prevail
future.
If
rates
the
l
o
ng
receives
settlement.
below the contract
rate. The short receives a payment if the specified rate falls to a level
LOS
6I.g
The payment to the long at settlement on an FRA is:
[ days in loan term
(reference
rate
at
settl
e
ment-FRA
rate)
360
]
. p amount
notion pnnct
[
d
a
,
y
_
_
s
m_o
_
an
_t
_
e
_
rm
_
1 reference rate at settlement _ 360 ]
The
numerator
isratethe and
difference
between
the rateandon atheloandenominator
for the specifiis toeddiscount
period atthithes
forward
contract
the
rate
at
settlement,
interest differential back to the settlement date at the market rate at settlement.
LOS
6l
h
.
Currencyatforward
that oneforpartya certain
will deliver
amountcurrency.
of one
currency
the settlcontracts
ement datespecify
in exchange
amounta certain
of another
Under cashbetween
settlement,
a single cashratepayment
is made
at settlement
based onexchange
the rate
difference
the
exchange
fi
x
ed
in
the
contract
and
the
market
at the settlement date.
.
Page 208
al
. al
{
X
+
©2012 Kaplan, Inc.
·
1
}
Study Session 1 7
Cross-Reference to CFA Institute Assigned Reading #61 - Forward Markets and Contracts
CONCEPT CHECKERS
1. A.Thehasshortnoindefaul
a delit vrisk.
erable forward contract:
B.C. makes
is obligaatedcashtopayment
deliver theto thespecifilongedatasset.
settlement.
2. A.On thethe settlement
date
of
a
forward
contract:
may besellrequired
toorsellmaketheaasset.
B.C. theat leastshort
longonemust
the
asset
cash payment.
party must make a cash payment
to the other.
of
the
foll
o
wi
n
g
statements
regardi
n
g
early
termination
of
a
forward
3. Which
is who enters into an offsetting contract to terminate has no risk.
A.contract
A
party
partytermination
who terminthrough
ates a forward
contract
early mustwimake
aoriginal
cash payment.
C.B. AEarly
an
offsetti
n
g
transaction
t
h
the
counterparty eliminates default risk.
4. AA.dealcannot
er in betheaforward
contract market:
bank.
B.C. may
enter
into
a
contract
wi
t
h
another
dealer.
gets a small payment for each contract at initiation.
5. Which of the following statements regarding equity forward contracts is
A.B. Dividends
Equity forwards
may
be
settled
i
n
cash.
are neverin anincluded
in indexcould
forwards.
C. Aofshort
position
equi
t
y
forward
not hedge the risk of a purchase
that equity in the future.
of
the
foll
o
wi
n
g
statements
regarding
forward
contracts
on
90-day
T-bills
6. Which
A.B.is The
faceis novaluedefault
mustribesk paid
by theforwards
long atbecause
settlement.
There
on
these
T-bills are
government-backed.
C. will
If short-term
s increase unexpectedly after contract initiation, the short
profit on yiel
thedcontract.
lar ontimaediscount
deposit: basis.
7. AA.Eurodol
i
s
priced
B.C. may
be issued
a Japanesedenominated
bank. in Euros.
is a certi
ficate ofbydeposit
differenceis forbetween
LIBOR
and Euribor is that:
8. A.OneLIBOR
London
deposits.
B.C. they
currencies.
LIBORare isforslidightlfferent
y higher
due to default risk.
most accurate?
least
accurate?
most accurate?
©20 12 Kaplan, Inc.
Page 209
Study Session 17
Cross-Reference to CFA Institute Assigned Reading #61 - Forward Markets and Contracts
9. Which of the following statements regarding a LIBOR-based FRA is
short
wi
l
l
settl
e
the
contract
by
making
a
loan.
A.B. The
can beincreases
based onunexpectedly
interest ratesoverforthe30-,contract
60-, orterm,
90-daytheperiods.
C. FRAs
Ifrequired
LIBOR
long will be
to make a cash payment at settlement.
10. 60-day
ConsiderLIBOR
a $2 million
FRA
with
a
contract
rate
of
5o/
o
on
60-day
LIBOR.
If
is 6o/o at settlement, the long will:
A.B. pay
$3,333.
recei
v
e
$3,300.
C. receive $3,333.
A hasrateentered
a 8currency
forward
contracttheto purchase
10 mill
ion97atperan
11. Party
exchange
of
$0.
9
per
euro.
At
settlement,
exchange
rate
i
s
$0.
If thea payment
contract iofs settled
in cash, Party A will:
A.B.euro.make
$100,000.
C. recei
receivvee aa payment
payment ofof $100,
$103,0090.00.
12. 3.15o/o
If the quoted
discount
yield
onhasa the128-day,
$1ofmillion
T-billgaineddecreases
from
to
3.
0
7o/o,
how
much
holder
the
T-bill
or
lost?
A.B. Lost
$284.$284.
Gained
C. Gained $800.
13. maturi
90-daytLIBOR
is
quoted
as
3.
5
8o/o.
How
much
i
n
terest
woul
d
be
owed
at
y6for12.a 90-day loan of $1.5 million at LIBOR 1.3o/o?
A.B. $17,
$18,3900.25.
$32,
treasurer
needs
toandborrow
10 million
euros fortake180to days,
60thedays
14. Afromcompany
now.
The
type
of
FRA
the
position
he
should
hedge
interest
rate riskPosition
of this transaction are:
FRA
A.B. 22 x 68 Short
Long
2 8 Short
most
accurate?
€
+
c.
c.
Page 2 1 0
X
X
©2012 Kaplan, Inc.
Study Session 1 7
Cross-Reference to CFA Institute Assigned Reading #61 - Forward Markets and Contracts
ANSWERS - CONCEPT CHECKERS
1.
B
The short in a forward contract is obligated to deliver the specified asset at the contract
price on the settlement date. Either party may have default risk if there is any probability
that the counterparty may not perform under the terms of the contract.
2.
A
A forward contract may call for settlement in cash or for delivery of the asset. Under a
deliverable contract, the short is required to deliver the asset at settlement, not to make a
cash payment.
3.
C
Terminating a forward contract early by entering into an offsetting forward contract
with a different counterparty exposes a party to default risk. If the offsetting transaction
is with the original counterparty, default risk is eliminated. No cash payment is required
if an offsetting contract is used for early termination.
4.
B
Forward contracts dealers are commonly banks and large brokerage houses. They
frequently enter into forward contracts with other dealers to offset long or short
exposure. No payment is typically made at contract initiation.
5.
B
Index forward contracts may be written as total return contracts, which include
dividends. Contracts may be written to settle in cash, or to be deliverable. A long
position is used to reduce the price risk of an expected future purchase.
6.
C
When short-term rates increase, T-bill prices fall and the short position will profit.
The price of a T-bill prior to maturity is always less than its face value. The deliverable
security is a T-bill with 90 days to maturity. There is default risk on the forward, even
though the underlying asset is considered risk free.
7.
B
Eurodollar time deposits are U.S. dollar-denominated accounts with banks outside the
United States and are quoted as an add-on yield rather than on a discount basis.
8.
B
LIBOR is for U.S. dollar-denominated accounts while Euribor is for euro-denominated
accounts. Neither is location-specific. Differences in these rates are due to the different
currencies involved, not differences in default risk.
9.
B
A LIBOR-based contract can be based on LIBOR for various terms. They are settled in
cash. The long will receive a payment when LIBOR is higher than the contract rate at
settlement.
x
(60 I 360)
x
1 I (1
+
0.06 I 6) = $3,300.33.
(0.06 - 0.05)
11. A
($0.98 - $0.97) x 10 million = $ 100,000 loss. The long, Party A, is obligated to buy
euros at $0.98 when they are only worth $0.97 and must pay $0.01 x 1 0 million
= $ 1 00,000.
12. B
The actual discount has decreased by:
(0.03 1 5 - 0.0307) x
128
-
360
=
$2 million
x
10. B
0.0284% of $ 1 ,000,000, or $284.
A decrease in the discount is an increase in value.
©20 12 Kaplan, Inc.
Page 2 1 1
Study Session 17
Cross-Reference to CFA Institute Assigned Reading #61 - Forward Markets and Contracts
13. B
(0.0358
+
0.013)
( )
90
360
1 . 5 million = $ 1 8,300. Both LIBOR and any premium to LIBOR
are quoted as annualized rates.
14. B
Page 2 1 2
This requires a long position in a 2
x
8 FRA.
©2012 Kaplan, Inc.
The following is a review of the Derivatives principles designed to address the learning outcome
statements set forth by CFA Institute. This topic is also covered in:
FUTURES MARKETS AND CONTRACTS
Study Session 1 7
EXAM FOCUS
Candidatestheshould
focusofonmargi
the terminology
of futures
markets,
how futures
differOther
from
forwards,
mechanics
n
deposits,
and
the
process
of
marking
to
market.
concepts
herefinancial
includefutures
limit pricontracts.
ce moves,Learn
delivtheery options,
and theposition
characteristi
cs
ofimportant
the
basic
types
of
ways
a
futures
can
be
to contract expiration
understand how cash settlement is accomplished
byterminated
the finalprior
mark-to-market
at contractandexpiration.
LOS 62.a: Describe the characteristics of futures contracts.
LOS 62.b: Compare futures contracts and forward contracts.
CFA® Program Curriculum, Volume 6, page 43
Futures
are
very
much
l
i
k
e
the
forward
contracts
we
learned
about
in
the
previous topic review. They are in that both:
Canpribeceiedtherto have
delivzero
erablevalue
or cashat thesettlement
contracts.enters into the contract.
Are
time an investor
Futures contracts from forward contracts in the following ways:
Futures
contracts trade on organized exchanges. Forwards are private contracts and
doFutures
not trade.
contracts
areofhighl
y standardized.
Forwards are customized contracts
satisfyi
n
g
the
needs
the
parties
invol
v
ed.
Acontracts
single clearinghouse
ins atithengcounterparty
to all futures contracts. Forwards are
with
the
origi
counterparty.
The
government regulates futures markets. Forward contracts are usually not
regulated.
contracts
similar
•
•
differ
•
•
•
•
Characteristics of Futures Contracts
A major diffcontract
erence between
forwardscontracts
and futures
is that
futuresand
contracts
have
standardized
terms.
Futures
specify
the
quality
quantity
of
goods
that
can
be
delivered,
the
deli
v
ery
time,
and
the
manner
of
deli
v
ery.
The
exchangethealsobasic
sets price
the minimum
priceor fltick,uctuation
(whi
ch is calledgrainthecontract
tick size).is a
For
example,
movement,
for
a
5,
0
00-bushel
quartera dailof ay point
(1mpoint
=ch$0.sets0 1)thepermaximum
bushel, orprice
$12.movement
5 0 per contract.
Contracts
alsoe
have
price
li
i
t
,
whi
allowed
in
a
si
n
gl
day. For example, wheat cannot move more than $0.20 from its close the preceding day.
Standardization.
©20 12 Kaplan, Inc.
Page 2 1 3
Study Session 17
Cross-Reference to CFA Institute Assigned Reading #62
-
Futures Markets and Contracts
The
pricemonth.
limits expand
duringalperiods
gh volatitimes
lity andfor each
are notcontract.
in effect
durinmaximum
g the delivery
The exchange
so sets ofthehitrading
Ittrading.
wouldWhy?
appearStandardization
that these rulestells
wouldtraders
restrictexactltrading
actiisvbeing
ity, buttraded
in fact,andtheythe stimulate
y
what
conditions of the transaction.
The
purchaser
of
a
futures
contract
is
said
to
have
gone
long
or
taken
a
whileach
e thecontract
seller of traded,
a futurestherecontract
is saidandto have
goneTheshortlongorhastakencontracted
a to buy
For
is
a
buyer
a
sel
l
er.
the asset
atprice.
the contract
price
at contract
expiration,
and theto gain
shortexposure
has an obligation
toin
sell
at
that
Futures
contracts
are
used
by
to
changes
thecontracts
price ofto thereduceassetexposure
underlyingto price
a futures
contract.
Aasset (hedgein contrast,
wilpril usece risk).
futures
changes
i
n
the
thei
r
asset
Anthe exampl
e
i
s
a
wheat
farmer
who
sells
wheat
futures
to
reduce
the
uncertainty
about
price of wheat at harvest time.
Clearinghouse.
Each exchange
hasll honor
a their obligations.
The clearinghouse
guarantees
thatthis
traders
in
the
futures
market
wi
The
clearinghouse
does
by splitting
each trade
once
itbuyer
is madeto and
actiselnlgerasandthetheopposite
sideeveryof each
position.
The
cl
e
ari
n
ghouse
acts
as
the
every
sel
l
er
to
buyer.
By
doing
this,
the havi
clearingnghouse
allowsthe eiother
ther side
ofof thethe trade
totrade.
reverseThispositions
at a future
date
withethout
to
contact
si
d
e
initial
al
l
ows
traders
to
enter
market
knowing
that
they
wi
l
l
be
able
to
reverse
their
position.
Traders
are
also
freed
from
having to worryIn theabouthistory
the counterparty
defaulting
since
the counterparty
is now
thedefaulted
clearinghouse.
of
U.
S
.
futures
trading,
the
clearinghouse
has
never
on a trade.
Uniformity promotes market Liquidity.
Long position,
short position.
speculators
hedger,
clearinghouse.
Professor's Note: The terminology is that you "bought" bond futures ifyou
entered into the contract with the Long position. In my experience, this
terminology has caused confusion for many candidates. You don't purchase the
contract, you enter into it. You are contracting to buy an asset on the Long side.
"Buy" means take the Long side, and "sell" means take the short side in futures.
LOS 62.c: Distinguish between margin in the securities markets and margin
in the futures markets, and explain the role of initial margin, maintenance
margin, variation margin, and settlement in futures trading.
CFA® Program Curriculum, Volume 6, page 48
In usecurities
markets,Initialmargin
on ofa stock
or bond
purchase
is a percentage
of the market
valthe
eremai
of theningasset.
l
y,
50%
the
stock
purchase
amount
may
be
borrowed,
and
amount,
theamount,
equity ithen themargin
account,loan.must
bemargin
paid ipercentage,
n cash. Theretheispercent
interest
charged
on
the
borrowed
The
ofminimum
the security
value thatof market
is owned,value.will vary over time and must be maintained at some
percentage
Page 214
©2012 Kaplan, Inc.
Study Session 1 7
Cross-Reference t o CFA Institute Assigned Reading #62 - Futures Markets and Contracts
In thethefutures
markets,
margiThere
n is a performance
guarantee.
Itconsequentl
is money deposited
by
both
l
o
ng
and
the
short.
i
s
no
l
o
an
i
n
vol
v
ed
and,
y
,
no
i
n
terest
charges.
Each
futures
exchange
has
a
clearinghouse.
To
safeguard
the
clearinghouse,
the
exchange
requitrader
res traders
todeposi
postt margin
andledsettle
thein)rwith
accounts
on a(who,
daily inbasis.turn,Before
trading,
themargin
must
funds
(cal
margi
a
broker
wil
l
post
with the clearinghouse).
In securities
markets,
theprice
cashprovi
deposited
isthepaidbroker.
to theThis
sellerisofwhythethesecuriunpaid
ty, withbalance
the is a
balance
of
the
purchase
d
ed
by
loan, with interest charged to the buyer who purchased on margin.
Initial
margin
is
the
money
that
must
be
deposited
i
n
a
futures
account
before
any
trading
Itequal
is sets about
for eachonetypeday'ofs maximum
underlyingprice
asset.fluInitial
margionnthepertotal
contract
iofs reltheaticontract'
vtakes
ely lowplace.
and
ctuation
value
s underlying asset.
Maintenance
margin
isbalance
the amount
ofaccount
marginfalthatls below
must bethemaintained
in margin
a futuresdue
account.
If
the
margi
n
i
n
the
maintenance
to a changetoinbring
the contract
e for thebackunderlup ytoingtheasset,
funds must be
deposited
the marginpricbalance
initialadditional
margin requirement.
This is ipercentage
n contrast toupequi
margimargin,
ns, whichnotrequire
to bringlevel.the
margin
to thety account
maintenance
back toinvestors
the initialonlymargin
Variation
is theamount.
funds Ifthataccount
must bemargin
deposited
intothetheinitial
account
to bring
it back
tofundsthe can
initialmargin
margin
exceeds
margin
requirement,
be withdrawn or used as initial margin for additional positions.
The
settlement
price
is
analogous
to
the
closing
price
for
a
stock
but
i
s
not
simply
the
priof trading,
ce of thecalled
last trade.
It is anperiod,
averagewhich
of theisprisetcesbyofthetheexchange.
trades during
thefeaturelast ofperiod
the
closing
This
themake
settlement
price
prevents
manipulation
by
traders.
The
settl
e
ment
price
i
s
used
to
margin calculations at the end of each trading day.
Initial
and
minimum
margi
n
s
in
securities
accounts
are
set
by
the
Federal
Reserve,
althoughmarket
brokerage
houses
canclearinghouse
require more.andIniaretialbased
and maintenance
margi
nprice
s in the
futures
are
set
by
the
on
historical
dail
y
volMargiatilityn inoffutures
the underlying
asset
sincelymargin is resettl
epercentage
d daily in futures
accounts.
accounts
is
typical
as
a
of
the
value
of
the
assets
covered byis much
the futures
s means that the leverage, based on the actual
cash required,
highercontract.
for futuresThiaccounts.
much lower
How a Futures Trade Takes Place
Into thecontrast
to
forward
contracts
i
n
whi
c
h
a
bank
or
brokerage
i
s
usually
the
counterparty
is a buyerthatandwiallseller
futures oftrade.
The futures
exchangecontract,
selects there
the contracts
trade.onTheeachasset,sidetheof aamount
the asset,
and the
©20 1 2 Kaplan, Inc.
Page 2 1 5
Study Session 17
Cross-Reference to CFA Institute Assigned Reading #62
-
Futures Markets and Contracts
settlement/delivery
date
areamount
standardized
in this manner
(e.gthere
., a Juneis afutures
contract
on
90-day
T-bills
wi
t
h
a
face
of
$1
million).
Each
time
trade,
the
del
i
very
price
for
that
contract
i
s
the
equi
l
i
b
ri
u
m
pri
c
e
at
that
point
i
n
ti
m
e,
which
depends
on
supply (by those wishing to be short) and demand (by those wishing to be long).
The
mechanismlocation
by whionch supply
and demand
determine
thiEachs equilibrium
is opentooutcry
atexchange
a particular
the
exchange
fl
o
or
called
a
trade
i
s
reported
so that the equilibrium price, at any point in time, is known to all traders.the
pit.
LOS 62.d: Describe price limits and the process of marking to market, and
calculate and interpret the margin balance, given the previous day's balance and
the change in the futures price.
CPA® Program Curriculum, Volume 6, page 48
Many
futures
contracts
have
price
limits,
whi
c
h
are
exchange-imposed
limits
on
how
much the arecontract
price from
can change
fromtrades
the previous
day'outside
s settlement
price.IfExchange
members
prohibited
executing
at
prices
these
limits.
the or
(equilibrium)
price
at
which
traders
woul
d
wil
l
i
n
gl
y
trade
is
above
the
upper
limit
below the lower limit, trades cannot take place.
Consider
a
futures
contract
that
has
daily
price
limits
of
two
cents
and
settled
the
previousofdaychanges
at $1.0in4.market
If, on theconditions
followinorg tradi
ng day, traders
wishwitolltrade
at $1.0The7
because
expectations,
no
trades
take
place.
settlement
pril bece saiwildl tobe have
reported
asa$1.lim0it6 (for
theandpurposes
of marking-to-market).
The
contract
wil
made
move,
the
price
i
s
sai
d
to
be
li
m
it
(from theareprevious
day).tradeIf imarket
conditions
had
changed
such
that theprice,
priceandat whithech
traders
wi
l
ling
to
s
below
$1.
0
2,
$1.
0
2
wil
l
be
the
settlement
priup core idown,
s said tothebeprilimit
down.
If
trades
cannot
take
pl
a
ce
because
of
a
l
i
mit
move,
ei
t
her
is said topositions.
be locked limit since no trades can take place and traders
are locked into theirceexisting
Marking-to-market
is theinprocess
ofofadjusting
the margi
n from
balancetheinprevious
a futurestrading
accountday,
each
day
for
the
change
the
value
the
contract
assets
based on the new settlement price.
The
futures exchanges
can require a mark-to-market more frequently (than daily) under
extraordinary
circumstances.
up
Page 216
©2012 Kaplan, Inc.
Study Session 1 7
Cross-Reference to CFA Institute Assigned Reading #62 - Futures Markets and Contracts
Computing the Margin Balance
Example: Margin balance
ConsiderAssume
a long position
ofcontract
five Julypricewheatis $2.contracts,
eacheachof whicontract
ch coversrequi5,r0es00an
bushels.
that
the
0
0
and
that
initial
margi
n
deposit
of
$150
and
a
maintenance
margi
n
of
$100.
The
total
initial
margin
requi
red forCompute
the 5-contract
trade
is $750.forThethismaintenance
margin
fordecrease
the
account
i
s
$500.
the
margi
n
balance
position
after
a
2-cent
ionn price
on
Day
1,
a
1-cent
increase
in
pri
c
e
on
Day
2,
and
a
1-cent
decrease
in
price
Day 3.
Answer:
Each
contractvalisufore by5,$50,
000 bushels
change of(0.01)(5)(5,
$0. 0 1 per0bushel
changes00.
the contract
or $250soforthattheafiprice
ve contracts:
00) = $250.
The
followingchanges
figure ileach
lustrates
the change
in initial
the margibalanncebalaisncetheasinitial
the price
of
thirequis contract
day.
Note
that
the
margin
change.rement of $750 and that the required deposit is based on the previous day's price
Margin Balances
Day
Required Deposit
Price/Bushel
Daily Change
Gain/Loss
Balance
$750
$2.00
0
0
$750
0
$ 1 .98
-$0.02
-$500
$250
2
$500
$ 1 .99
+$0.01
+$250
$ 1 ,000
3
0
$ 1 .98
-$0.01
-$250
$750
0 (Purchase)
Atmaintenance
the close onmargin
Day 1,leveltheofmargi
n balance
has gone
beloofw the$500minimum
or to bring
$500.
Therefore,
a
deposit
is
required
thebalamargi
nanybackpoint
to theas initial
marginthelevelinvestor
of $750.
Wereali
canzinterpret
the margin
nce
at
the
amount
would
e
i
f
the
position
were
closedmargioutnbybalance.
a reversing trade at the most recent settlement price used to calculate
the
©20 12 Kaplan, Inc.
Page 2 1 7
Study Session 17
Cross-Reference to CFA Institute Assigned Reading #62
-
Futures Markets and Contracts
LOS 62.e: Describe how a futures contract can be terminated at or prior to
expiration.
CPA® Program Curriculum, Volume 6, page 53
There are
1. Atheshort
can
termi
n
ate
the
contract
by
del
i
veri
n
g
the
goods,
and
a
long
can
terminate
by The
accepting
deliforverydeliandverypayi(forngphysical
the contract
pricetermsto the delshort.ivery,Thisandis
caldetails
ledcontract
location
assets),
of
exactly
what
i
s
to
be
del
i
vered
are
al
l
specified
in
the
contract.
Deli
v
eries
represent less than 1% all contract terminations.
2. Inmarked-to-market
a
account is
based on thedelivery
settlementis notpricean onoption.
the laThest dayfutures
of trading.
3. You
maywemakedescribed
a exiting
or a forward trade
in thepriorfutures
market. This
isfutures,
similar to
thehowever,
way
contract
to
expiration.
Wi
t
h
the othertrade
side of(maturi
yourtposition
is held
bygood)the clearinghouse-if
you makethe
anclearinghouse
exact opposite
y,
quantity,
and
to
your
current
position,
will positions
net your positions
out,Theleaving
youprice
withcana zerodifferbalance.
Thistheis
how
most
futures
are
settled.
contract
between
two
contracts.sellIf you
initially
areposition
long onein)contract
at $370golperd contract
ounce ofwhen
goldtheand
subsequently
(take
the
short
an
i
d
entical
is deducted
$350/oz.,from
$20 tithemesmargi
the nnumber
of ounces
ofaccount.
gold specified
in ofthethecontract
wilprice
l
be
deposit(s)
in
your
The
sale
futures
contract hasendsbeen
the exposure orto future pricebyfluactuationstrade.
on the first contract. Your
position
positionwithmayanalsoopposite
be settled
through
an own and deliver the goodsHere,andyousettlfinde up
4. Aa trader
position
to
your
between
yourselves,
off
the
fl
o
or
of
the
exchange
(call
e
d
an
ex-pit
transaction).
This
isthetheflosole
exception
to theYoufederal
lawthenthatcontact
requiresthethatclearinghouse
all trades takeandplace
on
or
of
the
exchange.
must
tel
l
them
what
happened.
Antheexchange
forcontract
physicalsisdiffers
from
a delitheveryfloorinofthatthetheexchange,
traders
actually
exchange
goods,
the
not
cl
o
sed
on
and
the
two
traders
pri
v
ately
negotiate
the
terms
of
the
transaction.
Regular
del
i
very
involves only one trader and the clearinghouse.
four ways to terminate a futures contract:
delivery.
of
of
cash-settlement contract,
reverse,
offsetting,
reversed,
closed out,
closing
exchange for physicals.
Delivery Options in Futures Contracts
Some tofutures
contracts
grant bond contractstogivthee theshort;shortoptions
one ofwhat,severalwhere,
and
when
deliver.
Some
Treasury
a
choi
c
bonds
that
are Physi
acceptabl
e to delsuch
iver andgoloptions
as tomaywhenoffertoadelichoice
ver during
the expiration
month.
c
al
assets,
d
or
corn,
of
del
i
very
locations
toin
the
short.
These
options
can
be
of
signifi
c
ant
val
u
e
to
the
holder
of
the
short
position
a futures contract.
delivery options
as
Page 2 1 8
©2012 Kaplan, Inc.
Study Session 1 7
Cross-Reference t o CFA Institute Assigned Reading #62 - Futures Markets and Contracts
LOS 62.f: Describe the characteristics of the following types of futures
contracts: Treasury bill, Eurodollar, Treasury bond, stock index, and currency.
CFA® Program Curriculum, Volume 6, page 57
Let'
s
introduce
fi
n
ancial
futures
by
first
examining
the
mechanics
of
a
T-hill
futures
contract.
Treasury
billsettlfutures
contracts
are based
onarea $1100million
facethe valannualized
ue 90-day
(13-week)
T-hi
l
l
and
e
in
cash.
The
price
quotes
minus
discount in percent on the T-bills.
Afrompricefacequote
of98.
5 2(90represents
an annualized discount of 1.48%, an actual discount
of
0.
0
148
360)
= 0. 0 037, and a delivery price of (1 - 0. 0 037)
1 million = $996,300.
T-hill
futures
contracts
are
not
as
important
as
they
once
were.
Their
prices
are
heavi
l
y
influencedhavebylostU.S.importance
Federal Reserve
operations
and overall
monetary
policy.
T-hill
futures
in
favor
of
Eurodollar
futures
contracts,
which
represent
aborrowers
more free-market
and
more
global
measure
of
short-term
interest
rates
to
top
quality
for U.S. dollar-denominated loans.
Eurodoiiar
futures
are
based
on
90-day
LIBOR,
whi
c
h
is
an
add-on
yield,
rather
than
a
discount
yielared. calculated
By convention,
however,
the priLIBOR
ce quotesinfollow
theThese
same convention
as e
T-bills
and
as
(100
annualized
percent).
contracts
settl
i0.01
n cash,%, representi
and the minimum
price
change
i
s
one
which
is
a
price
change
of
0.
0
001
=
ngof$25(1 00per- $197 .million
contract. A quote of 97.60 corresponds to an
annualized
LIB
OR
6
)
= 2.4% and an effective 90-day yield of 2.4 4 =
0.6%.
x
x
I
tick,
I
Professor's Note: Eurodollar futures are priced such that the long position gains
value when interest rates decrease. This is different from forward rate agreements
and interest rate call options, where the long position gains when interest rates
mcrease.
Q
One of the first things a new T-bill futures trader learns is that each change in
price of 0. 0I in the price ofa T-bill futures contract is worth $25. Ifyou took a
long position at 98.52 and the price fell to 98.50, your loss is $50 per contract.
Because Eurodollar contracts on 90-day LIB OR are the same size and priced in
a similar fashion, a price change ofO.OI represents a $25 change in value for
these as well.
Treasury bond futures contracts:
Are
traded
for Treasury
bonds with maturities greater than 15 years.
Are
a
deli
v
erable
contract.
Havequoted
a face asvaluea percent
of $100,and000.fractions of 1% (measured in 1132nds) of face value.
Are
The
shortthatinwiallTreasury
bonddelifutures
contract
hascontract.
the option
tois deliver
anydelivery
of several
bonds
satisfy
the
very
terms
of
the
This
cal
l
ed
a
option
and
is
val
u
able
t
o
the
short
because
at
expiration,
one
particular
Treasury
bond
will
be
the cheapest-to-deliver bond.
•
•
•
•
©20 12 Kaplan, Inc.
Page 2 1 9
Study Session 17
Cross-Reference to CFA Institute Assigned Reading #62
-
Futures Markets and Contracts
Each
whichreceiis used
to adjustpayment.
the long'These
s payment
ataredelmultipl
ibond
very isoiesrsgithatforventhethea more
valuable
bonds
v
e
a
higher
factorsat
futures
price
at
settlement.
The
long
pays
the
futures
price
expiration times the conversion factor.
Stocktrades
indexinfutures.
most popular
futureonis thea multiplier
S&P 500ofIndex
that
Chicago.TheSettlement
is in stock
cash andindexis based
250. Future
The
val
u
e
of
a
contract
i
s
250
times
the
level
of
the
i
n
dex
stated
in
the
contract.
Wi
t
h
anfutures
indexpricelevelrepresents
of 1,000, athegaivalue
of each
contract
is $250,000.
Eachstockindexindexpointfutures
in the
n
or
loss
of
$250
per
contract.
A
long
position
on
S&P
500
i
n
dex
futures
at
1,051
would
show
a
gain
of$1,750
i
n
the
trader'
s
account iifs thetradedindexonwere
1,058index
at theandsettlhasement
date ($250
contract
the same
a multipli
er of 50.7 = $1,750). A smaller
Futurescontract
contracts
covering
severalsame,otheralthough
populartheindices
are traded,
andfromthe contract
pricing to
and
val
u
ation
are
the
multiplier
can
vary
contract.
Currency
futures.
The
currency
futures
market
is
smaller
i
n
volume
than
the
forward
currency
market
wetrade
described
ineurothe previous
topic revipeso
ew. In(MXP),
the UniandtedyenStates,
currency
contracts
on
the
(EUR),
Mexican
QPY),
among
others.
Contracts
are
set
i
n
units
of
the
forei
g
n
currency,
and
the
price
i
s
stated
inon USD/unit.
The
sizechange
of theinpeso
contractof theis MXP500,000,
and the euro0001contract
is
EUR125,
0
00.
A
the
price
currency
unit
ofUSD0.
translates
into a gain or unit
loss ofUSD50
EUR125,000
contract. on a MXP500,000 unit contract and US012.50 on a
conversion foetor,
x
Page 220
©2012 Kaplan, Inc.
Study Session 1 7
Cross-Reference t o CFA Institute Assigned Reading #62 - Futures Markets and Contracts
KEY CONCEPTS
LOS 62.a
Like
forward and
contracts,
futures
contracts
aredate
mostandcommonly
for delivery
delivery ofor settlement
commodities
fi
n
ancial
assets
at
a
future
can
require
in cash.
Compared
to forward
contracts,
futures contracts:
Are
more
liquid,
trade
on
exchanges,
and can be closed
by an offsetting
Dothe contract.
not have counterparty risk; the clearinghouse
acts asoutcounterparty
to eachtrade.
side of
Have
lower
transactions
costs.
Requi
r
e
margin
deposits
andas areto asset
markedquantity,
to market
daity,ly.settlement dates, and delivery
Are
standardi
z
ed
contracts
qual
i
requirements.
LOS 62.b
•
•
•
•
•
LOS 62.c
Futures
deposits are not loans, but deposits to ensure performance under the
terms ofmargin
the contract.
Initial margin is the deposit required to initiate a futures position.
Maintenance
is the minimum
marginvariation
falls belowmargin.
this
amount, it mustmargin
be brought
back up tomargin
its initialamount.
level byWhen
depositing
Margin
calculations
based onset theby thedailyexchange.
settlement price, the average of the prices for
trades during
a closingareperiod
Trades
cannotthe take
place
atandpricesare saithatd todifbeferlifrom
the previous
day'thes settlement
prices by
more
than
pri
c
e
limit
m
i
t
down
(up)
when
new
equilibrium
price is below (above) the minimum (maximum) price for the day.
