Download Global Fixed Income Portfolio

Asset Management
Global Fixed Income Portfolio
CfBS Center for Business Studies AG
Dr. Enzo Mondello, CFA, FRM, CAIA
August 2014
Content
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2
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Risks Associated with Investing in Bonds
Fixed-Income Valuation
Term Structure of Interest Rates
Yield Measures
Interest Rate Risk: Duration and Convexity
Credit Risk: Fundamentals of Credit Analysis
Managing Bond Portfolio
Relative-Value Methodologies for Global
Corporate Bond Portfolio Management
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10
11
12
Exchange Rate Risk: International Bond Investing
Managing Interest Rate Risk with Derivatives
Managing Credit Risk with Derivatives
Currency Risk Management
© Dr. Enzo Mondello, CFA, FRM, CAIA
August 2014
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Risks Associated with Investing in Bonds
Overview of Risk Factors
Interest rate risk is the risk that when interest rates increase, bond prices decline. Interest rate risk is the greatest
risk faced by bond market investors.
Call risk is the risk that a bond will be paid off before its maturity date. The risks are:
– Higher uncertainty of the cash flows of the bond.
– Risk that principal proceeds will have to be reinvested at lower rates.
– Reduced capital gain potential in a falling rate environment.
© Dr. Enzo Mondello, CFA, FRM, CAIA
August 2014
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Risks Associated with Investing in Bonds
Yield curve risk is the risk that the value of a bond portfolio might deteriorate because of a change in the shape
of the yield curve
Reinvestment risk is defined as the risk that the received cash flows must be reinvested at a rate lower than the
original investment. If coupon payments must be reinvested at lower rates, overall returns of the investment will be less
than initially projected.
Credit (default) risk is the possibility that the issuer will be unable to repay the coupon payments and/or the principal
amount to the bondholder as defined by the indenture
Liquidity risk is the risk that a security will not be able to be sold quickly without giving up a large price concession.
This bid-ask-spread is the best measure of liquidity risk; the wider the spread, the greater the liquidity risk is.
© Dr. Enzo Mondello, CFA, FRM, CAIA
August 2014
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Risks Associated with Investing in Bonds
Exchange rate risk is the risk that the exchange rate between the currency in which a bond is denominated
and the currency of the investor’s home country might change
Volatility risk describes the risk that changes in volatility of interest rates will affect the value of options embedded
in a bond
Inflation risk is the risk that the purchasing power of the cash flows received from a bond (interest and principal) will
decline over time because of inflation
Event risk is the risk that some unusual event could cause the price of bonds to decrease (e.g. natural disaster,
corporate takeover, a regulatory change, or political factors)
Sovereign risk has two components:
1. A sovereign may be unable to service its bonds (no ability to pay)
2. A sovereign may be unwilling to service its bonds even though it has the resources to do so
© Dr. Enzo Mondello, CFA, FRM, CAIA
August 2014
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Risks Associated with Investing in Bonds
Bond Price and Risk Factors
Interest rate risk is the major risk faced by fixed-income investors
The bond price is the present value of the sum of future cash flows (coupon payments plus the principal
amount)
Bond Price 
C3
C1
C2
Cn  P



.........

(1 r) 1 (1 r) 2 (1 r) 3
(1 r) n
Therefore, if the discount rate r, which is the yield required by the market (which is related to interest rate levels)
increases, the price of the bond decreases, and vice versa. This is true for almost all bonds.
© Dr. Enzo Mondello, CFA, FRM, CAIA
August 2014
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Risks Associated with Investing in Bonds
Coupon Rate > Required Market Yield:
Bond Price > Par Value (Premium Bond)
Coupon Rate < Required Market Yield:
Bond Price < Par Value (Discount Bond)
Coupon Rate = Required Market Yield:
Bond Price = Par Value (Par Bond)
© Dr. Enzo Mondello, CFA, FRM, CAIA
August 2014
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Risks Associated with Investing in Bonds
The volatility of a bond (i.e. by what percentage the price of a bond will change for a given basis point change
in interest rates) depends upon:
–
Maturity: Long-term bonds are more volatile than short-term bonds, all other factors being equal
–
Coupon: The lower a bond’s coupon is, the greater its volatility will be
–
Yield: The higher the yield at which a bond trades, the lower its price sensitivity for a given basis point change in
interest rates will be, all other factors being equal
© Dr. Enzo Mondello, CFA, FRM, CAIA
August 2014
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Risks Associated with Investing in Bonds
Call Risk
Some bonds are callable. Therefore, they have a call option embedded in their price structure. This means that the
owner of a callable bond can be viewed as owning a portfolio consisting of an option-free (straight) bond
and a short position in a call option on the bond. The investor has a short position in the embedded call
option because the issuer has the right to call the bond from the bondholder.
Therefore, the price structure of a callable bond can be modeled as follows:
Price Callable Bond = Price Noncallable Bond Price – Price of embedded Options
© Dr. Enzo Mondello, CFA, FRM, CAIA
August 2014
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Risks Associated with Investing in Bonds
Call and prepayment risk is the risk that a bond will be paid off before its maturity date. The reasons why this is
disadvantageous for an investor are:
–
–
–
The cash flows are unknown.
Reinvestment risk because bonds are usually called when interest rates are low so that the investor is forced to
reinvest the proceeds at lower interest rates.
The appreciation potential of a callable bond is limited (price compression).
© Dr. Enzo Mondello, CFA, FRM, CAIA
August 2014
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Risks Associated with Investing in Bonds
Interest Rate Risk of a Floating-rate Security
The future cash flows of floating-rate notes are not fixed. They rise and fall directly with changes in interest rates.
Consequently, the price of a typical floating-rate security should change very little when interest rates
change because the dollar value of its coupon (future cash flows) will change in the same direction as the rate at
which the future cash flows will be discounted.
There are three reasons why floating-rate security prices can be affected by changes in interest rates:
–
–
–
Reset dates: the longer the time between reset dates, the greater the interest risk will be.
Reference rate: the quoted margin above the reference interest rate that the market requires can change.
Cap risk: this is the risk that the reference interest rate will rise enough that a floating-rate security’s coupon rate
will be capped out.
© Dr. Enzo Mondello, CFA, FRM, CAIA
August 2014
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Risks Associated with Investing in Bonds
Yield Curve Risk
The yield curve risk is the risk that the value of a bond portfolio will deteriorate because of the change in the shape
of the yield curve
The yield curve is a graphical representation of interest rates across all maturities. When interest rates move, they do
not change in an equal amount for all maturities.
Duration has a very restrictive interpretation: it is the percentage change in the value of a bond that will occur if the
entire yield curve shifts in a parallel manner (all maturities move by the same increment)
Since a parallel shift is an unlikely scenario, duration is considered at best to be an approximation of a bond’s
sensitivity, and is only accurate for small changes in interest rates
© Dr. Enzo Mondello, CFA, FRM, CAIA
August 2014
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Risks Associated with Investing in Bonds
Reinvestment Risk
The factors that affect the reinvestment risk of a security are:
Changes in interest rates: The greater the change, the higher the risk
The size of the cash flows: The larger the cash flows to be reinvested, the greater the risk
The timing of the reinvestment cash flows: The faster the cash flows are received, the greater the reinvestment
risk
© Dr. Enzo Mondello, CFA, FRM, CAIA
August 2014
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Risks Associated with Investing in Bonds
Amortizing securities, such as mortgage-backed securities, have more reinvestment risk than non-amortizing
securities, such as conventional bonds. There are two reasons for this:
– The periodic cash flows paid by amortizing securities consist of both coupon interest and the repayment of a
portion of principal
– Amortizing securities typically pay their cash flows monthly, rather than semi-annually. The more frequently the cash
flows are paid, the more frequently the reinvestments occur, and the higher the reinvestment risk.
Note that with zero-coupon bonds, there are no coupon payments to be reinvested over their term to maturity, and
thus have no reinvestment risk
© Dr. Enzo Mondello, CFA, FRM, CAIA
August 2014
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Risks Associated with Investing in Bonds
Types of Credit Risk
Default risk: is the risk that an issuer will fail to make interest or principal payments when they are due. If a bond
defaults, the investors do not necessarily suffer a total loss. The recovery rate is the percentage of the investor’s
investment that is not lost, but recovered.
Credit spread risk: is the risk that the market yield (due to the credit spread) will rise, causing the price of the bond to
decline
Downgrade risk: is the risk that the price of a bond might fall because the credit rating agencies reduce its credit
rating
© Dr. Enzo Mondello, CFA, FRM, CAIA
August 2014
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Risks Associated with Investing in Bonds
AAA (or Aaa)
AA (or Aa)
A
BBB (or Baa)
Prime Grade
High Quality Grade
Upper Medium Grade
Medium Grade
BB (or Ba)
B
CCC (or Caa)
CC (or Ca)
C
CI
DDD, DD, D
Low Grade
Speculative
Poor Grade (substantial risk)
Very Speculative
Extremely Speculative
Noninterest Bearing Income Bonds
Default
Investment
Grade
© Dr. Enzo Mondello, CFA, FRM, CAIA
Non
Investment
Grad
August 2014
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Risks Associated with Investing in Bonds
Liquidity Risk
Liquidity risk is the risk that a security will not be able to be sold quickly without giving up a large price concession
The bid/asked spread is the best measure of liquidity risk: the wider the spread, the greater the liquidity risk
The market bid/asked spread can be determined by simply taking the difference between the lowest dealer
asked and the highest dealer bid for an issue at a particular point in time
Liquidity risk is mostly a concern for investors who do not expect to hold a security to maturity or who must periodically
mark it to market
© Dr. Enzo Mondello, CFA, FRM, CAIA
August 2014
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Risks Associated with Investing in Bonds
Liquidity risk can change for a number of reasons:
– If the structure of a bond structure is popular, the bid-ask-spread will narrow. If the structure of a bond is
unpopular, the bid-ask-spread will widen
– When interest rates become more volatile, the demand of bonds decline which will cause the bid-ask-spread to
widen
– When important traders of a certain type of bond exit the market, the spreads will tend to widen because of a lack
of liquidity
© Dr. Enzo Mondello, CFA, FRM, CAIA
August 2014
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Risks Associated with Investing in Bonds
Exchange Rate Risk
Exchange rate risk is the risk that the exchange rate between the currency in which a bond is denominated and the
currency of the investor’s home country might change
Inflation Risk
Inflation risk is the risk that the purchasing power of the cash flows received from a bond (interest and principal) will
decline over time because of inflation
If an investor buys a bond with a 7% return but inflation is 6% the real return is only 1%
© Dr. Enzo Mondello, CFA, FRM, CAIA
August 2014
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Risks Associated with Investing in Bonds
Volatility Risk
Volatility risk is the risk that changes in the expected volatility of interest rates can affect the value of any embedded
options in a bond’s pricing structure, thereby affecting the value of the bond.
Price Callable Bond = Price Noncallable Bond – Price embedded Call Option
Price Putable Bond = Price Nonputable Bond + Price embedded Put Option
The value of both puts and calls increase if volatility increases. Because the embedded option values are affected by
changes in volatility, the price of bonds with embedded options will also be affected.
© Dr. Enzo Mondello, CFA, FRM, CAIA
August 2014
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Risks Associated with Investing in Bonds
Event Risk
Event risk is the risk that some unusual event could cause the price of bonds to decline:
– Natural disasters such as famine, war etc.
– Takeover, leveraged buy-out, or corporate debt restructuring that substantially increases an issuer’s debt-to-equity
ratio and causes downgrading of its credit rating
– A regulatory change that requires an issuer to conduct its affairs in ways that result in a downgrading of its credit
rating (i.e. lower regulatory capital for banks)
– Political factors or actions taken by government that impair an issuer’s ability or willingness to pay its debt service
© Dr. Enzo Mondello, CFA, FRM, CAIA
August 2014
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Content
1
2
3
4
5
6
7
8
Risks Associated with Investing in Bonds
Fixed-Income Valuation
Term Structure of Interest Rates
Yield Measures
Interest Rate Risk: Duration and Convexity
Credit Risk: Fundamentals of Credit Analysis
Managing Bond Portfolio
Relative-Value Methodologies for Global
Corporate Bond Portfolio Management
9
10
11
12
Exchange Rate Risk: International Bond Investing
Managing Interest Rate Risk with Derivatives
Managing Credit Risk with Derivatives
Currency Risk Management
© Dr. Enzo Mondello, CFA, FRM, CAIA
August 2014
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Fixed-Income Valuation
Valuation Principles
Interest rate risk is the major risk faced by fixed-income investors
The bond price is the present value of the sum of future cash flows (coupon payments plus the principal
amount)
Bond Price 
C3
C1
C2
Cn  P



.........