Marki
addingingaisettlement
ns to or subtracting
fromtothethe next.
marginng-to-market
account daily,is thebasedprocess
on theofchange
prices fromlosses
one day
The
mark-to-market
adjustment
either
adds
the
day'
s
gains
in
contract
value
to
the
long'
s margin
balance
andvalsubtracts
them
froms margin
the short'balance
s marginandbalance,
or subtracts
the
day'
s
loss
i
n
contract
u
e
from
the
long'
adds
them
to the
short's margin balance.
A futures
positiontrade,
can beenteri
terminated
iann theopposite
followiposition
ng ways:in the same contract.
AnCashoffsetting
n
g
i
n
to
payment
atassetexpiration
(cash-settlement
contract).
Deli
v
ery
of
the
specifi
e
d
in
the
contract.
An exchange for physicals (asset delivery off the exchange).
LOS 62.d
LOS 62.e
•
•
•
•
©20 12 Kaplan, Inc.
Page 221
Study Session 17
Cross-Reference to CFA Institute Assigned Reading #62
-
Futures Markets and Contracts
LOS 62.lfar futures contracts are for a face value of $1,000,000, are quoted as 100 minus
Eurodol
annualized 90-day LIBOR in percent, and settle in cash.
Treasury
bond
contracts
are
for
a
face
value
of
$100,
0
00,
give
the
short
a
choice
of
bonds
iver, and use conversion factors to adjust the contract price for the bond
that is todelidelvered.
Stock indexvalue,futures
haveeainmultiplier
contract
and settl
cash. that is multiplied by the index to calculate the
Currency futures are for delivery of standardized amounts of foreign currency.
Page 222
©2012 Kaplan, Inc.
Study Session 1 7
Cross-Reference t o CFA Institute Assigned Reading #62 - Futures Markets and Contracts
CONCEPT CHECKERS
1. A.WhichHedgers
of thetrade
followito nreduce
g statements
about
futures
markets
is
some that
preexisting
risk
exposure.
clearinghouse
guarantees
traders
in
the
futures market will honor
B. The
their
obligations.
C. deposit
If an account
to ornexceeds
variationrisesmargi
. the maintenance margin, the trader must
2. A.Thevaridailaytionprocess
ofn.adjusting the margin in a futures account is called:
margi
marking-to-market.
C.B. maintenance
margin.
buysat 98.14
(takes and
a longclosesposition
in)at aa price
Eurodollar
futures
contract
($1 million
3. Afacetrader
value)
it
out
of98.
2
7.
On
this
contract,
the
trader
has:
A.B. gained
lost $325.$325.
C. gained $1,300.
4. Innotthepermifutures
market,
a
contract
does
not
trade
for
two
days
because
trades
are
tted at the equilibrium price. The market for this contract is:
A.B. limit
up.
limit
down.
C. locked limit.
existence of a delivery option with respect to Treasury bond futures means
5. The
that
the:
A.B. short
short has
can thechooseoptionwhichto settl
bonde iton cash
deliver.or by delivery.
C. long chooses which of a number of bonds will be delivered.
6. Assume
thefutures
holderposition
ofa longtofutures
position tonegotiates
privatel
y with
theandholder
ofshorta short
accept
delivery
close
out
both
the
long
positions.
Which
of
the
fol
l
owing
statements
about
the
transaction
is
The transaction
is:
as
del
i
very.
A.B. alalssoo known
known
as
an
exchange
for
physicals.
C. the most common way to close a futures position.
factortheinnumber
a Treasuryof bonds
bond contract
is:vered.
7. A.A conversion
used
to
adjust
to
be
deli
i
ed
by
the
face
value
to
determine
the
deli
v
ery
price.
B.C. multipl
multiplied by the futures price to determine the delivery price.
least accurate?
most
accurate?
©20 12 Kaplan, Inc.
Page 223
Study Session 17
Cross-Reference to CFA Institute Assigned Reading #62
-
Futures Markets and Contracts
125,pric0e00settleuroes atfutures
contracts
are sold at a priceforofthi$1.s account
0234. Thechanges
next
8. Three
day
the
$1.0180.
The
mark-to-market
the
previous
day'
s
margin
by:
A.B. -$675.
+$675.
+$2,025.
futureswhimarket,
the
clearinghouse
is
to:
9. A.In thedecide
ch contracts
will margins.
trade.
and
maintenance
B.C. setact initial
as the counterparty to every trade.
to
meet
a
margi
n
cal
l
are
termed:
10. A.Fundsdaideposited
margin.costs.
B.C. vari
settllyaetion
ment
margin.
11. A.Compared
to
forward
contracts,
futures
contracts
are
to
be:
standardiin size.
zed.
B.C. larger
less subject to default risk.
c.
least likely
least likely
Page 224
©2012 Kaplan, Inc.
Study Session 1 7
Cross-Reference t o CFA Institute Assigned Reading #62 - Futures Markets and Contracts
ANSWERS - CONCEPT CHECKERS
1.
C
If an account rises to or exceeds the maintenance margin, no payment needs to be made,
and the trader has the option to remove the excess funds from the account. Only if an
account falls below the maintenance margin does variation margin need to be paid to
bring the level of the account back up to the level of the initial margin.
2.
B
The process is called marking-to-market. Variation margin is the funds that must be
deposited when marking-to-market draws the margin balance below the maintenance
margtn.
3.
B
The price is quoted as 100 minus the annualized discount in percent. Remember that
the gains and losses on T-hill and Eurodollar futures are $25 per basis point of the price
quote. The price is up 1 3 ticks, and 13 x $25 is a gain of $325 for a long position.
4.
C
This describes the situation when the equilibrium price is either above or below the
prior day's settle price by more than the permitted (limit) daily price move. We do not
know whether it is limit up or limit down.
5.
A
The short has the option to deliver any of a number of permitted bonds. The delivery
price is adjusted by a conversion factor that is calculated for each permitted bond.
6.
B
When the holder of a long position negotiates directly with the holder of the short
position to accept delivery of the underlying commodity to close out both positions, this
is called an exchange for physicals. (This is a private transaction that occurs ex-pit and is
one exception to the federal law that all trades take place on the exchange floor.) Note
that the exchange for physicals differs from an offsetting trade in which no delivery takes
place and also differs from delivery in which the commodity is simply delivered as a
result of the futures expiration with no secondary agreement. Most futures positions are
settled by an offsetting trade.
7.
C
It adjusts the delivery price based on the futures price at contract expiration.
8.
C
(1 .0234 - 1 . 0 1 80) x 125,000 x 3 $2,025. The contracts were sold and the price
declined, so the adjustment is an addition to the account margin.
9.
A
The exchange determines which contracts will trade.
=
10. C
When insufficient funds exist to satisfY margin requirements, a variation margin must be
posted.
11. B
Size is not one of the things that distinguishes forwards and futures, although the
contract size of futures is standardized, whereas forwards are customized for each party.
©20 1 2 Kaplan, Inc.
Page 225
The following is a review of the Derivatives principles designed to address the learning outcome
statements set forth by CFA Institute. This topic is also covered in:
OPTION MARKETS AND CONTRACTS
Study Session 17
EXAM FOCUS
Thi
s
deri
v
ati
v
es
revi
e
w
introduces
options,
descri
b
es
their
terms
and
trading,
and
provides
deri
vations nofg how
severalthe options
valuati
on results.
Candidates
should spendThisome
tidesme
understandi
payoffs
on
several
types
of
options
are
determined.
s
incl
u
options
on
stocks,
bonds,
stock
i
n
dices,
i
n
terest
rates,
currencies,
and
futures.
The
assi
g
ned
material on must
establlearn
ishingatupper
and oflowerthe bounds
iparity
s extensirelations
ve, so iand
t should
notto construct
be ignored.an
Candidates
l
e
ast
one
put-cal
l
how
arbi
tinragethestrategy.
The
notation,whatformulas,
andonrelisasayi
tionsngmay(andseem
daunting,
but
if youthe
put
ti
m
e
to
understand
the
notati
why),
you
can
master
important points.
LOS 63.a: Describe call and put options.
CFA® Program Curriculum, Volume 6, page 72
Antransaction involvinggianvesunderlying
its owner theassetrigatht,a butpredetermined
not the legalfuture
obligation,
to conduct
a
date
(the
exercise
date)
and
at
a
predetermined
price
(the
or
Options
give
the
option
the righasht tothedecide
whetherto perform
or not theif thetradebuyerwil exercises
eventuallthey takeoption.
place. The
seller ofbuyer
the option
obligation
The
owner
of a ed time period.
has the right to purchase the underlying asset at a specific
price
for
a
specifi
The
for aowner
specifieofd atime period. has the right to sell the underlying asset at a specific price
For
mustpossible
be a seloptions
ler. Thepositions:
seller of the option is also
calledeverythe owner of an option,
Therethere
are four
1. Long call: the buyer of a call option-has the right to buy an underlying asset.
2. asset.
Short call: the writer (seller) of a call option-has the obligation to sell the underlying
3. Long pur: the buyer of a put option-has the right to sell the underlying asset.
4. asset.
Short put: the writer (seller) of a put option-has the obligation to buy the underlying
To acquire these rights,
to the owners
seller ofoftheoptions
option.must buy them by paying a price called the
option contract
exercise price
•
call option
•
put option
option writer.
option premium
Page 226
©2012 Kaplan, Inc.
strike price).
Study Session 1 7
Cross-Reference to CFA Institute Assigned Reading #63 - Option Markets and Contracts
Listed After
stock issuance,
option contracts
trade contracts
on exchanges
andustedare normally
for 1 00butshares
of
stock.
stock
option
are
adj
for
stock
splits
not
cash
dividends.
To$55seeandhowhasana caloption
contract
works,
consider
the
stock
of
ABC
Company.
It
sells
for
that sells fordatea inpremium
of $10. This call option
has an exercise pricel option
of $50avaiandlablhase onanitexpiration
five months.
Professor's Note: The option premium is simply the price of the option. Please do
not confuse this with the exercise price of the option, which is the price at which
the underlying asset will be bought/sold if the option is exercised.
If theoption
ABCselcallleroption
is purchased
for $10,forthe$50.buyerThecansellpurchase
ABC
stock
from
the
over
the
next
fi
v
e
months
er,
or
wri
t
er,
of
the
option
gets
keep thebuyer$10exercises
premiumthenooption,
matterthewhatsellerthe wistock
doesveduring
thisstritikme price
e period.
Ifmustthetodeloption
l
l
recei
the
$50
andor
i
v
er
to
the
buyer
a
share
of
ABC
stock.
If
the
pri
c
e
of
ABC
stock
fall
s
to
$50
below,
the
buyer
i
s
not
obli
g
ated
to
exerci
s
e
the
option.
Note
that
option
holders
wi
l
l
y exercise thei
act if it ofis profitable
do so. The option writer, however, has
anonlobligation
to actr rigathttheto request
the optiontoholder.
option onhasABCthestock
itos thesellsame
as aofcallABCoption,
except
thetime
buyerduring
of thetheputnext
A(loputng position)
right
a
share
for
$50
at
any
fiexerci
ve months.
The
put
wri
t
er
(short
position)
has
the
obligation
to
buy
ABC
stock
at
the
se price in the event that the option is exercised.
The
ofhasthevalue,
optiontheis thebuyeronemaywhoeither
decidexerci
es whether
oroption
not toorexerci
se theoptionoption.
Ifanother
theowner
option
s
e
the
sell
the
to
buyer in the secondary options market.
LOS 63 .b: Distinguish between European and American options.
CFA® Program Curriculum, Volume 6, page 73
American
expiration options
date. may be exercised at any time up to and including the contract's
European options can be exercised only on the contract's expiration date.
� Professor's Note: The name ofthe option does not imply where the option trades­
� they arejust names.
Atsameexpiration,
an
Ameri
c
an
option
and
a
European
option
on
the
same
asset
wi
t
h
the
strike however,
price are identical.
They
mayandeither
behaveexercised
orvalalluoes,wedsotoyouexpire.
Before
expiration,
they
are
di
f
ferent
may
different
must
distinguish between the two.
©20 12 Kaplan, Inc.
Page 227
Study Session 17
Cross-Reference to CFA Institute Assigned Reading #63
If two opti
oone
ns areis aidentical
(maturity,
underlying
stock,
strike
price,option,
etc.) intheallvalways,ue of
except
that
European
option
and
the
other
i
s
an
American
theearlyAmerican
option
wi
l
l
equal
or
exceed
the
val
u
e
of
the
European
option.
Why?
The
Americanmore.
option gives it more flexibility, so it should be
worthexercise
at leastfeature
as muchofandthe possibly
Option Markets and Contracts
LOS 63.c: Define the concept of moneyness of an option.
CPA® Program Curriculum, Volume 6, page 75
refersoption
to whether
an optiona positive
is payoff,orit is in the money. IfIfimmediate
immediate
exercise
of
the
would
generate
exercise
would
resultthe inexerci
a lossse price,
(negativeexercise
payoff),
igenerate
t is out ofneither
the money.
When
theandcurrent
asset
pri
c
e
equals
wi
l
l
a
gain
nor
loss,
the
option is
The following describe the conditions for a call to be in, out of, or at the money.
Ifholder
S - X would
0, a calreceive
l optionfromis inimmediate
the money.exercise,
S X isbuyitheng a
amount
of
the
payoff
a
call
share for and selling it in theIfmarket
for
a
greater
price
S.
a callisoption
money.
If S = X,S -Xa call 0,option
said toisbeoutatofthethemoney.
The following describe the conditions for a
to be in, out of, or at the money.
If iXS 0, aexercise,
put option
is inathesharemoney.
X-Sexercisi
is theng
amount
of
the
payoff
from
m
mediate
buying
for
Sand
the put to receive for the share.
the stock'IfsX-priceS is0,greater
amoney.
put option is said to be out When
of the money.
a put than
optiontheisstrioutkeofprice,
the
If S = X, a put option is said to be at the money.
Moneyness
in the money
out ofthe money.
at the money.
option
•
•
•
In-the-money call options.
>
X
-
<
Out-ofthe-money call options.
At-the-money call options.
put option
•
•
•
In-the-money put options.
>
X
Out-ofthe-money put options.
<
At-the-money put options.
Example: Moneyness
Consi
der a Calculate
July 40 calhow
l andmuch
a Julythese
40 put,options
bothareon ianstock
$37/share.
or outthatof theis currently
money. selling for
Professor's Note: A july 40 call is a call option with an exercise price of$40 and
an expiration date in july.
Answer:
The
becausecallX-is $3S out= $3.of0the0. money because S-X= -$3.00. The put is $3 in the money
Page 228
©2012 Kaplan, Inc.
Study Session 1 7
Cross-Reference to CFA Institute Assigned Reading #63 - Option Markets and Contracts
LOS 63.d: Compare exchange-traded options and over-the-counter options.
CPA® Program Curriculum, Volume 6, page 76
Exchange-traded
orCorporation
listed optionsfor Chi
are cregulated,
standardized,
liquid,transactions.
and backed byMostthe
Options
Clearing
ago
Board
Options
Exchange
exchange-l
isted options
have
expiration
datesanticipatory
within twosecurities
to four months
of the
current
date.
Exchanges
al
s
o
li
s
t
long-term
equity
(LEAPS),
which
are
equity options with expiration dates longer than one year.
Over-the-counter
(OTC) options
on stocks
for1970s.
the retail
trade
all buthowever,
disappeared
with
themarket
growthin OTC
of theoptions
organized
exchanges
i
n
the
There
is
now,
an
active
onmarket,
currencies,
swaps,options
and equities,
pris largel
mariylyunregulated,
for institutional
buyers.
Like
the
forward
the
OTC
market
i
consists
customwayoptions,
much theofsame
forwardsinvolves
marketscounterparty
are. risk, and is facilitated by dealers in
LOS 63.e: Identify the types of options in terms of the underlying instruments.
CPA® Program Curriculum, Volume 6, page 80
The
types of options
and (3)threecommodity
options.we consider are (1) financial options, (2) options on futures,
Financial
optionsinterest
includerates,
equityandoptions
and other
optionspricebasedfor fionnancial
stock indices,
Treasury
bonds,
currencies.
The
strike
options
can
be in terms of yield-to-maturi
ty on bonds, an indexhavelevelpayoffs
, or anbased
exchange
ratedifference
for
LIBOR-based
on
the
between LIBOR at expiration and the strike rate in the option.
aretivelmost
often
based
on Treasury
bonds because
of their active trading.
There
are
rel
a
y
few
l
i
sted
options
on
bonds-most
are
over-the-counter
options.
Bond
options
can beoptions,
deliverable
or settle
inoncash.bondThepricesmechanics
of bondfaceoptions
areof the
lbond.
ike those
of
equity
but
are
based
and
a
specific
value
The
buyer
of
a
call
option
on
a
bond
wi
l
l
gai
n
if
i
n
terest
rates
fal
l
and
bond
pri
c
es
rise. A put buyer will gain when rates rise and bond prices fall.
settle
i
n
cash,
nothi
n
g
is
deli
v
ered,
and
the
payoff
is
made
directly
to
the
option
holder'
s account.
The payoffexceeds
on an ithendexincalldex (long)
is theedamount
(if any) (the
by
whi
c
h
the
i
n
dex
level
at
expiration
level
specifi
in
the
option
strifromketheprice),account
multiplied
by
the
An
equal
amount
wi
l
l
be
deducted
of the index call option writer.
foreign
currency options.
interest rate options
Bond options
Index options
contract multiplier.
©20 1 2 Kaplan, Inc.
Page 229
Study Session 17
Cross-Reference to CFA Institute Assigned Reading #63
-
Option Markets and Contracts
Example: Index options
Assume
thatmultipl
you ownieraforcallthisoption
on theis 250.
S&P Compute
500 Indexthewithpayoff
an exercise
price
equal
toassuming
950. The
contract
on
this
option
that the index is 962 at expiration.
Answer:
This is a call, so the expiration date payoff is (962-950) $250 = $3,000.
x
sometimes
give theat aholder
the rightprice,to buythe
orstrisellke price.
a specified futures
contractcalled
on orfutures
beforeoptions,
a given date
given futures
on
futures
contracts
give
the
holder
the
right
to
enter
into
the
long
side
ofonaafutures
contractat 98at a(percent
given futures
price.
Assume
that you
hold a callpriceoption
bond
future
of
face)
and
at
expiration
the
futures
onfutures
the
bond
contract
i
s
99.
By
exercising
the
call,
you
take
on
a
long
position
i
n
the
contract,
and
the
account
is
i
m
mediately
marked
to
market
based
on
the
settlement
accountof thewouldbondsbe credited
wittheh cashcontract.
in an The
amountsellerequal
to exerci
1 o/o (99sed- call98)
ofwiprice.lthel takeYour
faceonvalue
covered
by
of
the
the
short
position
i
n
the
futures
contract,
and
the
mark-to-market
value
of this position
will generate
thegicash
deposited
to your
account.
on
futures
contracts
v
e
the
holder
the
option
totertake
on aobligation
short futuresto
position
at
a
futures
price
equal
to
the
stri
k
e
price.
The
wri
has
the
take on the opposite (long) position if the option is exercised.
holder theprice.right to either buy or sell a fixed quantity of
some physical asset atgiavfiextheed (strike)
Some capital
investment
projectswhilehaveit isprovisions
that(forgivexample,
e the company
flexitobilabandon
ity to
adjust
the
project'
s
cash
Rows
i
n
progress
an
option
the project
beforea completion).
have value that should be considered
when
evaluating
project's NPV.Such
Options on futures,
•
•
Call options
Put options
Commodity options
real options
� Professor's Note: Evaluating projects with real options is covered in the Study
� Session on corporate finance at Level II.
LOS 63.f: Compare interest rate options with forward rate agreements (FRAs).
CPA® Program Curriculum, Volume 6, page 81
are similar asset
to theisstock
optionsrateexcept
that
the exercise
pricerateis an
ioptions
nterest rate
and
the
underlying
a
reference
such
as
LIBOR.
Interest
are
also
simil
a
r
to
FRAs
because
there
is
no
deli
v
erabl
e
asset.
Instead
they
are
settl
ed in cash,
a notional
amountareandEuropean
the spreadoptions.
between
the strike
rate andin antheamount
referencethatrate.is based
Most oninterest
rate options
Interest rate options
Page 230
©2012 Kaplan, Inc.
Study Session 1 7
Cross-Reference to CFA Institute Assigned Reading #63 - Option Markets and Contracts
Tointerest
see how
interest
ratewith
optionsa notional
work, consider
aoflo$1,ng 0position
in a a1-year
LIBOR-based
rate
call
option
amount
00,
0
00
and
stri
k
e
rate
of 5%.
For
our
example,
l
e
t'
s
assume
that
this
option
is
cosdess
for
simplicity.
If
at
expiration,
LIBOR
is00greater(LIBORthan 5%,5%).theIfLIBOR
option canis belessexercised
andthetheoption
ownerexpiwillresrecei
ve ess
$1,
0
00,
0
than
5%,
worthl
and the owner receives nothing.
Now,samelet'sfeatures
considerasatheshortcallposition
injusta LIBOR-based
interest
rate putis option
withto be
thecostless,
that
we
discussed.
Again,
the
option
assumed
withs below
a strik5%,
e ratetheofoption
5% andwrinotional
amount
ofpay$1,the000,put000.holderIf atanexpiration,
LIBOR
fall
t
er
(short)
must
amount
equal
to
$1,
0
00,
0
00
(5%LIBOR).
If
at
expiration,
LIBOR
is
greater
than
5%,
the
optiononeexpires
worthlpayoff
ess andis adjtheusted.
put wriForterexample,
makes noif thepayments.
Ifrate
the rate
is foroption
less is
than
year,
the
reference
for
the
60-day
LIBOR,ratetheandpayoff
be $1,are000,annualized
000 (5%actual LIBOR
the would
strike rate
rates. LIBOR)(60/360) because the
Noti
c
e
the
one-sided
payoff
on
these
interest
rate
options.
The
long
call
recei
v
es
a
payoff
when
LIBOR
exceedshand,thethestrishort
ke rateputandposition
receivesmakes
nothingpayments
ifLIBORif LIBis below
thebelowstrikethe
rate.
On
the
other
OR
i
s
strike rate, and makes no payments when LIBOR exceeds the strike rate.
The
ofasthea forward
long interest
rate call option
plusToaseeshortthis,interest
ratetheput option
hasfixed-rate
thecombination
samepayerpayoff
rate
agreement
(FRA).
consider
in thea 5%fixfied-rate
xed-rate,payer$1,will
000,receive
000 notional,
LIBOR-based
FRA.5%).LikAnd,
e our
long
cal
l
position,
$1,
0
00,
0
00
(LIBORlike our short put position, the fixed-rate payer will pay $1,000,000 (5%- LIBOR).
x
x
x
x
x
� Professor's Note: For the exam, you need to know that a long interest rate call
� combined with a short interest rate put can have the same payoffas a long
position in an FRA.
LOS 63.g: Define interest rate caps, floors, and collars.
CFA® Program Curriculum, Volume 6, page 83
Ancorrespond to the resetis adates
seriesonofainterest
rate callloan.options,
having
expirati
onprotect
dates thata
fl
o
ating-rate
Caps
are
often
used
to
fllimit)
oating-rate
from an increase
in interestloan.
rates. Caps place a maximum (upper
on theborrower
interest payments
on a floating-rate
Caps
pay
when rates
risel above
thewicapth strirate.ke Inratesthisequal
regard,to thea capcapcanrate.be Each
viewedoption
as a in a
seri
e
s
of
interest
rate
cal
opti
o
ns
cap is called a
Ancorrespond to thefloorresetisdates
a seriesonofa flinoterest
rate put
dates that
ating-rate
loan.options,
Floors arehaving
oftenexpiration
used to protect
interest rate cap
caplet.
interest rate
©20 12 Kaplan, Inc.
Page 231
Study Session 17
Cross-Reference to CFA Institute Assigned Reading #63
-
Option Markets and Contracts
a floating-rate
nder from
a decline
limit)
on the inleterest
payments
that arein interest
receivedrates.
fromFloors
a floatiplace
ng-ratea minimum
loan. (lower
Anminimum
interestraterateonfloortheonpayments
a loan operates
just the opposite
on a floating-rate
loan. of a cap. The floor rate is a
Floorsofpayinterest
when rate
ratesputfalloptions
below thewithfloorstrikerate.ratesIn this
regard,
aflflooororrate.
can beEachviewed
as ina
series
equal
to
the
option
a floor is called a
Anmayinteresta caprateforcollar
combines
a
cap
and
a
fl
o
or.
A
borrower
wi
t
h
a
fl
o
ating-rate
loan
some of the cost ofprotection
the cap. against rates above the cap and a floor in order to defray
Let'oor.s reviOneweachthereset
information
infloFigure
1, which
illtheustrates
theforpayments
from
a cap(e.g.and, 90a
fldays)
date
of
a
ating-rate
loan,
interest
the
next
period
is determined
Here,onwetheassume
the reference
rate andonthatthe webasishaveof some
quarterlreference
y paymentrate.dates
loan. that LIBOR is
The
fig10%,
ure shows
thewieffect
of aacappayment
that istosettheatcap10%.buyerIn theto offset
event any
thatinterest
LIBO Rexpense
rises
above
the
cap
l
l
make
inof periods
excess oforanforannual
rate oflife10%.
Aloan.capThemaycapbe will
structured
topayment
cover a certain
number
the
entire
of
a
make
a
at
any
future
interest
payment
due date inwhenever
thethereference
rate (LIBOR
in our
example)
exceeds
thebetween
cap rate.
As
indicated
the
fi
g
ure,
cap'
s
payment
i
s
based
on
the
difference
the
reference
rate
and
the
cap
rate.
The
amount
of
the
payment
will
equal
the
notional
amount specifi
ed in theusedcapto contract
timesthethenotional
differenceamount
betweenis usually
the cap equal
rate
and
the
reference
rate.
When
hedge
a
loan,
to the loan amount.
1 also iratellustrates
a loan
floorfallofs5%belowfor our
LIBOR-based
loan. Forpayment
any payment
where
thebyFigtheurereference
on
the
5%,
there
i
s
an
additional
required
floor toNotebringthatthethetotalissuerpayment
toating-rate
5% (1.2 note
5% quarterly
ona acap90-day
LIBOR­
based
loan).
of
a
fl
o
wi
t
h
both
and
a
floor when
(a
collar)
is
long
a
cap
and
(has
sold)
a
fl
o
or.
The
note
issuer
recei
v
es
a
payment
rates
are
above
the
cap,
and
makes
an
additional
payment
when
rates
are
below
the
floor
(compared to just paying the reference rate).
jloorlet.
buy
sell
short
Page 232
©2012 Kaplan, Inc.
Study Session 1 7
Cross-Reference to CFA Institute Assigned Reading #63 - Option Markets and Contracts
Figure 1: Interest Rate Caps and Floors
Loan Rate
Loan Rate without Caps or Floors
1 Oo/o -
5%
0%
- --
-
-- --
- -
- - -- - -- -- - -- -
-- - -
- -
- --
-
--
1 0% Cap
5% Floor
5%
LIB OR
10%
LOS 63.h: Calculate and interpret option payoffs and explain how interest rate
options differ from other types of options.
CFA® Program Curriculum, Volume 6, page 83
or other typea callof option
wireceives
th a monetary­
based
exerci
s
e
pri
c
e,
i
s
strai
g
htforward.
At
expiration,
owner
any amount
bywillwhich
the
asset
price
exceeds
the
strike
price,
and
zero
otherwise.
The
holder
ofanda put
recei
v
e
any
amount
that
the
asset
price
is
below
the
stri
k
e
price
at
expiration,
zero otherwise.
While
areandquoted
in termsas ofanyield-to-maturi
tthey, T-bill
s principle
in discountapplies.
yield,That
indicesis,
iinn each
indexbonds
points,
currencies
exchange
rate,
same
theandpayofftheperstrikeunitpriceof the(orrelevant
asset, weto aneeddollarto strike
translaprice.
te theWeasset
valcanuethentocase,
amuldoltotliply
argetvalue
rate,
or
yield)
options contract. this payoff times however many units of the asset are covered by the
For
a stock index
option,levelweandsawthethatstrithese
dollarby thevalumultipli
es were eobtained
from
multiplying
the
index
k
e
l
e
vel
r
specifi
e
d
in
the
contract.
Theonresulting
dolfutures
lar payoffsis thearecashper thecontract.
The
payoff
options
on
optionis holder
when he
exercises the option and the resulting futures position
markedreceives
to market.
Calculating the payoff for a stock option,
•
•
©20 1 2 Kaplan, Inc.
Page 233
Study Session 17
Cross-Reference to CFA Institute Assigned Reading #63
The
areondifaferent.
Fornotional
example,
a callandoption
based on
90-day
LIBOR
makes
a
payment
based
stated
amount
the
difference
between
90-day
LIBOR
and
the
option'
s
stri
k
e
rate,
times
90
360
to
adj
u
st
for
the
interest rate period.
Thetermpayment
is made, not
atForoption
expiration,
but based
at a future
date
corresponding
to
the
of
the
reference
rate.
example,
an
option
on
90-day
LIBOR
wil
l
make
a
payment
90
days
after
the
expiration
date
of
the
option.
This
corresponds
date on which a LIBOR-based borrower
wouldpayment
make thedatenextofteninterest
paymenttoonthea loan.
Option Markets and Contracts
payoffs on interest rate options
I
Example: Computing the payoff for an interest rate option
Assume
you
bought
a
60-day
call
option
on
90-day
LIBOR
with
a
notional
principal
of
$190-day
millionLIBOR
and aisstri6%keatratecontract
of 5%.expiration,
Compute and
the payment
thatwhenyouthewillpayment
receive ifwill be
determine
received.
Answer:
The interest savings on a $1 million 90-day loan at 5% versus 6% is:
1 million (0.06-0.05)(90 360) = $2,500
This is the amount that will be paid by the call writer 90 days after expiration.
x
I
LOS 63.i: Define intrinsic value and time value, and explain their relationship.
CFA® Program Curriculum, Volume 6, page 88
Anamount
optiothat
n's the optionvalueowneris thewould
amount
byve which
the option
isexercised.
in-the-money.
It is thehas
recei
i
f
the
option
were
An
option
zero
intrinsic
value
i
f
it
is
at
the
money
or
out
of
the
money,
regardl
e
ss
of
whether
i
t
i
s
a
call or a put option.
Let'
s
look
at
the
value
of
a
call
option
If
the
expiration
date
price
of
the
stock
exceeds
theIf thestrikepricepriceof theof thestockoption,
thethancallorowner
wiltheexercise
the option
and
recei
v
e
S
-X.
i
s
less
equal
to
strike
price,
the
call
holder will let the option expire and get nothing.
The
option is the greater of (S -X) or 0. That is:
= max[O, S -X]
Similarly, the
option is {X - S) or 0, whichever is greater. That is:
P = max[O, X- S]
intrinsic
at expiration.
intrinsic value ofa call
C
intrinsic value ofa put
Page 234
©2012 Kaplan, Inc.
Study Session 1 7
Cross-Reference to CFA Institute Assigned Reading #63 - Option Markets and Contracts
Example: Intrinsic value
Consider
call option
h a stri$50,ke priandce$45.
of $50. Compute the intrinsic value of this
option forastock
prices wioft$55,
Answer:
stock price = $55: C = max[O, S -X] = max[O, (55 - 50)] = $5
stock price = $50: C = max[O, S -X] = max[O, (50- 50)] = $0
stock price = $45: C = max[O, S -X] = max[O, (45 - 50)] = $0
NoticeBecause
that at expiration,
if the stock
iswiworth
$50exercior sbele theow,calltheoption
call option
is worth
$0.
Why?
a
rati
o
nal
option
holder
l
l
not
and
take
the
loss.
Thi
s
one-sided
feature
of
call
options
i
s
i
l
l
u
strated
i
n
the
option
payoff
di
a
gram
presented in Figure 2 for the call option we have used in this example.
Professor's Note: Option payoffdiagrams are commonly used tools to illustrate
the value ofan option at expiration.
Figure 2:
Call
Option Payoff Diagram
Value
Long call
$5
o �n-r............
. ....
. ........
. ....
. ,.,.,
'....
' .·
'
·
-$5
I
----------------------------
·
.
.
.
.
'
'
·.
I
j_ - - - - - - - -
�·•.
·
·
·
·
·
·
·.
.·
.
..
·
Short call
'------'---'- Srock p ri �e
ar exp1ranon
X = $50 $55
indicated
intheFigure
2,isthein theexpiration
dateFor payoff
to the wriowner
is eitherthezeropayoff
or theis
amount
that
option
money.
a
call
option
t
er
(seller),
eioption
ther zero
or
mi
n
us
the
amount
it
i
s
i
n
the
money.
There
are
no
positive
payoffs
for
an
optiongaiwriter
whateverwriter.
the callTheowner
ns. receives the premium and takes on the obligation to pay
As
©20 12 Kaplan, Inc.
Page 235
Study Session 17
Cross-Reference to CFA Institute Assigned Reading #63
With reference to Figure 2, you should make the following observations:
The
payoff
call position
(thethesolidstrike
line)price,
is a flat line which angles upward
toThethepayoff
right totoat athea long
45writer
degree
angl
e
from
ofangl
a calle from
(dottedtheline),
isprice,
a flat line which angles downward
toOptitheonsrigareht ata zero-sum
a 45 degreegame.
strike
If youpayoff
addofthezero.long call option's payoff to the short
option'
s
payoff,
you
will
get
a
net
At a stock price of $55, the payoff to the long is $5, which is a $5 loss to the short.
Similarvaltououres forpayoff
dioption.
agram forAs aindicated
call option,here,Figure
3price
illustrates
thestockat-expiration
payoff
a
put
i
f
the
of
the
ithes lessprithan
thethe
strike
price,
the
put
owner
wil
l
exerci
s
e
the
option
and
receive
(
X
S).
If
c
e
of
stockreisandgreater
than or (0).equalAttoa thestockstrike
price,
thetheputpayoff
holderonwilallong
let theputputis $1option
expi
get
nothing
price
of
$40,
0;stock
the
selat l$50er ofandtherecei
put v(the
short)
would
have
a
negati
v
e
payoff
because
he
must
buy
the
e stock worth $40.
3:
Option Markets and Contracts
•
X.
•
X.
•
•
Figure
Put Option Payoff Diagram
Value
X
$10
0
I
-$10
·
..··
..
•
•
•
- - - - - - - - - - - - �··
..
..··
·
·
.·
.
-X
·
.·
.
.
.
•
Short
put
$40
Stock price
X = $50
The
of
an
option
i
s
the
amount
by
which
the
option
premium
exceeds
therelationshi
intrinsicp canvaluebeandwritten
is sometimes
as: called the speculative value of the option. This
option value = intrinsic value time value
Asoption
we discussed
earlier, theAt anyintrinsic
valduring
ue ofthean option
is theoptions
amountcontract,
by whiitschvaltheue
i
s
in
the
money.
point
l
i
f
e
of
an
withatll typi
cstock
ally bepricegreater
than
its inintrinsic
value.thatThigis visesbecause
therea ipositive
s some probability
the
wil
l
change
an
amount
the
option
payoff
at expiration greater than the (current) intrinsic value. Recall that an option's intrinsic
time value
+
Page 236
©2012 Kaplan, Inc.
Study Session 1 7
Cross-Reference to CFA Institute Assigned Reading #63 - Option Markets and Contracts
value
(toan aoption
buyer)reaches
is the amount
of thetherepayoff
attimeexpiration
andandis bounded
byvaluezero.is
When
expiration
i
s
no
remaining
the
time
zero.
For
American
options
and
in
most
cases
for
European
options,
the
longer
the
time
to expiration,
premium
(price).the greater the time value and, other things equal, the greater the option's
LOS 63.j: Determine the minimum and maximum values of European options
and American options.
CFA® Program Curriculum, Volume 6, page 91
The following is some option terminology that we will use when addressing these LOS:
s{ = the price of the underlying stock at time
exerci
se expiration
price of the option
XT == the
the
ti
m
e
to
cr = thetimeprice
of a European call at any time prior to expiration at
=
T
= thetimeprice
of
an
American
cal
l
at
any
time
prior
to
expiration
at
= thetimepri==cTTe of a European put at any time prior to expiration at
= thetimepri= cTe of an American put at any time prior to expiration at
RFR = the risk-free rate
t
t
c{
t
t
Pr
Pr
t
Professor's Note: Please notice that lowercase letters are used to represent
European-style options.
Theoreti
c
all
y
,
no
option
wi
l
l
sell
for
less
than
its
intrinsic
value
and
no
option
zero. can take on a negative value. This means that the lower bound for any option is
Thetime-t
maximum
valueofoftheeitherunderlying
an American
orThisa European
option
at
any
ti
m
e
tis
the
share
price
stock.
makesthe
sense
because
no
one
would
pay
a
price
for
the
ri
g
ht
to
buy
an
asset
that
exceeded
asset's boundary
value. It woul
d be cheaper
toexpressed
simply buyrespectivel
the underlyi
ng asset. AtandtimeEuropean
t = 0, thecall
upper
condition
can
be
y
for
American
options as:
Lower bound.
The lower bound ofzero applies to both American and European options.
Upper bound for call options.
call
Theexerci
priceseforvaluean American
puttheoption
cannotstock
be moreprice
than
its
stri
k
e
price.
This
i
s
the
in
the
event
underlying
goes
to
zero.
However,
since
European
puts
cannot
be
exercised
prior
to
expiration,
the
maximifumthevalstockue isprice
the present
of theis expected
exercise price
Even
goes to value
zero, and
to staydiscounted
at zero, theat theintririnssick-freevalue,rate.
Upper bound for put options.
©20 12 Kaplan, Inc.
Page 237
Study Session 17
Cross-Reference to CFA Institute Assigned Reading #63
X,condition
will notcanbe recei
ved untilfortheAmeri
expiration
At timeputt = options,
0, the upper
boundary
be expressed
can anddate.European
respectivel
y, as:
X
X and (1+ RFR)
The
minimum
and maximum
boundary
any time
tare summari
zed in Figure
4. conditions for the various types of options at
P0 :S
Option Markets and Contracts
T
Po :S
Figure 4: Option Value Limits
Option
Minimum VaLue
Maximum VaLue
European call
c, 2: 0
c, :::; s,
American call
c, 2: 0
c, :::; s,
European put
p, 2: 0
American put
P, 2: 0
P, :::; X/(1
+
RFR)tT-•l
p, _
<X
Professor's Note: The values in the table are the theoretical limits on the value of
options. In the next section, we will establish more restrictive limits for option
prices.
LOS 63.k: Calculate and interpret the lowest prices of European and American
calls and puts based on the rules for minimum values and lower bounds.
CFA® Program Curriculum, Volume 6, page 91
Professor's Note: The option boundary conditions that we discuss below will be
important when you study option pricing models. For now, ifyou follow the
logic leading up to the results presented in Figure 5, you will be prepared to deal
with these LOS. Knowing and understanding the results in Figure 5 satisfy the
requirements of these LOS; the following derivation of those results need not be
memorized.
Atexercithissed,point,the weminimum
know thatpriceforhasAmerican-style
options,
whichvalue.
can For
be immediately
to
be
the
option'
s
intrinsic
at-the-money
and
out-of-the
money
options,
thi
s
minimum
i
s
zero,
because
options
cannot
haveintrinsic
negati
v
e
values.
For
in-the-money
American
options,
the
minima
are
simply
the
valoption
ues Sfor- Xlessforthancalls,itsandintrinsic
X- S value
for puts.and Ifimmediately
this were notexerci
the scase,
youa guaranteed
could buy theprofit.
e
it
for
So,priorfor toAmerican
options,
we
can
express
the
at
any
time
expiration as:
= max[O, S,-X]
= max[O, X- S ]
however, Tothedetermine
minima arethenotlower
so obvious
these options
areFor notEuropean
exercisabloptions,
e immediately.
boundsbecause
for European
options,
lower bound on the option price
t
Cr
P,
Page 238
,
©2012 Kaplan, Inc.
Study Session 1 7
Cross-Reference to CFA Institute Assigned Reading #63 - Option Markets and Contracts
weshortcanposition
examineinthethevalstock
ue ofanda portfolio
in whichbond.
the option is combined with a long or
a pure discount
For a
construct the following portfolio:
At =loT.ng at-the-money European call option with exercise price X, expiring at time
Aexpiration.
long discount bond priced to yield the risk-free rate that pays X at option
A short position in one share of the underlying stock priced at S0 = X.
The current value of this portfolio is c0 -S0 + X (1 + RFR)T.
At =expiration
time,
t on= T,thethicals portfoli
o wipayll pay
- ST our+ X.short
Thatstock
is, weposition,
will collectand
max:[O,
S
-X]
l
option,
S
to
cover
T
collect X fromTthe maturing bond.
IftheSTcall� pays
X, theS call-X,is thein-the-money,
andandthe portfolio
willtohave
a our
zeroshort
payoffposition.
because
bond
pays
+X,
we
pay
-S
cover
T t= T payoff is: ST -X+ X- ST = 0. T
is,
the
time
That
call istheout-of-the-money,
and
theweportfoli
oXhason thea posibond,
tive payoff
equal
Ifto X>X-SST thebecause
cal
l
value,
c
,
is
zero,
collect
and
pay
to cover Tthe short position. So, theT time t = T payoff is: 0 +X-ST =X- ST . -ST
Note
that nothematter
whether
thewiloption
expiresto orin-the-money,
at-the-money,
or out-of­
the-money,
portfolio
value
l
be
equal
greater
than
zero.
We
will
never
have
to make a payment.
To prevent
possibili
of a negative
have
a negatiarbitrage,
ve value.anyThus,portfol
we canio that
statehasthenovalue
of thetyportfoli
o payoff= cannot
as:
c0 -S0 + X ( 1 + RFR)T � 0
which allows us to conclude that:
European call option,
•
•
•
I
Cr
Cr
•
•
at time t 0
I
Combining this result with the earlier minimum on the call value of zero, we can write:
T is the present value of a pure discount bond with a face value
Note
that
X
(1
+
RFR)
of
Basedas:on these results, we can now state the lower bound for the price of an American
call
C0 � max[O, S0 -X (1 + RFR?J
X.
I
I
©20 12 Kaplan, Inc.
Page 239
Study Session 17
Cross-Reference to CFA Institute Assigned Reading #63
-
Option Markets and Contracts
How can we say this? This conclusion follows from the following two facts:
se feature
1. The
equivalearlyentexerci
European
call (i.one.an, CAmerican
t ;::: ct) . call makes it worth at least as much as an
2. The
lower bound
for theforvaluean American
of a European
calForl isexampl
equal eto, max[O,
or greater thanX I the
theoretical
lower
bound
cal
l
.
max[O,
(1 +
RFR) T] ;:::
S0 -
S0 - X] .
Professor's Note: Don't get bogged down here. We just use the fact that an
American call is worth at least as much as a European call to claim that the
lower bound on an American call is at least as much as the lower bound on a
European call.
Derive theat time t = 0:
by forming the following
portfolio
AA long
at-the-money
European
put
option
with
exercise
price
X,
expi
r
ing
at
t
= T.
short nposition
on a riequal
sk-freetobond
priced
at X I (1 + This is the same as
borrowi
g
an
amount
X
I
(1
+
A long position in a share of the underlying stock priced at
At= max[O,
expiratiX-on timeont =theT, put
this option,
portfolioreceiwilvlepay from+ the-X.stock,Thatandis,paywe-Xwilloncollect
the bond
issue (loan).
IfIf X,X,thethepayoff
payoffwilwilllequal:
be zero. + -X = X.
Again,
a
no-arbitrage
argument
can
be
made
that
the
portfolio
val
u
e
must
be
zero
or
greater, because there are no negative payoffs to the portfolio.
At time t = 0, this condition can be written as:
minimum value of a European put option
•
•
•
50 .
S T]
•
•
RFR) T.
RFR) T_
ST
ST >
S T :::;
PT
ST
PT
ST
PT
ST -
and rearranged to state the minimum value for a European put option at time t = 0 as:
X I (1 +
We
as: have now established the
max[O, X I (1 +
Po ;:::
RFR) T - S0
minimum bound on the price of a European put option
Po ;:::
Page 240
RFR) T - S0]
©2012 Kaplan, Inc.
Study Session 1 7
Cross-Reference to CFA Institute Assigned Reading #63 - Option Markets and Contracts
Professor's Note: Notice that the lower bound on a European put is below that of
an American put option (i.e., max[O,
SJ). This is because when it's in the
money, the American put option can be exercised immediately for a payoff of
X-
X-50.
FiandgureEuropean
5 summarizes
now know
the boundary
optionswhat
at anywetime
prior regardi
to expinrgation
at time t =prices
T. for American
t
Figure 5 : Lower and Upper Bounds for Options
Option
Minimum Value
Maximum Value
European call
American call
Cr 2: max[O, Sr -X I (1
European put
Pr 2: max[O, X I ( 1
+
+
r
RFR)T- ]
r
RFR) T- - Sr]
X I (1
+
r
RFR) T-
X
American put
Professor's Note: For the exam, know the price limits in Figure 5. You will not be
asked to derive them, but you may be expected to use them.
Example: Minimum prices for American vs. European puts
Compute
the
lowest
possible
price
for
4-month
Ameri
c
an
and
European
65
puts
on
a
stock that is trading at 63 when the risk-free rate is 5%.
Answer:
American put: :2: max[O, = max[0,2l = $2
European put: $0.95max[O, (1 RFR)T - = max[O, 65 1 1.05°·333-631 =
P0
X - S0l
Po :2:
XI
+
S0l
Example: Minimum prices for American vs. European calls
Compute
lowestatpossible
3-monthrateAmeri
stock
that theis trading
68 whenprithece forrisk-free
is 5%.can and European 65 calls on a
Answer:
C max[O,
c max[O,
0 :2:
S0 - X I
0 :2:
S0 - X I
(1 RFR)Tl = max[O, 68-65 1 1.05°·251 = $3.79
(1 + RFR)T] = max[O, 68-65 1 1.05°·25] = $3.79
+
©20 12 Kaplan, Inc.
Page 241
Study Session 17
Cross-Reference to CFA Institute Assigned Reading #63 - Option Markets and Contracts
LOS 63.1: Explain how option prices are affected by the exercise price and the
time to expiration.
CPA® Program Curriculum, Volume 6, page 96
The
result
we
are
aft
e
r
here
i
s
a
simple
and
somewhat
intui
t
i
v
e
one.
That
is,
gi
v
en
two
putsse prithatce wilarelidentical
inastallasrespects
exceptas exercise
price,
theloonewerwiexerci
th these price.
higher
exerci
have
at
l
e
much
value
the
one
wi
t
h
the
Thi
is because
the underl
ying stock
canexcept
be soldexerciat asehigher
price.
Similarl
y, gilower
ven two
calexercilss that
are
identical
in
every
respect
price,
the
one
with
the
price wilthel have
at least stock
as muchcanvalue
as the oneatwia tlohwerthe price.
higher exercise price.
This issebecause
underlying
be purchased
Professor's Note: The derivation of this result is included here although it is not
explicitly required by the LOS.
The
method
here,intofora portfoli
both putso andandexamine
calls, istheto combine
twopayoffs
options
with different
exercise
prices
portfolio
at
expiration
for
the
three possible
stock
prichave
e ranges.
We usevaltheue tofactestablish
that a portfoli
o withrelnoatiopossibility
of a
negati
v
e
payoff
cannot
a
negative
the
pricing
ns
for
options
with differing times to expiration.
For X1 X2, consider a portfolio at time that holds the following positions:
ct(X1) = a long call with an exercise price ofX1
ct(Xz) = a short call with an exercise price ofXz
three expiration
date 6.(t = T) conditions and payoffs that need to be considered here
areThesummari
zed in Figure
<
t
Figure 6: Exercise Price vs. Call Price
Expiration Date
Condition
Option Value
Portfolio Payoff
ST ::; X1
�(X1) = �(X2) = 0
0
X , < ST < Xz
Xz ::; ST
�(X,) = ST
�(Xz) = 0
- x,
�(X I ) = ST - XI
�(Xz) = ST - Xz
ST - XI > 0
(ST - XI) - (ST - Xz)
= Xz - XI > 0
Wi
t
h
no
negati
v
e
payoffs
at
expiration,
the
current
portfoli
o
of
c
(X
)
c
(
X
)
must
0
0
2
1
have a value greater than or equal to zero, and we have proven that c0 (X1) � c0 (Xz).
Page 242
©2012 Kaplan, Inc.
Study Session 1 7
Cross-Reference to CFA Institute Assigned Reading #63 - Option Markets and Contracts
Simi
larlse yprice
, consider
a portfolio short
a put
wiration
th exerci
sepayoffs
price X1thatandweloneed
ng a toputconsider
with
exerci
X
,
where
.
The
expi
date
are summarized2in Figure 7. 2
Figure 7: Exercise Price vs. Put Price
X1
Expiration Date
Condition
<
Option Value
ST � �
pT (X ,)
� > ST > X1
PT(X ,)
PT(X2)
X1 � ST
X
PT(X ,)
PT(X2)
=
PT(�)
Portfolio Payoff
=
X2 - sT > o
=
0
=
X2 - ST
=
=
0
0
x, - ST
X2 - ST
(X2 - ST) - (X, - ST)
X2 - X1 > 0
=
Here again, withmust
no negati
vaevalue
payoffsgreater
at expiration,
the current
portfoli
oproves
of that
have
than
or
equal
to
zero,
whi
c
h
�
In summary, we have shown that, all else being equal:
Callprices
pricesarearedirectl
inversely
relatedtotoexercise
exerciseprice.
prices.
Put
y related
Inmoney
general,options,
a longer
time totimexpiration
willno increase
anweoption'
ssayvalue.
For far out-of-the­
the
extra
e
may
have
effect,
but
can
the
longer-term
option
will be no less valuable that the shorter-term option.
The
case
that
doesn'
t
fi
t
this
pattern
is
the
European
put.
Recal
l
that
the
minimum
value
T
r - Sr.
ofWhianleinlo-the-money
European
put
at
any
ti
m
e
t
pri
o
r
to
expi
r
ati
o
n
i
s
(1
RFR
nger
time to valexpiration
inoption
creasespayoff
optionatvalue
throughForincreased
volatility,
it
decreases
the
present
u
e
of
any
expiration.
this
reason,
we
cannot
state
positivelyput.that the value of a longer European put will be greater than the value of a
shorter-term
If volatility
is high
and the put
discount
ratemorelow,valuable.
the extraLowtimevolatil
valueitywiand
ll behitheghdominant
factor
and
the
longer-term
wi
l
l
be
rates have the opposite effect and the value of a longer-term in-the-money putinterest
option
can be less than the value of a shorter-term put option.
p 0 (�) - p0 (X)
Po (�) Po (X l).
•
•
XI
+
)
LOS 63.m: Explain put-call parity for European options, and explain how
put-call parity is related to arbitrage and the construction of synthetic options.
CFA® Program Curriculum, Volume 6, page 98
derivation
of put-call
aOurfiduciary
call and
a protectiparity
ve put.is based on the payoffs of two portfolio combinations,
©20 12 Kaplan, Inc.
Page 243
Study Session 17
Cross-Reference to CFA Institute Assigned Reading #63
-
Option Markets and Contracts
is a combination
of apayoff
pure-discount,
risklaryesscalbond
thatratipayson Xis Xat when
maturity
and
a
call
with
exerci
s
e
price
The
for
a
fi
d
uci
l
at
expi
the call is out of the money, and (S = S when the call is in the money.
is
a
share
of
stock
together
with
a
put
option
on
the
stock.
The
expi
payofftheforputa protecti
is S) S = when the put is in the
money,rationanddate5 when
is out ofvetheputmoney.
A fiduciary
call
X.
A protective put
X+
- X)
(X -
+
X
Professor's Note: When working with put-call parity, it is important to note that
the exercise prices on the put and the call and the face value of the riskless bond
are all equal to X.
When
the put is in the money, the call is out of the money, and both portfolios pay X at
expiration.
Simi5larlatyexpiration.
, when the put is out of the money and the call is in the money, both portfolios
pay
Put-call arbi
paritytrage.holdsWethatcanportfolios
identical
fs must sellas:for the same price to
prevent
express thewithput-call
paritypayof
relationship
c
RFR)T = S p
valenciesas:for each of the individual securities in the put-call parity relationship can
beEquiexpressed
TT
Sp == c-c-pS
RFR)
T
c = S pRFR)
- T = S RFR)
RFR)
p- c
The
si
n
gl
e
securiti
e
s
on
the
left-hand
side
of
the
equations
all
have
exactly
the
same
payoffs
as the portfoli
os eonntstheofright-hand
side.onThe
portfolios
on thetheright-hand
side
arebe European-styl
the synthetic
equival
the
securi
t
ies
the
left.
Note
that
options
must
relations to hold.e and the puts and calls must have the same exercise price for these
For
to synthetically
use theexample,
following
relationship:produce the payoff for a long position in a share of stock,
S = c-p
RFR)T
This
on a inlonga ristock
be synthetically
a shortmeans
put, that
and athelongpayoff
position
sk-freecandiscount
bond. created with a long call,
The
other
securities
in
the
put-call
parity
relationship
can
be
constructed
in
a
similar
manner.
+
+ X I (1 +
+
X I (1 +
+ X I (1 +
+ X I (1 +
X I (1 +
+
+ X I (1 +
Page 244
©2012 Kaplan, Inc.
Study Session 1 7
Cross-Reference to CFA Institute Assigned Reading #63 - Option Markets and Contracts
Professor's Note: After expressing the put-call parity relationship in terms ofthe
security you want to synthetically create, the sign on the individual securities will
indicate whether you need a long position (+ sign) or a short position (- sign) in
the respective securities.
Example: option valuation using put-call parity
Suppose
thata 3-month
the currentputstock
pricewitihs $52
and these price
risk-free
rateTheis 5%.putYoupricehaveis $1.50,
found
abutquote
for
option
an
exerci
of
$50.
due to$50lightcall.tradiEstimate
ng in thethecallpriceoptions,
was notcallaoption.
listed quote for the
3-month,
of thethere
3-month
Answer:
Rearranging put-call parity, we find that the call price is:
call = put+ stock-present value (X)
call= $1.50 +$52- 1.0$505 . = $4.11
This means that if a 3-month, $50 call is available, it should be priced at $4.11 per
share.
Call
0 25
LOS 63 .n: Explain how cash flows on the underlying asset affect put-call parity
and the lower bounds of option prices.
CFA® Program Curriculum, Volume 6, page I 04
positivevalcash
fltheowscash
overfltheows.period
of thethinoption,
the costa stock
of theforasset
isIfsimultaneously
ltheess asset
by thehaspresent
u
e
of
You
can
k
of
buying
Sand
borrowing
theloan(s),
present and
valuetheofloan(s)
the cashwifllloreduce
ws, PVthe. netThecostcashoffltheow(s)asset
will
provide
the
payoff
of
the
. Therefore,
for assets
with
positive
cash flows over the term of the option,
to Scan- PVsubstitute
weand
thi
s
(lower)
net
cost,
- PV , for S in the lower bound conditions
in all the parity relations.
The lower bounds for European options at time t = 0 can be expressed as:
T], and
cPo0 �� max[O,
X
(1
+
RFR)
S
PV
0
T
max[O, X (1 + RFR) - (S0 -PV
The
put-call parity relations can be adjusted to account for asset cash flows in the same
manner.
(S0 - PV = C-TP =+ (SX -(1PV+ RFR)+ PT, and
C + X (1 + RFR) 0
CF
CF
S
I
I
CF)
CF -
I
I
CF
cp) ]
cF)
©20 12 Kaplan, Inc.
Page 245
Study Session 17
Cross-Reference to CFA Institute Assigned Reading #63 - Option Markets and Contracts
LOS 63.o: Determine the directional effect of an interest rate change or
volatility change on an option's price.
CPA® Program Curriculum, Volume 6, page I 05
When
i
n
terest
rates
increase,
t
h
e
value
of
a
cal
l
option
i
n
creases
and
the
val
u
e
of
a
put
option
decreases
(holding
the pricerateofoptions
the underlying
security
constant).
This
general
resul
t
may
not
appl
y
to
interest
or
to
bond
or
T-hill
options,
where
a change
in the risk-free rate may affect the value of the underlying asset.
The no-arbitrage relations for puts and calls make these statements obvious:
TT
=S
RFR)
P= S
RFR)
T. This will have the
Here
we
can
see
that
an
i
n
crease
in
RFR
decreases
RFR)
effect
of increasing
value ofthethevaluecall,ofanda calldecreasing
value ofthethevalue
put. Aofdecrease
ioption.
n interest
rates willthedecrease
option andthe increase
a put
C
+ P - X I (1 +
C - + X I (1 +
X I (1 +
Professor's Note: Admittedly, this is a partial analysis of these equations, but it
does give the right directions for the effects of interest rate changes and will help
you remember them ifthis relation is tested on the exam.
Greater
vol
a
ti
l
i
t
y
in
the
val
u
e
of
an
asset
or
i
n
terest
rate
underlying
an
option
contract
ioptions
ncreasesaretheone-sided.
values of both
puts
and cals lvalue
s (andfalcapsls noandlowerfloors).
Thezeroreason
isit that
Since
an
option'
than
when
expifrom
res
out
of
the
money,
the
increased
upside
potential
(wi
t
h
no
greater
downsi
d
e
ri
s
k)
increased volatility, increases the option's value.
Page 246
©2012 Kaplan, Inc.
Study Session 1 7
Cross-Reference to CFA Institute Assigned Reading #63 - Option Markets and Contracts
KEY CONCEPTS
LOS 63.a
Athecallobligation,
option ontoabuy
financial
or ephysical
asset
githevesasset
the option'
s owner
thewriright,
butthenot
a
specifi
d
quanti
t
y
of
from
the
option
t
er
at
exerci
s
e
price
specifi
e
d
in
the
option
for
a
gi
v
en
time
period.
The
wri
t
er
of
a
cal
l
option
it.is obligated to sell the asset at the exercise price if the option's owner chooses to exercise
Anotputtheoption
on a financial
or physical
asset gives
theasset
option'to thes owner
thewriter
right,atbutthe
obligation,
to
sell
a
specifi
e
d
quantity
of
the
option
exerci
ed inthetheassetoptionat theforexerci
a givense price
time period.
The wris owner
ter ofchooses
a put option
iexercise
s oblisgeatedit.pricetospecifi
purchase
if the option'
to
owneris(buyer)
is said to be long the option, and the writer (seller) of
anTheoption
said to ofbeanshortoption
the option.
LOS 63.b
American options can be exercised at any time up to the option's expiration date.
European options can be exercised only at the option's expiration date.
Moneyness
for puts
s is determined
and
the market
priceandof thecallunderlying
stockby the difference between the strike price (X)
LOS 63.c
(5):
Moneyness
Galt Option
Put Option
In the money
At the money
Out of the money
LOS 63.d
Exchange-traded
options
arearestandardized,
regulated,custom
and options
backed bythata have
clearinghouse.
Over-the-counter
options
largely
unregulated
counterparty
risk.
Options
are
avai
l
abl
e
on
fi
n
ancial
securities,
futures
contracts,
interest
rates,
and
commodities.
LOS 63.e
©20 12 Kaplan, Inc.
Page 247
Study Session 17
Cross-Reference to CFA Institute Assigned Reading #63 - Option Markets and Contracts
63.frate option payoffs are the difference between the market and strike rates,
Interest
adjusted for the loan period, multiplied by the principal amount.
Atstrikexpiration,
an
i
n
terest
rate
call
receives
a
payment
when
the
reference
rate
is
above
the
the strie rate,
ke rate.and an interest rate put receives a payment when the reference rate is below
An FRA can be replicated with two interest rate options: a long call and a short put.
63.grate caps put a maximum (upper limit) on the payments on a floating-rate loan
Interest
and
are
equi
v
alent
(
f
rom
the
borrower'
s
perspective)
to
a
series
of
long
interest
rate
call
s
at the cap rate.
Interest
ratevflalent
oors put
a minimum
(lower
limit) on theto apayments
on a flinoterest
ating-rate
loan
and
are
equi
(
f
rom
the
borrower'
s
perspective)
series
of
short
rate
puts
at the floor rate.
Anfloatiinterest
combinesa capa cap
ng-raterateloancollbyarbuying
andandsellinga floaor.floor.A borrower can create a collar on a
63.
h
The
payoffoccurs
to theatholder
of a call
put option on a stock is the option's intrinsic value.
Payment
expiration
of theor option.
Payoffs
on interest
are paid after expiration, at the end of the interest rate
(loan) period
specifrateied ioptions
n the contract.
63.i value of an option is the payoff from immediate exercise if the option is in
The
intrinsic
the money, and zero otherwise.
The
time
(speculative)
value
of
an
option
i
s
the
difference
between
its
premium
(market
price) and its intrinsic value. At expiration, time value is zero.
63.j,kand maximum option values:
Minimum
LOS
LOS
LOS
LOS
LOS
Option
sr
RFR) T-1
t
RFR)T- - St]
st
American call
Cr 2: max[O, St- X I ( 1
European put
Pr 2: max[O, X I ( 1
+
Maximum Value
RFR)T-1
ct 2: max[O, St - X I (1
American put
Page 248
Minimum Value
European call
+
+
P 2: max[O, X - S ]
©2012 Kaplan, Inc.
X I (1
+
t
RFR) T-
X
Study Session 1 7
Cross-Reference to CFA Institute Assigned Reading #63 - Option Markets and Contracts
LOS
63.1
Cal
l
s
with loexercise
wer exercise
worthly more).
at least as much as otherwise identical calls
with higher
pricesprices
(and aretypical
Puts
wi
t
h
hi
g
her
exerci
s
e
prices
are
worth
at
l
e
ast
as
much
as
otherwise
identical
puts
with lower exercise prices (and typically more).
Otherwise
identical options are worth more when there is more time to expiration, with
two
exceptions:
out-of-the-money
options
withe todiexpiration
fferent expiration
dates anmayoptibeoequal
in value.
WiFar
t
h
European
puts,
l
o
nger
ti
m
may
decrease
n'
s
value
when
they are deep in the money.
63.m call (a call option and a risk-free zero-coupon bond that pays the strike price
ALOSfiatduciary
expiration)
and
a
protective
put
(a
share
of
stock
and
a
put
at
have
the
same
payoffs
trages establishes
will force these
equal options.
prices:
c at expiration,
RFR? = Sso arbip. Thi
put-callpositions
parity forto have
European
Based
on theby put-call
paritylongrelation,
a synthetic
security
(stock,threebond,securities.
call, or put) can
be created
combining
and
short
positions
in
the
other
cp == Sc - Sp - RFR)
RFR)TT
T
S = c -pRFR)T = S RFR)
p-c
LOS 63.n
When
the
underl
y
ing
asset
has
positive
cash
fl
o
ws,
the
minima,
maxima,
and
put-call
parity
relations
are adjusted
bythesubtracting
the present
valuebe replaced
of the expected
cash
flows
from
the
assets
over
the
l
i
f
e
of
option.
That
is,
S
can
by
(S
PV
of
expected cash flows).
63.o in the risk-free rate will increase call values and decrease put values (for
AnLOS
increase
options that do not explicitly depend on interest rates or bond values).
Increased
call
values.volatility of the underlying asset or interest rate increases both put values and
•
•
X
X)
+ X I (1 +
+
•
•
•
•
X I (1
+
+
X I (1 +
+ X I (1 +
+ X I (1 +
+
©20 12 Kaplan, Inc.
Page 249
Study Session 17
Cross-Reference to CFA Institute Assigned Reading #63
-
Option Markets and Contracts
CONCEPT CHECKERS
1.
of theis following
statements
aboutmoney.
moneyness is
When:
A.Which
S
0,
a
call
option
i
s
i
n
the
B. SS =a 0,puta calloptionoptionis inistheat themoney.
money.
Which of the following statements about American and European options is
wibecause
ll alwaysofbeexchange-rate
some price dirisk.
fference between American and European
A. There
options
B. European
options allanowAmerican
for exercioption
se on ormaybefore
thea higher
optionvalexpiration
date.
Priequiorvaltoentexpiration,
have
u
e
than
an
European option.
ofprithece follof theowioption
ng statements
about
putthanandthecalprice
l options
isunderlying stock.
A.Which
The
is
less
vol
a
ti
l
e
of
the
B. Option
prices
are
general
l
y
higher
the
longer
the
time
until
the
option
expues.
For
the strike price relative to the stock's underlying
price,puttheoptions,
more thetheputhigher
is worth.
Which
of
the
foll
o
wi
n
g
statements
about
options
i
s
A. The
wriputteroption.
of a put option has the obligation to sell the asset to the holder
of
the
B. The
holders price
of a callrisesoption
hasthe thestrikeobligati
on to sell to the option writer if
theThestock'
above
price.
holder of a put option has the right to sell to the writer of the option.
the and
risk-free
rate of interest will:
A.AB. idecrease
ncreaseinput
call
prices.
put
prices
and
i
n
crease
call
prices.
increase put prices and decrease call prices.