(1 r) 1 (1 r) 2 (1 r) 3
(1 r) n
Therefore, if the discount rate r, which is the yield required by the market (which is related to interest rate levels)
increases, the price of the bond decreases, and vice versa. This is true for almost all bonds
© Dr. Enzo Mondello, CFA, FRM, CAIA
August 2014
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2
Fixed-Income Valuation
The appropriate discount rate is the sum of the risk-free rate and a risk premium (nominal spread).
The yield on a U.S. Treasury security with the same maturity as the bond being valued can be used as a proxy for the
risk-free rate.
Discount Rate for the Bond = Yield-to-Maturity
= Yield-to-Maturity of Treasury Security + Nominal Spread
Pr ice 
C1
C2
Cn
Par


...


(1  r)1 (1  r)2
(1  r)n (1  r)n
where:
C
Par
r
t1 ... n
=
=
=
=
Coupon payments
Par value of the bond at maturity
Yield for maturity (discount rate)
Life time of the bond
© Dr. Enzo Mondello, CFA, FRM, CAIA
August 2014
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Fixed-Income Valuation
The appropriate discount rate (i) is the sum of the risk-free rate and a risk premium (i.e. the nominal spread).
Discount Rate = Yield to Maturity = Risk-free Rate + Nominal Spread
Example (valuing annual-pay bonds):
A 3-year corporate bond has an annual coupon rate of 5% and a face value of USD 1,000. The discount rate is 4%. The
bond is paid back at par at maturity. Calculate the price of the bond!
© Dr. Enzo Mondello, CFA, FRM, CAIA
August 2014
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Fixed-Income Valuation
Example (valuing semiannualy-pay bonds):
A 3-year corporate bond has a coupon rate of 5%, coupons are paid semiannualy and the bond has a face value of USD
1,000. The discount rate is 4%. The bond is paid back at par at maturity. Calculate the price of the bond!
© Dr. Enzo Mondello, CFA, FRM, CAIA
August 2014
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Fixed-Income Valuation
Relationships among a Bond’s Price, Coupon Rate, Maturity, and Market Discount Rate (Yield-to-Maturity)
The farther into the future a cash flow is received, the lower its present value will be. The higher the discount rate
(yield to maturity) is, the lower the value of the bond will be, all other factors being equal.
A bond’s price and YTM are inversely related. An increase in YTM decreases the price and vice versa.
Prices are more sensitive to changes in YTM for bonds with lower coupon rates and longer maturities, and less
sensitive to changes in YTM for bonds with higher coupon rates and shorter maturities.
If the yield-to-maturity of a bond is higher (lower) than its coupon rate, the bond will sell below (above) its par value. If
the yield-to-maturity equals its coupon rate, the bond will sell at its par value.
© Dr. Enzo Mondello, CFA, FRM, CAIA
August 2014
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Fixed-Income Valuation
Coupon Rate > Yield-to-Maturity:
Bond Price > Par Value (Premium Bond)
Coupon Rate < Yield-to-Maturity:
Bond Price < Par Value (Discount Bond)
Coupon Rate = Yield-to-Maturity:
Bond Price = Par Value (Par Bond)
© Dr. Enzo Mondello, CFA, FRM, CAIA
August 2014
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Fixed-Income Valuation
There is a convex relationship between a bond’s price and its yield-to-maturity:
(Bond Price)
(Yield-to-Maturity)
© Dr. Enzo Mondello, CFA, FRM, CAIA
August 2014
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Fixed-Income Valuation
At a bond’s maturity date, the bond’s value is equal to its par value. As a bond moves closer to maturity (constant
discount rate assumed), a bond’s value:
–
–
A bond selling at a premium decreases over time
A bond selling at a discount increases over time
Example:
A 7% coupon, 4-year semiannual paid bond is priced at 96.63 and has a yield-to-maturity of 8%. If the yield to maturity
remains unchanged, what will the bond’s price be in one year?
© Dr. Enzo Mondello, CFA, FRM, CAIA
August 2014
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Fixed-Income Valuation
Spot Rates and the Price of a Bond
Spot rates are market discount rates for single payments to be made in the future. The discount rates for zero-coupon
bonds are spot rates because these rates do have no reinvestment risk.
Example:
The spot rates over the next 6 months, 12, months, 18 months, and 24 months are 4.0%, 4.2%, 4.4%, and 4.5%.
Therefore the no-arbitrage price of a 2-year, 6% coupon Treasury note is:
P
3
3
3
103



 102.86
1.02 1.0212 1.0223 1.02254
The YTM of this issue is 4.489% (2,244% x 2);
N = 4, PMT = 3, PV = -102.86, FV = 100  I/Y = 2.244
© Dr. Enzo Mondello, CFA, FRM, CAIA
August 2014
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2
Fixed-Income Valuation
Flat Price, Accrued Interest, and Full Price
Full Price = Flat Price + Accrued Interest
The full price (dirty price) of a bond includes interest accrued between coupon dates. The flat price (quoted or clean
price) of a bond is the full price minus accrued interest.
Accrued interest for a bond transaction is calculated as the coupon payment times the portion of the coupon period
from the previous payment date to the settlement date
Methods for determining the period accrued interest include actual (typically used for government bonds) or 30-day
months and 360-day years (typically used for corporate bonds)
© Dr. Enzo Mondello, CFA, FRM, CAIA
August 2014
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Fixed-Income Valuation
The full price of a fixed-income bond between two coupon payments given the market discount rate resp. the
YTM can be calculated as:
Full Pr ice 
C1
C2
Cn  Par


...

(1  YTM)1 t / T (1  YTM)2 t / T
(1  YTM)n  t / T
The next coupon payment (C) is discounted for the remainder of the coupon period, which is 1 – t / T. The second
coupon payment is discounted for that fraction plus another full period, 2 – t / T. This equation is simplified by
multiplying the numerator and denominator by the expression (1 + YTM) ^ t/T:
C1
C2
Cn  Par 

t/T


Full Pr ice  


...


1

YTM

1
2
(1  YTM)n 
 (1  YTM) (1  YTM)
© Dr. Enzo Mondello, CFA, FRM, CAIA
August 2014
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Fixed-Income Valuation
Example
A 6% German corporate bond is priced for settlement on 18 June 2015. The bond makes semi-annual coupon payments
on 19 March and 19 September of each year and matures on 19 September 2026. The corporate bond uses the 30/360
day-count convention for accrued interest. Calculate the full price, the accrued interest, and the flat price per EUR 100 par
value for a yield-to-maturity of 6,2%?
© Dr. Enzo Mondello, CFA, FRM, CAIA
August 2014
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2
Fixed-Income Valuation
Matrix Pricing
Matrix pricing is a method used to estimate the YTM for bonds that are not traded or infrequently traded. The yield is
estimated based on the yields of traded bonds with the same credit quality. If these bonds have different maturities than
the bond being valued, linear interpolation is used to estimate the subject bond’s yield.
For example, suppose that an analyst needs to value a 3-year, 4% semi-annual coupon payment corporate bond, Bond
X. This bond is not actively traded. However, there are quoted prices for four corporate bonds that have similar credit
quality:
–
–
–
–
Bond A: 2-year, 3% semi-annual coupon paying bond with a price of 98.500,
Bond B: 2-year, 5% semi-annual coupon paying bond with a price of 102.25,
Bond C: 5-year, 2% semi-annual coupon paying bond with a price of 90.250
Bond D: 5-year, 4% semi-annual coupon paying bond with a price of 99.125
© Dr. Enzo Mondello, CFA, FRM, CAIA
August 2014
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Fixed-Income Valuation
The semi-annual YTM of the four bonds are:
–
–
–
–
Bond A: YTM = 3.786% (N = 4, PMT = 1.5, PV = - 98.5, FV = 100  I/Y = 1.8929)
Bond B: YTM = 3.821% (N = 4, PMT 2.5, PV = -102.25, FV = 100  I/Y = 1.9104)
Bond C: YTM = 4.181% (N = 10, PMT = 1, PV = -90.250, FV = 100  I/Y = 2.0906)
Bond D: YTM = 4.196% (N = 10, PMT = 2, PV = -99.125, FV = 100  I/Y = 2.0979)
The average yields for the 2-year bonds of 3.8035% and for the 5-year bond of 4.1885% are calculated:
0.03786  0.03821
 0.038035
2
0.04181 0.04196
 0.041885
2
© Dr. Enzo Mondello, CFA, FRM, CAIA
August 2014
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2
Fixed-Income Valuation
The estimated 3-year YTM can be obtained with linear interpolation. The interpolated yield is 3,9318%:
 3  2
0.038035  
  (0.041885  0.038035)  0.039318
5

2


Thus, the 3-year Bond X has an estimated price of 100.191 (N = 6, PMT = 2, I/Y = 1.9659, FV = 100)
© Dr. Enzo Mondello, CFA, FRM, CAIA
August 2014
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Fixed-Income Valuation
Example
An analyst needs to assign a value to an illiquid 4-year, 4.5% annual coupon payment corporate bond. The analyst
identifies two corporate bonds that have similar credit quality: One is a 3-year, 5.5% annual coupon payment bond priced
at 107.5 per 100 of par value, and the other is a 5-year, 4.5% annual coupon payment bond priced at 104.75 per 100
of par value. Using matrix pricing, the estimated price of the illiquid bond per 100 of par value is closest to:
A. 103.895
B. 104.991
C. 106.125
© Dr. Enzo Mondello, CFA, FRM, CAIA
August 2014
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Content
1
2
3
4
5
6
7
8
Risks Associated with Investing in Bonds
Fixed-Income Valuation
Term Structure of Interest Rates
Yield Measures
Interest Rate Risk: Duration and Convexity
Credit Risk: Fundamentals of Credit Analysis
Managing Bond Portfolio
Relative-Value Methodologies for Global
Corporate Bond Portfolio Management
9
10
11
12
Exchange Rate Risk: International Bond Investing
Managing Interest Rate Risk with Derivatives
Managing Credit Risk with Derivatives
Currency Risk Management
© Dr. Enzo Mondello, CFA, FRM, CAIA
August 2014
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3
Term Structure of Interest Rates
The three different shapes of the yield curve are:
– Normal: upward sloping (short rates < long rates)
– Flat: no slope (short rates = long rates)
– Inverted: (short rates > long rates)
Historically the yield curve has been upward sloping more often than the other shapes.
The slope of the yield curve captures what the market is willing to pay for bonds of different maturities.
The yield curve expresses the relationship between yield and maturity.
Typically the yields being measured are U.S. Treasury yields as these are default risk-free yields.
© Dr. Enzo Mondello, CFA, FRM, CAIA
August 2014
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Term Structure of Interest Rates
Treasury Yield Curve
(Yields)
Normal Yield Curve
Flat Yield Curve
Inverted Yield Curve
(Maturity)
© Dr. Enzo Mondello, CFA, FRM, CAIA
August 2014
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Term Structure of Interest Rates
The problems with using on-the-run Treasury issues are:
–
–
–
On-the-run Treasury curve consists only of 6 points. Interpolation is needed
Due to the strong dealer demand Treasury yields tend to be abnormally low, reducing their usefulness as a good
benchmark
They tend to have abnormally low reinvestment rate risk, and abnormally high interest rate risk
Despite the drawbacks of the on-the-run Treasury yield curve as the benchmark for valuing other fixed-income
securities, it is the most widely used benchmark
An alternative to the on-the-run Treasury yield curve that is sometimes used is the yield curve for zero-coupon Treasury
securities
The yield on zero-coupon bond securities is called the spot rate, with the yield on Treasury strips called the Treasury
spot rate. When Treasury spot rates are plotted versus their maturities, the resulting curve is called the term
structure of interest rates
© Dr. Enzo Mondello, CFA, FRM, CAIA
August 2014
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Term Structure of Interest Rates
A shift in the yield curve occurs when yields change.
In a parallel shift all yields change across the term structure by the same amount. A nonparallel shift occurs when
the changes in yield are different for different maturities.
Yield
Yield
Initial
Curve
Initial
Curve
Maturity
Maturity
© Dr. Enzo Mondello, CFA, FRM, CAIA
August 2014
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Term Structure of Interest Rates
A yield curve twist occurs when the curve (the slope of the curve) flattens or steepens due to a nonparallel shift.
The yield curve can become flatter (less difference between long and short rates) or steeper (more difference between
long and short rates).
A butterfly twist occurs when the curvature of the curve changes.
–
–
Positive butterfly: the curve becomes more straight (less humped).
Negative butterfly: the curve becomes less of a straight line (more humped).
© Dr. Enzo Mondello, CFA, FRM, CAIA
August 2014
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Term Structure of Interest Rates
Factors that Drive U.S. Treasury Security Returns
Researchers generally agree that three factors are responsible for changes in Treasury returns:
–
–
–
Changes in the level of interest rates. This is by far the most important factor. It accounts for about 90% of
historical returns and is measured by duration.
Changes in the slope of the yield curve (distant second most influential factor). It accounts for about 8.5% of
historical returns and is measured by key rate duration.
Changes in the curvature of the yield curve (slight impact). It accounts for about 1.5% of historical bond
returns.
Bond portfolio managers who want to hedge their interest rate risks, therefore, should be most concerned about
protecting against the adverse effects of changes in the level of interest rates.
© Dr. Enzo Mondello, CFA, FRM, CAIA
August 2014
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Term Structure of Interest Rates
Various Universes of Treasury Securities used to Construct the Theoretical Spot Rate Curve
Constructing a theoretical spot rate yield curve is not simple. Ideally we would use the yield on default risk-free zero
coupon bonds (to abstract from the coupon effect) for each maturity in the maturity spectrum.
There are several different combinations of Treasury securities that can be used to construct a default-free theoretical
spot rate curve:
–
On-the-run Treasury issues are the most recently auctioned issues of a given maturity. The Treasury is currently
issuing bills with maturities of 1, 3, and 6 months, notes and bonds with maturities of 2, 5, 10, and 30 years. The
bills are issued at a discount while the notes and bonds carry coupons. The resulting on-the-run yield curve is a par
coupon curve because the notes and bonds are issued at par. Securities issued at par eliminate the tax effect that
exist for securities issued at a discount or premium. The bootstrapping methodology is used to generate the
theoretical spot rate curve. A potential criticism is that large maturity gaps exist, particularly after 5 years.
© Dr. Enzo Mondello, CFA, FRM, CAIA
August 2014
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3
Term Structure of Interest Rates
Selected off-the-run Treasury issues can be added to the on-the-run issues to bridge the caps in on-the-run
maturities. The par coupon yield curve is estimated and remaining gaps are filled by interpolation. Like with all on-therun issues, bootstrapping is used to generate the theoretical spot rate curve.
All Treasury issue so that all coupon securities and bills are used. As a practical matter issues that have special
circumstances such as tax advantages, illiquid markets, futures contract delivery are usually omitted to avoid yield
distortions. Adjustments are made for taxes and call features. The advantage is that all information available in prices
can be used.
Treasury coupon strips are observable zero-coupon securities that can be used directly to create an actual spot rate
curve. The relative illiquidity in the strips market implies that strip rates include a premium.
© Dr. Enzo Mondello, CFA, FRM, CAIA
August 2014
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3
Term Structure of Interest Rates
Swap Rate Curve (LIBOR Curve)
LIBOR is the rate at which high quality banks will borrow or lend U.S. dollars outside the U.S. amongst themselves,
and 3 months LIBOR is the most common floating rate used in interest rate swap agreements. The LIBOR spot rate
curve is calculated using the same bootstrapping procedure used to calculate Treasury spot rates.
The swap rate curve represents the swap rates available at various future time periods to convert fixed rates to
floating rates and vice versa
The swap rate curve is used to hedge interest rates, to value bonds, and for performance evaluation
© Dr. Enzo Mondello, CFA, FRM, CAIA
August 2014
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3
Term Structure of Interest Rates
The swap rate curve tends to be better benchmark than the government bond curve for the following reasons:
–
–
–
–
There is little or no government regulation of the swaps market.
A large demand for government bonds in the repo market can unrealistically change the yield curve. The swaps
market does not have these yield problems.
The swap curve has the credit risk of the underlying banks. Credit risks are thus more similar in the swaps market
(LIBOR) than when comparing various government bond market.
The swaps market has more bond maturities to construct a yield curve than the government bond market. Swap
rates quoted in the swap market have maturities of 2, 3, 4, 5, 6, 7, 8, 9, 10, 15, and 30 years.
© Dr. Enzo Mondello, CFA, FRM, CAIA
August 2014
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3
Term Structure of Interest Rates
Theories of the Term Structure of Interest Rates
Expectations
Theory
Segmentation
Theory
Biased Expectations
Theory
Pure Expectations
Theory
Broadest
Interpretation
Local
Expectations
Liquidity
Theory
© Dr. Enzo Mondello, CFA, FRM, CAIA
Preferred
Habitat Theory
August 2014
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3
Term Structure of Interest Rates
Pure (unbiased) expectations theory says the investor’s expectations of future interest rates alone creates the
shape of the yield curve. Forward rates are the expected future spot rates. This implies that if the yield curve is upward
(downward) sloping, short-term rates are expected to rise (fall), and if the yield curve is flat, the market expects shortterm rates to be constant. The drawback is that it fails to consider price risk and reinvestment risk, but interest risk
increases as the term to maturity increases.
–
The broadest interpretation is that given any investment horizon, investors expect the same return, regardless of
the maturity of the investment vehicle selected. This ignores the price risk associated with selling a bond prior to its
maturity.
–
The local expectations form of the pure expectation theory is an interpretation that suggests that the return on
bonds with different maturities will be identical over a short-term investment period, commencing immediately. This
is the only interpretation of the pure expectation theory that can be sustained in equilibrium.
© Dr. Enzo Mondello, CFA, FRM, CAIA
August 2014
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3
Term Structure of Interest Rates
The two form of biased expectations theory are the liquidity theory and the preferred habitat theory.
–
Liquidity theory: duration measures the price risk of holding a bond. Duration increases as the bond’s maturity
lengthens. Liquidity theory says that investors will demand a risk premium for holding bonds with long maturities
because the risk of this bonds is higher. - The yield curve will typically be upward sloping as investors demand
higher yields on longer bonds. The yield curve could slope downwards, however, if expectations for lower rates in
the future overwhelm the risk premium.
–
Preferred habitat theory also proposes that forward rates represent expected future spot rates plus a premium,
but it does no support the view that this premium is directly related to maturity. The existence of an imbalance
between supply and demand for funds in a given maturity range will induce lenders and borrowers to shift from
their preferred habitat (maturity range) to one that has the opposite imbalance. To do so, they must be offered a
risk premium to compensate for the price and/or reinvestment risk.
© Dr. Enzo Mondello, CFA, FRM, CAIA
August 2014
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3
Term Structure of Interest Rates
Market segmentation theory is similar to the preferred habitat theory in that it agrees that lenders and borrowers
have preferred maturity ranges and there is no premium (or discount) large enough to induce investors out of their
preferred maturity range.
Instead, the shape of the yield curve is proposed to be determined by the supply and demand for securities within a
given maturity range. In the extreme, the segmentation theory implies that rates for a given maturity segment will be
determined independently of all other maturities.
The shape of the yield curve depends exclusively on the supply and demand within maturity segments. Under this
theory the yield curve can take any shape.
© Dr. Enzo Mondello, CFA, FRM, CAIA
August 2014
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3
Term Structure of Interest Rates
Spot Rate Curve, Yield Curve on Coupon Bonds, Par Curve, and Forward Rate Curve
A yield curve shows the term structure of interest rates by displaying yields across different maturities (i.e., yields of
U.S. Treasury coupon bonds). Yields are calculated for several maturities and yields for bonds with maturities between
these are estimated by linear interpolation.
The spot rate curve is a yield curve for single payments in the future, such as 0%-bonds or stripped Treasury par
bonds. Yields on zero-coupon government bonds are spot rates.
The par curve shows the coupon rates for bonds of various maturities that would result in bond prices equal to their
par values. It is not calculated from yields on actual bonds but is constructed from the spot rate curve.
© Dr. Enzo Mondello, CFA, FRM, CAIA
August 2014
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3
Term Structure of Interest Rates
With spot rates of 1%, 2%, and 3%, a 3-year annual par bond will have payments that are:
PMT PMT PMT  100


 100  PMT  2.96
2
3
1.01 (1.02)
(1.03)
Thus, the payment is 2,96 and the par bond coupon rate is 2.96%
A forward curve is a yield curve composed of forward rates, such as 1-year rates available at each year over a future
period
© Dr. Enzo Mondello, CFA, FRM, CAIA
August 2014
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3
Term Structure of Interest Rates
Forward Rates
The general formula to calculate a semi-annual forward is:
where:
1fm
zm
zm+1
(1  zm 1)m 1
1
1 fm 
m
(1  zm )
forward rate that starts in m semi-annual periods for 6 months
spot rate for a period of m semi-annual periods
spot rate for a period of m semi-annual periods plus 6 months
Doubling the forward rate 1fm gives the bond equivalent yield for the forward rate that starts in m months
for 6 months
© Dr. Enzo Mondello, CFA, FRM, CAIA
August 2014
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3
Term Structure of Interest Rates
Example
The spot rates for 6-month Treasury bills and 1-year Treasury bills are 2.50% and 2.80% respectively, expressed as bond
equivalent yields. The 6-month forward rate expressed as bond equivalent yields is closest to:
A) 2.96%
B) 3.00%
C) 3.10%
© Dr. Enzo Mondello, CFA, FRM, CAIA
August 2014
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3
Term Structure of Interest Rates
Example
Given the following spot rate curve, the implied forward rate in 12 months for 6 months is closest to:
Maturity
Spot Rate
6 months
12 months
18 months
24 months
3.00%
4.00%
5.00%
6.00%
A) 6.55%
B) 7.02%
C) 7.54%
© Dr. Enzo Mondello, CFA, FRM, CAIA
August 2014
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3
Term Structure of Interest Rates
The relationship between a T-period spot rate (zT), the current 6-month spot rate (z1), and the 6-month forward rates
is stated as:
z T  (1  z1 )(1 1 f1 )(1 1 f 2 )......(1 1 f T 1 
1/ T
1
where:
1f1
1f2
forward rate that starts in 6 months for 6 months
forward rate that starts in 12 months for 6 months
Just know that a spot rate is a package of forward rates and that discounting at either the forward rates
or the spot rate will give the same present value.
© Dr. Enzo Mondello, CFA, FRM, CAIA
August 2014
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3
Term Structure of Interest Rates
Example
The following forward rates are given:
Semi-annual Periods
1
2
3
4
Notation
1f0
1f1
1f2
1f3
Forward Rate
4.00%
4.60%
5.00%
5.20%
The 2-year spot rate is closest to:
A) 4.40%
B) 4.70%
C) 4.95%
© Dr. Enzo Mondello, CFA, FRM, CAIA
August 2014
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3
Term Structure of Interest Rates
Example
The following forward rates are given:
Semi-annual Periods
1
2
3
4
Notation
1f0
1f1
1f2
1f3
Forward Rate
4.00%
4.60%
5.00%
5.20%
A 6% coupon bond pays the coupons semi-annually and has a remaining maturity of 1.5 years. The price of the bond is
closest to:
A) 101.56%
B) 102.00%
C) 102.12%
© Dr. Enzo Mondello, CFA, FRM, CAIA
August 2014
61
Content
1
2
3
4
5
6
7
8
Risks Associated with Investing in Bonds
Fixed-Income Valuation
Term Structure of Interest Rates
Yield Measures
Interest Rate Risk: Duration and Convexity
Credit Risk: Fundamentals of Credit Analysis
Managing Bond Portfolio
Relative-Value Methodologies for Global
Corporate Bond Portfolio Management
9
10
11
12
Exchange Rate Risk: International Bond Investing
Managing Interest Rate Risk with Derivatives
Managing Credit Risk with Derivatives
Currency Risk Management
© Dr. Enzo Mondello, CFA, FRM, CAIA
August 2014
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4
Yield Measures
Yield Measures for Fixed-Rate bonds, Floating Rate Notes, and Money Market Instruments
The effective yield of a bond depends on its periodicity, or annual frequency of coupon payments. For an annual-pay
bond the effective yield is equal to the yield-to-maturity. For bonds with greater periodicity, the effective yield is greater
than the YTM. For example, a semi-annual coupon paying bond with a YTM of 8% has a yield of 4% every 6 months
and an effective yield of 1.04 ^2 – 1 = 8.16%.
A YTM quoted on a semi-annual basis is two times the semi-annual discount rate: 2 x 4% = 8%.
© Dr. Enzo Mondello, CFA, FRM, CAIA
August 2014
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4
Yield Measures
An important tool used in fixed-income analysis is to convert an annual yield from one periodicity to another. These are
called periodicity, or compounding, conversions. A general formula to convert an annual percentage rate for m
periods per year, denoted as APRm, to an annual percentage rate for n periods per year, APRn, is the following
equation:
m
n
 APRm 
 APRn 
1