A $40 call on a stock trading at $43 is priced at $5. The time value of the option
A.B. $2.$5.
$8.
expiration,
an- AmericanRFR)
putToption
on a stock:
A.B.Priowiirstobounded
by
S
.
lcanl never
never sellsell forfor more
less thanthanitsitsintrinsic
value.
intrinsic value.
ownerexerciofsae callthe option
onandoiltakefutures
withofa thestrikoil.e price of $68.70:
A.The
can
option
del
i
very
can exercineverse theexercise
optiontheandoption
takewhen
a longtheposition
i
n
oil
futures.
B. would
spot price of oil is less than the
strike price.
C.
2.
-X
-X
> X,
Least accurate?
>
most accurate?
C.
3.
least accurate?
C.
4.
most accurate?
C.
5.
decrease
C.
6.
IS:
c.
7.
X I (1
+
C.
8.
C.
Page 250
©2012 Kaplan, Inc.
Study Session 1 7
Cross-Reference to CFA Institute Assigned Reading #63 - Option Markets and Contracts
lower bound
for a European put option is:
9. A.Themax(O,
S
-X).
T-S].
max[O, XS -X
I (1 I+(1RFR)
B.C. max[O,
+ RFR?J.
10. A.Themax(O,
lower bound
for an American call option is:
S
-X).
T- S].T
B.C. max[O,
max[O, XS -X
1(1 +I (1RFR)+ RFR)
].
11. Totheaccount
forparitypositive
cashby:flows from the underlying asset, we need to adjust
put-call
formula
A.B. adding
adding the
the future
future valvaluuee ofof thethe cash
cash flfloowsws toto
C. subtracting the present value of the cash flows from
12. AA.forward
rate
agreement
is equivalent to the following interest rate options:
long
a
call
and
a
put.
a
call
and
long
a
put.
B.C. short
long a call and short a put.
payoffonly
on anatiexerci
nterestse.rate option:
13. A.Thecomes
greatersometheperiod
higherafter
the "strike"
rate.
B.C. iscomes
option expiration.
14. Anequiivnalent
teresttoratea serifloores onof: a floating-rate note (from the issuer's perspective) is
interest
rate
puts.
A.B. long
interest rate
C. short
short interest
rate puts.
calls.
relati
oTns. is
accurate?
15. A.WhichP =ofC-theS fol+ Xlowing
I
(1
+
RFR)
T.
B.C. XC =I (1S -+ PRFR)
+ XTI -(1P+=RFR)
S - C.
isselling
sellingforat $40,
a 3-month
put atrate$50is is6%.selling
formuch,
$11,ifa anything,
3-month callcan
16. Aat stock
$50
i
s
$1,
and
the
ri
s
k-free
How
an arbitrage?
A.beB. made
$0$0.2(no8.onarbitrage).
$0.72.
the follinowivolati
ng wility.ll the value of a put option?
17. A.WhichAn ofincrease
the exerci
se price.
C.B. AA decrease
decrease iinn time
to expiration.
S.
X.
S.
least likely
c.
increase
©20 12 Kaplan, Inc.
Page 25 1
Study Session 17
Cross-Reference to CFA Institute Assigned Reading #63 - Option Markets and Contracts
ANSWERS - CONCEPT CHECKERS
Page 252
>
<
1.
C
A put option is out of the money when S
statements are true.
2.
C
American and European options both give the holder the right to exercise the option
at expiration. An American option also gives the holder the right of early exercise, so
American options will be worth more than European options when the right to early
exercise is valuable, and they will have equal value when it is not, C � c and Pr � P ·
r
r
r
3.
A
Option prices are more volatile than the price of the underlying stock. The other
statements are true. Options have time value, which means prices are higher the longer
the time until the option expires, and a higher strike price increases the value of a put
option.
4.
C
The holder of a put option has the right to sell to the writer of the option. The writer of
the put option has the obligation to buy, and the holder of the call option has the right,
but not the obligation to buy.
5.
C
Interest rates are inversely related to put prices and directly related to call prices.
6.
A
The intrinsic value is S - X = $43 - $40 = $3. So, the time value is $5 - $3 = $2.
7.
B
At any time t, an American put will never sell below intrinsic value, but may sell for
more than that. The lower bound is max[O, X - SJ.
8.
B
A call on a futures contract gives the holder the right to buy (go long) a futures contract
at the exercise price of the call. It is not the current spot price of the asset underlying
the futures contract that determines whether a futures option is in the money, it is the
futures contract price {which may be higher).
9.
B
The lower bound for a European put ranges from zero to the present value of the
exercise price less the prevailing stock price, where the exercise price is discounted at the
risk-free rate.
10. C
The lower bound for an American call ranges from zero to the prevailing stock price less
the present value of the exercise price discounted at the risk-free rate.
11. C
If the underlying asset used to establish the put-call parity relationship generates a cash
flow prior to expiration, the asset's value must be reduced by the present value of the
cash flow discounted at the risk-free rate.
12. C
The payoff to a FRA is equivalent to that of a long interest rate call option and a short
interest rate put option.
13. C
The payment on a long put increases as the strike rate increases, but not for calls. There
is only one payment and it comes after option expiration by the term of the underlying
rate.
14. B
Short interest rate puts require a payment when the market rate at expiration is below
the strike rate, j ust as lower rates can require a payment from a floor.
15. B
The put-call parity relationship is S + P = C + X I ( 1 + RFR) T. All individual securities
can be expressed as rearrangements of this basic relationship.
X and in the money when S
©2012 Kaplan, Inc.
X. The other
Study Session 1 7
Cross-Reference to CFA Institute Assigned Reading #63 - Option Markets and Contracts
16. C
A synthetic stock is: S C - P + X I ( 1 + RFR) T $ 1 - $ 1 1 + 50 I ( 1 .06) 0 · 25 $39.28.
Since the stock is selling for $40, you can short a share of stock for $40 and buy the
synthetic for an immediate arbitrage profit o f $0.72.
17. A
Increased volatility of the underlying asset increases both put values and call values.
=
=
©20 12 Kaplan, Inc.
=
Page 253
The following is a review of the Derivatives principles designed to address the learning outcome
statements set forth by CFA Institute. This topic is also covered in:
SWAP MARKETS AND CONTRACTS
Study Session 17
EXAM Focus
This
topic
revi
e
w
introduces
swaps.
The
fi
r
st
thing
you
must
learn
is
the
mechanics
of
swaps
so that
youbecanablcalculate
the payments
oncashanyflofowstheoftypes
of can
swapsbecovered.
Beyond
that,
you
should
e
to
recognize
that
the
a
swap
duplicated
with
capital
markets
transactions
(make
a
loan,
issue
a
bond)
or
wi
t
h
other
deri
v
ati
v
es
(a
series
of forward
rate agreementsfloating
or inrate
terestdetermi
rate options).
Common
mistakes
include
forgetti
ng
that
the
current-period
n
es
the
next
payment,
forgetti
n
g
to
adj
u
st
the
interestfiedrates
forswap,
the payment
period,
forgetti
ng toswaps
add anyinvolmargin
above theofflocurrencies
ating rate
speci
i
n
the
and
forgetti
n
g
that
currency
v
e
an
exchange
at the initiation and termination of the swap. Don't do these things.
SwAP CHARACTERISTics
Before wethegetdifferent
into thetypes
detailofs ofswaps.
swaps,Youa simple
introduction
mayswapshelpasastheyouexchange
go of
through
can
vi
e
w
interest
rate
one
loan
for
another.
If
you
lend
me
$10,
0
00
at
a
fl
o
ating
rate,
and
I
lend
you
$10,
0
00
atchange
a fixedhands.
rate, The
we have
created
a swap.makeTherethisispointless.
no reasonAtforeachthepayment
$10,000date,
to actual
llyl
two
equal
loans
I
wi
make
a
payment
to
you
based
on
the
fl
o
ati
n
g
rate,
and
you
wi
l
l
make
one
to
me
based
onthethelargerfixedpayment
rate. Again,
it makes
no sense
to exchange
thedifference
full amounts;
the oneThiwisth
liability
wi
l
l
make
a
payment
of
the
to
the
other.
describes the payments of a fixed-for-floating or "plain vanilla" swap.
Aratecurrency
swapandcanyoube vilendewedmethethesame
way. Ifiamount
lend youof yen1,000,at 0today'
00 euros
at the euro
of
interest,
equivalent
s
exchange
rate atsame
the yenamounts
rate ofofincurrency
terest, weathave
done a currency
swap.twoWeloans.
will "swap"
back I
these
the
maturity
date
of
the
In
the
interim,
borrowed
yen, so Iinmake
interest payments
euros.yen interest payments, and you borrowed euros and must make
For
other
types
of
swaps,
we
just
need
to
describe
how
the
payments
are
calculated
on
Fortoantheequity
swap,
Istock
couldindex,
promiseandtoyoumakecouldquarterly
payments
onfixed-rate
your loan
tothe(ormeflloans.
equal
return
on
a
promise
to
make
ovating-rate)
payments
toed-rate
me. Ifpayment
the stocktoindex
goesa down,
myequal
payments
todecline
you are
negati
e
(i.
e
.
,
you
make
a
fi
x
me
payment
to
the
in the indexbasedoveronthethequarter).
If theincrease
indexiwent
upindex.overAgain,
the quarter,
I would coul
maked bea
payment
percentage
n
the
the
payments
"netted" so that only the difference changes hands.
This
intui
t
i
v
e
expl
a
nation
of
swaps
should
make
the
fol
l
owing
a
bit
easier
to
understand.
Now let's dive into the mechanics and terminology of swaps. We have to specify exactly
and
Page 254
©2012 Kaplan, Inc.
Study Session 1 7
Cross-Reference to CFA Institute Assigned Reading #64 - Swap Markets and Contracts
howloaned,
the interest
payments
wiloans
l be calareculfor.ated,Swapshowareoftencustom
they instruments,
are made, howandmuch
is to
bespecify
and
how
l
o
ng
the
we
can
any terms both of us can agree on.
LOS 64.a: Describe the characteristics of swap contracts and explain how
swaps are terminated.
CPA® Program Curriculum, Volume 6, page 120
Swaps
are
agreements
to
exchange
a
series
of
cash
flows
on
periodic
over
aswap,
certainonetime
period
(e.g., quarterly
payments
overontwotheyears).
In theprincipal
simplestspecif
typeiedof in
party
makes
interest
payments
notional
the swapthe two
in return
for are sopayments
from
the other
party.isAtmade.
eachThe
settlement
date,
payments
that
only
one
(net)
payment
party
witermed
th thethegreater liability
makesanda payment
to theendsother
party.termination
The lengthdate.of theA swap
swapcanis
of
the
swap
the
contract
on
the
bedates.decomposed into a series of forward contracts (FRAs) that expire on the settlement
In many respects, swaps are similar to forwards:
Swaps typical
ly require
no payment by either party at initiation.
Swaps
are
custom
instruments.
Swaps
areare largely
not traded
in anyated.organized secondary market.
Swaps
unregul
Default
risk
i
s
an
important
aspect
of
the
contracts.
Most
particiarepantsrarelinytheswapsswapsmarket
marketparticipants.
are large institutions.
Individuals
There
areThere
swaps arefacilitators
who large
bringbanks
togetherandparties
withfirms,
needswho
for theact opposite
sides
ofin swaps.
also
dealers,
brokerage
as
principals
trades just
as theycontracts
do in forward
contracts.
rge business; the total notional
principal
of swaps
is estimated
at overIt is$50a latrillion.
settlement dates
fixed-rate
floating-rate
netted
tenor
•
•
•
•
•
•
•
How Swaps are Terminated
There are ways terminate a swap prior to its original termination date.
Aforwards,
cash payment
cancan beaccumulate
made by one
party
that isprices
acceptable
to
theratesother
party.
Li
k
e
swaps
value
as
market
or
interest
change.
If
the
party
that
has
been
disadvantaged
by
the
market
movements
is
wicounterparty
lling to makeis will
a payment
of theit,swap'theys value
to the ycounterparty,
ing to accept
can mutuall
terminate theandswap.the
2. offers for early termination
Just as wiareth forwards,
if thethetermsalternati
oftheveoriginal
counterparty
unacceptable,
is
to
enter
an
offsetting
swap.
Ifprice
our 5-year
quarterly-pay
flveoating
swapswap
has two
years
to go, weourcanfloseek
a
current
on
a
pay-fi
x
ed
(recei
fl
o
ating)
that
will
provide
ating
payments and leave us with a fixed-rate liability.
four
to
1 . Mutual termination.
Offsetting contract.
©20 12 Kaplan, Inc.
Page 255
Study Session 17
Cross-Reference to CFA Institute Assigned Reading #64 - Swap Markets and Contracts
Just
aswewitrecei
h forwards,
exixedtinong aourswaporiginal
may in5-year
volve pay
takinflgoatia loss.
Consider
the casepay
where
v
e
3o/o
fi
n
g
swap,
but
must
4o/o
fi
x
ed
on
the
offsetting
swap.
We
have
locked
in
a
loss
because
we
must
pay
1
o/o
higher
ratesquarterly
on the offsetti
ng swapfor thethannextwe recei
vyears,
e on theandswap
wee nothing
are offsetting.
We
must
make
payments
two
recei
v
i
n
return.
Exiting
a
swap
through
an
off
s
etting
swap
with
other
than
the
original
counterparty
will also expose the investor to default risk, just as with forwards.
3. counterparty
It is possible
to
sell
the
swap
to
another
party,
with
the
permission
of
the
to the swap.market.
This would be unusual, however, as there is not a
functioning secondary
4. offsetting Aswap providesis anan option
toto enter
into aanswap.
The
optionConsider
to enterthat,
into iann the
option
terminate
existi
n
g
swap.
case ofpaythe fiprevious
5-year
pay. Exercising
floating swap,
we purchased
a 3-year
call optionswap
on ato
2-year
x
ed
swap
at
3o/o
this
swap
would
give
us
the
offsetting
exit our original swap. The cost for such protection is the swaption premium.
Resale.
Swaption.
swaption
LOS 64.b: Describe, calculate, and interpret the payments of currency swaps,
plain vanilla interest rate swaps, and equity swaps.
CPA® Program Curriculum, Volume 6, page 123
Inpayments
a from the other
one party
makes
payments
denominated
in
one
currency,
whi
l
e
the
party are made
in currencies
a second currency.
Typically,
the notional
amounts
of
the
contract,
expressed
i
n
both
at
the
current
exchange
rate,
are
exchanged
at
contract
initiation
and
returned
at
the
contract
termination
date
in
the
same amounts.
Aninitiation
examplein ofreturn
a currency
swapmillion.
is as follows:
Party
1 pays
Party 2dates,
$10 million
athavicontract
for
On
each
of
the
settlement
Party
1,
ngto
received
euros,
makes
payments
at
a
6o/
o
annualized
rate
in
euros
on
the
million
Party
2.
Party
2
makes
payments
at
an
annualized
rate
of
5o/
o
on
the
$10
million
to
Party
These settlement
single 1.currency
interest ratepayments
swap. are both made. They are not netted as they are in a
Aswishes
an exampl
e ofishwhat
motivatesin Australia
a currencyandswap,wantsconsider
that thea U.costs
S. firm,in Australian
Party A,
to
establ
operations
to
finance
dollars (AUD).
The firmUSD-denominated
finds, however, thatdebt,issuing
debttheyin AUD
is relativelyunknown
more in
expensive
than
issuing
because
are
relatively
Austral
i
a
n
financial
markets.
An
al
t
ernative
to
issuing
ADD-denominated
debt
is
to
issue
USD
debtfindsandanenter
into a USD/AUD
currency
swap.theThrough
a swapsinfacilitator,
the
U.
S
.
firm
Australian
firm,
Party
B,
that
faces
same
situation
reverse.
They wish to issue AUD debt and swap into a USD exposure.
There are four
available.
1. Party
A
pays
a
fi
x
ed
rate
on
AUD
received,
and
Party
B
pays
a
fi
x
ed
rate
on
USD
received.
currency swap,
€9.8
€9.8
possible types of currency swaps
Page 256
©2012 Kaplan, Inc.
Study Session 1 7
Cross-Reference to CFA Institute Assigned Reading #64 - Swap Markets and Contracts
2. Parry
received.A pays a floating rate on AUD received, and Parry B pays a fixed rate on USD
A
pays
a
fi
x
ed
rate
on
AUD
received,
and
Parry
B
pays
a
fl
o
ati
n
g
rate
on
USD
3. Parry
received.
4. Parry
received.A pays a floating rate on AUD received, and Parry B pays a floating rate on USD
Following are the steps in a fixed-for-fixed currency swap:
The
notional
principal
actualBlyandchanges
handsback.
at theWhy?
beginning
ofthethemotivation
swap.
Party
A
gi
v
es
USD
to
Party
gets
AUD
Because
of Parry A was to get AUD and the motivation of Parry B was to get USD.
Interestianpayments
areratemade
without
netting.
Parryof AUD
A, whotogotParryAUD,
pays B,the
Austral
interest
on
the
notional
amount
B.
Parry
who
got toUSD,ParrypaysA. Since
the U.theS. inpayments
terest rateareonmade
the notional
amount
ofUSDnetting
received
in
di
f
ferent
currencies,
is not a typical practice.
Ateachtheother
termination
the swap notional
agreementamounts.
(maturity), the counterparties give
back theofexchanged
currency swap are illustrated in Figure 1. The cash flows associated with this
Step 1 :
Notional principal is swapped at initiation.
Step 2:
Full interest payments are exchanged at each settlement
date, each in a different currency.
Step 3:
Notional principal is swapped
again at the termination ofthe agreement.
Figure 1: Fixed-for-Fixed Curren cy Swap
SWAP INITIATION
The Australian firm wanes USD.
Swaps AUD for USD
Has or can borrow AUD.
Swaps USD for AUD
The U.S. firm wants AUD.
Has or can borrow USD.
SWAP INTEREST PAYMENTS
TI1e Australian firm
Australian pays USD interest
has use of the USD.
The U.S . firm has
use of the AUD.
U.S. firm pays AUD interest
SWAP TERM INATION
The Australian firm returns
--------+�
USD returned
the USD borrowed.
AUD returned
©20 1 2 Kaplan, Inc.
The U.S. firm returns
the AUD borrowed.
Page 257
Study Session 17
Cross-Reference to CFA Institute Assigned Reading #64 - Swap Markets and Contracts
Calculating the Payments on a Currency Swap
swap
BBUnited
can borrow
in
the
United
States
for
9o/o,
whil
e
AA
has
to
pay
1
Oo/
o
to
borrow
in
the
States.
AAl becandoing
borrowbusiness
in Australia
for 7o/oa and, whilneeds
e BBAUD,
has towhipayle8o/AAo towiborrow
in
Australia.
BB
wil
i
n
Australi
l
l
be
doinneeds
g business
i1.n0themillion
UnitedandStates
and needs
USD.
The exchange
rate itos 2AUD/USD.
AA
USD
BB
needs
AUD2.
0
million.
They
decide
borrow
the
funds lhave
ocallypaidandhadswaptheytheborrowed
borrowedinfunds,
charging
each other
the rateperiodthe isother
party
would
the
forei
g
n
market.
The
swap
for
fi
ve
years. Calculate the cash flows for this swap.
Example: Fixed-for-fixed currency
Answer:
AA and BB each go to
their own domestic bank:
AA
borrows
AUD2.0 million, agreeing to pay the bank 7o/o, or AUD 140,000
annual
l
y
.
BBannuall
borrows
USD
1.0
million,
agreeing
to
pay
the
bank
9o/o
,
or
USD90,
0
00
y.
AA and BB swap currencies:
AA
gets AUD2.
USDI.O0 million,
interestininAUD
USDannuall
annualyly. .
BB gets
million, agreeing
agreeing toto pay
pay BBAA 10o/o
8o/o interest
•
•
•
•
They pay each other the annual interest:
•
•
AA
owes AA
BB AUD
USD 100,
BB owes
160,000000 inin interest
interesttoto bebe paid
paid onon each
each settlement
settlement date.
date.
They each owe their own bank the annual interest payment:
•
•
•
AA pays the000Australian
bankAUD140,000 (but getsAUD160,000 from BB, an
AUD20,
gain).
BBUSD10,
pays 0the00U.gain).
S. bank USD90,000 (but gets USD100,000 from AA, a
They
both
gain
by
swapping
(AA
is
ahead
AUD20,
0
00
and
BB
is
ahead
USD
10,000).
In jive years, they reverse the swap. They return the notionalprincipal.
•
•
AA
gets AUD2.
million from
fromAABB and
and then
then pays
pays back
backthethe Australian
BB gets
USDI.O0 million
U.S. bank. bank.
Interest Rate Swaps
flThe
ng-rate) payments. (A
foroatianother.
ininvolves
volves traditrading
ng fixoneed interest
for
set of florateatingpayments
rate payments
plain vanilla interest rate swap
basis swap
Page 258
©2012 Kaplan, Inc.
Study Session 1 7
Cross-Reference to CFA Institute Assigned Reading #64 - Swap Markets and Contracts
Thetheparty who wants
flotheatinswap.
g-rateTheinterest
payments who
agreesreceives
to paythefixed-rate
interest andand
has
si
d
e
of
counterparty,
fi
x
ed
payments
agrees to pay variable-rate interest, has the
side of the swap and is called the
flat
orTheplusfloating
a spread.rate quoted is generally the
Let's look at the cash flows that occur in a
notional principal
is thetosame
for both
counterparties
and is
iBecause
n the samethe currency
units, thereswapped
iins sinonglneed
actually
exchange
the
cash.
eatcurrency
swaps. of the settlement
The
determi
n
ati
o
n
of
the
variabl
e
rate
is
the
beginning
period,
and
the
cash
interest
payment
is
made
at
the
end
of
the
settlement
period.
Because
the interest
payments
are ithen thecash.sameThecurrency,
therebetween
is no need
forxed-rate
both
counterparties
to
actual
l
y
transfer
di
f
ference
the
fi
payment
and the variable-rate payment is calculated and paid to the appropriate
counterparty.
Atno thetransfer
conclusion
of funds.of the swap, since the notional principal was not swapped, there is
You
loses.should note that swaps are a zero-sum game. What one party gains, the other party
The net is:formula for the
based on a 360-day year and a floating rate of
(
)
(=(
360
If this Ifnumber
is positive,
the fixed-rate
payer
apayer
net payment toa nettheflow
floating-rate
party.
this
number
is
negative,
then
the
fixed-rate
from
the
floating-rate payer.
pay-fixed
pay-floating
floating-rate payer.
London Interbank Offered Rate (LIBOR),
plain vanilla interest rate swap.
•
Notional
•
principal is generally not swapped
Net interest is paid by the one who owes it.
•
fixed-rate payer,
LIBOR
(net fixed-rate payment)
swap fixed rate - LIBOR c-l )
number of days
(notional principal)
owes
receives
Professor's Note: For the exam, remember that with plain vanilla swaps, one
party pays fixed and the other pays a floating rate. Sometimes swap payments are
based on a 365-day year. For example, the swap will specify whether 90/360 or
90/365 should be used to calculate a quarterly swap payment. Remember, these
are custom instruments.
Example: Interest rate risk
Consi
d
er
a
bank.
Its
deposi
t
s
represent
liabilities
and
are
most
li
k
el
y
short
term
in
Inloans.
other words,
deposits
represent
floofating-rate
liabilities.
The
bank
assets
are
prinature.
m
arily
Most
loans
carry
fi
x
ed
rates
interest.
The
bank
assets
are
fi
x
ed-rate
and
bank
liabilities
are
fl
o
ating.
Explai
n
the
nature
of
the
interest
rate
ri
s
k
that
the
bank
faces, and describe how an interest rate swap may be used to hedge this risk.
©20 12
Kaplan, Inc.
Page 259
Study Session 17
Cross-Reference to CFA Institute Assigned Reading #64 - Swap Markets and Contracts
Answer:
The
risk
the
bank
faces
i
s
that
short-term
interest
rates
will
rise,
causing
cash
payment
depositsrates
to increase.
This
would
not beloana major
problem
ifwilcashl not.inflows
albank
so increase
asonremains
interest
ri
s
e,
but
with
a
fi
x
ed-rate
portfoli
o
they
If
the
unhedged as interest rates rise, cash outflows rise and bank profits fall.
The
bank
can
hedge
thi
s
ri
s
k
by
entering
into
a
fi
x
ed-for-fl
o
ating
swap
as
the
fi
x
ed-rate
payer. Theonflodeposits.
ating-rateNote
payments
received
would
offsets costs
any idoncrease
in thestillfloating-rate
payments
that
if
rates
fall,
the
bank'
not.
They
pay fitoxed
fortheirthelower
termcosts
of theonswap
and
recei
v
e
(l
o
wer)
fl
o
ati
n
g-rate
payments
that
correspond
deposits.
Calculating the Payments on an Interest Rate Swap
Example: Calculating the payments on an interest rate swap
Bank
A enters
intoat aafi$1,xed000,rate0of006%quarterly-pay
plai
n vanilla
interest
rate
swap aspayer
the
fiagrees
xed-rate
payer
based
on
a
360-day
year.
The
fl
o
ating-rate
to pay 90-day LIBOR plus a 1 o/o margin; 90-day LIBOR is currently 4%.
now
90-day LIBOR rates are: 5.0%
4.5% 90180daysdaysfrom
from
now
360 days
days from
from now
now
6.5.5%
0% 270
Calculate the amounts Bank A pays or receives 90, 270, and 360 days from now.
Answer:
The
payment
90
days
from
now
depends
on
current
LIBOR
and
the
fixed
rate
(don'
t
forget the 1 o/o margin).
Fixed-rate payer pays:
[o.o6 (;;o)-(o.o4 o.o1)(;6°0 )jx 1,ooo,ooo = $2,500
+
Page 260
©2012 Kaplan, Inc.
Study Session 1 7
Cross-Reference to CFA Institute Assigned Reading #64 - Swap Markets and Contracts
270
days
from
now,
the
payment
i
s
based
on
LIBOR
180
days
from
now,
whi
c
h
is
5%.
Addi
makes payment.
the floating-rate 6%, which is equal to the fixed rate, so
therenigs nothenet1%thimargin
rd quarterly
The bank's "payment" 360 days from now is:
[o.o6(;6°0 )-(0.055 o.o 1)(;6°0 )] 1,ooo,ooo -$1,250
Because
ating-rate
payment
$1,250 atthetheflofourth
payment
date.exceeds the fixed-rate payment, Bank A will
+
x
=
receive
Equity Swaps
Inby anoneequity
swap,
the
return
on
a
stock,
a
portfolio,
or
a
stock
index
is
paid
each
period
party
in returnorfortheatotal
fixed-rate
orincluding
floating-rate
payment.
Thestock,
returnportfolio,
can be theor
capital
appreciation
return
dividends
on
the
index.
Inpayorder
to
reduce
equity
risk,
a
portfolio
manager
might
enter
into
a
1-year
quarterly­
S&Peach500quarter
indexisswap
andagainst
agree tothereceive
a fixedto determine
rate. The percentage
increase
in the
index
netted
fixed
rate
the
payment
to
be
made.
Ifinthethe index
return
is negative,manager.
the fixed-rate
payeramong
mustswaps,
also payequity
the percentage
decline
index
to
the
portfolio
Uniquely
swap
payments
can
be floating
on bothratesidesswaps,
and thebothpayments
areandnotfloating
knownpayments
until the areendknown
of the at the
quarter.
With
interest
the
fixed
beginning of period for which they will be paid.
Aoverswaptheonperiod
a singleof thestockswap.canTobe protect
motivateda large
by acapital
desire gain
to protect
the
value
of
a
position
in ana single
stock,
and
to avoid
aequity-returns
sale for tax orpayer
controlandreasons,
an
investor
could
enter
into
equity
swap
as
the
receive
a
fixed
rate
i
n
return.
Any
decline
i
n
the
stock
price
would
be paid to thetheinvestor
the settlement
dates, pluslessthethefixed-rate
payment. If the
stock appreciates,
investoratmust
pay the appreciation
fixed payment.
©20 12 Kaplan, Inc.
Page 261
Study Session 17
Cross-Reference to CFA Institute Assigned Reading #64 - Swap Markets and Contracts
Calculating the Payments on an Equity Swap
Example: Equity swap payments
Ms.
Smi
t
h
enters
into
a
2-year
$10
million
quarterly
swap
as
the
fi
x
ed
payer
and
will
receive they atindex
return
on theof theS&Pnext500.three
Thequarters,
fixed ratetheis 8%,
andleveltheis:in1030,
dex is 968,
currentl
986.
At
the
end
i
n
dex
and 989.
Cal
c
ul
a
te
the
net
payment
for
each
of
the
next
three
quarters
and
identify
the
direction
of the payment.
Answer:
The
percentage
change in the index each quarter, Q, is: Q1 = 4.46%, Q2 = -6.02%,
and
Q3
= 2.17%. The index return payer will receive 0. 0 8 I 4 = 2% each quarter and
pay the index return, therefore:
Q1: Index
Index return
return payer
payer pays
4.46%
- 2.02.0%00%= 2.=46%
or $246,
000.000.
Q2:
receives
6.
0
2%
8.
0
2%
or
$802,
Q3: Index return payer pays 2.17% - 2.00% = 0.17% or $17,000.
+
Page 262
©2012 Kaplan, Inc.
Study Session 1 7
Cross-Reference to CFA Institute Assigned Reading #64 - Swap Markets and Contracts
KEY CONCEPTS
LOS
64.aare based on a notional amount of principal. Each party is obligated to pay a
Swaps
percentage
return
onPercentage
the notionalpayments
amountareat periodic
settlement
datesfiover
the liorfe the
(tenor)
of
the
swap.
based
on
a
fl
o
ating
rate,
x
ed
rate,
return on an equity index or portfolio.
Except
in periodic
the case ofpayments
a currencyare swap,
no(themoney
changes
hands
atargerthe amount
inceptionpaysof thethe
swap
and
netted
party
that
owes
the
l
difference to the other).
Swaps
instruments,
are largely(defaul
unregulated,
markets,areandcustom
are subject
to counterparty
t) risk. do not trade in secondary
SwapsEntering
can be into
terminated
prior toswap,theirsometimes
stated termination
datesa by:swaption (most
an
offsetting
by
exercising
common).with the counterparty to terminate (likely involves making or receiving
Agreeing
compensation).
Selling the swap to a third party with the consent of the original counterparty
(uncommon).
64.b vanilla (fixed-for-floating) interest-rate swap, one party agrees to pay a floating
InLOS
a
plain
rate
of
interest
on
the
notional
amount
and
the
counterparty
agrees
to
pay
a
fi
x
ed
rate
of
interest.
The
formula
for
the
net
payment
by
the
fi
x
ed-rate
payer,
based
on
a
360-day
year
and
the number of days in the settlement period is:
(net fixed rate payment )r
= (swap fixed rate-LIBORr-I ) ( number360of days ) (notional principal)
In an equityor swap,
thein exchange
returns payer
makes
payments
basedpayments.
on the return
onstock,
a stock,
portfolio,
index,
for
fi
x
edor
fl
o
ating-rate
If
the
portfolio,
or index,anddeclines
in value
the returns
interest payment
a payment
basedoveron thethe period,
percentage
decline payer
in value.receives the
In thea currency
swap,of thetheswap,
notional
principal
(in two
differentin twocurrencies)
iscurrencies
exchangedare
atexchanged
inception
periodic
i
n
terest
payments
different
on
settlement
dates,
and
the
same
notional
amounts
are
exchanged
(repaid)
on the termination date of the swap.
•
•
•
©20 12 Kaplan, Inc.
Page 263
Study Session 17
Cross-Reference to CFA Institute Assigned Reading #64 - Swap Markets and Contracts
CONCEPT CHECKERS
1. A.WhichIn anof ithenterest
following
statements
about principal
swaps is is swapped.correct?
rate
swap,
the
notional
B.C. The
defaulvanill
t problem
is theratemostswap,important
In a plain
a interest
fixed rateslimitation
are tradedto thefor swap
variablemarket.
rates.
following
statements
about
swaps
is
correct?
2. A.WhichTheoftimethe frame
of
a
swap
i
s
cal
l
e
d
i
t
s
tenor.
currency swap,
swap, only
net interest
payments
are made.
B.C. InIn aa currency
the
notional
principal
is
actually
twice, once at
the beginning of the swap and again at the terminationswapped
of the swap.
oflithettlefollowing
statements is
an advantage of swaps? Swaps:
3. Which
A.B. have
or
no
regulation.
minimize
defaultcontracts.
risk.