1 

m 
n 


© Dr. Enzo Mondello, CFA, FRM, CAIA
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4
Yield Measures
Example
A 5-year, 4.5% semi-annual coupon payment government bond is priced at 98 per 100 of par value. Calculate the annual
yield-to-maturity stated on a semi-annual bond basis, rounded to the nearest basis point. Convert the annual yield to:
A. An annual rate that can be used for direct comparison with otherwise comparable bonds that make quarterly coupon
payments and
B. An annual rate that can be used for direct comparison with otherwise comparable bonds that make annual coupon
payments
© Dr. Enzo Mondello, CFA, FRM, CAIA
August 2014
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4
Yield Measures
Investors of fixed-income securities obtain their total return from the following three sources:
–
–
–
Coupon interest
Capital gains / losses resulting from buying at a different price than the one received when the security is sold or
matures
Reinvestment income from investing interim cash flows (interest on interest)
© Dr. Enzo Mondello, CFA, FRM, CAIA
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4
Yield Measures
Current Yield
The current yield on a security is simply its coupon rate, divided by its market price:
Current Yield 
Cash Coupon Payment per Year
Bond Price
This yield calculation ignores potential capital appreciation / depreciation and reinvestment income, and does not
incorporate the influence of the time value of money.
© Dr. Enzo Mondello, CFA, FRM, CAIA
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4
Yield Measures
Yield to Maturity (YTM)
This yield is the single discount rate that when applied to all of the cash flows generated by a fixed-income security
over its term to maturity, will make the present value of those cash flows equal to the current price of the bond:
Pr ice 
C1
C2
Cn
Par


...


(1  YTM)1 (1  YTM) 2
(1  YTM) n (1  YTM) n
The yield to maturity takes into account the time value of money and the potential for capital appreciation
This measure does not consider the reinvestment rate. In reality, the reinvestment rate rarely ever equates to the YTM.
The YTM also is based upon the assumption that the bond will be held to maturity.
© Dr. Enzo Mondello, CFA, FRM, CAIA
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4
Yield Measures
Example:
Suppose we have a 10-year, USD 1‘000 par value, 7% semi-annual coupon paying bond. The bond price today is USD
895.80. Compute the current yield and the yield to maturity!
© Dr. Enzo Mondello, CFA, FRM, CAIA
August 2014
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4
Yield Measures
Yield to Call (YTC)
Callable bonds might not reach maturity because they can be called before their maturity date. Therefore, the yield-tocall was developed to measure the return on a bond if it were to be called on a particular date. The yield to first call is
the same as yield to maturity, calculated through the first call date with the call price as the maturity value.
C1
C2
Cn
Call Price
Pr ice 

 ... 

1
2
n
(1  YTC) (1  YTC)
(1  YTC)
(1  YTC) n
where: n = number of periods to first call date
The YTC should be used whenever a callable bond is trading at a price greater than or equal to its par value. Any
additional premium above this price could be lost if the bond were called away, and thus the YTC will be a more
conservative return measure.
© Dr. Enzo Mondello, CFA, FRM, CAIA
August 2014
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4
Yield Measures
There are several problems with these yield-to-call measures:
–
–
–
They assume the bond is held to the call date
They assume the issuer calls the bond on the call date
They assume the coupons are reinvested at the yield-to-call
Example
Compute the yield-to-first-call and the yield-to-first-par-call for a 8% coupon (paid semi-annually), 7-year bond priced at 93
that is callable in 4 years at 106 and in 6 years at 100!
Yield to first par call date
This measure is the same as YTC, using expected cash flows to the first date at which the issuer can call the bond
at par
© Dr. Enzo Mondello, CFA, FRM, CAIA
August 2014
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4
Yield Measures
Yield to Worst (YTW)
Yield to worst involves the calculation of YTC for every possible call date as well as the YTM, and determining which
of these results is the lowest expected return. This yield is supposed to be the worst possible yield that can be realized
by the investor.
In reality, the YTW measure has little meaning because it does not identify a bond’s true return, except in the rare event
that the worst possible conditions do happen to materialize
Furthermore, the YTW measure incorporates a conglomeration of different reinvestment risk exposures
© Dr. Enzo Mondello, CFA, FRM, CAIA
August 2014
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4
Yield Measures
The yield to worst is a commonly cited yield measure for fixed-rate callable bonds used by bond dealers and investors.
However, a more precise approach is to use an option pricing model and an assumption about future interest rate
volatility to value the embedded call option.
Option-adjusted price = flat price of bond + value of embedded call
The investor bears the call risk, so the embedded call option reduces the value of the bond from the investor’s
perspective. The investor pays a lower price for the callable bond than if it were option-free. If the bond were noncallable, its price would be higher. The option-adjusted price is used to calculate the option-adjusted yield. – The
option-adjusted yield is the required market discount rate whereby the price is adjusted for the value of the embedded
call option.
Value of Call = Price of option-free Bond – Price of Callable Bond
© Dr. Enzo Mondello, CFA, FRM, CAIA
August 2014
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4
Yield Measures
Floating-rate Note Yields
Floating rate notes have a quoted margin relative to a reference rate, typically LIBOR
The quoted margin is positive for issuers with more credit risk than the banks that quote LIBOR and may be negative
for issuers that have less credit risk than loans to these banks
The required margin on a floating rate note may be greater than the quoted margin if credit quality has decreased,
or less than the quoted margin if credit quality has increased
© Dr. Enzo Mondello, CFA, FRM, CAIA
August 2014
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4
Yield Measures
The valuation of a floating-rate note needs a pricing model:
(Index  QM )  FV
(Index  QM )  FV
 FV
m
m
P
 ... 
1
N
 Index  DM 
 Index  DM 
1 

1 

m
m




where:
Index
QM
FV
m
DM
N
reference rate,
quoted margin
future value paid at maturity or par value of bond
periodicity of the floating-rate note (number of payment
periods per year)
discount margin
number of evenly spaced periods to maturity
© Dr. Enzo Mondello, CFA, FRM, CAIA
August 2014
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4
Yield Measures
Example
A 4-year, French floating-rate note pays three-month Euribor plus 1.25%. The floater is priced at 98 per 100 of par value.
Calculate the discount margin for the floater assuming that three-month Euribor is constant at 2%. Assume the 30/360
day-count convention and evenly spaced periods.
© Dr. Enzo Mondello, CFA, FRM, CAIA
August 2014
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4
Yield Measures
Yields for Money Market Instruments
For money market instruments yields may be quoted on a discount basis or an add-on basis, and may use 360-day
or 365-day years. A bond-equivalent yield is an add-on yield based on a 365-day year.
Commercial papers, T-bills, and bankers’ acceptances often are quoted on a discount basis
Bank certificates of deposits, repos, and such indices as LIBOR and Euribor are quoted on an add-on basis
© Dr. Enzo Mondello, CFA, FRM, CAIA
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Yield Measures
The pricing formula for money market instruments quoted on a discount rate basis is:
 Years   FV  PV 
 Days

PV  FV  1
 DR  DR  
  

Days
FV
 Year





where:
PV
FV
Days
Year
DR
present value, or price of the money market instrument
future value paid at maturity, or face value of the money market
instrument
number of days between settlement and maturity
number of days in the year
discount rate (stated as an annual percentage)
© Dr. Enzo Mondello, CFA, FRM, CAIA
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4
Yield Measures
Example
91-day U.S. Treasury bill with a face value of USD 1 million is quoted at a discount rate of 2.25% for an assumed 360-day
year. What is the price of the T-bill?
Example
91-day U.S. Treasury bill with a face value of USD 1 million is quoted at a price of USD 976,450 for an assumed 360-day
year. What is the quoted discount rate of the T-bill?
© Dr. Enzo Mondello, CFA, FRM, CAIA
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4
Yield Measures
The pricing formula for money market instruments quoted on an add-on rate basis is:
PV 
where:
PV
FV
Days
Year
AOR
FV
 Years   FV  PV 
 AOR  
  

Days
Days
PV






 AOR 
1 
 Year

present value, or price of the money market instrument
future value paid at maturity, or face value of the money market
instrument
number of days between settlement and maturity
number of days in the year
add-on rate (stated as an annual percentage)
© Dr. Enzo Mondello, CFA, FRM, CAIA
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4
Yield Measures
Yield Spread Measures
Yield Spread = Bond Yield – Benchmark Yield
If the benchmark is a government bond yield, the spread is known as a government spread or G-spread.
If the benchmark is a swap rate, the spread is known as an interpolated spread or I-spread.
A disadvantage of G-spreads and I-spreads is that they are theoretically correct only if the spot yield curve is flat and
approximately the same across maturities. However, the spot yield curve is normally upward-sloping.
© Dr. Enzo Mondello, CFA, FRM, CAIA
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4
Yield Measures
A zero-volatility spread or Z-spread is the percent spread that must be added to each spot rate on the benchmark
yield curve to make the present value of a bond equal to its price. – Thus, the Z-spread accounts for the shape of the
yield curve.
P
C2
Cn  Par


...

(1 z1  Z)1 (1 z2  Z)2
(1 zn  Z)n
C1
where:
z
Z
benchmark spot rates
Z-spread
In practice, the Z-spread is usually calculated in a spreadsheet using a goal seek function or similar solver function.
© Dr. Enzo Mondello, CFA, FRM, CAIA
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Yield Measures
Example
A 6% annual coupon corporate bond with two years remaining to maturity is trading at a price of 100.125. The 2-year, 4%
annual payment government benchmark bond is trading at a price of 100.750. The 1-year and 2-year government spot
rates are 2.1% and 3.635%, respectively, stated as effective annual rates.
1. What is the G-spread?
2. Demonstrate that the Z-spread is 234.22 bps
© Dr. Enzo Mondello, CFA, FRM, CAIA
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Yield Measures
Investors will require a larger spread for an issue with an embedded option that is favourable to the issuer
(call option). If interest rates fall, the issuer will call the bond forcing the investor to reinvest at lower rates and
reducing their return. The option-adjusted spread (OAS) is used to price bonds with embedded options. The OAS for a
callable bond is calculated as follows:
OAS (bps.) = Z-Spread (bps.) – Option Value (bps.)
Since embedded options will clearly impact the spread one way or another, a Z-spread calculation does not give nearly
as accurate a picture as an option-adjusted spread calculation.
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Yield Measures
Option-adjusted spread (OAS) removes the effect of the embedded options and shows the average spread the
investor will actually earn over a comparable Treasury security.
Credit
Quality
AA
AA
Baa
7-Year Maturity Bonds
First Call in
Z-Spread
OAS
1-year
3-years
3-years
55 bps.
89 bps.
77 bps.
30 bps.
28 bps.
40 bps.
The Z-spreads cannot be used to compare the bonds because they are based only on spot rates and do not take into
account the impact of call features. The OAS is lower then the Z-spread for all the callable bonds because it considers
the adverse affect of the embedded call.
© Dr. Enzo Mondello, CFA, FRM, CAIA
August 2014
85
Content
1
2
3
4
5
6
7
8
Risks Associated with Investing in Bonds
Fixed-Income Valuation
Term Structure of Interest Rates
Yield Measures
Interest Rate Risk: Duration and Convexity
Credit Risk: Fundamentals of Credit Analysis
Managing Bond Portfolio
Relative-Value Methodologies for Global
Corporate Bond Portfolio Management
9
10
11
12
Exchange Rate Risk: International Bond Investing
Managing Interest Rate Risk with Derivatives
Managing Credit Risk with Derivatives
Currency Risk Management
© Dr. Enzo Mondello, CFA, FRM, CAIA
August 2014
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5
Interest Rate Risk
Duration and Convexity
Macaulay Duration
Macaulay duration is named after Frederick Macaulay, a Canadian economist who first wrote about the statistic in
1938.
Macaulay duration is the weighted average of the time to receipt of the bond’s promised payments, where the
weights are the shares of the full price that correspond to each of the bond’s promised future payments.
© Dr. Enzo Mondello, CFA, FRM, CAIA
August 2014
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5
Interest Rate Risk
Duration and Convexity
Example
A 4-year 5% annual coupon paying bond is trading at par. What is the Macaulay duration?
Period
1
2
3
4

Cash Flow
PV
Weight
Period x Weight
5
5
5
105
4.76
4.54
4.32
86.38
100.00
0.0476
0.0454
0.0432
0.8638
1.0000
0.0476
0.0908
0.1296
3.4552
3.7232
The Macaulay duration is 3.7232 years
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There is also a general closed-form solution which can be used to calculate the Macaulay duration (MD):
 1  r 1 r  N  (c  r) 
  (t / T)
MD  

N
c  1  r   1  r 
 r
where:
r
c
N


expected return (yield-to-maturity)
coupon rate
maturity of the bond
 1.05 1.05  4  (0.05  0.05) 
  0  3.7232
MD  

4

 0.05 0.05  1.05  1  0.05 


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Duration and Convexity
Modified Duration
The calculation of the modified duration statistic of a bond requires a simple adjustment to Macaulay duration.
Modified Duration 
Macaulay Duration
1 r
where:
r
expected return (yield-to-maturity)
For the example, the modified duration of the 4-year, 5% annual coupon paying bond is 3.546:
Modified Duration 
3.7232
 3.546
1.05
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Duration and Convexity
Interpretation of duration:
1st interpretation of duration:
– Effective duration is the first derivative of the price-yield relationship of a security, divided by the initial price of the
security:
DE  
–
dP/dy
P
While correct, this interpretation is mathematically.
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Duration and Convexity
2nd interpretation of duration:
–
Unadjusted duration (Macaulay duration) is a weighted average of time. – The Macaulay duration may be
meaningful to an investment professional who understands that a bond with a duration of 6 years is more volatile
than a bond with a duration of 2 years, but it does not have much meaning to most clients.
3rd interpretation of duration:
–
Effective duration is a measure of how sensitive the return on a bond is to small changes in interest rates
DE  
–
dP/P
dy
This interpretation is easily understood by almost anybody. It indicates that if a bond has a duration of 4.0, its price
will rise or fall by 4% every time interest rates fall or rise by 100 basis points.
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Approximate Modified Duration
An alternative approach is to approximate modified duration directly:
Approx . Modified Duration 
where:
P–
P+
P  P
2  (Yield )  P0
Price of the bond after a decrease in yield
Price of the bond after an increase in yield.
Let’s assume a yield change of 50 bps. for your 4-year, 5% annual coupon paying bond. The approx. modified duration
is:
Approx . Modified Duration 
101.794  98.247
 3.547
2  (0.005)  100
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Example:
An option-free bond has a remaining maturity of 5 years and a coupon of 4.5% which is paid semi-annually. The yield to
maturity of the bond is 4.8%. Calculate the approximate modified duration and (based on the duration) the new bond price
if interest raise by 50 basis points.
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Effective Duration
Another approach to assess the interest rate risk of a bond is to estimate the percentage change in price given a
change in a benchmark yield curve. – The effective duration of a bond is the sensitivity of the bond’s price to a
change in a benchmark yield curve:
Effective Duration 
P  P
2  (Curve )  P0
The difference between approximate modified duration and effective duration is in the denominator. Modified duration is
a yield duration statistic in that it measures interest rate risk in terms of a change in the bond’s own YTM. Effective
duration is a curve duration statistic in that it measures interest rate risk in terms of a change in the benchmark yield
curve ( Curve).
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Duration and Convexity
Modified duration is the approximate price change in a bond‘s price for a 100 basis point change in yield, assuming
that the bond‘s expected cash flows do not change when the yield changes (option-free bonds). When calculating Pand P+, the same cash flows used to calculate P0 are used.
Effective (or option-adjusted) duration also estimates a bond‘s price sensitivity to a change in yield, but accounts
for how changes in yield will affect cash flows.
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Duration and Convexity
Modified and Macaulay Duration assume that the cash flows of a bond will not change as yields change. – Thus
effective duration is the appropriate measure of interest rate risk for bonds with embedded options because changes in
interest rates may change their future cash flows.
Pricing models are used to determine the prices that would result from a given size change in the benchmark yield
curve
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Duration and Convexity
How a Bond’s Maturity, Coupon, Embedded Option, and Yield Level Affect its Interest Rate Risk
Holder other factors constant:
–
–
–
Duration increases (decreases) when maturity increases (decreases).
Duration decreases (increases) when the coupon rate increases (decreases).
Duration decreases (increases) when YTM increases (decreases).
With a call provision, the value of the call increases as yields fall, so a decrease in yield will have less effect on the
price of the callable bond (price callable bond = price straight-bond – price of call)
With a put provision, the bondholder’s option to sell the bond back to the issuer at a set put price reduces the
negative impact of the yield increases on the price of a putable bond (price putable bond = price straight-bond + price
of put)
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Duration of a Portfolio
A portfolio‘s duration is the weighted average duration of the component securities
Example
Compute the duration of the following portfolio:
Bond:
A
B
C
Market Value:
USD 3,000,000
USD 4,000,000
USD 5,000,000
Duration:
3.75
4.25
2.55
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Duration and Convexity
A second approach to calculate portfolio duration is to calculate the weighted average number of periods until cash
flows will be received using the portfolio’s IRR (its cash flow yield). This method is better theoretically but cannot be
used for bonds with embedded options. This approach is also inconsistent with duration capturing the relationship
between price and YTM.
Duration will not provide meaningful percentage value change estimates for portfolios unless the yield curve shifts
in a parallel manner
Bullet and barbell portfolios with the same durations have the same interest rate risk if the yield curve shifts in a parallel
manner
Even if the bullet and barbell portfolios have the same durations, they do not have the same interest rate risk with
respect to a non-parallel shift in the yield curve
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Duration and Convexity
Money Duration and Price Value of a Basis Point (PVBP)
The money duration of a bond (dollar duration) is expressed in currency units and calculated as follows:
Money Duration = Annual Modified Duration x Full Price of Bond
Money duration is sometimes expressed as money duration per 100 of bond par value:
Money Duration = Annual Modified Duration x Full Price of Bond per 100 of Par Value
The change in bond price can be calculated:
Change in Bond Price = Money Duration x Change in YTM
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Duration and Convexity
Example
A life insurance company holds a USD 10 million (par value) position in a 4.50% ArcelorMittal bond that matures
on 25 February 2017. The bond is priced (flat) at 98.125 per 100 of par value to yield 5.2617% on a street-convention
semi-annual bond basis for settlement on 27 June 2014. The total market value of the position, including accrued interest,
is USD 9,965,000 or 99,65 per 100 par value. The bond’s (annual) Macaulay duration is 2.4988.
1. Calculate the money duration per 100 in par value for the ArcelorMittal Bond?
2. Using the money duration, estimate the loss on the position for each 1 bp increase in the yield-to-maturity for that
settlement date?
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Duration and Convexity
The price value of a basis point is the change in the value of a bond, expressed in currency units, for a change in
YTM of one basis point (0.01%):
PVBP 
P  P
2
Example
A newly issued, 10-year, 5% annual coupon paying bond is priced at 92.64. The price value of a basis point for this bond
assuming a par value of USD 1 million is closest to:
A.
B.
C.
USD 10
USD 700
USD 1,400
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Duration and Convexity
Approximate Convexity and Effective Convexity
The divergence from the bond price curve to the straight line (duration) is called convexity
Positive convexity is a larger increase in price than decrease in price, for the same change in interest rates – The
upside is greater than the downside
All option-free bonds have positive convexity, but the actual degree of duration and convexity of bonds will vary,
depending on the level of interest rates, coupon, and maturity. A longer maturity, a lower coupon rate, or a lower YTM
will all increase convexity, and vice versa. For two bonds with equal duration, the one with cash flows that are more
dispersed over time will have the greater convexity.
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Duration and Convexity
Convexity, is used to approximate the change in price that is not explained by duration.
The approximate convexity of a bond can be computed as follows:
approx . Convexity 
P  P  2P0
P0 (change in Yield )2
Example:
Compute the convexity of a 6-year, 7% seminannual corporate bond which actually has yield to maturity of 5% when we
assume a change in interest rates by 100 basis points
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Duration and Convexity
Effective convexity, like effective duration, must be used for bonds with embedded options. The approximate
effective convexity of a bond can be computed as follows:
approx . effective Convexity 
P  P  2P0
P0 (change in Curve )2
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Interest Rate Risk
Duration and Convexity
For callable bonds: The decline in yield will reach the point where the rate of increase in the price of the bond will
start slowing down and eventually level off → negative convexity. – This is due to the fact that the issuer has
the right to retire the bond prior to maturity at some specified call price.
As long as yields remain below a certain level, callable bonds will exhibit price compression, or negative convexity.
As long as yields are above a certain level, those same callable bonds will exhibit all the properties of positive
convexity.
With putable bonds as interest rates move from high to low the duration will increase. Convexity will be positive
at all rate levels and convexity will be highest when interest rates are in the area where the put begins to acquire value.
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Duration and Convexity
Taylor Approximation
Given values for approximate annual modified duration and approximate annual convexity, the percentage change in the
full price of a bond can be calculated as follows:
Estimated price change in % = –Duration ( y) + 0.5 Convexity ( y)2
Example:
Compute the estimated price change in % when the duration is 5.5 and the convexity is 30.5 and assuming an interest
shift by 120 basis points!
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Duration and Convexity
Duration predicts a straight linear-relationship between changes in yield and changes in price. In reality, the price/yield
relationship for a bond is convex. Duration therefore underestimates the price increase and overestimates
the price decline.
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Content
1
2
3
4
5
6
7
8
Risks Associated with Investing in Bonds
Fixed-Income Valuation
Term Structure of Interest Rates
Yield Measures
Interest Rate Risk: Duration and Convexity
Credit Risk: Fundamentals of Credit Analysis
Managing Bond Portfolio
Relative-Value Methodologies for Global
Corporate Bond Portfolio Management
9
10
11
12
Exchange Rate Risk: International Bond Investing
Managing Interest Rate Risk with Derivatives
Managing Credit Risk with Derivatives
Currency Risk Management
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Credit Risk
Fundamentals of Credit Analysis
Overview
Default risk: This is the risk that the interest or principal on a bond will not be paid.
Credit risk has two components:
–
–
Default risk (probability of default)
Loss severity or loss given default
Expected credit loss = Default risk x Loss severity
Recovery rate is the percentage of a bond’s value an investor will receive if the issuer defaults
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Credit Risk
Fundamentals of Credit Analysis
Credit spread risk: This is the risk that the yield spread on a fixed-income security over some benchmark yield (such
as a comparable Treasury security) will widen due to a change in the return the market demands for taking credit risk.
Downgrade risk: This is the risk that the price of a fixed-income security may fall because its credit rating is
downgraded by one or more of the credit-rating agencies
Market liquidity risk: Selling a bond less than its market value and is reflected in the size of the bid-ask spread.
This risk is greater for bonds with less creditworthy issuers and for bonds of smaller issuers with relatively little publicly
traded debt.
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Credit Risk
Fundamentals of Credit Analysis
Each category of debt from the same issuer is ranked in accordance to a priority of claims in the event of default
Secured debt is backed by a collateral
Unsecured debt or debentures reflect a general claim to the issuer’s assets and cash flows
General seniority rankings for debt repayment priority are:
–
–
–
–
–
–
–
First lien or first mortgage (specific asset is pledged)
Senior secured debt
Junior secured debt
Senior unsecured debt
Senior subordinated debt
Subordinated debt
Junior subordinated debt
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Credit Risk
Fundamentals of Credit Analysis
All debt with the same category is ranked as pari passu (same priority of claim)
A bankruptcy reorganization plan is confirmed by a vote among all classes of investors with less than 100%
recovery rate. Typically a reorganization plan does not strictly conform to the original priority of claims.
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Credit Risk
Fundamentals of Credit Analysis
Issuer credit ratings, or corporate family ratings, represent a debt issuer’s overall creditworthiness and typically apply
to a company’s senior unsecured debt
Issue-specific ratings, or corporate credit ratings, represent the credit risk of a specific debt issue
Cross default provision: default in one of the outstanding bonds may trigger default on the remaining issues
Notching refers to the practice of adjusting an issue credit rating upward or downward from the issuer credit rating to
reflect the seniority and other provisions of a debt issue. Notching is less common for highly rated issues than for
lower-rated issues. For lower-rated issues, higher default risk results in significant differences between recovery rates
of debt with different seniority rankings, leading to more notching.