C. have
customized
4. A.In ansettlequity
swap:
e
ment
i
s
made
only
at
swap
termination.
notionalforprincipal.
B.C. shares
returnsareonexchanged
an index canforbetheswapped
fixed-rate payments.
vanillaprincipal
interest rateis swapped.
swap:
5. A.In atheplainnotional
the net iprincipal
nterest payments
B.C. only
the notional
is returnedareatmade.
the end of the swap.
the follorate
wingswap
statements
about
swap markets
is
correct?
6. A.WhichIn anofinterest
only
the
net
interest
i
s
exchanged.
notional
principal is swapped at inception and at termination of a
B. The
currency
swap.
C. exchanged
Only the netin dia fcurrency
ference between
swap. the dollar interest and the foreign interest is
least likely
least likely
least likely
least likely
Page 264
©2012 Kaplan, Inc.
Study Session 1 7
Cross-Reference to CFA Institute Assigned Reading #64 - Swap Markets and Contracts
Use the following data to answer Questions 7 through
Consider
a 3-year units
annualandcurrency
swap(USF)
that takes
place
betweenunits.
a foreign
firmthe(FF)
wirate
thpayer
FC currency
a
U.
S
.
firm
with
$
currency
USF
is
fixed­
andandFF8o/ois theat thefloating-rate
payer.
The
fixed
interest
rate5%atcurrently;
the initiation
ofthethe
swap
i
s
7%,
end
of
the
swap.
The
variable
rate
i
s
6o/o
at
endswap,
of year$1.1;08o/omillion
at theisendexchanged
of year 2;at and
7% at therateendofofFC2.
year03.= At$1.the0 . Atbeginning
of
the
an
exchange
the
end
of
the swap period, the exchange rate is FC 1.5 = $1.0.
Note: Wiinterest
th thisrates.
currency swap, end-of-period payments are based on beginning-of­
period
the initiation of the swap, which of the following statements is
7. Atcorrect?
FF gigivesvesUSFFF $1.0
million.
A.B. USF
$1.0
million.
C. USF gives FF FC2.0 million.
8. AtA. theUSFendpaysof year
2:
FC140,
000;00;FFFFpayspays$70,$60,0000.00.
B.C. USF
USF pays
FC60,
0
pays USD70,000; FF pays FC60,000.
9. Atamounts?
the termination of the swap, FF gives USF which of the following notional
A.B. $1FC2,million.
000,0000.00.
C. FC1,500,
of
year
3,
FF
wi
l
l
pay
whi
c
h
of
the
followi
n
g
total
amounts?
10. A.At the$1,end
B.C. FC2,
$1,0070,80,160,0000.00.000
10.
most likely
©20 1 2 Kaplan, Inc.
Page 265
Study Session 17
Cross-Reference to CFA Institute Assigned Reading #64 - Swap Markets and Contracts
13.
Lambda
Corp.quarterly-pay
has a floating-rate
liability
and wants a fixed-rate
exposure.
Theypayer.
enter
into
a
2-year
$4,000,
0
00
fixed-for-floating
swap
as
the
fixed-rate
The
Gamma
Corp. The
is 6o/o year.
and theRealizations
floating rateofLIBOR
is 90-dayare:
LIBORcounterparty
1 o/o, withisboth
calculated
basedfixedon arate360-day
Annualized
LIBOR
5.0%
Current
InIn 21 quarter
5.5%
quarters
5.4%
InIn 34 quarters
5.8%
quarters 6.0%
first swap
payment
is:
11. A.Thefrom
Gamma
to Lambda.of the swap.
B. known
at
the
initiation
$5,000.
second from
net swap
payment
is:
12. A.The$5,000
Lambda
to Lambda.
Gamma.
000 from
Gamma
to
B.C. $4,$5,000
from Gamma to Lambda.
fi
f
th
net
quarterly
payment
on
the
swap
is:
13. The
A.B. 0.$10,000.
$40,000.
Use the following information to answer Questions 11 through
+
c.
c.
Page 266
©2012 Kaplan, Inc.
Study Session 1 7
Cross-Reference to CFA Institute Assigned Reading #64 - Swap Markets and Contracts
ANSWERS - CONCEPT CHECKERS
1.
A
In an interest rate swap, the notional principal is only used to calculate the interest
payments and does not change hands. The notional principal is only exchanged in a
currency swap.
2.
B
In a currency swap, payments are not netted because they are made in different
currencies. Full interest payments are made, and the notional principal is also exchanged.
3.
B
Swaps do not minimize default risk. Swaps are agreements between two or more parties,
and there are no guarantees that one of the parties will not default. Note that swaps do
give traders privacy and, being private transactions, have little to no regulation and offer
the ability to customize contracts to specific needs.
4.
C
Equity swaps involve one party paying the return or total return on a stock or index
periodically in exchange for a fixed return.
5.
B
In a plain vanilla interest rate swap, interest payments are netted. Note that notional
principal is not exchanged and is only used as a basis for calculating interest payments.
6.
C
In a currency swap, full interest payments are made, and the notional principal is
exchanged.
7.
B
Because this is a currency swap, we know that the notional principal is exchanged.
Because USF holds dollars, it will be handing over dollars to FF.
8.
A
Remember, the currency swap is pay floating on dollars and pay fixed on foreign.
Floating at the end of year 1 is 6o/o of $ 1 .0 million. Since payments are made in arrears,
FF pays $60,000 and USF pays FC140,000 at the end of year 2.
9.
A
The notional principal is exchanged at termination. FF gives back what it borrowed,
$ 1 .0 million, and the terminal exchange rate is not used.
10. A
FF is the floating-rate dollar payer. FF will pay the return of $ 1 . 0 million in principal
at the termination of the swap, plus the floating rate payment (in arrears) of 8% x $ 1 .0
million $80,000. The total payment will be $ 1 ,080,000.
=
11. B
The first payment is based on the fixed rate and current LIBOR + 1 o/o, which are both
6o/o. There is no net payment made at the first quarterly payment date and this is known
at the initiation of the swap.
12. C
The second quarter payment is based on the realization of LIBOR at the end of the first
90
4, 000,000 = $65,000. The fixed
quarter, 5.5%. The floating rate is: (5.5% + 1 o/o)
360
( )
rate payment is $60,000, making the net payment $5,000 from Gamma to Lambda.
13. B
The fifth quarterly floating-rate payment is based on the realization of LIBOR at the
end of the fourth quarter, which is 6o/o. With the 1 o/o margin, the floating rate is 7o/o
compared to 6o/o fixed, so the net payment is $ 1 0,000.
©20 12 Kaplan, Inc.
Page 267
The following is a review of the Derivatives principles designed to address the learning outcome
statements set forth by CFA Institute. This topic is also covered in:
RISK MANAGEMENT APPLICATIONS
OF OPTION STRATEGIES
Study Session 17
EXAM Focus
The
mostdiaigrams
mportantfor aspect
ofputthiors topi
c erevicalelwpositions
is the interpretation
ofoption
profi
t diarevi
grams.ew.
Payoff
singl
e
si
n
gl
were
covered
in
our
options
Inththioptions.
s review,Inwea protective
introduce put
profiposition,
t diagramsweandcombine
two option
strategi
es andthatacombine
stock
wistrategy,
a
share
of
stock
put.
With
this
we
essenti
a
l
y
purchase
downsi
d
e
protection
for
the
stock
(li
k
e
insurance).
A
covered
positing othen consists
of buyingona share
of stockin return
and selliforntheg a caladded
l on income
it. This from
strategytheequates
tothecallsellicall.
upside
potential
the
stock
salebutof
On
the
Level
CFA®
Exam,
you
wi
l
not
be
required
to
draw
payoff
di
a
grams,
you
are
expected
to
know
how
to
interpret
them
and
fi
n
d
the
breakeven
price,
maxi
m
um
gains and losses, and the gains and losses for any stock price at option expiration.
I
LOS 65.a: Determine the value at expiration, the profit, maximum profit,
maximum loss, breakeven underlying price at expiration, and payoff graph of
the strategies of buying and selling calls and puts and determine the potential
outcomes for investors using these strategies.
CPA® Program Curriculum, Volume 6, page 144
Call Option Profits and Losses
Consider
a $5calltooption
witer.th aAtpremium
of $5if theandpria cstrie ofkethepricestockof $50.
Thisthanmeans
the
buyer
pays
the
wri
expiration,
i
s
less
or
equal
to thewri$50
strike
price (theis ahead
option$5.hasAszerothe value),
the buyer
of the$50,option
is outof$5,theand
the
t
er
of
the
option
stock'
s
price
exceeds
the
buyer
option
starts
to
gai
n
(breakeven
wi
l
come
at
$55,
when
the
value
of
the
stock
equals
the
strike
pricofe and
the optionstartspremium).
However,figasuresthewilprice
ofatthe$55,stockwhenmovesthe upward,
thethe seller
the
option
to
lose
(negative
l
start
value of
stock equals the strike price and the option premium).
The
profit/loss
diagram
for theis buyer
(long)in Figure
and wri1.terThi(short)
of the calldiagram
optionillustrates
we have
been
discussing
at
expiration
presented
s
profit/loss
the following:
The
mum$50).loss for the buyer of a call is the loss of the $5 premium
(atTheanymaxi
S
(at S breakeven
= $55). point for the buyer and seller is the strike price plus the premium
•
•
Page 268
:S
©2012 Kaplan, Inc.
Cross-Reference to CFA Institute Assigned Reading #65
-
Study Session 1 7
Risk Management Applications of Option Strategies
The profitlopotential
to theter buyer
ofcalltheoption
optionis unlimited.
is unlimited, and, conversely, the
potential
ss
to
the
wri
of
the
The
call
holder
wil
l
exerci
s
e
the
option
whenever
the
stock'
s
price
exceeds
the
stri
k
e
pricegreatest
at the expi
ration
date.
The
profi
t
the
writer
canthemake
is theand$5sellerpremium
(at anyoptionS ::;is$50).
The
sum
of
the
profi
t
s
between
buyer
of
the
call
al
w
ays
zero;
thus,
tradingprofitsis aequal the short losses.
There are no net profits or losses in the
market.options
The long
•
•
•
•
zero-sum game.
Professor's Note: Please notice that option profit diagrams show the gain or loss
to the long and/or short option positions. They differ from the payoffdiagrams
that we used in our options review in that profit diagrams reflect the cost of the
option (i.e., the option premium).
Figure 1: Profit/Loss Diagram for a
Call
Option
Proflr
Long call
+$5
0
-$5
Shorr call
L..._-----�--'-
X = $50 $55
Srock price
Put Option Profits and Losses
Towithexami
n
e
the
profi
t
s/losses
associated
with
trading
put
options,
consider
a
put
option
a $5 premium.
The
buyer
paysto $5theto$50thestrike
writer.price,
Whenthetheputpricehas ofzerothevalue.
stockTheat
expiration
i
s
greater
than
or
equal
buyer
of
the
option
has
a
loss
of
$5,
and
the
wri
t
er
of
the
option
has
a
gain
of
$5.
As
thellstock'
falwhen
ls belothew $50,
theof thebuyerstockof theequalsputtheoption
startspricetolessgainthe(breakeven
wipremium).
comes atprice
$45,
val
u
e
strike
option
However,
as
the
price
of
the
stock
moves
downward,
the
seller
of
the option
starts
to
lose
(negative
profits
wi
l
l
start
at
$45,
when
the
val
u
e
of
the
stock
equals
the
strike price less the option premium).
©20 12 Kaplan, Inc.
Page 269
Study Session 17
Cross-Reference to CFA Institute Assigned Reading #65 - Risk Management Applications of Option Strategies
Fioption
gure 2thatshowswe have
the profi
diagramThisfor profi
the buyer
er (short)
beent/loss
discussing.
t/loss (long)
diagramandillsellustrates
that: of the put
The
maximum
loss
for
the
buyer
of
a
put
is
the
loss
of
the
$5
premium
(at anymaximum
S � $50).gain to the buyer of a put is limited to the strike price less the
The
premi
um ($50- $5 = $45). The potential loss to the writer of the put is the same
amount.
The
breakeven
price$5 =of$45).
a put buyer (seller) is at the strike price minus the option
premium
($50The
greatest
profiprofit thets writer
ofthea putbuyer
can make
is theof$5thepremium
(S is� al$50).
The
sum
of
the
between
and
seller
put
option
w
ays
zero.
Trading
put options is a
In other words, the buyer's profits equal the
writer's losses.
•
•
•
•
•
zero-sum game.
Figure 2: Profit/Loss Diagram for a Put Option
Profit
$45
$5
0
-$5
Breakeven (X - Premium)
Shorr pur
Lon g pur
-$45
'-------'-- Stock price
$45 X = $50
Page 270
©2012
Kaplan,
Inc.
Cross-Reference to CFA Institute Assigned Reading #65
-
Study Session 1 7
Risk Management Applications of Option Strategies
Example: Option profit calculations
Suppose
thatce both
a callTheoption
andstock
a putpriceoptionis $42,haveandbeenthewritten
onputa stock
with anare
exerci
s
e
pri
of
$40.
current
cal
l
and
premiums
$3 and $0.75, respectively.
Cal
c
ul
a
te
the
profi
t
to
the
l
o
ng
and
short
positions
for
both
the
put
and
the
call
with
an
expiration day stock price of $35 and with a price at expiration of $43.
Answer:
will be computed as ending option valuation-initial option cost.
Profit
Stock at $35:
•
•
•
•
Long
cal
l
:
$0
$3
= -$3. The option finished out-of-the-money, so the
premium
is$3lost.- $0 = $3. Because the option finished out-of-the-money, the
Short
call:
call
writer'
s$5gai-$0.
n equals
the premium.
Long
put:
7
5
= $4. 2 5. You paid $0. 7 5 for an option that is now
worth
$5. $0.75 -$5 = -$4.25. You received $0.75 for writing the option,
Short
put:
but you face a $5 loss because the option is in-the-money.
Stock at $43:
•
•
•
•
Long
calyour
l: -$3net profit
$3 = $0.is zero.
You paid $3 for the option, and it is now worth $3.
Hence,
Short
call:
$3
$3
= $0. You received $3 for writing the option and now face
aLong
-$3 put:
valuation
for5 -$0
a net= prof
i7t 5.ofYou
zero.paid $0.75 for the put option and the
-$0.
7
-$0.
option
is now$0.7worthless.
Your net profit is -$0.75.
Short
put:
5
-$0
= $0.75. You received $0.75 for writing the option and
keep the premium because the option finished out-of-the-money.
+
Adecreases.
buyer ofAputsbuyeror ofa selcallsler ofor calla sells wier lofl profi
t wilwhenl profithetprice
ofthethepriceunderlying
asset
puts
when
of
the
underlying
asset
increases.
In
general,
a
put
buyer
bel
i
eves
the
underl
y
ing
asset
i
s
overvalued
and
will decline in price, while a call buyer anticipates an increase in the underlying asset's
pnce.
©20 12 Kaplan, Inc.
Page 271
Study Session 17
Cross-Reference to CFA Institute Assigned Reading #65
-
Risk Management Applications of Option Strategies
LOS 65.b: Determine the value at expiration, profit, maximum profit ,
maximum loss, breakeven underlying price at expiration, and payoff graph
of a covered call strategy and a protective put strategy, and explain the risk
management application of each strategy.
CPA® Program Curriculum, Volume 6, page 151
�
�
Professor's Note: Whenever we combine options with assets or other options, the
net cost ofthe combined position is simply the sum ofthe prices paid for the long
options/assets minus the proceeds from the option/asset sales (short positions). The
profits and losses on a position are simply the value ofall the assets/options in the
positions at expiration minus the net cost.
In writing covered
calls,
theassumed
term in wrimeans
thatcall.owning
the stockyoucovers
thecovered
obligation
to
del
i
ver
stock
t
i
n
g
the
Why
would
wri
t
e
a
call?
You
feel
the
stock'
s
price
will
not
go
up
any
time
soon,
and
you
want
to
increase
your
income
bycallcollecting
thethecallcaloption
premium.
Toout-of-the-money
add some insurance
that
theshould
stock
won'
t
get
e
d
away,
l
writer
can
wri
t
e
call
s
.
You
know that this strategy for enhancing one's income is not without risk.
covered
The call writer is
trading the stock's upside potentialfor the call premium.
Figure the3 illcallustrates
the profithet/lossstock'of as covered
call$50.position
at'option
expiration
date.and
When
was
written,
price
was
The
call
s
strike
price
was
$55,
the callat expiration:
premium was $4. The call is out-of-the-money. From Figure 3, we can observe
that
Ifwritheter'stock
closes
below
$50,
the
option
will
expire
worthless,
and
the
option
s loss is offset by theispremium
income of $4.
Breakeven
at
$46
= $50 - $4. Breakeven price =
callBecause
premium.
Ifthistheoption
stockwas
closesanbetween
$50
and
$55,
the
option
wil
l
expire
worthless.
out-of-the-money
call, theandoption
writheterstrike
will price.
get anySostock
appreciation
above
the
original
stock
price
below
the gain
(premium
plus
stock
appreciation)
wil
l
be
between
$4
and
$9.
Ifmaxistockmumclosesgainabove
$55,
thecovered
strike price,
the writer wicall.
ll get nothing more. The
i
s
$9
on
the
our-of-the-money
The
price goes
to zero;
net cost ofloss.the position
($46maximum
= $50 stocklosslossoccurs
offsetifbythe$4stock
premium
income)
is thethemaximum
•
•
•
S0 -
for the position
•
•
Page 272
©2012 Kaplan, Inc.
Cross-Reference to CFA Institute Assigned Reading #65
3:
Profit
Figure
Covered Call Profit and
Loss S =
for
50, C
= 4, X =
-
Study Session 1 7
Risk Management Applications of Option Strategies
55
stock
.
maxt
m
um
gam
$9
, ------------- covered call
,
$4 call premium
0
,,
,,
, ,,
-$46 ,
-$50
Stock
pri
c
e
Breakeven=$46
$50
X=$55
0
The
desirability
of writing
a covered
call stoe price
enhanceat which
incomethedepends
upon thethe chance
that
the
stock
price
wil
l
exceed
the
exerci
trader
writes
call.
In
this exampl
e, theThewribuyer
ter ofofthethecallcalthil isnpaying
ks the stock'
sgetupside
potential
is$55,
less than
thethe
buyer
expects.
$4
to
any
gai
n
above
whi
l
e
seller has traded the upside potential above $55 for a payment of $4.
Afrom a declineputin isvalanue.inItvestment
management
technique
protecton athatstockstock.
is constructed
by buying
a stockdesigned
and put tooption
Look at thethe profi
t/loss
diastock'
gramss valin uFigure
4.your
The profi
diagram
on the leandft isifthetheprofi
t from
holding
stock.
If
the
e
i
s
up,
t
i
s
positive
stock'
s
value
is down,is, profi
yourt profi
t-Sis negati
vdie.agram
Profit onequalthes ritheghtendsideprice,
Sp le4ssisthetheinprofi
itial tprice
St.
.
The
of
Figure
graph
That
=
S
t
T put. If the market is up, you lose your premium payment, and if the
from
holding
a
l
o
ng
market is down, you have a profit.
The
val
u
e
of
the
put
at
termination
wi
l
l
be
max[O,
X-S
].
Your
profit
wi
l
l
be
T
max[O, X- ST] less the price of the put.
.
- - - - - - - - - - - - - - - - - - - - - - - - - - - "1- -
-
-
-
-
-
- -- - -- -
- - - -
-
- --
-
-
-
- 1/
.,
,
- - - - - - - - - - - - - - - - �- - - ,
,
,
,
,
I
I
I
I
,
protective
©20 12 Kaplan, Inc.
Page 273
Study Session 17
Cross-Reference to CFA Institute Assigned Reading #65 - Risk Management Applications of Option Strategies
Figure
4: Protective Put
Components
Stock
Long put
Profit
Profit
_
_
..__
_,_
_
_
_
_
-
Stock
value
'-
X
Stock
- value
Figure 5 shows
theHereprofiit ists assumed
from thethat
combination
ofis purchased
a long put atand a longandstock
(i.pute., a
protective
put).
the
stock
that
a
wiat ttheh amoney.
strike price of is purchased for Note that the put described in Figure 5 is
Figure
$ 100
$ 1 00
$4.
5: Protective Put
Profit
Stock
'\. ,- - - - -
+---
Protective put
--�
��
- -�
0�
:�< :
----;-;__¥
',
-$4 t--'
'
'
'
-- -
:
� - --------- -- ·
'
.
.
.
'------'--
0
$ 1 00 $ 1 04
u
long p t
Stock value
What we should observe in Figure 5 is that:
Aupside
protectipotential
ve put alone
cuts your
downsideupside
lossesgains).
(maximum loss = but leaves the
(unlimited
Your
maximum
lossandoccursoccur
at anyforpricestockbelow
Losses
between
prices
between
and
.
You
will notpricemake= a profipremium
t until the. stock price exceeds (breakeven) .
Breakeven
Note
It couldthatbe replicated with a bond that pays (X-premium) at expiration and a call at X.
•
$4)
•
•
•
•
$ 1 00 .
$0
$4
50
$ 1 00
$ 1 04
+
$ 1 04
a protective put (stock plus a put) has the same shape profit diagram as a long call.
Proftssor's Note: Recall that this relation was the basis for our derivation ofput­
callparity. The payoffi at expiration are identicalfor a protective put (S + P) and
a fiduciary call
X )T C
X
(1 + Rr
-r
pure discount bond that pays
Page 274
+
,
a call with an exercise price equal to
at expiration.
©2012 Kaplan, Inc.
X
and a
Study Session 1 7
Cross-Reference to CFA Institute Assigned Reading #65 - Risk Management Applications of Option Strategies
KEY CONCEPTS
65.a value at expiration is Max -X) and profit (loss) is
Cal
l
option
Max -X) - option cost.
LOS
(0, S
(0, S
Call Option
Maximum Loss
Maximum Gain
Buyer (long)
Option Cost
Unlimited
Seller (short)
Unlimited
Option Cost
Breakeven
X
+
Option Cost
Put valueX-at expirati
on is cost.
Max X- and profit (loss) is
Max
- option
(0,
S)
(0,
S)
Put Option
Maximum Loss
Maximum Gain
Buyer (long)
Option Cost
X - Option Cost
Seller (short)
X - Option Cost
Option Cost
Breakeven
X - Option Cost
Aasset.call buyer (call seller) anticipates an increase (decrease) in the value of the underlying
Aasset.put buyer (put seller) anticipates a decrease (increase) in the value of the underlying
65.b call position is a share of stock and a short (written) call. Profits and losses are
Ameasured
covered
relati
v
e
to
the
net
cost
of
thi
s
combination
premium).
The
purpose
of selforlintheg acallcovered
call is to enhance income by trading the stock's
upside
potential
premium.
The
upsi
d
e
potential
on
a
covered
call
i
s
limi
t
ed
to
(X+
call
premium
received.
The maximum loss is the net cost premium).
Aareprotecti
v
e
put
consists
of
buying
a
share
of
stock
and
buying
a
put.
Profits
and
losses
measured
aputtive istoathestrategy
net costto protect+ premium).
AMaximum
protectiverelgains
against
a decline
in the value
ofputthepremium
stock.
on
a
protective
put
are
unlimited,
but
reduced
by
the
paid. Maximum losses are limited to -X) + put premium paid.
LOS
(S0 -
•
•
•
•
(50 -
S0)
(S0
(S0
©20 12 Kaplan, Inc.
Page 275
Study Session 17
Cross-Reference to CFA Institute Assigned Reading #65
-
Risk Management Applications of Option Strategies
CONCEPT CHECKERS
1.
Afolcalllowingoptionstatements
sells foris$4 on a $25 stock with a strike price of $30. Which of the
A. Atpricexpiration,
the buyer of the call will not make a profit unless the stock's
e
exceeds
$30.
B. Atof theexpiration,
the wri$34.
ter of the call will only experience a net loss if the price
stock
exceeds
C. Amaximum
covered calllossposition
at these
a maximum gain of $9 and the
of the stock
priceprices
less thehaspremium.
An$5 premium.
investor buys
amaximum
put on a stock
selling for $60, with a strike price of $55 for a
The
gain
is:
A.B. $50.
$55.
$60.
Which
of
the
foll
o
wi
n
g
is
the
ri
s
kiest
single-option
transaction?
A.B. Wri
tingaaput.
call.
Buying
C. Writing a put.
AnA. investor
wi
l
l
exerci
s
e
a
put
option
when
the
price
of
the
stock
is:
thethe stristrikeke price.
B.C. above
below
price plus the premium.
below the strike price.
Ais put with a striThe
ke price
of $75 sells for $10. Which of the following statements
greatest:
A.B. profit
thethe wri
ter ofofatheputputoption
optioncancanmakemakeis $65.
is $10.
profit
buyer
C. loss the writer of a put option can have is $75.
AtA. expiration,
the
value
of
a
cal
l
option
must
equal:
of theminus
strikethepricestrikeless price,
the stock
pricetrageor zero.
stock
price
or
arbi
l occur.
B.C. thethethe larger
larger of zero, or the stock's price less the strikewilprice.
Ana premium
investorofwrites
a
covered
cal
l
on
a
$40
stock
with
an
exercise
price
of
$50
for
gainwiwillllbebe$2.$40.
$12.The investor's maximum:
A.B. loss
C. loss will be unlimited.
Which
ofilatherly follshaped
owinprofit/loss
g combinations
of options
and underlying investments
have
si
m
diagrams?
A:
A.B. covered
caloption
l, and combined
a short stockwitcombined
wil toption,
h a longandcall.a protective put.
short
put
h
a
long
cal
C. long
call option combined with a short put option, and a long stock
position.
least accurate?
2.
c.
3.
4.
5.
6.
7.
8.
Page 276
likely
least accurate?
©2012 Kaplan, Inc.
Study Session 1 7
Cross-Reference to CFA Institute Assigned Reading #65 - Risk Management Applications of Option Strategies
ANSWERS - CONCEPT CHECKERS
1.
A
The buyer will not have a net profit unless the stock price exceeds $34 (strike price plus
the premium). The other statements are true. At $30 the option will be exercised, but
the writer will only lose money in a net sense when the stock's price exceeds
X + C $30 + $4. The covered call's maximum gain is $4 premium plus
$5 appreciation.
=
2.
A
This assumes the price of the stock falls to zero and you get to sell for $55. Your profit
would be $55 - 5 $50.
=
3.
A
When buying either a call or a put, the loss is limited to the amount of the premium.
When writing a put, the loss is limited to the strike price if the stock falls to zero
(however, the writer keeps the premium). When writing an uncovered call, the stock
could go up infinitely, and the writer would be forced to buy the stock in the open
market and deliver at the strike price-potential losses are unlimited.
4.
C
The owner of a put profits when the stock falls. The put would be exercised when
the price of the stock is beLow the strike price. The amount of the premium is used to
determine net profits to each party.
5.
C
The greatest loss the put writer can have is the strike price minus the premium received
equals $65. The other statements are true. The greatest profit the put writer can make is
the amount of the premium. The greatest profit for a put buyer occurs if the stock falls
to zero and the buyer makes the strike price minus the premium. Since options are a
zero-sum game, the maximum profit to the writer of the put must equal the maximum
loss to the buyer of the put.
6.
C
At expiration, the value of a call must be equal to its intrinsic value, which is
Max[O, S - X] . If the value of the stock is less than the strike price, the intrinsic value is
zero. If the value of the stock is greater than the strike price, the call is in-the-money and
the value of the call is the stock price minus the strike price, or S - X.
7.
A
As soon as the stock rises to the exercise price, the covered call writer will cease to realize
a profit because the short call moves into-the-money. Each dollar gain on the stock
is then offset with a dollar loss on the short call. Since the option is $ 1 0 out-of-the­
money, the covered call writer can gain this amount plus the $2 call premium. Thus,
the maximum gain is $2 + $ 1 0 $ 1 2. However, because the investor owns the stock,
he or she could lose $40 if the stock goes to zero, but gain $2 from the call premium.
Maximum loss is $38.
=
8.
C
�
�
A combined long call and a short put, with exercise prices equal to the current stock
price, will have profits/losses at expiration nearly identical to those of a long stock
position.
ProJ:ssor's !"_ote: The easiest way to see this is to draw the payoffdiagram for the combined
optzon posztzons.
©20 1 2 Kaplan, Inc.
Page 277
The following is a review of the Alternative Investments principles designed to address the learning
outcome statements set forth by CFA Institute. This topic is also covered in:
INTRODUCTION TO ALTERNATIVE
INVESTMENTS
Study Session 1 8
EXAM FOCUS
'traditional
Alternativedefiinvestments"
coll
e
ctivel
y
refers
to
the
many
asset
classes
that
fall
outside
the
nitions
of stocks and
bonds.alternati
This category
includesprimarily
hedge funds,
private
equity,
real
estate,
commodities,
and
other
v
e
investments,
collectibles.
Each
of
these
al
t
ernative
investments
has
unique
characteristi
c
s
that
require
a
di
f
ferent
approach
by theandanalyst.
You
shouldandbe aware
of thereturns
differentwithstrategi
eofs, thefee alternative
structures,
due
diligence,
issues
i
n
valuing
calculating
each
investments discussed in this topic review.
LOS 66.a: Compare alternative investments with traditional investments.
CFA ® Program Curriculum, Volume 6, page 170
Alternative
investments
differ
from
traditional
investments
(publicl
y
traded
stocks,
bonds,
cash) bothofithen theinvestment
types of assets
andinsecurities
included
inarethisheld.assetManagers
class andof
ialternative
n the structure
vehicles
which
these
assets
investment
portfol
i
os
may
use
deri
v
ati
v
es
and
l
e
verage,
i
n
vest
i
n
illiquid
assets,
and short
securities.investment
Many typesas ofwell.realTypes
estateofinvestment
areinvestment
consideredstructures
alternatives
to
traditional
alternative
inclusome
de hedge
funds,
private equity
funds, various
types ofarerealdifferent
estate inthan
vestments,
and
ETFs.
Fee
structures
for
alternati
v
e
i
n
vestments
those
of traditionalincenti
investments,
withonhigher
management
fees on investments
average and asoftena group
with have
additional
v
e
fees
based
performance.
Alternative
had
l
o
w
returns
correlations
wi
t
h
traditional
investments.
Compared
to
tradi
t
i
o
nal
investments, alternative investments exhibit:
Less
lispeci
quidiatliyzofationassetsby held.
More
investment managers.
Less
regulation
and
transparency.
More
problematic
and
less
available
historical
return
and
volatility
data.
Different legal issues and tax treatments.
•
•
•
•
•
LOS 66.b: Describe categories of alternative investments.
CFA ® Program Curriculum, Volume 6, page 174
WeHerewiwel exami
n
e
fi
v
e
categori
e
s
of
alternati
v
e
i
n
vestments
in
detai
l
in
thi
s
topic
revi
e
w.
introduce each of those categories.
Page 278
©2012 Kaplan, Inc.
Study Session 1 8
Cross-Reference to CFA Institute Assigned Reading #66 - Introduction to Alternative Investments
These
funds
may useassets.
leverage,
hold oflonghedge
and funds
short positions,
use
derivatives,
and
invest
in
illiquid
Managers
use
a
great
many different
ng toimgenerate
necessaril
y hedgestrategies
risk as thein attempti
name might
ply. investment gains. They do not
Asnotthepublicly
name traded
suggests,or priin vtheateequity
equityoffunds
investtraded
in thefirequity
ofthatcompanies
that
are
publicly
ms
thetofundpurchase
intendsequity
to takein establi
private.shedLeveraged
buyout
(LBO)
fundsthe usemajborrowed
money
companies
and
comprise
ority of
pricapital
vate funds,
equity iinnvest
vestment
funds.
A
much
smal
l
er
portion
of
these
funds,
venture
in orForfinourancepurposes
young unproven
companies
at various
stagesin the
early
i
n
thei
r
exi
s
tence.
here
we
wil
l
also
consider
i
n
vesting
securities
of
fi
n
anci
a
ll
y
distressed
companies
to
be
pri
v
ate
equi
t
y,
although
hedge
funds may hold these also.
Real estate
investments
include
residential
or commercial
properties
as
well
as
real
estate
backed
debt.
These
investments
are
held
in
a
vari
e
ty
of
structures
including
ful
l
or
l
e
veraged
ownershi
p
of
individual
properties,
individual
real
estate
backed
publicly traded securities backed by pools of properties or
mortgages,loans,andprivate
limitedandpartnerships.