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Credit Risk
Fundamentals of Credit Analysis
Lenders and bond investors should not rely exclusively on credit ratings from rating agencies for the following reasons:
–
–
–
–
Credit ratings are dynamic and can change during the life of a debt issue
Rating agencies are not perfect and cannot always judge credit risk accurately
Event risk is difficult to asses: unforeseen events are not reflected in credit ratings
Market prices of bonds often adjust more rapidly than credit ratings
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Credit Risk
Fundamentals of Credit Analysis
Non-Investment Grade
“Jun”“ or “High Yield”
Investment Grade
Moody’s
S&P
Fitch
Aaa
AAA
AAA
High-Quality
Aa1
AA+
AA+
Grade
Aa2
AA
AA
Aa3
AA 
AA
A1
A+
A+
Upper-Medium
A2
A
A
Grade
A3
A
A
Baa1
BBB+
BBB+
Low Medium
Baa2
BBB
BBB
Grade
Baa3
BBB 
BBB 
____________________________________________________________________________________
Ba1
BB+
BB+
Low Grade or
Ba2
BB
BB
Speculative Grade
....
....
.....
C
C
C
____________________________________________________________________________________
Default
C
D
D
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Credit Risk
Fundamentals of Credit Analysis
Components of Traditional Credit Analysis
In traditional credit analysis, the following four C’s of credit are considered: capacity, collateral, covenants, and
character
Character: Management’s ability to manage potential crises is a key factor in assessing a borrower’s character.
Management should have demonstrated their ability to define and execute a strategic plan. The track record
can be used to measure the character of the management.
Assessing the quality of the management by the rating agencies include:
– Understanding of business strategies and policies
– Financial philosophy and strategic direction
– Conservative approach to business
– Track record
– Succession planning (continuity of management)
– Well-developed business plans
– Well-developed control systems
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Fundamentals of Credit Analysis
Capacity to repay: A firm will receive the funds to service its debt (interest and principal payments) from its cash flow.
Sales less operating expenses must be enough to cover interest charges. An analyst can calculate the capacity to
repay the debt burden by the use of ratios and cash flows derived from the financial statements.
Analysis of collateral (underlying capital): A corporate debt obligation can be secured or unsecured. In a
liquidation, the proceeds from bankruptcy are distributed to creditors based on the absolute priority rule (risk of loss is
reduced for secured debt). However, in the case of a reorganization the absolute priority rule does typically not hold.
A secured creditor may receive only a portion of its claim, while unsecured creditors may receive distributions for their
entire claim. This is the case because a reorganization requires approval of all parties. – As a consequence, analysts
place less emphasis on the collateral.
Issue covenants: Covenants include limitations and restrictions on the borrower’s activities
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Credit Risk
Fundamentals of Credit Analysis
The bond indenture should contain terms and conditions that are appropriate to ensure payment of the debt. Covenants
are usually imposed by the bondholders to restrict companies from taking action that might not be in the
bondholders’ best interest.
There are two general types of covenants:
–
–
Affirmative covenants (the debtor promises to take action)
Negative covenants (the debtor promises not to do certain things)
Examples of affirmative covenants are to make interest and principal payments and to keep the equipment in good
working order
Examples of negative covenants are not to incur additional debt and not to exceed limits on solvency, capitalization,
or coverage ratios
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Credit Risk
Fundamentals of Credit Analysis
Sources of liquidity are:
Liquid assets are needed to pay debt obligations as they come due
The primary source is cash flow which is derived from net sales less operating costs
Additional sources of liquidity come from the firm’s ability to obtain additional financing to meet immediate needs.
These additional sources include:
–
–
–
A line of bank credit
Securitization of loans or receivables
Third party guarantees
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Credit Risk
Fundamentals of Credit Analysis
Factors that Influence the Level and Volatility of Yield Spreads
Yield of option-free bond = Real risk-free rate + Expected inflation rate + Maturity premium + Liquidity premium +
Credit Spread
Yield spread = Liquidity premium + Credit Spread
The level and volatility of yield spreads are affected by:
–
–
–
–
Credit and business cycles
Performance of financial markets as a whole
Availability of capital from broker-dealers, and
Supply and demand for debt issues
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Credit Risk
Fundamentals of Credit Analysis
Yield spreads tend to narrow when:
–
–
–
–
Credit cycle is improving
Economy is expanding
Financial markets are strong, and/or
Investor demand for new debt issues is strong
On the other hand, yield spreads tend to widen when:
–
–
–
–
–
Credit cycle is weakening,
Economy is weakening,
Financial markets are weakening,
Broker-dealer capital is insufficient for market making, and/or
Supply of new debt issues is heavy
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Credit Risk
Fundamentals of Credit Analysis
Example:
Which bonds are likely to exhibit the greatest spread volatility?
A. Bonds from issuers rated AA
B. Bonds from issuers rated B
C. Bonds from issuers rated A
Example:
If investors become increasingly worried about the economy – say, as shown by declining stock prices- what is the most
likely impact on credit spreads?
A. No change to credit spreads because they are not affected by equity markets
B. Narrower spreads will occur because investors will move out of equities into debt securities
C. Wider spreads will occur because investors are concerned about weaker creditworthiness
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Credit Risk
Fundamentals of Credit Analysis
Return Impact of Spread Changes
Small spread changes:
Return impact  ( Modified Duration) x ( Spread)
Larger spread changes:
Return impact  ( Modified Duration) x ( Spread) + 0.5 x (Convexity) x ( Spread)^2
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Credit Risk
Fundamentals of Credit Analysis
Longer maturity bonds have higher duration and as a consequence higher spread sensitivity. Longer maturity bonds
have higher credit spreads. Longer maturity bonds also tend to have larger bid-ask spreads (i.e., higher transaction
costs), implying investors in longer maturity bonds would require higher spreads.
Credit curves are typically upward sloping
Active bond managers have to forecast spread changes and expected credit losses for individual bonds and for the
overall bond portfolio in order to improve portfolio performance
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Credit Risk
Fundamentals of Credit Analysis
Yield = Benchmark Yield + Risk Premium (Spread)
where:
Benchmark yield =
risk-free rate = expected inflation rate + expected real rate
Risk premium =
credit risk + liquidity risk + taxation
Estimated price change in % = –Duration ( spread) + 0.5 Convexity ( spread)2
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Credit Risk
Fundamentals of Credit Analysis
Example
The flat price on a fixed-rate corporate bond falls one day from 92.25 to 91.25 per 100 of par value because of poor
earnings and an unexpected ratings downgrade of the issuer. The (annual) modified duration for the bond is 7.24. Which of
the following is closest to the estimated change in the credit spread on the corporate bond, assuming benchmark yields are
unchanged?
A.
B.
C.
15 bps.
100 bps.
129 bps.
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Credit Risk
Fundamentals of Credit Analysis
High Yield Bonds
High yield bonds are more likely to default than investment grade bonds, which increases the importance of
estimating loss severity. Analysis of high yield debt should focus on:
–
–
–
–
Liquidity
Projected financial performance
The issuer’s corporate and debt structures
Debt covenants
A credit analyst will need to calculate leverage for each level of the debt structure when an issuer has multiple layers
of debt with a variety of expected recovery rates
High yield issuers for whom secured bank debt is a high proportion of the capital structure are so called top heavy
and have less capacity for additional bank borrowings in financially stressful period
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Credit Risk
Fundamentals of Credit Analysis
Issuers of high-yield bonds typically have a holding company structure. The assets and cash flows that are
available to pay the debt service will reside in operating subsidiaries.
A financial analysis of every subsidiary may be necessary in order to determine if the individual subsidiaries will be
able to generate sufficient excess cash flow to pay to the parent so that the parent can meet its debt service
requirements
High-yield issuers are risky in the first place. It is, therefore, very important to analyze the covenants in their indentures
to determine whether or not they are sufficiently limiting so as to “force” the company to preserve cash and assets as
collateral.
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Credit Risk
Fundamentals of Credit Analysis
Important covenants for high yield debt include:
–
–
–
–
Change of control put: debt holders have the right to require the issuer to buy back debt (at or above par)
in the event of an acquisition
Restricted payments: amount of cash that may be paid to equity holders is limited
Limitations on liens: amount of secured debt that a borrower can carry is limited
Restricted versus unrestricted subsidiaries: restricted subsidiaries’ cash flows and assets can be used to service
the debt of the parent holding company
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Credit Risk
Fundamentals of Credit Analysis
High-yield debt is not as risky as equity investments, but it is more risky than investment quality bonds. –
The empirical evidence is that the returns on high-yield debt are more closely correlated with the returns
on equities than the returns on bonds.
The best way to analyze high-yield bonds is to perform the same type of long-term cash flow projection that is used to
analyze the value of equity because these bonds tend to have below average solvency and interest coverage ratios and
above average debt-to-capital ratios
For example, analysts can compare companies based on the difference between their EV/EBITDA and Debt/EBITDA
ratios. Companies with a wider difference between these two ratios have greater equity relative to their debt and
therefore have less credit risk.
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Credit Risk
Fundamentals of Credit Analysis
Sovereign Bonds
Sovereign debt is the debt of foreign governments. This kind of debt is unique insofar as it is necessary to analyze
both
–
–
A sovereign government’s ability to pay its debt
And its willingness to pay its debts.
Rating agencies consider the following factors:
–
–
–
–
–
–
–
–
Political risk
Income and economic structure
Economic growth prospects
Fiscal flexibility
Public debt burden
Price stability (inflation)
Balance of payment flexibility
External debt and liquidity
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Credit Risk
Fundamentals of Credit Analysis
S&P assigns two ratings:
–
–
Local currency denominated debt rating
Foreign currency denominated debt rating
Historically the risk of defaults has been greater on debts not denominated in the issuer’s local currency. While a
country can levy taxes (or print money) to repay its local currency debts, it must generate real economic activity to
repay debts in another currency.
Sovereign defaults can be caused by events such as war, political instability, severe devaluation of the currency, or large
declines in the prices of the country’s export commodities. Access to debt markets can be difficult in bad economic
times.
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Content
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2
3
4
5
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Risks Associated with Investing in Bonds
Fixed-Income Valuation
Term Structure of Interest Rates
Yield Measures
Interest Rate Risk: Duration and Convexity
Credit Risk: Fundamentals of Credit Analysis
Managing Bond Portfolio
Relative-Value Methodologies for Global
Corporate Bond Portfolio Management
9
10
11
12
Exchange Rate Risk: International Bond Investing
Managing Interest Rate Risk with Derivatives
Managing Credit Risk with Derivatives
Currency Risk Management
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Introduction
Set investment objectives
– It depends upon the institution and is typically expressed in terms of return and risk
Establish investment policy
– It begins with asset allocation. Client and regulatory constraints in addition to tax and financial reporting implications
must be considered
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Select portfolio strategy
– The portfolio strategy must be consistent with objectives and guidelines. May be active, passive, or a combination
of the two
Select assets
– This is an attempt to construct a portfolio with the greatest return for the given level of risk
Measure and evaluate performance (monitoring)
– The performance should be assessed relative to a predetermined benchmark
Adjusting the portfolio
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There are two broad investment objectives that are associated with two different types of benchmark.
If the investment objective is to satisfy liabilities, then the benchmark should be structured to provide an index of those
liabilities  Benchmark in terms of its liability structure
If the objective is to provide performance in excess of some benchmark, then the benchmark should be a suitable bond
index  Benchmark as a bond index
The benchmark specified must reflect the client’s investment objectives from a risk/return perspective. The objective
returns must be appropriate.
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Using liabilities as a benchmark is most appropriate for investors whose primary concern is the satisfaction
of those liabilities when they come due
Investors who follow an investment policy of strategic asset allocation on the other hand, will want to compare
investment performance to a bond index
Occasionally, investors with liabilities, like pension plan sponsors, will pursue a bond index strategy on the assumption
that over a long time period bond performance that mimics an index will be sufficient to satisfy the liabilities
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Managing a Fixed-Income Portfolio against a Bond Market Index
Investors must choose an index with characteristics that match the objectives of their portfolios. In order to choose
the appropriate index the most important characteristics to examine are:
–
Market value risk:
It is the change in the market value of a portfolio as interest rates shift
Investors who are most adverse to market value risk should invest in portfolios with short or intermediate
durations and use short or intermediate-term indexes as performance benchmarks. Only less risk averse
investors should compare their higher risk portfolios to long-term indexes.
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Income risk:
– It refers to the instability and unpredictability of the income generated by the portfolio.
– Investors who are seeking a stable income stream that will persist for years into the future should choose longerterm portfolios and judge them against long-term indexes. – Short-term assets create an unpredictable income
stream that can vary from the income needs of the investor.
Credit risk:
– The average credit risk and diversification of the benchmark index should be compatible with the amount of credit
risk the investor is willing to take and the amount of diversification that is desired
Liability framework risk:
– Investors who must fund long-term liabilities such as a pension fund should invest in long-term fixed-income assets
to fund their long-term liabilities
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Taxable investors face a tax liability. They should attempt to maximize their after-tax portfolio returns. Therefore,
managers with clients whose returns are fully taxable should choose a benchmark index made up of either taxable
or non-taxable bonds, depending upon which is expected to produce the higher after-tax return for their clients.
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Example
A portfolio manager has three fixed-income clients, a risk-averse individual who does not want to risk much of a loss
in the value of his portfolio, a college endowment fund that wants stable long-term income to fund future expansion
programs, and a property and casualty insurance company that relies on the fund to meet short-term automobile accident
claims. The manager’s firm has three benchmark portfolios available for investment:
Portfolio A, which is made up of A-rated, 1–3 year corporate bonds
Portfolio B, which is made up of high yield (junk) bonds
Portfolio C, which is made up of A-rated, 5–7 year corporate bonds
Portfolio D, which is made up of Baa or better, 10–25 year corporate bonds
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(1) Passive management
–
The manager’s primary job is to select the bond index that best matches the risk and constraint profile of his client,
and attempt to construct a portfolio that matches the chosen index and tracks its return closely
–
A passive (indexing) strategy has three advantages:
Indexing is a low-cost strategy
It is difficult to outperform an index, so indexing may not sacrifice returns
Indexing produces excellent diversification, which reduces risk
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A passive (indexing) strategy has the following disadvantage:
–
Management and transaction costs that produce a net return to the client that is less than the return
of the benchmark index
a) Pure bond indexing
–
–
–
It attempts to replicate the index by owning all the bonds in the index and in the same percentage
by market weight
Disadvantages: With this technique is difficult to beat the benchmark because the portfolio pays expenses
and transaction costs where the index does not. The approach is difficult to implement because not all the bonds
in the index will be available to purchase (highly illiquid). – This approach will lag the benchmark index by the
amount of manager’s expenses and transaction costs.
Advantage: It will perfectly match the benchmark
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b) Enhanced indexing by matching primary risk factors
–
–
–
–
This approach invests in a large sample of bonds such that the portfolio risk factors such as duration, cash flow
distribution, sector, quality and call exposure match the index
Advantage: It does not require owning all the index’s bonds, therefore implementation costs are lower
Disadvantage: The portfolio will have a higher tracking error than pure bond indexing. Tracking error can be kept
relatively low, by making sure that the portfolio is constructed to match the risk profile of the benchmark as closely
as possible.
Through the use of under-priced securities and efficient construction, it is possible to slightly outperform the index’s
return
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The risk profile of a bond index is a detailed analysis of its risk exposure. The most important risk exposures relate
to the yield curve. These include:
–
–
–
Interest rate risk: the index’s sensitivity to parallel shifts in the yield curve, measured by the index’s duration
and convexity
Yield curve risk: the index’s sensitivity to yield curve reshapings (non-parallel changes of the yield curve),
measured by key rate durations. Key rate durations are used to measure the price change of a bond or bond
portfolio to changes in yields at specific points on the yield curve.
Spread risk: the index’s sensitivity to the spread between non-Treasury and Treasury yields, due to changes
in the creditworthiness of specific issue, or to changes in the credit conditions either generally or within specific
sectors of the market
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–
–
Call risk: the likelihood that the index will not respond very favorably if interest rates fall to very low levels because
of the likelihood that certain callable bonds within the index will be called
Event risk: the index’s exposure to credit rating changes because of restructurings and other idiosyncratic factors
unique to individual issues or sectors
Therefore, an enhanced indexer must make sure that he constructs a portfolio that is exposed to these risks in exactly
the same way as is the benchmark bond index whose risk exposures are to be replicated
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The following strategies can be used to align the interest rate risk and yield curve risks of a portfolio to those
of a benchmark index:
–
–
–
Cell-matching (stratified planning): The bonds within the benchmark index are categorized into “cells” that
represent the various risk exposures within index. The manager then selects a (random) sample of the bonds from
each cell for inclusion in the portfolio, making sure that the weight given to each cell in the portfolio matches that
cell’s weighting in the benchmark index.
Multifactor modeling: The manager must construct a portfolio that has the same effective duration, effective
convexity and important key rate duration as the benchmark index. Simulations should be run to ensure the desired
interest rate behavior of the portfolio vs. the benchmark index.
Cash flow matching: The manager constructs a portfolio so that the percentage of the present values of all the
cash flows generated by the bonds in it that fall into a series of non-overlapping time periods match period-toperiod with the same percentages for the benchmark index
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To align the spread risk exposure of the portfolio with that of the benchmark bond index, the enhanced indexer
should make sure:
–
–
–
–
Sector and quality weightings of the portfolio match those of the benchmark index
The sector contributions to the overall portfolio’s duration are the same, sector-by-sector,
for the constructed portfolios as for the benchmark index
The amount of duration that comes from various quality sectors in the portfolio matches that
of the benchmark index
Managers should make sure that their portfolio’s spread risk is the same as that of the benchmark index
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Spread Duration
Spread is the difference between the yield on a bond and a reference rate, typically U.S. Treasury securities of similar
maturity
Spread duration measures the percentage change in the value of a bond or portfolio of non-Treasury bonds
for a change in the yield spread between those assets and their benchmark Treasury bond.
Spread duration is important because as spreads change the value of the portfolio may change far in excess of its
modified duration
In addition, it can be used to measure the sensitivity of the value of a portfolio as a result of spread changes
independent of changes in Treasury
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Example:
A 8-year, A-rated, corporate bond yields 8%, and an 8-year Treasury bond yields 7%. What will happen to the price
of the corporate bond if the nominal spread between the two widens to 125 basis points? – The spread duration
of the corporate bond is 6.2.
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There are three spreads used in determining spread durations:
–
Nominal spread (or G-Spread) is the difference between the yield of a non-Treasury security and the yield
of a Treasury security of comparable maturity. The nominal spread duration measures the percentage price change
in price of the non-Treasury for a change in the nominal spread.
–
Zero volatility spread is the spread over the Treasury spot rate. Zero volatility spread duration measures
the change in price of the non-Treasury for a change in the zero-volatility spread.
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–
Option-adjusted spread is determined using a binomial interest rate tree. It can be interpreted as measuring the
average incremental return of the non-Treasury compared to the return of the benchmark Treasury over a range of
possible future interest rate paths and the bond cash flows that would occur along each such path. – The option
adjusted spread duration measures the percentage change in price of the non-Treasury for a change in the
OAS.
The manager should always use the spread duration that matches the method in which the spread was measured.
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Call risk exposure can be matched by
–
making sure that the callable bond weighting of the portfolio matches that of the benchmark index. The sector,
coupon, and maturity weightings of callable bonds in the portfolio should match those of the callable bonds
in the benchmark index as well.
Event risk exposures can be matched by making sure that
–
the number of issues in the portfolio is large. Bond indexes contain thousands of issues. This high degree
of diversification reduces event risk in the benchmark to a very low level.
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c) Enhanced indexing with small risk factor mismatches
–
This approach is similar to the one above except that it allows minor mismatches in the risk factors (except
duration). Duration is matched to control interest rate risk because changes in interest rates account for 90%
of the benchmark index’s return. Then the manager attempts to enhance the portfolio’s return by a small amount
by using the following techniques:
Tight cost controls (low trading costs and management fees)
Issue selection: undervalued bonds are included in the portfolio and overvalued issues are avoided.
The manager performs independent credit analyses to select bonds whose credit rating will likely be upgraded
and avoid issues that are likely to be downgraded.
Yield curve positioning: Overweight maturities along the yield curve that are undervalued and underweight
those that are overvalued
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–
–
Sector and quality positioning: Tilt toward short duration corporate issues, which is where the best yield spread
per unit of duration is usually found.
Anticipate yield changes: When credit conditions will be expected to deteriorate, tilt the portfolio from corporate
bonds slightly toward an overweighting in Treasuries, and vice versa.
Call exposure positioning: Underweight callable issues that are likely to be called due to an expected decline
in interest rates
Tracking error should still be low
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(2) Active management
–
Active management requires the manager to successfully challenge the market’s expectations with his own
superior forecasting ability
–
If the manager can forecast the interest rate outlook, credit market conditions, or some other relevant factors with
better accuracy than the market, he should be able to “tilt” the portfolio away from the benchmark indexes
weightings in ways that will generate higher returns than those produced by the benchmark index
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d) Active management with risk factor mismatches
–
–
–
–
–
This strategy involves larger mismatches in the risk factors to add greater value. – Duration may also be
mismatched to some degree, allowing the portfolio to take some interest rate risk.
The portfolio is tilt in the direction of attractive sectors and to adopt an aggressive posture with risk factors where
the manager believes there is mispricing
Advantage: It can enhance returns relative to the benchmark index without incurring undue risk
Disadvantage: It is more costly and somewhat more risky than the purely passive strategies
The tracking error risk will be more substantial
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e) Full-blown active management (unrestricted active management)
–
–
–
–
–
This is the riskiest approach, with large duration and sector bets being made
The manager deviates from the benchmark to a much greater degree as long as his forecasts about the level
of interest rates, the shape of the yield curve, or credit conditions differ from those implied by the market’s behavior
Advantage: The manager can outperform the index by a wide margin if his forecasts are consistently better than
those of the market
Disadvantage: The manager can underperform the benchmark by a wide margin if his forecasts are (even
occasionally) significantly wrong
The tracking error is the highest with this approach
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In attempting to outperform the benchmark index by a significant amount, active managers must undertake a number
of activities that are not required of passive managers such as:
–
–
–
–
Identifying which index mismatches to exploit. This depends on the manager’s areas of expertise (interest
rate risk and credit risk expertise)
Determining the market’s expectations regarding the mismatches that might be exploited. Market data
can provide insight as to what market expectations are. – For example, calculating forward rates along the yield
curve can provide some insight as to what the market expects interest rates will be doing in the future.
Making independent forecasts in the areas where the manager has the most expertise in order to find
overvalued or undervalued issues. An exploitable opportunity exists whenever the market’s expectations differ from
that of the manager.
Identifying areas of under- or overvaluation using relative value analysis of securities in the market,
which the active manager can exploit
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Tracking risk describes the risk that the return of the portfolio will be different from the return of the benchmark
portfolio. It is measured by computing the tracking error of a portfolio’s returns. It is the standard deviation
of the portfolio’s active return (actual return – benchmark returns) over a period of time.
Average 
 Active