To gain exposure
to changesderiinvatives,
commodities
prices,ofinvestors
can
own
physical
commodities,
commodities
or
the
equity
commodity
producing
firms.by holding
Some funds
seek exposure
to that
the returns
on various
commodity
indices,
often
derivatives
contracts
are
expected
to
track
a specific
commodity index.
Thi
s
category
includes
investment
in
tangible
collectible
assets
such
as
fiintangible
ne wines,asset.
stamps, automobiles, antique furniture, and art, as well as patents, an
1 . Hedge funds.
2.
3.
4.
5.
Private equity funds.
Real estate.
Commodities.
Other.
LOS 66.c: Describe potential benefits of alternative investments in the context
of portfolio management.
CFA ® Program Curriculum, Volume 6, page 177
Alinvestments
ternative investment
returns have
had low moti
correlvatiations
witholding
h those alternati
of traditional
over
long
periods.
The
primary
o
n
for
ve
investments
is
thei
r
historically
low
correlation
of
returns
wi
t
h
those
of
traditional
investments,
which
canforreduce
an investor'
s overall
portfolio
risk.to However,
therisk
risk
measures
we
use
traditional
assets
may
not
be
adequate
capture
the
characteristics
of alternative
investments.
Managers
oftenmonth
consider
measuresfrequency
of risk of
other
than
standard
devi
a
tion
of
returns,
such
as
worst
or
historical
downside returns.
Historical
returns
for
al
t
ernative
investments
have
been
higher
on
average
than
for
traditi
onalexpected
investments,
soTheaddingreasons
alternative
investments
to a traditional
portfolio
may
increase
returns.
for
these
higher
returns
are
thought
to
be
that
some alternative investments are less efficiently priced than traditional assets (providing
©20 12 Kaplan, Inc.
Page 279
Study Session 1 8
Cross-Reference to CFA Institute Assigned Reading #66 - Introduction to Alternative Investments
for skilled
alternativeoften
investments
may offer extra returns
foropportunities
being illiquid,
and thatmanagers),
alternativethatinvestments
use leverage.
Whi
le it seems
thatexpected
adding alternative
investments
to a portfolio
wiallocation
ll improvetoboth
portfolio
ri
s
k
and
return,
choosing
the
optimal
portfol
i
o
alternatidata
ve inand
vestments
is compl
emeasures.
x and there are potential problems
withethupward
historicalbias of
returns
traditional
risk
refers
to
if data
onlthose
y forthatcurrentl
ybetter-than-average
existing (surviving)returns,
firms isexcluding
included.theSincereturns
surviving
fiforreturns
rmsfailtend
to
be
had
data
ed firms results
in averagethe returns
thatperformance
are biased data
upward.
refers
toto a
bibenchmark
as introduced
by
including
previous
for
fi
r
ms
recently
added
i
n
dex.
Si
n
ce
firms
that
are
newly
added
to
an
i
n
dex
must
be
those
that
have
survived
andthedone
better
thancurrent
average,returns
including
theithat
r returns
fornotprior
years
(without
including
previ
o
us
and
for
funds
have
been
added
to the
index) tends to bias index returns upward.
Survivorship bias
Backfill bias
LOS 66.d: Describe hedge funds, private equity, real estate, commodities,
and other alternative investments, including, as applicable, strategies, sub­
categories, potential benefits and risks, fee structures, and due diligence.
LOS 66.e: Describe issues in valuing, and calculating returns on, hedge funds,
private equity, real estate, and commodities.
CFA ® Program Curriculum, Volume 6, page 178
HEDGE FUNDS
Hedgemorefundsflexiemploy
a largemanagers
numberofoftraditional
different strategies.
HedgeHedgefundfunds
managers
have
b
ility
than
i
n
vestments.
can use
leverage,
take
short
equity
positions,
and
take
long
or
short
positions
i
n
derivatives.
The
complex
nature
ofmany
hedgeservices
fund transacti
onscustodial
leads managers
toadministrative
trade throughservices,
prime
brokers,
who
provide
including
services,
money
lending,
securities
lending
for
short
sales,
and
trading.
Hedge
fund
managers
can
negotiate various service parameters with the prime brokers, such as margin
requirements.
fundbasisreturn
objectives
canabove
be stated
onfanic benchmark
absolute basisreturn)(e.gdepending
., Oo/o) or onon
atheHedge
relative
(e.
g
.
,
returns
5o/o
a
speci
fund
strategy.
Hedge
funds
are
than
traditional
investments.
Like
pritheviatenvestors
equityasfunds,
hedge (lifunds
are partners.
typically Asethedge
up as fund
limitedlimited
partnerships,
withmay
the
l
i
mited
a
bility)
partnership
not include
more
than atproscribed
numbereofdegree
investors,
who
mustsophistication.
possess adequateThe
wealth,
suffi
c
i
e
nt
liquidi
y,
and
an
acceptabl
of
i
n
vestment
management
firm isoftheassetsgeneral
partnerandandan typi
callyverecei
es bothon afund
management
based
on the value
managed
incenti
fee vbased
returns. fee
Hedge fund oninvestments
are less
liquid
thana lockup
traditional,
publicly
traded
investments.
Restrictions
redemptions
may
include
period
and/or
a
notice
A lockup period is a time after initial investment during which withdrawalsperiod.
are not
1
less regulated
Page 280
©2012 Kaplan, Inc.
Study Session 1 8
Cross-Reference to CFA Institute Assigned Reading #66 - Introduction to Alternative Investments
allreceiving
owed. a notice
period,request
typicaltolyfulfiltothe request.
days, is theAdditional
amount feesof timay
me abefundcharged
has after
redemption
atoftenredemption.
All
of
these,
of
course,
discourage
redemptions.
Hedge
fund
managers
incurthese
significosts.
cantNoti
transactions
costsallowwhentimetheyfor redeem
shares.
Redemption
feesin
can
offset
c
e
periods
managers
to
reduce
positions
anoverorderl
y
manner.
Redemptions
often
i
n
crease
when
hedge
fund
performance
i
s
poor
a period,interests.
and theThis
costsisofanhonoring
the value of
partnership
additionalredemptions
source of riskmayforfurther
hedgedecrease
fund investors.
is an hedge
investment
company
that
invests
insmal
hedgeler funds,
givtoingaccess
investors
dihedge
versififunds
cationinamong
fund
strategi
e
s
and
al
l
owing
investors
whi
c
h
they
may
not
be
abl
e
to
i
n
vest
di
r
ectl
y
.
Fund
of
funds
managers
charge
an additional layer of fees beyond the fees charged by the individual hedge funds
in the portfolio.
A
30
90
A fund of funds
Hedge Fund Strategies
Simi
l
ar
to
categori
z
i
n
g
alternati
v
e
i
n
vestments,
cl
a
ssifyi
n
g
hedge
funds
can
also
be
enginfund
g. Accordi
ofchallhedge
strateginges:to Hedge Fund Research, Inc., there are four main classifications
are typi
cally based onfora long
corporate
restructuring
orcommon
acqui
s
iti
o
n
that
creates
profi
t
opportunities
or
short
positions
in
equity, preferred equity,Buyor debt
of a specifi
crmcorporation.
Subcategories
are: the firm
the
shares
of
a
fi
being
acquired
and
sell
short
making the acquisition. Buy the (undervalued) securities of firms in
firestructuri
nancial distress
wheny short
analysisovervalued
indicatessecurity
value wiltypes
l be increased
bytime.
a successful
ng; possibl
at
the
same
Buy
suffi
c
ient
equity
shares
to
infl
u
ence
a
company'
s
policies with the goalInvest
of inincreasi
nsecurities
g companyof fivalue.
the
rsellmsithat
are issuing
or
repurchasing
securities,
spinning
off
divisions,
n
g
assets,
or
distributing
capital.
2. with the goal of profitinginwhen
volveabuying
a security
anddiscrepancy
selling short
a relathetedtwo
security
perceived
pricing
between
is
resolved.
Exploioft thepricing
discrepancies
between
convertible bonds and the common
stock
issuing
companies.
Exploitorpricing
discrepancies
among
various
mortgage-backed securities
(MBS)
asset-backed
securities
(
A
BS).
t pricing discrepancies between fixed income
securities ofExploi
varioust pricing
types.Exploidiscrepancies
arising from
differencesofbetween
returnsity.
volatility impliedExploi
by options
prices
and
manager
expectations
future
volatil
t pricingy ldiscrepancies
asset classes
different from those previousl
isted and acrossamong
assetsecurities
classes andin markets.
1 . Event-driven strategies
•
Merger arbitrage:
•
Distressed/restructuring:
•
Activist shareholder:
•
Special situations:
Relative value strategies
•
Convertible arbitrage fixed income:
•
Asset-backed fixed income:
•
General fixed income:
•
Volatility:
•
Multi-strategy:
©20 12 Kaplan, Inc.
Page 28 1
Study Session 1 8
Cross-Reference to CFA Institute Assigned Reading #66 - Introduction to Alternative Investments
Macro
are basedin equities,
on globalfixeconomic
and events
and may involve
long orstrategies
short positions
ed income,trends
currencies,
or commodities.
Equity
hedge fund
strategies
seek
toequities
profit from
longunderlying
or short positions
in publicly
tradedMarket
equities
and
derivatives
with
as
their
assets.
neutral:
Uselong,technical
orselect
fundamental
analysis
to toselectbe solundervalued
equities
to
be
held
and
to
overval
u
ed
equi
t
ies
d short, in
approximately
equal
amounts
to
profi
t
from
their
rel
a
ti
v
e
price
movements
wiFundamental
thout exposure
to market
risk. analysis to find high-growth companies.
growth:
Use
fundamental
Identify
equities
of companies that are expected to sustain relatively
hiFundamental
gh ratesandof buy
capital
appreciation.
value: Buyanalysis.
equityHere
sharesitthat
arehedge
believed
tostructure,
be undervalued
based
on
fundamental
is
the
fund
rather ve
than
the
type
of
assets
purchased,
that
results
in
classifi
c
ati
o
n
as
an
alternati
investment.
Quantitative
directional:
Buybe overval
equity usecurities
beli
eved to beanalysis.
undervalued
and
short
securities
believed
to
ed
based
on
technical
Market
exposure may vary depending on relative size of long and short portfolio
positions.
Short
positions
in overvalued
equities,overall.
possiblybias:withEmploy
smallerpredominantly
long positions,short
but with
negative
market exposure
Many
hedge
funds
tend
to
specialize
i
n
a
specifi
c
strategy
at
fi
r
st
and
over
ti
m
e
may
develop or add additional areas of expertise, becoming multi-strategy funds.
3.
4.
•
•
•
•
•
Hedge Fund Potential Benefits and Risks
Hedge
fund returns
havelagtended
to beofbetter
thanequities
thoseinofupglobal
equitiesDifferent
in downhedge
equi
t
y
markets
and
to
the
returns
global
markets.
fund
strategieand
s havediversifi
the bestcatireturns
duringof hedge
differentfundstimeareperiods.
Statements
about
the
performance
o
n
benefits
problematic
because
of
the
great
vari
e
ty
of
strategies
used.
Less-than-perfect
correlation
wi
t
h
gl
o
bal
equity
returns
may
of finoffer
anciasome
l crisis.diversification benefits, but correlations tend to increase during periods
Hedge Fund Valuation
Hedge
fund
values
are
based
on
market
val
u
es
for
traded
securities
i
n
thei
r
portfolios,
but
must
useconservative
model (estitomuseated)thevalues
forat which
non-traded
securities.
Forbe cltraded
securities
mostpositions
prices
a
position
coul
d
o
sed:
bid prices
ifort islong
and
ask
pri
c
es
for
short
positions.
Some
funds
use
the
average
of
the
bid and askfor thepricesdegree
instead.of illiqui
In theditcase
of illiquid
securities,
quoted market
prices
may
be
reduced
y,
based
on
position
size
compared
to
the
total
value
such securities
outstanding
and their average
trading Trading
volume. NAV
Someisfunds
calculfrom
ate
atheof"trading
NAV"
using
such
adjustments
for
illiquidity.
di
f
ferent
calculoramodel
ted netprices.
asset value required by accounting standards, which is based on either
market
Page 282
©2012 Kaplan, Inc.
Study Session 1 8
Cross-Reference to CFA Institute Assigned Reading #66 - Introduction to Alternative Investments
Hedge Fund Due Diligence
Selecting
hedge This
fundsmay(or funds
of funds)hampered
requires bysignifi
cckantofintransparency
vestigation ofbythefunds
avai
l
able
funds.
be
somewhat
a
l
a
that
consider
their
strategies
and
systems
to
be
proprietary
information.
The
fact
that
the regulatory
requirements
for hedge
fund disclosures
are minaimal
presents
additional
chall
e
nges.
A
partial
list
of
factors
to
consider
when
selecting
hedge
fund
or
a fund of
funds includes an examination of the fund's:
Investment
strategy
.
Investment
process
.
of competi
tive advantages.
HiValSource
sutorical
returns
.
ation
and
returns
calculation
methods
.
Longevityof. assets under management.
Amount
Management
style. .
Key
person
risk
Reputatiplona.ns .
Growth
Systems
for
ri
s
k
management
.
Appropriateness of benchmarks.
The
analthatysisfunds
of these
factors
is challengireturns
ng because
a laprovide
ck of persistence
in returns may
mean
with
better
historical
will
not
better-than-average
returns
in theriskfuture.
Additionall
y, manyandofmanagement
the items forstyle,
due diligence,
suchto quantify
as in
reputation,
management
systems,
are
diffi
c
ult
astrategies
way thattoprovi
doesit pricing
clear choices
foriencipotential
investors.
Further,lesspreviously
profi
table
expl
ineffi
c
e
s
are
likel
y
to
become
profi
t
able
as
more
funds pursue the same strategy.
•
•
•
•
•
•
•
•
•
•
•
•
•
PRIVATE EQUITY
The majoritytheyofintend
privatetoequity
fundsvateinvest
eitherbuyout
in privatefunds),
companies
or public
companies
take
pri
(l
e
veraged
or
in
early
stage
companies
capital investment
funds). Twofunds
additional,
but smaller, categories
of private
equity funds(venture
are distressed
and developmental
capital funds.
Adoesprivnotatehappen,
equity fund
so charge asset
fees fordivesti
arrangi
fees for a deal that
or feesmayforalhandling
turesngaftbuyouts,
er a buyout.
Private Equity Strategies
buyouts
(LBOs)
are
the
most
common
type
of
pri
v
ate
equity
fund
investment.is funded
"Leveraged"
refersbytodebt.
the factThisthatmaythebefund'
s debt
purchase
of the debt),
portfolhigh­
io
company
primarily
bank
(l
e
veraged
yishares
eld bonds,
or
Mezzanine
fi
n
ancing
refers
to
debt
or
preferred
that arefeatures
subordinate
high-yiel
d bonds iinssuedequityandvalue
carryincreases.
warrants or
conversion
that givetointhevestors
participation
Leveraged
mezzanine financing.
©20 12 Kaplan, Inc.
Page 283
Study Session 1 8
Cross-Reference to CFA Institute Assigned Reading #66 - Introduction to Alternative Investments
Professor's Note:
We
will use a similar term, "mezzanine-stage financing, "
� when referring to a late-stage investment in a venture capital company that is
� preparing to go public via an !PO. Here we are referring to a type ofsecurity
rather than a type of investment.
Two
types
ofLBOs
are
management
buyouts
(MBOs),
in
whi
c
h
the
existing
management
teammanagement
is involved inteam
the purchase,
buy-ins (MBis),
which
an external
will replaceandthemanagement
existing management
team. in
Incombination
an LBO, theof prinewvatemanagement,
equity firm management
seeks to increaseincentives,
the valuerestructuring,
of the firm through
some
cost
reduction,
orbecause
revenuetheienhancement.
Firms
wi
t
h
high
cash
fl
o
w
are
attracti
v
e
LBO
candidates
for acquisition.r cash flow can be used to service and eventually pay down the debt taken on
Venture
capital (VC)
funds
investforminofcompanies
incanthebeearlinyconvertible
stages of theirpreferred
development.
The
investment
often
is
i
n
the
equity
but
shares
orsuccessful
convertiblcompanies
e debt. Whil
e
the
ri
s
k
of
start-up
companies
i
s
often
great,
returns
on
the case
to the point where it iscansoldbe (atveryleasthigh.in This
part) istooften
the publi
c viawhen
an IPO.a company has grown
The
companies
in whicapital
ch a venture
capital fund
isoselinvested
are referred
to as its portfolio
companies.
Venture
fund
managers
are
cl
y
i
n
volved
i
n
the
development
portfolio companies, often sitting on their boards or filling key management roles. of
Categorization
of venture capital
investments
is basedfirmoninvestment
the company'at sdistage
ofstages of
development.
Terminology
used
to
i
d
enti
fy
venture
f
ferent
the company's life includes the following:
The
formative
stage
refersphases.
to investments made during a firm's earliest period and
distinct
three
comprises
Angel
investing
refers
to
investments
made
very
early
in
a
fi
r
m'
s
life,
often
the
"idea"
stage,
and theTheinfunding
vestmentsource
fundsisareusually
used forindividual
businesss ("angels")
plans andrather
assessing
market
potential.
than
venture
capital
funds.
The
seed stageresearch.
refers This
to investments
made
for product
development,
marketi
ng,
and
market
i
s
typi
c
all
y
the
stage
during
whi
c
h
venture
capi
t
al
funds stage
make refers
initialtoinvestments,
through
ordinary
or convertibl
e preferred
shares.
Early
investments
made
to
fund
initial
commercial
production
and sales.
2. Later
stage investment
refers
tois operating
the stage ofas development
where
aInvestment
company already
hasfundsproduction
and
sal
e
s
and
a
commercial
entity.
provided
at
this
stage
are
typical
l
y
used
for
expansion
of
production
and/
or
increasing sales though an expanded marketing campaign.
financing
refersof theto capi
tal provided
to prepare
the firm forandanpublic
IPO.
3. Mezzanine-stage
The
term
refers
to
the
timing
fi
n
ancing
(between
pri
v
ate
company
company) rather than the type of financing.
1.
•
•
•
Page 284
©2012 Kaplan, Inc.
Study Session 1 8
Cross-Reference to CFA Institute Assigned Reading #66 - Introduction to Alternative Investments
Other Private Equity Strategies
Developmental
capitalor restructuring.
or minority equity
investing
refersmayto bethepubl
provision
of capitalIn the
forcase
business
growth
The
fi
r
ms
fi
n
anced
i
c
or
private.
of public
equities
(PIPEs).companies, such financing is referred to as private investment in public
Distressed
investing
i
n
vol
v
es
buyi
n
g
debt
of
mature
companies
that
are
experiencing
fiInvestors
nancial diffi
culties (potentially
ortakecurrently
ine role
default,in theor turnaround
in bankruptcyby proceedings).
in
distressed
debt
often
an
acti
v
workinshould
g
witake.th management
on
reorganizati
o
n
or
to
determine
the
direction
the
company
Distressed
debt
investors
are
sometimes
referred
to
as
Note
that
althoughinvestdistressed
debt ofinvesti
ng islyincluded
the privateasequiwellty. category, some hedge
funds
in the debt
financial
distressedin companies
vulture investors.
Private Equity Structure and Fees
Similar
to
hedge
funds,
pri
v
ate
equity
funds
are
typi
c
al
l
y
structured
as
limited
partnerships.
Committed
capital
is the amount
ofallycapital
provided
toimmedi
the fundatelyby
investors.
The
committed
capi
t
al
amount
i
s
typi
c
not
all
i
n
vested
but
i
s
"drawn
down"
(invested)
as
securiti
e
s
are
i
d
entifi
e
d
and
added
to
the
portfolio.
Committed
capital
is usuallyof thedrawn
down
over Management
three to five years,
buttypically
the 1 to 3o/o
is
at
the
discretion
fund
manager.
fees
are
of committed capital, rather than invested capital.
Incentiearned
ve feesuntiforl after
privatetheequity
fundsreturned
are typiinvestors'
cally initial
of profits,
butIt these
fees arethat
not
fund
has
capital.
is
possible
incentive feeshavepaibeen
d overliquidated.
time mayThis
exceedsituationofarithesesprofi
ts returns
realizedonwhenportfolio
all portfolio
companies
when
companies
are high early
andve fees
declitoneinlavestors
ter. A clawback
provision
requi
res thereceimanager
to
return
any
periodic
i
n
centi
that
would
result
in
investors
v
i
n
g
less
than of the profits generated by portfolio investments as a whole.
drawdown
o/o
period
20o/o
20o/o
80o/o
Private Equity Exit Strategies
The
average
holdi
n
g
peri
o
d
for
companies
in
private
equity
portfol
i
os
i
s
fi
v
e
years.
There
are several primary methods of exiting an investment in a portfolio company:
1. Trade sale: Sell a portfolio company to a competitor or another strategic buyer.
Sell all or some shares of a portfolio company to the public.
Recapitalization:
TheThicompany
issues
debt
to thefundfunda dividend
distribution
to equity
hol
d
ers
(the
fund).
s
i
s
not
an
exi
t
,
in
that
still
controls
the
company,
but is often a step toward an exit.
2.
IPO:
3.
©20 12 Kaplan, Inc.
Page 285
Study Session 1 8
Cross-Reference to CFA Institute Assigned Reading #66 - Introduction to Alternative Investments
4. of investors. Sell a portfolio company to another private equity firm or a group
Reassess and adjust to take losses from an unsuccessful
5. outcome.
Secondary sale:
Write-off/liquidation:
Private Equity Potential Benefits and Risks
There ions evidence
that
over
thestock
last returns.
years returns
on private correlation
equity fundsofhave
been
higher
average
than
overall
Less-than-perfect
private
equity
returns
wibenefi
th traditional
investment
returns
suggests
that thereThemaystandard
be portfolio
diversifi
c
ation
t
s
from
i
n
cludi
n
g
private
equity
i
n
portfolios.
deviation
of
private
equi
t
y
returns
has
been
higher
than
the
standard
deviati
o
n
of
equity
index returns,
suggesti
ngfromgreatersurvirisk.vorshiAspwibiasth hedge
fund returns
data,leprivate
equity
returns
data
may
suffer
and
backfill
bias
(both
ad
to
overstated
returns). Because
portfolio
companies
arereturns
revaluedwithinfrequently,
reported
standard
deviations
of
returns
and
correl
a
ti
o
ns
of
equity
returns
may
both
be
biased
downward.
Evidencethesuggests
thatto choosing
skilfunds
led fundandmanagers
is important.
Diarefferences
between
returns
top
quartile
bottom
quarti
l
e
funds
significant and
performance rank shows persistence over time.
20
Private Equity Company Valuation
Valuation
for private
equityalthough
portfoliothecompanies
is essentially
the used
same may
as valuing
a
publicly
traded
company,
discount
rate
or
multiples
be
different
for private companies.
Market
or private
transactionnetvalincome,
ues of orsimilar
companies
may
be
used
to
estimate
multiples
of
EBITDA,
revenue
to
use in estimating the portfolio company'
s value.discount model falls into this category,
A
dividend
asequity.
does calculating the present value of free cash flow to the firm or free cash flow to
Either
thewiliquidation
values
orarefaivalr market
values
ofbeassets
can
be
used.
Liquidation
values
l
l
be
lower
as
they
u
es
that
could
real
i
z
ed
quickly in area situation
of fisonancial
distress
or termination
ofthecompany
operations.
Liabilities
subtracted
that
onl
y
the
equity
portion
of
fi
r
m'
s
value
is being
estimated.
Page 286
•
Market/comparables approach:
•
Discounted cash flow approach:
•
Asset-based approach:
©2012 Kaplan, Inc.
Study Session 1 8
Cross-Reference to CFA Institute Assigned Reading #66 - Introduction to Alternative Investments
Example: Portfolio company comparables approach
Aandprimarket
vate equivalues
ty fundfor isfourvaluing
a
French
private
manufacturi
n
g
company.
EBITDA
are shown in the following publicly
table (intraded
millionsEuropean
of euros):companies in the same industry
EBITDA Market Value
Company
Company
Company
Company
The
estimated
EBITDA
company
is the million.
thecompany.
four
companies
as theforinthedustryFrench
multiple,
estimate
market valUsing
ue forantheaverage
Frenchof
1:
2:
3:
4:
€ 1 ,000
€2,000
€ 1 ,500
€2,200
€ 1 00
€250
€250
€275
€ 175
Answer:
EBITDA
Multi
p
le
Company
II ==
Company
Company
Company
II == 6x
The
average
mul
t
iple
for
these
four
companies
is
Based
on
the
French
company'
s
expectedorEBITDAbillion. million, its estimated value is million =
million
1:
2:
3:
4:
€ 1 ,000
€2,000
€ 1 ,500
€2,200
€100
€250
€250
€275
of € 175
lOx
8x
8x
8x.
€ 1 .4
€ 1 75
x 8
€ 1 ,400
Private Equity Due Diligence
Because ofhowtheinterest
high leverage
typicall
y usedlabilforitypriofvcapital
ate equity
funds,
investors
should
consider
rates
and
the
avai
may
affect
any
required
refiimportant
nancingandof portfol
io thecompany
debt.
The
choice
of manager
(general
partner)
is quitote
many
of
factors
we
l
i
sted
for
hedge
fund
due
dil
i
gence
al
s
o
apply
prithevmanager,
ate equitythefundvaluati
investments.
Specifical
l
y,
the
operating
and
financial
experi
e
nce
of
on methods
structures, and drawdown
procedures are all important
areas toused,
investithegateincentive
prior tofeeinvesting.
REAL ESTATE
Investment
real
estate
can
provide
i
n
come
i
n
the
form
of
rents
as
well
as
the
potential
capitals portfolio
gains. Realandestate
as an asset
class
can provide
divrents
ersifiand
cationrealbenefi
tsvalues
to an
ifortend
nvestor'
a
potential
infl
a
tion
hedge
because
estate
to
increase
with
inflation.
Real
estate
i
n
vestments
can
be
differenti
a
ted
accordi
n
g
toinclude:
their underlying assets. Assets included under the heading of real estate investments
Residential property-single-family homes.
in
•
©20 12 Kaplan, Inc.
Page 287
Study Session 1 8
Cross-Reference to CFA Institute Assigned Reading #66 - Introduction to Alternative Investments
•
•
Commercial
property-produces
income.
Loans
wi
t
h
residential
or
commercial
property as collateral-mortgages ("whole
loans"), construction loans.
Forms of Real Estate Investment
isaconsidered
a direct investment
inTherealissuer
estate.(lSome
buyers
pay
cash
but
most
take
on
mortgage
(borrow)
to
purchase.
e
nder)
of
the
mortgage
hassela ldirect
investmenttheyin aoriginate
whole loanandandthe imortgages
s said to "hold
the mortgage.
"
Issuers
often
the
mortgages
are
then
pooled
(securitized)
as publiclin ythetraded
mortgage-backed
securitiespurchased
(MBS), whi
charepresent
anis
indi
r
ect
i
n
vestment
mortgage
loan
pool.
Property
wi
t
h
mortgage
referred
to as a loan amount. Changes
and ithen property
owner's value
equityoveris thetime,property
valueaffect
minusthe
the
outstanding
therefore,
property owner's equity in the property.
properties
generate
income
from
rents.
Homes
purchased
for
rentalofficincome
are considered
investment
in commercial
property. Large
properties
(e.g.,
aneither
epurchased
building)
are
a
form
of
direct
investment
for
institutions
or
wealthy
individuals,
for cashtimeorhorizons,
leveragedilliquidity,
(a mortgagetheloanlargeis sitaken
forinvestment
a portionneeded,
of the and
purchase
price).
Long
z
e
of
theinvestors.
complexity
of the inrealvestments
make commercial
real
estatebyinappropriate
for manyin
Commercial
estate
properties
can
also
be
held
a
limited
partnership
which
the
partners
have
limited
liability
and
the
general
partner
manages
the
investment
and the properties, or by a real estate investment trust (REIT).
Asconsidered
with residenti
a
l
mortgages,
whole
loans
(commercial
property
mortgages)
are
a direct
investment,
but loansancaninbedirectpooledinvestment.
into commercial mortgage­
backed securiti
es (CMBS)
that represent
(REITs)
issue
shares
thatestatetradeassetspublicly
like shares
of
stock.
REITs
are
often
identi
f
i
e
d
by
the
type
of
real
they
hold:
mortgages,
hotel
properties,
malls,
offi
c
e
buildings,
or
other
commercial
property.
Income
i
s
used
to payondithis
vidends.
Typical
lywoul
, d have
of intocomebe paid
mustbybethedisREIT
tributedbefore
to shareholders
totoavoid
taxes
income
that
distribution
shareholders.
Residential property
leveraged investment
Commercial real estate
Real estate investment trusts
90o/o
Other Real Estate Assets
Two additional
assets considered
ascomes
real estate
are timberland
andagricultural
farmland, products.
for
which
one
component
of
returns
from
sales
of
timber
or
Timberland returns
alsoprices
includein price
changesandonhowtimberland,
whichhasdepend
on
expectations
of
lumber
the
future
much
timber
been
harvested.
Farmltheandqualreturns
based onofland
price changes,
and
ity andarequantity
the crops
produced.changes in farm commodity prices,
Page 288
©2012 Kaplan, Inc.
Study Session 1 8
Cross-Reference to CFA Institute Assigned Reading #66 - Introduction to Alternative Investments
Potential Benefits and Risks of Real Estate
Real estate
performance
is measured
byNatithree
different
types
ofEstate
indices.Investment
An appraisal
index,
such
as
those
prepared
by
the
o
nal
Council
of
Real
Fiduciaries
(NCREIF),
is based
onthoseperiodic
estionmactual
ates ofsalproperty
valuthees. Appraisal
ideviation
ndex returns
are
smoother
than
based
e
s
and
have
l
o
west
standard
ofproperties
returns ofthat
the various
indexmultipl
methods.
A The
repeatsample
sales ofindexproperties
is basedsoldon price
changes
for
have
sold
e
times.
and
thus
included
in
the
i
n
dex
is
not
necessarily
random
and
may
not
be
representati
v
e
of
theindices
broadarespectrum
e (anofexampl
of samplesimilarselection
bias).indices.
REIT
based onoftheproperties
actual tradiavainglablprices
REITeshares,
to equity
Historical
ly,(onREITthe iorder
ndex returns
and globalbusiness
equitycycles
returnsaffecthaveREITs
had aandrelativel
y strong
correl
a
ti
o
n
of
because
gl
o
bal
equities
similarl
y
.
The
correlation
between
global
bond
returns
and
REIT
returns
has
been
very
low historical
ly. In eis tportfolio.
her case diversi
ficationthe benefi
ts canof iresul
t construction
from including
real
estate
i
n
an
i
n
vestor'
However,
methods
n
dex
g., appraisal
or repeat
indices)benefimaytsbemaya factor
the low
reported correlations,
i(e.n which
case actual
diversisalfesication
be lessinthan
expected.
0.6)
Real Estate Valuation
Three methods are commonly used to value real estate:
The
comparable
sales
approach include
bases valuation
on recent
sales of similar
properties.
Values
for
i
n
divi
d
ual
properties
adj
u
stments
for
differences
between
the
characteristi
cs ofavaithelable,specific
property
and thosecondition,
of the properties
for which recent
sales
prices
are
such
as
age,
location,
and
size.
The
incomefutureapproach
estimates
property ownership
values by calculating
theing present
valoperating
ue of
expected
cash
fl
o
ws
from
property
or
by
divi
d
the
net
income
(NOa I)growth
for a property
byestia capi
talizati
on on(cap)factors
rate.such
The ascapgeneral
rate is business
a discount
rate
minus
rate
and
is
m
ated
based
conditions,
property
qualities,
management
eff
e
ctiveness,
and
sales
of
comparable
properties.
Note(1thatI dividing= 8).by a cap rate of is the same as using a multiple
ofThe8 times
NOI
costcostapproach
estimates
the replaconstruction
cement cost costs
of a property.
Theto esticostmofateland
and
the
of
rebui
l
ding
at
current
are
added
replacement cost.
Value
estimates forapproach
real estateisinsimi
vestment
trustsincome
can beapproach
income based
or assetc property
based.
The
income-based
l
ar
to
the
for
a
specifi
and
uses
some
measure
of
cash
fl
o
w
and
a
cap
rate
based
on
the
factors
we
noted
previooperations
usly for the(FFO).
incomeFFOapproach.
One
measure
ofincome
cash flowith
w fordepreciation
a REIT is funds
from
i
s
cal
c
ul
a
ted
from
net
added
back
(because
depreciation
i
s
a
non-cash
charge)
and
wi
t
h
gains
from
property
salassumed
es
subtracted
and
losses
on
property
sales
added
(because
these
gains
and
losses
are
to(AFFO),
be nonrecurring).
A second
measure
of cashexpenditures
flow is adjusted
funds from
operations
which
i
s
FFO
with
recurri
n
g
capital
subtracted.
AFFO
is value
similarof
tothefreeREITcashbyflosubtracting
w. The asset-based
approach
provides
an
estimate
of
the
net
asset
lities from the total value of the real estate assets and
dividing by the number oftotalsharesliabioutstanding.
•
•
12.5%
•
0 . 125
©20 12 Kaplan, Inc.
Page 289
Study Session 1 8
Cross-Reference to CFA Institute Assigned Reading #66 - Introduction to Alternative Investments
Real Estate Investment Due Diligence
Propertyconditions,
values fluctuate
because
of global
and
natispecifi
onal ceconomic
factors,variation
local in
market
and
i
n
terest
rate
levels.
Other
risks
include
theDecisiabilities
of
managers
to
select
and
manage
properties,
and
changes
in
regulations.
ons regardingThe
selecting,
fiofnancing,
andusedmanaging
realestateestateinvestment
projects idirectl
y
affect
performance.
degree
leverage
in
a
real
s
important
because leverage amplifies losses as well as gains.
investing
hasls andadditional
risk factorshistories.
compared to investing in
properties
with
sound
fi
n
anci
a
stable
operating
hasenviaddi
t
i
o
nal
risk
factors
including
regulatory
issues
such
as
zoning,
permitting,
and
ronmental
considerations
orperiod.
remediation,
andbleeconomic
changes
and financifinnancing
g
decisions
over
the
development
The
possi
inabi
l
i
ty
to
get
long-term
atfintheanciappropriate
time
for
properties
initially
developed
with
temporary
(short-term)
ng presents an additional risk.
Distressedproperties
Real estate development
COMMODITIES
Whi
l
e
it
is
possible
to
invest
directl
y
in
commodities
such
as
grain
and
gold,
the
most
commonly
usedthemselves
instrumentsare tophysigaincalexposure
to thus
commodity
pricesforarestorage
derivatiandves.
Commodities
goods
and
incur
costs
transportation. Returns are based on price changes and not on income streams.
Futures,trade
forwards,
options, andsomeswaps
are altrade
l available
forms ofwhicommodity
derivatioverves.
Futures
on
exchanges;
options
on
exchanges
l
e
others
trade
thedealcounter;
andandforwards
andareswapscontractual
are over-the-counter
instruments
originated
by at a
e
rs.
Futures
forwards
obligations
to
buy
or
sel
l
a
commodity
speci
fied priceatanda specifi
time.eOptions
convey
theOther
right,methods
but notoftheexposures
obligation,to commodities
to buy or sell
ainclude
commodity
d
price
and
time.
the following:
(commodity
ETFs)in commodities
are suitable fororincommodity
vestors whofutures
are limited
tocanbuying
equity
shares.
ETFs
can
i
n
vest
and
track prices or indices.
include
sharesgiveofinvestors
a commodity
producer,
such
as
an
oil
producer
or
a
gold
mining
fi
r
m,
and
exposure
to price
changes
ofisthethatproduced
commodity.
One
potential
drawback
to
commodity-l
i
nked
equities
the
price
movements
of
the
stock
and
the
price
movements of the commodity
may notmanaged.
be perfectl
y correlated.
are
actively
Some
managers
concentrate
on ed.
specifi
c
sectors
(e.
g
.
,
agricultural
commodities)
whi
l
e
others
are
more
diversifi
Managed
future(e.funds
canandbe structured
as limitedon thepartnerships
withworth,
fees likeandthose
ofliquidity
hedge offunds
g
.
,
and
restrictions
number,
net
the investors.
They
can also
be structured
likbenefi
e mutual
funds
with shares
that
are
publicly
traded
so
that
retai
l
investors
can
also
t
from
professional
management.
tionally,tosucha limited
a structure
allows astructure.
lower minimum investment and
greater liquidityAddicompared
partnership
•
Exchange-traded funds
•
Equities that are directly linked to a commodity
•
Managed futures funds
2
Page 290
20)
©2012 Kaplan, Inc.
Study Session 1 8
Cross-Reference to CFA Institute Assigned Reading #66 - Introduction to Alternative Investments
•
•
Individual
managed
accounts
provideAccounts
an alternative
toredpooled
funds
forof thehighspecifi
net c
worth
individual
s
and
institutions.
are
tail
o
to
the
needs
mvestor.
Specializedwefunds
indiscussed
specific and
commodity
sectors
cancommodities,
be organizedsuchunderas oianyl andofgas,
the
structures
have
focus
on
certain
grains, precious metals, or industrial metals.
Potential Benefits and Risks of Commodities
Returns
onSharpe
commodities
overcommodities
time have been
lower
than have
returnsbeenonlowglobalduestocks
orlowerbonds.
rati
o
s
for
as
an
asset
class
to
these
returnscanandearnthehighhighreturns
volatiliover
ty ofshort
commodities
prices.theiAsrwith
other investments,
speculators
periods
when
expectations
term commodity price movements are correct and they act on them. about short­
Historical
ly,been
correlati
otypicall
ns of commodi
ty returnsso with
thosengofcommodities
global equitiesto aandtraditional
global
bonds
have
l
o
w,
y
l
e
ss
than
that
addi
portfolio
provide
diversifcommodities
ication benefits.canBecause
commodity
prices
tend
to move
wiextent
th inflthatacan
tioncommodities
rates, holding
act
as
a
hedge
of
infl
a
tion
ri
s
k.
To
thebe
prices
move
wi
t
h
infl
a
tion
the
real
return
over
time
would
zero, although futures contracts may offer positive real returns.
0.2,
Commodity Prices and Investments
prices
forof commodities
arey toa function
ofandsupply
and demand.
Demand
is affected
bySpot
the
value
the
commodi
t
end-users
by
global
economic
conditions
andBoth
cycles.
Supply
is
affected
by
production
and
storage
costs
and
existi
n
g
inventories.
supply
and demand are affected by the purchases and sales of non-hedging investors
(speculators).
For
commodities,
supply
is inelastic
ins, theplantshortcrops,runorbecause
ofto long
leadlesstimes
tothem).
almany
terAsproduction
levels
(e.
g
.
,
drill
oil
well
decide
plant
ofcantly
a
result,
commodity
prices
can
be
volatile
when
demand
changes
signifi
over
the economic
cycle.
Production
of someby thecommodities,
especiallyto hiagrigh cprices
ulturalwhen
commodities,
can
be
signi
f
i
c
antly
affected
weather,
leading
production
i
s
low
and
l
o
w
prices
when
production
i
s
high.
Costs
of
extracting
oil
and
mineralsneeds,
increase
as more expensi
ve methods
oreconomic
more remote
areasgovernment
are used.policy,
To estimate
future
commodities
producers
anal
y
ze
events,
and
forecasts
of
future
supply.
Investors
anal
y
ze
inventory
levels,
forecasts
of
production,
changes
in
government
pol
i
c
y,
and
expectations
of
economic
growth
in
order
to
forecast
commodity prices.
Commodity Futures Pricing
Wheat
todaytoday
and wheat
erent whil
products.
Purchasingfor wheat
the
commodity
will givsiex themonths
buyerfrom
the usetodayof areit ifdiffneeded,
e contracting
©20 1 2 Kaplan, Inc.
Page 291
Study Session 1 8
Cross-Reference to CFA Institute Assigned Reading #66 - Introduction to Alternative Investments
to be delivered
six monthsthesefromaspects
todayis:avoids storage costs and having cash tied up. An
equation
that considers
futures price spot price risk-free rate) storage costs - convenience yield
is contract.
the value Ifofthihaving
the physical
commodity
for use over
the is
period
of
the
futures
s
equation
does
not
hold,
an
arbitrage
transaction
possible.
Ifsituation
there istermed
little or no convenience
yield,
futures
prices
wi
l
l
be
higher
than
spot
prices,
a
Whenreferred
the convenience
less than spot prices, a situation
to as yield is high, futures prices will be
Three sources of commodities futures returns are:
Roll
yield duetwotofutures
a difference
the spotexpiprice
futures price,
or a differenceThebetween
pricesbetween
with different
ratioand
n dates.
The interest earned on collateral required to enter into a futures
2. contract.
3. spot pricesin and theicconvergence
The totalofprice
return
i
s
a
combination
of
the
change
in
futures prices to spot prices over the term of the
futures contract.
�
(1
+
+
Convenience yield
contango.
backwardation.
1.
yield-
Collateral yield-
Change
spot pr es-
� Professor's Note: These three sources ofreturn are described more fully in the
� Investing in Commodities topic review.
Other Alternative Investments
Various
types
ofandtangistamps,
ble collectibl
esjewelry
are consianddered
investments,
including
rare wines,
art,
rare
coins
valuable
watches,
and
sports
memorabilia.
There
iautomobile.
s no incomeStorage
generaticosts
on butmayowners
do
get
enjoyment
from
use,
as
wi
t
h
a
collectible
be signifi
cant, collectibles
especially with
art and wiandne.gains
Specialized
knowledge
i
s
required,
the
markets
for
many
are
illiquid,
result
only from increases in the prices of these assets.
LOS 66.f: Describe, calculate, and interpret management and incentive fees
and net-of-fees returns to hedge funds.
CPA ® Program Curriculum, Volume 6, page 185
Hedge Fund Fees
The total fee paiThed bymanagement
investors infeea hedge
fundregardless
consists ofof investment
a
and anand
i
s
earned
performance
incentive fees are a portion of profits. The most common fee structure for a hedge fund
management fee
incentive fee .
Page 292
©2012 Kaplan, Inc.
Study Session 1 8
Cross-Reference to CFA Institute Assigned Reading #66 - Introduction to Alternative Investments
iisncenti
"2 andve 20"
"2 plus,of profi
" 2%ts.of the value of the assets under management plus an
fee ofor20%
Profi
ts can
ben(1)s inanyexcessgainsofina value, (2) anyA hurdle
gains inratevaluecaninbeexcess
ofthertheasmanagement
fee,
or
(3)
gai
set
ei
a
percentage
(e.ncenti
g., 4%)ve feesor aarerateearned
plus aonly
premionumreturns
(e.g., inLIBOR
2%).
A
means that
imeans
excess
of
the
benchmark.
A
s
o
ft
that incentive fees are paid on all profits, but only if the hurdle rate is met.
Another
feature
is often
a priwor losses.
r mark.ThusThisinmeans
thatfees
theare only
incentipaid
ve feeto that
ithes notextent
paidthatonincluded
gaithencurrent
s thatis called
justvaluoffset
centi
v
e
e
of
an
i
n
vestor'
s
account
is
above
the
highest
ensuresiothatvalues.investors will not be charged
incentivvalue
e fees previ
twiceouslonytherecorded.
same gaiThins sinfeature
their portfol
InvestorsA common
in funds offeefunds
incurfrom
additional
feesfunds
fromisthe"1 and
managers
of1%themanagement
funds of
funds.
structure
funds
of
10.
"
A
fee andfunds
a 10%within
incentithevefund-of-funds
fee are chargedstructure.
in addition to any fees charged by the individual
hedge
Fee
calculationsof rates
for both
management
feesfeeanddetermination.
incentive feesManagement
can differ notfeesonlymaybybe
thecalculschedule
but
also
method
of
ated on eiIncenti
ther theve fees
beginning-of-period
ornetend-of-period
valuesfeesof(value
assets under
management.
may
be
calculated
of
management
increase
less management
fees)tendor independent
of management
fees.1Although
theofmostfunds,common
hedge
fund
fee
rates
to
be
the
"2
and
20"
and
"1
and
0"
for
funds
fee
structures
can
vary.
Price
breaks
to
investors,
competitive
conditions,
and
historical
performance can influence negotiated rates.
Fee
structures
and
their
i
m
pact
on
i
n
vestors'
results
are
i
l
l
ustrated
in
the
following
example.
hurdle rate.
+
hard hurdle rate
hurdle rate
high
ate
Example: Hedge fund fees
BJI(an alFunds
ishiaghedge
fundFundswitcharges
h a valuea of2%$100
million atfeethebased
beginning
of theunderyear
l
-ti
m
e
h).
BJI
management
on
assets
management
at uses
the begi
ngnih nwater
g of themark.yearIncenti
and av20%
incentive
fee wionth agai5%ns hard
hurdle
rate
and
a
hi
e
fees
are
calculated
net of
management fees. The ending values before fees are:
Year
1:
$125.
7
5
million
Year
$127.4440 million
million
Year 2:3: $138.
Calculate the total fees and investor's net return for all three years.
©20 12 Kaplan, Inc.
Page 293
Study Session 1 8
Cross-Reference to CFA Institute Assigned Reading #66 - Introduction to Alternative Investments
Answer:
Year
1:
Management
fee:of100year (given):
2o/o = 2 $125.75 million
Gross
val
u
e
end
Incenti
v
e
fee:
[125.75100
2
(100
5o/o)]
20o/o
= $3. 7 5 million
Total fee:value2 net3.75offees:
= $5. 7 5 million
Ending
125.75I 100)- 5.751 == 20.$120.00%00 million
Net return to investors: (120
Year 2: fee: 120 2o/o = $2.40 million
Management
Gross
valveufee:e end[127.ofyear
(given):
$127.
4(120
0 milli5.on0%)] 20o/o = -$0.20 million. Since
Incenti
4
0120
-2.
4
0thirate.s result is negative there is no incentive fee. The return did not exceed the hurdle
Total
fee:value$2.4net0 million
Ending
of120)fee: -127.1 =44.17o/o
0- 2.40 = $125.00 million
Net
return:
(125
I
The net return of less than 5o/o is consistent with no incentive fee.
Year
3: fee: 125 2.0o/o = $2.50 million
Management
Gross
valveufee:e end[138.ofyear
(given):
$138.
44 mill
ion00 5.0o/o)] 20o/o = $0.94 million
Incenti
4
4125.
0
02.
5
0(125.
Total
fee:value
2.50net0.offee:
94 = $3.138.4444million
Ending
Net return: (135 I 125) - 1 = 8.0-0o/o3.44 = $135. 00 million
The
over hieachgh water
of the mark
three wasyears.never an issue because this hedge fund had positive returns
x
x
+
x
x
x
x
x
+
x
x
LOS 66.g: Describe risk management of alternative investments.
CPA ® Program Curriculum, Volume 6, page 219
Riunique
sk management
of alternatiforve each
investments
requi
rcanes additional
understanding
of the
set
of
circumstances
category.
We
summarize
some
of
the
more
important risk considerations as follows:
Standardreturns
devidistributions
ation of returnsaremay
be a misleadingnormal;
measuretheyof risktendfortotwobe leptokurtic
reasons.
First,
not
approximately
(fatalternative
tails) and negati
vthat
ely skewed
(possibilior tmodels
y of extreme
negativevalues,
outcomes).
Second,
forsmoothed
assets
use
appraisal
to
estimate
returns
areof
so
that
standard
deviation
of
returns
(and
correlations
wi
t
h
returns
traditional
will transactions
be understated.are Even
market-based
returns cancanhave
these same investments)
limitations when
infrequent.
These problems
bias
•
Page 294
©2012 Kaplan, Inc.
Study Session 1 8
Cross-Reference to CFA Institute Assigned Reading #66 - Introduction to Alternative Investments
Sharpe
measuresdownsi
upwarddeandriskmake
estimsuch
ates ofas beta misleading(VaR),
as well.whichInvestors
shoul
d
consider
measures
is an
estimate
of
the
si
z
e
of
a
potential
decline
over
a
period
that
wil
l
occur,
for
example,
less than 5o/oratherof thethantime;standard
or thedeviation. For publicly
which measures
risk as downside
deviation
traded
securities,
such
asmore
REITs
and
ETFs,
market
returns
are
used
and
standard
definitions
of
ri
s
k
are
applicable.
Use of derivatives
introduces
operational,
financial,
counterparty,
anddetermined
liquidity risk.
Performance
for
some
alternative
investment
categories
i
s
primarily
byclass
management
expertise
and
execution,
so
ri
s
k
is
not
just
that
of
holding
an
asset
but
alsofunds
risk ofandmanagement
underperformance.
Hedge
pri
v
ate
equity
funds are much
less transparent
thanstrategies
traditionalto be
investments
as
they
release
l
e
ss
information
and
may
consider
their
proprietary
information.
Many
alternative
investments
areinvestors
illiquid.forReturns
should
reflor theect ainability
premiumto forredeem
lack
of
liquidity
to
compensate
liquidity
risk
securi
t
i
e
s
at
all
duri
n
g
lockup
periods.
When
calculating
optimal
allocations,
indices
ofreturns
historicalandreturns
and
standard
deviations
may
not
be
good
indicators
of
future
vol
a
ti
l
i
t
y.
Correlations vary across periods and are affected by events.
value at risk
Sortino ratio,
•
•
•
•
•
•
Due Diligence
listing
of key items
for due diportfol
ligenceioformanagement,
alternative investments
includes
six risk
maj
o
r
categories:
organization,
operations
and
controls,
management, legal review, and fund terms.
Experience,
quality,
andfundcompensation
of management
andandstaff;
anal
y
sis
of
al
l
their
prior
and
current
results;
ali
g
nment
of
manager
investor interests; and reputation and quality of third-party service providers used.
Management
of
the
investment
process;
target
markets,
asset
types,
and strategies;
investment
sources;integrati
operatingon ofpartners'
roles; underwriting;
envi
r
onmental
and
engineeri
n
g
review;
asset
management,
acquisitions, and dispositions; and the process for dispositions.
3. statements; internal controls;Reporti
n
g
and
accounting
methods;
audited
financial
frequency of valuations; valuation approaches;
insurance; and contingency plans.
and limits;
4. constraints on leverageFundandpolicies
currencies
and hedgiportfoli
ng oforelrisaktedandriskeyks. factors; and
Fund legal structure; registrations; and current and past litigation.
5.
Fund
Fees,
both
management
and
incentive,
and
expenses;
contractual
terms;
termandandtermination
extensions; procedures
carried interest;
conflicts;investment
rights ofperiod;
limited fund
partners;
for keydistributions;
personnel.
A
1 . Organization:
2 . Portfolio management:
Operations and controls:
Risk management:
Legal review:
6.
terms:
©20 12 Kaplan, Inc.
Page 295
Study Session 1 8
Cross-Reference to CFA Institute Assigned Reading #66 - Introduction to Alternative Investments
'
KEY CONCEPTS
LOS 66.a
"Traditional
innvestments"
vestments" refers
refers toto some
long-only
positions
insuchstocks,
bonds,
andcommodities,
cash.
"and
Alternati
v
e
i
types
of
assets
as
real
estate,
various
collectables,
asequity
well asfundssome(including
specific structures
of investment
vehicles.
Hedge
funds
and
private
venture
capital
funds)
are
often
structured
partnerships;
estate ivnevestment
trustsas (REITs)
mutual funds;as limited
and ETFs
can containrealalternati
investments
well. are similar to
Comparedlessto traditional
investments,
alternati
vmanagement
e investmentsfeestypicall
ymore
havespeci
loweralized
liquidity;
regulation
and
disclosure;
higher
and
management;
potential
di
v
ersifi
c
ation
benefi
t
s;
more
use
of
leverage,
use
of
deri
v
ati
v
es;
potentially higher
returns;
historical
returns data;
problematic
historical
risk limited
measures;andandpossibly
uniquebiased
legal and
tax considerations.
LOS 66.b
Hedge
funds
are
investment
companies
that
use
a
vari
e
ty
of
strategies
and
may
be
hi
g
hly
leveraged, use long and short positions, and use derivatives.
Priwanting
vate equity
funds
usually
invest
in
the
equity
of
pri
v
ate
companies
or
companies
to become
private,
fifunds,
nancingwhich
theirprovi
assetsdewith
hightolevels
of debt.earlThis
category
also
i
n
cludes
venture
capital
capital
companies
y
in
their
development.
Real
estate
as
an
asset
cl
a
ss
includes
residential
and
commerci
a
l
real
estate,
individual
mortgages,orandloanspoolass wel
of mortgages
orinvestment
properties. inIt limited
includespartnerships,
direct investment
inaresingle
properties
l
as
indirect
which
privatearesecurities,
mortgage-backed securities and real estate investment trusts,
which
publiclyandtraded.
Commodities
refer
to
physical
assets
such
as
agri
c
ul
t
ural
products,
metals,
oil
and
gas,
material
used incation
production.
anandinflother
ationrawhedge
and sdiversifi
benefits.Commodities market exposure can provide
Various
typesasofwell.collectibles, such as cars, wines, and art, are considered alternative
investments
LOS 66.c
The
primary
moti
v
ati
o
n
for
adding
alternati
v
e
i
n
vestments
to
a
portfol
i
o
is
to
reduce
portfoli
o risk based
onreturns.
the less-than-perfect
correlatiinvestments,
on betweenthealternati
ve asset
returns
and
traditional
asset
For
many
al
t
ernative
expertise
of
the
manager can be an important determinant of returns.
Page 296
©2012 Kaplan, Inc.
Study Session 1 8
Cross-Reference to CFA Institute Assigned Reading #66 - Introduction to Alternative Investments
LOS 66.d
Hedge Funds
strategies
include
merger
arbitrage,
distressed/restructuring,
activi
s
t
shareholder andstrategi
speciales seek
situations.
profidown"
ts fromstrategies
unusualbased
pricingon global
issues. economic trends.
strategies
are
"top
are "bottomStrategies
up" strategies
thatmarket
take long
and short
positions
igrowth,
n equitiesfundamental
andstrategi
equityesvalderivatives.
include
neutral,
fundamental
ue, quantitative directional, short bias, and sector specific.
In periods
oftofinincrease,
ancial crisis,
thelimits
correlation
of returns
between asglobal
equities
andassethedge
funds
tends
whi
c
h
hedge
funds'
effectiveness
a
diversi
fy
ing
class.
Due diligenceadvantages,
factors fortrack
hedgerecord,
funds longevity
are investment
strategy,
investment
process,
competitive
of
fund,
and
size
(assets
under
management).investor
Otherrelations,
qualitativgrowth
e factorsplans,
includeandmanagement
key personrisk.risk,
reputation,
managementstyle,
of systematic
•
•
•
•
Event-driven
Relative value
Macro hedge
Equity hedge
Private Equity
(LBOs)
and
are
the
two
dominant
strategies.
Other
strategies include developmental capital and distressed securities.
Types
of LBOs
include
management
buyouts, buy-ins,
in whichinthewhich
existianngexternal
management
team
iteam
s involved
i
n
the
purchase,
and
management
management
replaces the existing management.
Stages
ofg,venture
capital
investi
ngtheinclude
the formati
ve stageand(composed
of the angel
investi
n
seed,
and
early
stages);
later
stage
(expansion);
the
mezzanine
stage
(prepare for IPO).
Methods
for
exiting
i
n
vestments
in
portfolio
companies
include
trade
sale
(sell
to
a competitor or (issue
anotherportfolio
strategiccompany
buyer); IPO
(sellsecondary
some orsaleall shares
toanother
investors);
recapitalization
debt);
(sell
to
private
equity firm or other investors); or write-off/liquidation.
Primustvateidentify
equity tophas performing
some historical
record
of
potential
diversifi
c
ation
benefi
t
s.
An
i
n
vestor
private equity managers to benefit from private equity.
Due diligused,
ence factors
for privandate equity
includeprocedures
the manager'
s experience,capivaluation
methods
fee structure,
drawdown
for committed
tal.
Leveraged buyouts
venture capital
Real Estate
Reasons
to investdiversifi
in realcatiestate
include potential
returns, income from
rent
payments,
on benefits,
and hedginglong-term
againsttotal
inflation.
©20 12 Kaplan, Inc.
Page 297
Study Session 1 8
Cross-Reference to CFA Institute Assigned Reading #66 - Introduction to Alternative Investments
Forms of real estate investing:
Public (Indirect)
Debt
Equity
.
.
.
.
Private (Direct)
Mortgage-backed securities
Collateralized mortgage obligations
Real estate corporation shares
Real estate investment trust shares
.
.
.
•
.
.
Mortgages
Construction loans
Sole ownership
Joint ventures
Limited partnerships
Commingled funds
Real estatemortgage-backed
investment categories
residential and
properties,
REITs,
securities,include
and timberland
farmland.commercial real estate,
Historical
ly,wireal
estatebond
returnsreturns.
are highl
y construction
correlated witmethod
h globalofequity
returnsindexes
but lessmay
correl
a
ted
t
h
global
The
real
estate
contribute to the low correlation with bond returns.
Due
diligence
factors
for
real
estate
include
global
and
national
economic
factors,
local
market conditions,
interest
rates,properties
and property-specifi
c risksrealincluding
regulationshave
and
abilities
of
managers.
Distressed
investing
and
estate
development
additional risk factors to consider.
Commodities
The
common way tofunds,
investequities
in commodities
is wityhlinked
derivatitoves.a commodity,
Other methods
imanaged
nclumost
de exchange-traded
that
are
directl
commodityfutures
sectors.funds, individual managed accounts, and specialized funds in specific
Beyond
the potential
forclahissgmay
her returns
andationlowerprotection.
volatilityCommodities
benefits to a portfolio,
commodity
as
an
asset
offer
infl
can offset
inflation, especially if commodity prices are used to determine inflation indices.
Spot
prices
for
commodities
are
a
function
of
supply
and
demand.
Global
economics,
production costs, and storage costs, along with value to user, all factor into prices.
LOS
66.efunds often invest in securities that are not actively traded and must estimate
Hedge
their
values,Hedge
and funds
investmay
in securi
tieastethata tradiarenilliquid
relati
ve to theforsizthee ofilliquidity
a hedge fund'
s
position.
calcul
g
NAV
that
adjusts
of
these securities.
A(multiple-based)
private equity portfoli
may becashvalued
using a market/comparables
approach
approach,o company
a discounted
flow approach,
or an asset-based approach.
Real
estateapproach
property(multiples
valuationorapproaches
include
thews),comparabl
e salesapproach.
approach,REITsthe can
income
discounted
cash
fl
o
and
the
cost
be valued using an income-based approach or an asset-based approach.
Arisk-free
commodity
futures
pri
c
e
i
s
approximately
equal
to
the
spot
price
compounded
at
the
rate, plus storage costs, minus the convenience yield.
Page 298
©2012 Kaplan, Inc.
Study Session 1 8
Cross-Reference to CFA Institute Assigned Reading #66 - Introduction to Alternative Investments
LOS total
66.f fee for a hedge fund consists of a management fee and an incentive fee. Other
The
feeincurstructure
speci
f
i
c
ati
o
ns
include
hurdle
rates
and
high
water
marks.
Funds
of
funds
calculations
both management fees
and inancentiadditional
ve fees canleveldifferof management
by the schedulefees.andFeemethod
of feefordetermination.
LOS
66.g of alternative investments requires understanding of the unique
Risk
management
circumstances
for each category.
Standard
deviation
of returns operational,
may be misleading
as acounterparty,
measure of risk.
Use
of
deri
v
ati
v
es
introduces
fi
n
ancial,
and liquidity
risks.
Performance
for
some
alternati
v
e
i
n
vestment
categori
e
s
depends
primarily
on
management
expertiprisve.ate equity funds are less transparent than traditional
Hedge
funds
and
investments.
Many
alternati
vecinvestments
arestandard
illiquid. deviations may not be good indicators of
Indices
of
histori
al
returns
and
future
returnsvaryandacross
volatility.
Correlations
periods and are affected by events.
Key
i
t
ems
for
due
di
l
i
g
ence
include
organization,
portfolio
management,
operations
and
controls, risk management, legal review, and fund terms.
•
•
•
•
•
•
•
©20 12 Kaplan, Inc.
Page 299
Study Session 1 8
Cross-Reference to CFA Institute Assigned Reading #66 - Introduction to Alternative Investments
'
CONCEPT CHECKERS
Compared
toaremanagers
ofhavetraditional
investments,on:managers of alternative
iA.nvestments
l
i
kely
to
fewer
restrictions
holding
cash.
C. buying
using deristocks.
vatives.
to alternative investments, traditional investments tend to:
A.Compared
bebe less
less liquid.
C. requireregulated.
lower fees.
which category of alternative investments is an investor
to use
3. Inderivatives?
A. Real
estate.
C. Commodities.
Collectibles.
4. Anis investor who
choosest from:
a fund of funds as an alternative to a single hedge fund
to
benefi
fees.
A. hilower
g
her
C. more duereturns.
diligence.
InA. arestrict
leveragedadditional
buyout, borrowing.
covenants in leveraged loans can:
require lenders
C. provide
protectionto provide
for the transparency.
general partners.
Direct
commercial
real
estate
ownership
requires
investing
in:
A. large
amounts.
i
l
liquid
assets.horizon.
C. a short time
7. liDiversifi
cation benefits from adding hedge funds to an equity portfolio may be
m
i
t
ed
because:
A. hedge
correlations
tend toareincrease
duringperfectly
periodscorrel
of fiantedancialwithcrisis.
fund
returns
less
than
globalareequities.
C. hedge funds tend to perform better when global equity prices
declining.
Atoprivate
equity
valuation
approach
that
uses
estimated
multiples
of
cash
fl
o
ws
ue a portfoliapproach.
o company is the:
A. valdiscount
asset-based
cash
fl
o
w
approach.
C. market/comparables approach.
1.
B.
2.
B.
most likely
B.
most likely
B.
5.
B.
least likely
6.
B.
B.
8.
B.
Page 300
©2012 Kaplan, Inc.
Study Session 1 8
Cross-Reference to CFA Institute Assigned Reading #66 - Introduction to Alternative Investments
realincome
estateapproach.
property valuation would
use a(n):
B.C. asset-based
approach.
comparable sales approach.
highfund.
waterThemarkend-of-year
of million
was established
twoyearyearswasago formillion.
a British
hedge
value
before
fees
for
last
This
year'
s
end-of-year
value
before
fees
i
s
million.
The
fund
charges
and
Management
are paiWhat
d independentl
ncentithisve fees
calcul20.ated" million.
on end-of-yearfeesvalues.
is the totaly feeof ipaid
year?and are
B.C. million.
million.
Standard
deviation
is
an appropriate measure of risk for:
hedge
funds.
B.C. publicly
traded
REITs.
exchange-traded funds.
9.
A
A.
10.
A
least likely
£150
£140
£155
A.
1 1.
"2
£3. 1
£4.1
£6. 1
least likely
A.
©20 12 Kaplan, Inc.
Page 301
Study Session 1 8
Cross-Reference to CFA Institute Assigned Reading #66 - Introduction to Alternative Investments
'
ANSWERS - CONCEPT CHECKERS
1.
C
Traditional managers can hold cash and buy stocks but may be restricted from using
derivatives.
2.
C
Traditional investments typically require lower fees, are more regulated, and are more
liquid than alternative investments.
3.
B
Commodities investing frequently involves the use of futures contracts. Derivatives are
less often employed in real estate or collectibles investing.
4.
C
A fund of funds manager is expected to provide more due diligence and better
redemption terms. Funds of funds charge an additional layer of fees. Investing in fund of
funds may provide more diversification but may not necessarily provide higher returns.
5.
A
Debt covenants in leveraged buyout loans may restrict additional borrowing by the
acquired firm. Covenants restrict and require borrowers' actions, not lenders' actions.
Covenants in leveraged loans provide protection for the lenders, not the general partners.
6.
C
Commercial real estate ownership requires long time horizons and purchasing illiquid
assets that require large investment amounts.
7.
A
Adding hedge funds to traditional portfolios may not provide the expected
diversification to an equity portfolio because return correlations tend to increase during
periods of financial crisis.
8.
C
The marketlcomparables approach uses market or private transaction values of
similar companies to estimate multiples of EBITDA, net income, or revenue to use in
estimating the portfolio company's value.
9.
B
10. B
The three approaches to valuing a property are income, comparable sales, and cost. An
asset-based approach can be used for real estate investment trusts, bur not for valuing
individual real estate properties.
Management fee is £ 1 5 5 million
x
0.02 = £3. 1 million.
Incentive fee is (£155 million - £ 1 50 million)
x
0.20 = £ 1 . 0 million.
Total fee is £3. 1 million + £ 1 .0 million = £4. 1 million.
11. A
Page 302
Hedge funds may hold illiquid assets that may use estimated values to calculate returns.
Risk as measured by standard deviation could be understated. For publicly traded
securities, such as REITs and ETFs, standard definitions of risk are more applicable.
©2012 Kaplan, Inc.
The following is a review of the Alternative Investments principles designed to address the learning
outcome statements set forth by CFA Institute. This topic is also covered in:
INVESTING IN CoMMODITIES
Study Session 1 8
EXAM Focus
There
are
only
three
LOS
here.
The
concepts
of
backwardation
and
contango
are
based
on the relation thebetween
currentof(spot)
pricescalleandd thefutures
prices which
and arestems
important
for
understanding
component
returns
roll
yield,
from
the
necessity
to
re-establish
long
commodity
positions
as
they
reach
thei
r
settl
e
ment
(deli
v
ery)
dates.
The
fact thatinpositions
must beactiperiodically
clotoseda loutong andequityre-established
makesng
even
a
commodity
dexi
n
g
strategy
v
e
compared
or
bond
i
n
dexi
strategy.
LOS 67.a: Explain the relationship between spot prices and expected future
prices in terms of contango and backwardation.
CFA® Program Curriculum, Volume 6, page 232
Contango
refersthetospota situation
in price
commodities
futures
contracts
where
theoffutures
price
i
s
above
price,
the
for
current
purchase
and
del
i
very
thefutures
physical
commodi
t
y.
Thi
s
is
the
current
situation
(as
of
the
time
of
writing)
in
the
oil
market.
One wayWithto oilviewprices
the expl
anatisharpl
on fory overthistheis based
on theusersneedsof oilofand
either long or
short
hedgers.
ri
s
ing
l
a
st
year,
oil-related
commodities
are
concerned
wi
t
h
the
risk
they
face
from
risi
n
g
oil
prices.
Airlines,
forancialexample,
sell ticketsof increases
at prices ibased
onprices
expected
fuelthoseprices
and areto exposed
toin the
fi
n
consequences
n
fuel
above
expected
prevail
the future.
When
an cende inuser
of awecommodity
buysfutures
futuresbuyer
contracts
to protect against
unexpected
future
pri
creases,
refer
to
that
as
a
as
they
are
hedgi
n
g
commodityin price
risk withislong
positions.
Ifsktheof price
predominant
reason
for futureswill be
positions
a
commodity
to
hedge
the
ri
increases,
long
hedgers
paying
forpricetheincreases.
protectionIn ofa situation
long futuresof contango,
positions,long
whichhedgers
will produce
gainsupas thethe price
futures
are
bidding
of commodity
in effect, paying a premium for the hedging benefit they get
from
taking longfutures
futuresand,positions.
Backwardation
refers totheaspot
situation
inIfcommodities
futures
contracts
where thefuture
futures
price
i
s
below
price.
the
dominant
traders
in
a
commodity
arefromproducers
of
the
commodity
hedgi
n
g
thei
r
exposure
to
financial
losses
arising
unexpected
pricearedeclines
in theprotection
future, theagairesult
willdeclines
be backwardation.
Inreflthisected
situation,
producers
paying
for
n
st
price
and
that
is
iproducers
n futures prices
whi
c
h
are
lower
than
current
market
prices
(spot
prices).
Historicall
y
,
hedging the price risk of future production have been dominant in futures
long hedger,
©20 12 Kaplan, Inc.
Page 303
Study Session 1 8
Cross-Reference to CFA Institute Assigned Reading #67 - Investing in Commodities
markets,backwardation.
so that backwardation was the typical situation and sometimes referred to as
normal
LOS 67.b: Describe the sources of return and risk for a commodity investment
and the effect on a portfolio of adding an allocation to commodities.
CPA® Program Curriculum, Volume 6, page 234
Anthisinexposure
vestor whothrough
desiresa deri
longvatiexposure
to a commodity
priceor futures.
will typicalSomely achiphysievecal
v
e
i
n
vestment
in
forwards
commoditi
s cannot
beveffecti
vely purchased
anda more
storedeffilong
term,
andofforgaining
others,longsuch
asexposure
preciousthanemetal
s
,
deri
ati
v
e
positions
may
be
c
ient
means
purchasing the commodities outright and storing them long term.
ToU. Stake
a position
iaren forwards
orasfutures,
a specul
acollateral
tor or hedger
must
post thecollyield
ateral.onIf
.
Treasury
bill
s
deposited
collateral,
the
yield
i
s
simply
the
T-bills.canActiinvcrease
e management
of theyieldcollateral,
n the T-bil
boundsl rate.ofwhat is acceptable
collateral,
the collateral
above thewithi90-day
The
pricevereturn
on a long-only
investment
in commodities
derivati
vesthecancommodity
be positive
orovernegati
depending
on
the
direction
of
change
in
the
spot
price
for
the life of the derivatives contract employed.
Since commodity
deriovervatitime
ve contracts
expire,
a specul
ator orderihedger
who
wantsandto
maintain
a
position
must
close
out
the
expiring
v
ati
v
e
position
re-establishto asa new positionthewiposition
th a settlement
dateto further
inlosses
the future.
This
processtheis
referred
and
leads
gai
n
s
or
whi
c
h
are
termed
roll
yield.
The
roll
yi
e
ld
can
be
positive
or
negati
v
e
depending
on
whether
the
derivati
v
e
contract
used
toeldestablish
the longor losses
exposure
iwoul
s in backwardation
orthecontango.
Youif thecanspot
viprice
ew this
roll
yi
as
the
gains
that
d
be
real
i
zed
on
position
remained unchanged over the life of the contract.
Asspota futures
contract
gets thecloserfutures
to expiration,
theequal
futuresthe price
converges
toward
theor
price.
At
expiration,
price
must
spot
price.
For
a
future
forward
inrollbackwardation
(i.e.,since
the futures/forward
priceprice
is lessatthan
the current
spot
price)
the
yield
i
s
positive,
an
unchanged
spot
contract
settlement
would
mean
thehave
futures/forward
price increased
over ortheforward
life of thein contango,
contract, andthe theroll
investor
would
gai
n
s
at
settlement.
For
a
future
yiprice,
eld isannegati
ve. Sincespotcontango
meansthe the
forward/futures
price ithes greater
thanpricethewillspot
unchanged
price
over
l
i
f
e
of
the
contract
means
futures
have fallen and losses will result when the position is closed out.
When
commodity
derivatiwereve markets
were
dominated by theshortrollhedgers
(commodity
producers)
and
markets
typical
l
y
i
n
backwardation,
yield
was
positive.
In
current
marketIt mayconditions,
withthatfutures
and forwards
typical
ly in contango,
the roll yield
isderinegative.
be
the
case
structural
changes
i
n
the
markets
for
commodities
v
atives
mean
that
a
zero
or
negative
roll
yield
has
become
the
new
norm
for
these
markets.
rolling over
Page 304
©2012 Kaplan, Inc.
Study Session 1 8
Cross-Reference to CFA Institute Assigned Reading #67 - Investing in Commodities
Adding a longforcommodities
inportfolios.
dex positionCommodities
to a portfoliprovide
o can provide
several
benefi
tts,s
particularly
pension
fund
di
v
ersi
f
i
c
ation
benefi
because
thei
r
prices
tend
to
be
uncorrelated
with
securities
prices,
and
they
can
serve
as
a
hedge against inflation.
LOS 67.c: Explain why a commodity index strategy is generally considered an
active investment.
CPA® Program Curriculum, Volume 6, page 239
Annecessary
index strategy
intheequities
is considered
a thepassive
strategy.
Whileinchanges
may ofbe
if
one
of
component
stocks
of
index
i
s
changed,
the
absence
any
changeBecause
in the ofcomponent
stocks,of clnoosiacti
voute management
of an index
portfolio
is
required.
the
necessity
n
g
and
re-establishing
long
deri
v
ative
positions
to maintain
long exposure
tostrategy.
changesManagers
in commodity
prices,
atocommodity
icommodity
ndex strategy
iindexs considered
an
acti
v
e
can
add
value
the long-only
strategy
by
choosing
the
maturities
of
the
deri
v
ati
v
e
contracts
they
buy
andlong-only
by theircommodity
decisions about
when
to roll overattempt
their positions.
To positions
the extentoverthatat
many
deri
v
ati
v
e
managers
to
roll
their
the sameand time,
premium
in transactions
costs, which reduces both the roll
yield
overalthey
l yielpay
d ofatheir
commodity
index strategy.
There
are
two
other
aspects
of
commodity
index
i
n
vesti
n
g
that
requi
r
e
acti
v
e
management.
Theinweiindexes
ghtingsdoofnotvarious
commodities
andwithcommodity
blocks
(such asve
metals
or
energy)
necessarily
change
the
values
of
the
derivati
positions
in
the
portfolio.
Si
n
ce
commodities
index
wei
g
htings,
whether
based
on
commodity
production
orvelyconsumption,
change
over
time, a manager
whocommodity
seeks to
match
an
i
n
dex
must
acti
manage
the
si
z
e
of
the
exposure
to
vari
o
us
marketsusedastopositions
arezerolderiledvatiover.ve positions
Additionalmust
ly, asbementioned
earlier,
theTheshort-term
debt
col
l
aterali
managed
as
wel
l
.
coll
a
teral
debt
securities
matureadvantage
and newofonesmarket
mustconditions
be purchased,
and the collateral
collateral debt
yieldsecurities
can be
enhanced
by
taking
as
maturing
are replaced.
©20 12 Kaplan, Inc.
Page 305
Study Session 1 8
Cross-Reference to CFA Institute Assigned Reading #67 - Investing in Commodities
'
KEY CONCEPTS
67.a futures market is in contango if futures prices are greater than the spot
Aprice.
commodity
The market is in backwardation if futures prices are less than the spot price.
Futurestomarkets
thatagainst
are dominated
by longtendhedgers
(users
of the Futures
commodity
who that
buy
futures
protect
price
increases)
to
be
i
n
contango.
markets
are dominated
hedgers tend
(producers
the commodity who short futures to
protect
against bypriceshortdecreases)
to be inofbackwardation.
67.b on a commodity investment includes:
The return
Collateral
yield:the thegainreturn
onduethetocollateral
posted
to satisfy
margin requirements.
Price
return:
or
loss
changes
i
n
the
spot
price.
Roll
yield:
the
gai
n
or
loss
resul
t
ing
from
re-establishi
n
g
positions
as
contracts
exptre.
is positive if the futures market is in backwardation and negative if the market
iRoll
s in yield
contango.
Commodities
can provide
a portfoliowiofthsecurities
commodity returns
tend notdiversi
to befichiation
ghlybenefi
positivelts toy correlated
securitiesbecause
returns.
67.c ty index strategy is considered an active investment because the manager has
Ato commodi
decide
whatovermaturi
tnew
ies tocontracts.
use for theActiforward
or futuresiscontracts
and determine
when
toportfolio
roll themwei
i
n
to
v
e
management
al
s
o
required
to
manage
ghtssecurities
to matchto post
thoseasofcolthelateral
benchmark
inthese
dex selected
and
to edetermine
the
best
choice
of
and
how
should
be
roll
d
over
as
they
mature.
LOS
LOS
•
•
•
LOS
Page 306
©2012 Kaplan, Inc.
Study Session 1 8
Cross-Reference to CFA Institute Assigned Reading #67 - Investing in Commodities
CONCEPT CHECKERS
commodities
marketby endtendsusersto beofithen backwardation
if:
ittheisspot
dominated
commodity.
price areis greater
C. futures prices
greaterthan
thanfutures
the spotprices.
price.
The
source
ofspot
returnpriceon aoverlong-only
commodity
investment
thatcontract
represents
theis
change
in
the
the
l
i
f
e
of
the
forward
or
futures
used
the: roll yield.
return.
C. price
spot yield.
For
a
commodity
market
that
is
i
n
contango,
an
unchanged
spot
price
over
the
life ofzero.a contract will result in a roll yield that is:
positive.
C. negative.
following a long-only commodity index strategy is
to
4. adjmanager
utost thereduceportfolio:
exposure
to
a
declining
commodity
market.
changesoutin expiring
the composition
commodity index.
C. forcontracts.
by closing
contractsofandthere-establishing
positions in new
1.
A
A.
B.
2.
A.
B.
3.
A.
B.
A
least likely
A.
B.
©20 12 Kaplan, Inc.
Page 307
Study Session 1 8
Cross-Reference to CFA Institute Assigned Reading #67 - Investing in Commodities
ANSWERS - CONCEPT CHECKERS
Page 308
1.
B
Backwardation refers to the situation in which futures prices are less than the spot
price. Commodity markets tend tO be in backwardation when they are dominated by
producers of the commodity.
2.
B
The price return results from the change in the spot price. The roll yield is the gain or
loss that results from closing a position in an expiring contract and re-establishing it in
a new contract. The collateral yield is the return on the collateral deposited tO establish
the position.
3.
C
For a commodities market in contango, if the spot price remains unchanged, the futures
price will decrease over its life and the investOr will realize a loss at expiration. Thus, the
roll yield is negative.
4.
A
A long-only commodity index strategy is always long the commodities in the index and
the weights are not adjusted based on the performance of the positions. The manager
must actively manage the roll out of expiring contracts, as well as matching any changes
in the commodity index weightings.
©2012 Kaplan, Inc.
SELF-TEST : DERIVATIVES AND ALTERNATIVE
INVESTMENTS
10 questions, 15 minutes
1. Which
of thebasedfollonowing is 1.5 % and
a simianlarity
between
a forward
rate
agreement
interest
rate
option
on
A. Arateslongincrease
positionabove
in either
one
wi
l
l
result
in
a
positive
payment
if
interest
the
contract
rate.
The
payments
to
ei
t
her
are
based
on the difference between a contract rate
and
a
market
(reference)
rate.
C. Ifreference
both haverate,thetheysamewilcontract
rate,
notional
principal,
expi
r
ati
o
n
date,
and
l make equal payments to their (long) owners.
tookgoladlongwasposition
in fourmargi1 00-ounce
Julypergoldcontract
futuresandcontracts
2. Adam
atmaintenance
685 Vernon
when spot
670.
Initial
n
i
s
$4,
0
00
margi
n
i
s
$3,
2
00
per
contract.
If
the
account
i
s
marked
to
market
when
spotmustgolddeposit
is 660 toandkeepthethefutures
priceopen
is 672,is the additional
margin the
iA.nvestor
position
to:
$2,$4,0000.00.
$5,000.
ue of a callin asset
optionpriceonvola stock
is
to increase as a result of:
3. A.Theanvalincrease
a
ti
l
i
t
y.
a
decrease
i
n
the
risk-free
rate
of
interest.
C. a decrease in the strike price of the option.
Kurt coveri
Crawford
purchased
shares
ofeach.
Acme,TheInc.sum, forof$38the and
sold calper-share
l optionsgain
at
4. $40,
n
g
all
hi
s
shares
for
$2
maximum
and
maximum
per-share
loss
(as
an
absolute
value)
on
the
covered
cal
l
position
is:
A. $36.
$40.
C. unlimited.
Grant hasstock
entered
i
n
to
a
$10
million
quarterly-pay
equity
swap
based
on
5. theCraigNASDAQ
index
as the 8o/o fixed rate payer when the index is at 2,750.
Which
of
the
foll
o
wi
n
g
i
s
A. iHendexwilisl make
a payment of $200,000 on the second payment date if the
2,
7
50.
Hethe wiindex
ll neither
make nor receive a payment on the first settlement date if
i
s
2,805.
C. Ifthethesecond
indexsettlement
at the firstdate.
settlement date is 2,782, he must make a payment at
that a risk.
forward contract on a zero-coupon bond:
6. A.It ishas counterparty
can
be
settl
e
d
i
n
cash.
C. requires a margin deposit.
least likely
LIBOR +
LIBOR?
B.
closest
B.
c.
least likely
B.
B.
most accurate?
B.
least likely
B.
©20 12 Kaplan, Inc.
Page 309
Self-Test: Derivatives and Alternative Investments
Survivorship bias in reported hedge fund index returns will
result in
index:
A. returns
and
risk
that
are
biased
upward.
risk thatdownward
are biasedanddownward.
C. returns
risk thatandis biased
returns that are biased upward.
fundve feewitand
h a management
and fee structure
has a hardindependently
hurdle rate ofand theIf
8. Athehedge
i
n
centi
fee
are
calculated
management
fee is based
onwhich
beginning-of-period
asset
values,
an iinnvestor'
s net
return
over
a
period
during
the
gross
value
of
the
fund
has
creased
isA.
most likely
7.
B.
2
20
5%.
22%
closest to:
16.4%
B. 16.6%
c. 1 7.0%
9. Measures
downside
areA. value ofat risk
to (VaR).
include:risk for asset classes with asymmetric return distributions
Sortino ratio. standard deviation.
C. thekurtosis-adjusted
The
type
of
real
estate
i
n
dex
that
exhibits
sample
selection
bias
i
s
A.a(n):appraisal
REIT index.index.
C. repeat sales index.
least likely
B.
most likely
10.
B.
Page 3 1 0
©2012 Kaplan, Inc.
Self-Test: Derivatives and Alternative Investments
SELF-TEST ANSWERS: DERIVATIVES AND
ALTERNATIVE INVESTMENTS
1.
C
Because the F RA pays at the expiration of the forward contract, it pays the present value
of the interest savings that would be realized at the end of the (hypothetical) loan term.
The interest rate option will pay the interest savings on the (hypothetical) loan after
expiration at the end of the loan term and its payment will be greater (since it's not
discounted back to the expiration date).
2.
C
The initial margin is 4 x $4,000 $ 1 6,000 and the maintenance margin is 4 x $3,200
$ 1 2 ,800. The loss on the position is (672 - 685) x 4 x 100 -$5,200, leaving a balance
of $ 1 6,000 - $5,200 $ 1 0,800. Because the account has fallen below the maintenance
margin, a deposit of $5,200 is required to bring the balance back up to the initial
margin.
=
=
=
=
3.
B
A decrease in the risk-free rate of interest will decrease call values. The other changes will
tend to increase the value of a call option.
4.
B
The net cost of the covered call position is 38 - 2 36, so the maximum loss (if the
stock price goes to zero) is $36. The maximum gain (if the stock price goes to 40 or
more) is $4. The sum is 36 + 4 40.
=
=
5.
B
If the index has risen to 2,805 ( +2%), the index payer's liability (2% x $ 1 0 million) just
offsets the fixed rate payer's liability (8% I 4 x $ 1 0 million). The payment at the second
settlement date cannot be determined without knowing the change in the index level
between the first and second settlement dates. The index level at the first settlement date
does not determine the payment at the second settlement date.
6.
C
Forward contracts typically do not require a margin deposit. They are custom
instruments that may require settlement in cash or delivery of the underlying asset, and
they have counterparty risk.
7.
C
Surviving firms are more likely to have had good past returns and have taken on less risk
than the average fund, leading to upward bias in index returns and downward bias in
index risk measures.
8.
B
The management fee is 2% of the beginning asset value, which reduces an investor's
gross return by 2% to 22 - 2 20%. The incentive fee is 20% of the excess gross return
over the hurdle rate, or 0.20(0.22 - 0.05) 3.4%. The investor return net of fees is
22% - 2% - 3.4% 1 6 .6%.
=
=
=
9.
C
10. C
Value at risk (VaR) and the Sortino ratio based on downside deviations from the mean
are measures of downside risk. Kurtosis-adjusted standard deviation is not a concept
presented in the curriculum.
A repeat sales index includes prices of properties that have recently sold. Because these
properties may not be representative of overall property values (may be biased toward
properties that have declined or increased the most in value of the period), there is the
risk of sample selection bias. An appraisal index or a REIT index is generally constructed
for a sample of representative properties or REIT property pools.
©20 12 Kaplan, Inc.
Page 3 1 1
FORMULAS
full price = clean price accrued interest
change in bond price
duranon. = percentage
yield change in percent
value of a callable bond = value of an option-free bond-value of the call
. anon-adJ
. .USted par value stated
coupon payment= mfl
--coupon-rate
absolute yield spread = yield on the higher-yield bond-yield on the lower-yield bond
yield spread
re anve yi.eld spread yieldabsolute
on the benchmark bond
subject bond yield
pe. ld rano. = benchmark
bond yield
after-tax yield = taxable yield - marginal tax rate)
. yi.eld tax-free--=---yield
taxable-equivalent
(1-marginal tax rate)
zero-coupon bond value= +maturity value
payment
current yie. ld = annual cashbondcoupon
price
bond equivalent yield = [(1 monthly CFY)6 J
= [�1 +annual-pay -1J
effective annual yield = ( + semiannual-pay ) +
_ .!.._
_
_
-==....!._
-
TIPS
1
.
x-
=
x
=
(1
-
-
(1 i)llumber of yearsX2
+
-1
YTM
1
YTM
x2
X2
2
2
spot rate from forward rates:
forward rate from spot rates:
Page
312
©2012
Kaplan, Inc.
1
--''-- 2
Book 5
-
Fixed Income, Derivatives, and Alternative Investments
Formulas
V_-V . = (bond price when yields fall-bond price when yields rise) = ---'
e ecuve. duratton
2 (initial price) (change in yield in decimal form) 2V0 (L�y)
percentage change in bond price = -effective duration change in yield in percent
ffi
+
X
X
x
percentage change in price = duration effect + convexivity effect
= {[-duration (�y)] + [convexity �y) ]
price value of a basis point = duration
bond value
return impact of a change in spread -duration Llspread 2.2 convexity (L:lspread)2
(floating -forward)( days )
value of a long FRA at settlement: {notional ptincipai) [ [days
(floating)
intrinsic value of a call: = Max[O, S -X]
intrinsic value of a put: P = Max[O, X- S]
option value = intrinsic value + time value
lower and upper bounds for options:
ct � Max[O, Sr-X I + RFR)T-rT]
st
� Max[O, St - X I + TRFR) -t] ]
st
-t
Pr � Max[O, X I + RFR) - St] X I + RFR)T-r
X
Pt � Max[O, X- St]
put-call parity: c + X I + RFR)T = S + p
put-call parity with asset cash flows: +X I + RFR)T = (S0 - PV + P
plain-vanilla interest rate swap:
(net fixed-rate payment)r =(swap fixed rate - LIBOR r-d (numb;��f days )
notional principal
x
x
x
0.000 1
2 } x
100
x
x
�
(
+
x
r
3
1+
360
C
Option
Minimum Value
European call
American call
Maximum Value
(1
(1
Cy
European put
(1
(1
American put
(1
C
(1
CF)
x
©20 12 Kaplan, Inc.
Page 3 1 3
INDEX
A
absolute basis 280
absolute yield spread 74
accelerated sinking fund provision 16
accrued interest 14
ad hoc auction 47
affirmative covenants 1 1 , 162
after-tax yield 77
agency bonds 49
alternative investments 278
American options 227
amortizing securities 14
angel investing 284
annual-pay yield to maturity 103
apprrusal index 289
appropriation-backed obligations 54
arbitrage 193
arbitrage-free Treasury spot rates 73
asset-backed securities 59
B
backwardation 292, 303
bankers acceptances 59
bank reserve requirements 69
bankruptcy remote entity 60
best efforts basis 57, 6 1
bid-ask spread 36
bond equivalent yield 103, 1 1 0
bond forwards 202
bondholder rights 56
bond indenture 1 1
bond options 229
bootstrapping 1 1 1
bought deal 6 1
c
callable bonds 29, 1 17, 137
call option 192, 226, 230
call option profits and losses 268
call protection 15
call provisions 1 5
call risk 25
cap 13, 17, 231
caplet 231
cap risk 30
cash flow yield 107
cash management bill 47
cash settlement (forwards) 198
Page 3 1 4
cash settlement (futures) 2 1 8
central bank 69
certificates of deposit (COs) 58
change in spot prices 292
cheapest-to-deliver 2 1 9
clawback 285
clean price 14
clearinghouse 2 1 4
closing trade 2 1 8
collar 1 3 , 232
collateralized debt obligation (COO) 60
collateralized mortgage obligation (CMO) 5 1
collateral trust bonds 55
collateral yield 292, 304
commercial paper 58
commercial real estate 288
committed capital 285
commodities 290, 303
comparable sales approach 289
contango 292, 303
contingent drum 1 9 1
contract multiplier 229
convenience yield 292
conversion option 1 6
convexity 137, 145
corporate credit ratings 159
corporate family ratings 1 59
cost approach 289
counterparty risk 198
coupon 12
coupon rate 28
coupon strips 49
covenants 1 1
covered call 272
credit curves 170
credit enhancements 55, 56
credit migration risk 158
credit rating 55, 159
credit risk 26, 157, 199
credit spread 35, 75, 169
credit spread risk 35
currency denomination of a bond 12
currency forward contract 205
currency futures 220
currency options 229
currency risk 37
currency swap 256
current yield 1 0 1
curtailment 5 1
©2012 Kaplan, Inc.
Book 5
-
Fixed Income, Derivatives, and Alternative Investments
Index
Federal National Mortgage Association (Fannie
Mae) 50
fiduciary call 244
financial options 229
firm commitment 6 1
floating-rate securities 1 3 , 29
floor 13, 17, 231
floorlet 232
foreign currency options 229
formative stage 284
forward commitment 1 9 1
forward contract 192, 197
forward discount factor 1 1 8
forward rate 1 1 8
forward rate agreement 203
four Cs of credit analysis 1 6 1
full price 1 4
full valuation approach 134
funded investor 79
fund of funds 281
futures contracts 192, 213
D
dealer-placed paper 58
debentures 50
debt service coverage ratio 177
default risk 35, 157, 198
deferred-coupon bonds 12
deliverable forward contract 198
delivery 218
delivery options 218
derivatives 191
criticism of 192
developmental capital 285
directly-placed paper 58
dirty price 14
discount rate 69
discount to par value 27
distressed investing 285
dollar duration 3 1
double-barreled bonds 54
downgrade risk 35, 15 8
duration 28, 30
of a portfolio 144
duration/convexity approach 134
G
general obligation bonds 53, 176
Government National Mortgage Association 50
government sponsored enterprises 50
E
early stage (venture capital) 284
effective convexity 147
effective duration 139
embedded options 16, 28, 76
enterprise value 175
equity forward contracts 200
equity hedge fund strategies 282
equity swap 261
equivalent annual yield 1 1 0
Euribor 203
Eurodollar deposit 202
Eurodollar futures 219
European options 227
event-driven strategies 281
event risk 26, 38
exchange for physicals 218
exchange rate risk 26, 37
exchange-traded derivatives 1 9 1
exchange-traded options 229
expected loss 157
external credit enhancement 60
H
high water mark 293
high yield 172
hurdle rate 293
I
F
face value 12
Federal Farm Credit System 50
Federal Home Loan Bank Corporation (Freddie
Mac) 50
Federal Home Loan Bank (FHLB) 49
federally related institutions 50
incentive fee 292
income approach 289
indenture 1 1
index options 229
inflation-indexed bonds 13
inflation risk 26, 37
initial margin 2 1 5
insured bonds 5 4
interest rate cap 231
interest rate collar 232
interest rate floor 231
interest rate options 229, 230, 234
interest rate policy tools 69
interest rate risk 25, 27
interest rate swaps 258
in-the-money call option 228
intrinsic value of an option 234, 235
inverse floater 13
investment grade 160
issuer 12
©20 12 Kaplan, Inc.
Page 3 1 5
Book 5
Index
-
Fixed Income, Derivatives, and Alternative Investments
J
N
junior debt 158
negative convexity 137
negative covenants 1 1 , 162
negotiable CDs 58
negotiated offering 6 1
net asset value 36
nominal spread 74, 1 1 5
non-investment grade 160
nonrefundable bonds 15
normal backwardation 304
notching 160
notice period 280
notional principal 257
K
key rate duration 33
L
later stage (venture capital) 284
law of one price 193
letters of credit 56, 60
leveraged buyouts (LBOs) 283
limit move (up, down) 2 1 6
liquidity preference theory 7 1
liquidity risk 26, 36
listed options 229
locked limit 216
lockup period 280
London Interbank Offered Rate (LIBOR) 78,
203, 230, 259
long forward position 197
long-term equity anticipatory securities (LEAPS)
229
loss severity 157
M
Macaulay duration 142
macro strategies 282
maintenance margin 215
management buy-ins 284
management buyouts 284
management fee 292
margin buying by institutional investors 1 7
market liquidity risk 158
market segmentation theory 71
marking to market 36, 2 1 6
maturity, relation to interest rate risk 28
maturity value 12
medium-term notes (MTNs) 56
mezzanine financing (in LBOs) 283
mezzanine-stage financing (venture capital) 284
minimum and maximum values of options 237
minimum value of a European put option 240
minimum value of an American call option 239
minority equiry investing 285
modified duration 142
moneyness 228
moral obligation bonds 54
mortgage-backed securities 50
mortgage passthrough security 5 1
municipal bonds 53, 176
mutual termination of a swap 255
Page 3 1 6
0
offsetting contract (to terminate a swap) 255
offsetting trade (to exit a futures position) 2 1 8
off-the-run issues 48
on-the-run issues 48
open market operations 69
option-adjusted spread (OAS) 1 17
option contract 226
option payoffs 233
option premium 226
option profit diagrams 268
options 1 9 1
options on futures 230
option writer 226
out-of-the-money call option 228
overnight repo 1 8
over-the-counter derivatives 1 9 1
over-the-counter options 229
p
parallel shift 33
pari passu 1 5 8
par value 12, 27
plain vanilla interest rate swap 258
portfolio companies 284
positive convexiry 137
preferred habitat theory 72
premium of an option 227
premium to par value 27
prepayable debt 137
prepayment option 14, 17, 34
prepayment risk 25, 5 1
prerefunded bonds 54
price limits 2 1 6
price return 304
price value of a basis point 147
price-yield profile 93
primary market for debt 6 1
prime brokers 280
©2012 Kaplan, Inc.
Book 5
principal strips 49
priority of claims 158
Private Export Funding Corporation 50
private investment in public equities 285
private placement 61
protective put 244, 273
public credit enhancement 54
pure expectations theory 71, 72
putable bond 1 17, 138
put-call parity 243, 244, 245
put option 192, 226, 230
put option profits and losses 269
put provisions 16
Q
quality spread 75
R
rating agencies 55, 159
real estate investment trusts (REITs) 288
realized yield 108
real options 230
recovery rate 157
redemption 1 6
reference rate (for a floating-rate security) 1 3
regular cycle auction 47
regular redemption 1 6
reinvestment income 108
reinvestment risk 25, 34, 1 0 1 , 109
REIT indices 289
relative basis 280
relative value strategies 281
relative yield spread 74
repeat sales index 289
repurchase agreement (repo) 1 8
resale of a swap 256
reset date 29
residential property 288
revenue bonds 53, 54, 176
reverse trade (to exit a futures position) 218
roll yield 292, 304
Rule 144A offering 6 1
s
scenario analysis approach (to measuring interest
rate risk) 134
secondary market for debt 6 1
SEC Rule 4 1 5 56
secured debt 55, 1 5 8
Securities and Exchange Commission (SEC) 5 0
seed stage (venture capital) 284
seniority ranking 1 58
serial bonds 53
-
Fixed Income, Derivatives, and Alternative Investments
Index
settlement date 198, 255, 257
settlement price 2 1 5
shelf registration 56
short forward position 197
sinking fund 1 5 , 17
Sortino ratio 295
sources of return from debt securities 101
sources of return from commodities 292, 304
sovereign bonds 46, 175
sovereign risk 26, 38
special purpose vehicle 60
special redemption 16
spot rate 73, 1 1 8, 120
spread risk 158
static spread 1 1 5
step-up notes 12
stock index futures 220
stress testing 134
stripped Treasury securities (STRIPS) 49
structural subordination 160
structured note 57
Student Loan Marketing Association
(Sallie Mae) 50
subordinated debentures 56, 1 5 8
swaps 191, 255
swaption 256
swap, ways to terminate 255
synthetic options 244
T
tap system 47
taxable-equivalent yield 77
tax-backed bonds 53
tax-free bonds 53
Tennessee Valley Authority 50
tenor 255
terminating a forward contract 199
terminating a futures contract 2 1 8
term repo 1 8
theoretical Treasury spot rate curve 73, 1 1 1
third-party guarantee 56
time value 236
tranches 5 1 , 52
Treasury bill futures 2 1 9
Treasury bond futures 2 1 9
Treasury Inflation-Protected Securities 48
Treasury securities (bills, notes, bonds) 47
u
unsecured debt 55, 56, 158
upgrade of a bond rating 35
upper bound for call options 237
upper bound for put options 237
©20 12 Kaplan, Inc.
Page 3 1 7
Book 5
Index
-
Fixed Income, Derivatives, and Alternative Investments
v
value at risk (VaR) 295
variation margin 215
venture capital 284
volatility risk 26, 38
y
yield curve risk 25, 32, 33
yield curve shapes 70
yield ratio 74
yield spread 157
yield to call 105
yield to first call 105
yield to maturity (YTM) 1 02
yield to put 106
yield to refunding 106
yield to worst 106
yield volatility 37
z
zero-coupon bonds 12
value of 89
zero-volatility spread 1 1 5
Page 3 1 8
©2012 Kaplan, Inc.
Notes
Notes