  Return Active Return
Tracking



Risk
n 1
Tracking errors arises in both active and passive strategies
In an actively managed bond portfolio, the portfolio characteristics are deliberately designed to deviate from
the characteristics of the benchmark. They are willing to accept a large amount of tracking risk in order to try to
produce larger returns than those of the benchmark index.
In a passively managed bond portfolio, the risk is likely to be very small and be positive or negative
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Tracking error risk will be higher when the managed portfolio differs from the benchmark. The bond weightings
in the portfolio do not match the weightings of the bonds in the index.
–
The managed portfolio may have a different risk profile because it includes securities or sectors that are not
included in the benchmark. For example, if the managed portfolio includes mortgage backed securities but
the benchmark does not, the managed portfolio will have higher exposure to prepayment risk which could give rise
to tracking error.
–
The more the managed portfolio deviates from the benchmark in terms of the types of bonds included,
the higher the tracking error will be
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Further reasons for tracking error are:
–
–
Tracking error risk will be higher when administrative problems occur, which include commissions paid on
security purchases and sales, getting new funds fully invested without delay, selecting a mix of securities that will
match the performance of the index
Management fee reduce the return of a managed portfolio relative to the return of a benchmark index
Passively managed portfolios tend to have little tracking error (consisting of management fees and other
administrative reasons). Actively managed portfolios can generate large, positive or negative tracking error.
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Content
1
2
3
4
5
6
7
8
Risks Associated with Investing in Bonds
Fixed-Income Valuation
Term Structure of Interest Rates
Yield Measures
Interest Rate Risk: Duration and Convexity
Credit Risk: Fundamentals of Credit Analysis
Managing Bond Portfolio
Relative-Value Methodologies for Global
Corporate Bond Portfolio Management
9
10
11
12
Exchange Rate Risk: International Bond Investing
Managing Interest Rate Risk with Derivatives
Managing Credit Risk with Derivatives
Currency Risk Management
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Relative-Value Methodologies for Global/Corporate Bond Portfolio
Management
Relative value analysis is defined as ranking fixed income sectors, structures, issuers, and issues by expected
return
A top-down approach begins with asset allocation and large-scale economic developments to identify attractive
sectors within the bond market
A bottom-up approach focuses on individual issues and their relative attractiveness. They will outperform their peer
group based on individual security misevaluation
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Management
Classic relative value analysis attempts to combine the best of top-down and bottom-up approaches. – The goal is to
pick the best sectors, find the best issues in those sectors, and select the issuers’ securities that best match the
investor’s opinions of the markets.
There are seven methodologies:
–
–
–
–
–
–
–
–
–
Total return analysis
Primary market analysis
Liquidity and trading analysis,
Secondary trading rationales and trading constraints
Spread analysis
Structure analysis
Corporate curve analysis
Credit analysis
Asset allocation/sector analysis
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Management
Primary market analysis focuses on supply and demand for new issues. The expectation is that more supply will
hurt spreads as demand is stretched over a larger number of issues. In contrast empirical evidence is that new supply in
the corporate market has not hurt spreads.
Globalization is listed as the most important development in the primary corporate bond market
On the supply side, medium term notes as well as structured securities have become more popular. The primary motive
is to satisfy a broad range of investor needs thereby lowering funding costs. Bonds with embedded options are scarce,
the supply of long-dated maturities has declined, and credit derivatives have become more popular.
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Relative-Value Methodologies for Global/Corporate Bond Portfolio
Management
Both short and long-term liquidity influence portfolio management decisions
Some managers are hesitant to purchase issues that are not liquid, such as smaller-sized issues, private placements,
and non-local corporate issuers. Other managers see the lack of liquidity as an opportunity to earn higher yields.
Liquidity varies with the economic cycle, credit cycle, yield curve shape, supply, and the season. In addition, shocks
to the system can dry-up liquidity quite quickly
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Management
Rationales for Secondary Market Trading
The secondary market trades seasoned issues while the primary market trades new issues
The rationales for secondary trading are:
– Yield/spread pickup trades
– Credit upside trades
– Credit defense trades
– New issue swaps
– Sector rotation trades
– Curve adjustment trades
– Structure trades
– Cash flow reinvestment
Constructing a secondary market trade simply means comparing the relative values and selecting
the most attractive
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Management
Yield/spread pickup trades: they account for most of the secondary trades that occur. The goal is to trade one
security for another in order to improve the yield or spread.
Credit-upside trades: they occur when the manager buys a bond in anticipation of an upgrade in the issuer’s credit
rating that is not already reflected in the bond price. Good credit analysis is required and are profitable in the crossover
sector (from speculative grade to investment grade).
Credit-defense trades: they are important when the firm deteriorates. Investors increase credit quality in reaction
to uncertainties arising from secular changes in a sector (or also due to a rating downgrade, mandated by the portfolio
guidelines).
New issue swaps: they occur when managers rotate their portfolios into more current (and often larger) issues
to improve liquidity
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Management
Sector rotation trading: It is a strategy where the manager shifts out of a sector expected to underperform and into a
sector expected to outperform (macro and micro sector rotation)
Yield curve adjustment trades are made to reposition a portfolio’s duration
–
For example if investor believes that corporate spreads will narrow, with other rates remaining relatively stable, the
investor may shift the portfolio’s exposure to longer duration issues in that specific sector
–
In contrast, portfolio duration should be reduced when interest rates are anticipated to increase so as to minimize
potential price declines
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Management
Example:
Given the following bond portfolio and anticipated changes in interest rates, recommend whether to sell the CDS
or Treasury bonds and replace them with the XXX bonds if the only objective is to maximize short-term price appreciation
2-year
5-year
30-year
Yield curve today
4.7%
5.2%
5.5%
Weight % Issuer
Maturity
30%
U.S. Treasury
40%
YYY
30%
CDS
Bond being considered for purchase
XXX
Anticipated yield curve
4.1%
4.7%
5.0%
Mod. Duration
2-year
5-year
30-year
5-year
Eff. Duration
2.8
4.2
12.3
4.2
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Structure trades: they involve swapping into structures (e.g., callable, bullet, or put structures) that are expected to
outperform based on projected movements in volatility and the shape of the yield curve
Cash flow reinvestment: this forces managers into the secondary market on a regular basis to reinvest any cash
flows received as a result of coupon payments or maturities
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Management
Often, a trading constraint for one portfolio manager can become a trading opportunity for another portfolio manager
Constraints of trading are:
–
–
(1) Portfolio restriction prevent a portfolio from trading even when it is otherwise beneficial. For example, some
funds prevent a portfolio manager from holding non-domestic bonds, or force managers to sell a security
immediately if it is downgraded. Thus, such securities can become very attractively priced to another manager who
is not constrained.
(2) “Story disagreement”: times, when there is little agreement about a security’s value often indicate an
opportunity to take a position that may be very profitable if the manager turns out to be right
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Management
–
–
(3) Buy-and-hold strategies: can be dictated by accounting constraints or by the desire to curb portfolio
turnover. A buy-and-hold manager is often prevented from buying and selling even when it would be advantageous
to do so.
(4) Seasonality: There are slow periods during the year when dealers and portfolio managers are more focused
on closing their books, preparing reports, etc. Trading is very light at these times of year and some securities can
become very attractively priced.
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Spread Analysis
Spread analysis is a common tool for identifying profitable bond trades:
–
–
–
When yield spreads are expected to narrow, the bond with the higher spread duration will outperform the bond with
the lower spread duration
If spreads are expected to widen, the bond with the lower spread duration should outperform
If spreads are expected to remain stable, the bond with the higher yield will outperform the bond with the lower
yield
Spread analysis can be done using:
– Nominal spreads
– Static spreads
– Option-adjusted spreads
– Swap spreads
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Management
Swap spread analysis is a relatively recent tool for comparing fixed to floating-rate bonds
Example:
On January 1, 2001, an investor owns USD 10 million of GMAC 8.0% bonds due 2011. These bonds are trading at the
bid side price of 145 basis points over the 10-year U.S. Treasury yield of 6.2%. Thus, the yield-to-maturity is 7.65%
(6.2% + 1.45%). On the same date, a 10-year interest-rate swap has the following terms:
fixed rate
floating rate
10-year Treasury + 95 basis points
LIBOR flat
The investor is considering selling the GMAC bond to buy a 10-year floating rate GMAC bond that pays LIBOR + 30 basis
points. Calculate the fixed rate GMAC bond’s spread over LIBOR and advise the investor on the trade.
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Management
The major advantage to a swaps framework is that it allows managers to more easily compare securities across fixedrate and floating rate markets. – This comparison cannot be done with traditional spread analysis tools.
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Mean-reversion analysis: The mean is the average spread over a defined period, usually one economic cycle.
This analysis assumes the yield spread will return to its average historical value. Mean reversion implies a bond should
be purchased when spreads are at historic highs as it assumes spreads will narrow and the price of the target bond will
increase. The main drawback to mean-reversion analysis is to successfully predict when spreads will return to their
historic values.
Quality spread analysis focuses on credit spread. It looks at spread between high and low-quality credits. Managers
may decide to swap into lower quality debt in anticipation of an economic expansion, or swap into higher quality debt
in anticipation of weak economic conditions. The spreads between the two levels of quality may help determine
whether these swaps are attractive.
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Percent spread analysis examines the ratio of corporate yields to government yields for securities of similar duration.
A contraction of corporate percent yield spreads is considered a risk for future underperformance of the corporate
asset class.
–
This methodology ignores other factors that determine attractiveness, including demand and supply, profitability,
defaults, and so forth. It is more a derivative than an explanatory, or predictive variable.
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Structure Analysis
Structural analysis investigates the performance of the different structures – bullet, callable, putable, and sinking
fund structures
The importance of structural analysis has declined as intermediate bullets have become the predominant bond type.
Credit differentiation is often more important than the structural differences.
Callable structures usually provide 5 to 10 years of call protection before the issuer can exercise the option to
refinance debt in a lower-interest rate environment. Typically, issuers pay an annual spread premium of 30-40 basis
points to entice investors to buy callable bonds. As would be expected, callables underperform bullets in periods of
declining interest rates due to the higher risk of call (negative convexity). In bear markets, callables often outperform as
they have little risk of being called and they pay a spread premium.
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Bullet structures
– Front-end bullets (1 to 5 year maturities) are used by investors pursuing a barbell strategy. They want to gain an
enhanced yield.
– Intermediate corporate bullets (5 to 12 year maturities) are extremely popular. Their durations are reasonably
high and many investors find them attractive relative to longer-term credits.
– Longer-term credits include the most popular long-term security, the 30-year maturity. These longer-term
securities provide high convexity, while only modestly increasing duration compared to intermediate-term bonds.
Sinking fund structures allow issuers to execute a series of partial calls prior to maturity. Investors use bonds with
sinking fund structures to help protect against rising interest rates as a portion of the calls are mandatory. Thus, these
bonds may outperform bullets and callables during periods of rising rates.
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Putables are bonds where investors have a put option to demand full repayment at par. Put structures provide
investors with a defense against sharp increases in interest rates. In addition, investors can choose to put a bond where
the credit quality is deteriorating (assuming the issuer can meet the obligation).
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Credit Curve Analysis
Corporate curve analysis
Many portfolio managers opt to take credit risk in short and intermediate term maturities and to use government
securities in long-duration buckets. Credit barbell strategy.
As the time to maturity lengthens, the credit curve for poorly rated securities is steeper than for investment-grade
securities. That means the spreads widen with the time to maturity.
Credit curves change shape in response to economic cycles and the economic outlook
– When the market is worried about interest rates and general credit risk, spreads widen and the spread curve
becomes steeper
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Example:
Which of the following portfolios reflect a credit barbell strategy? All portfolios have the same durations.
Portfolio
A
B
C
Tr.
0%
15%
30%
1 to 5 years
Corp.
30%
15%
0%
Tr.
25%
30%
30%
5 to 12 years
Corp.
25%
20%
20%
Long
Tr.
Corp.
20%
0%
10%
0%
20%
10%
Identify the economic environment in which portfolio A would be most likely to underperform portfolio B, and explain why
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Credit Analysis
Good credit analysis identifies credit upgrades and downgrades before market prices and credit ratings reflect the
credit changes
However, such analysis requires detailed bottom up analysis of financial statements, corporate management and
industry trends. – This takes time and is challenging as global privatization of assets creates a growing list of credits to
analyze.
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Content
1
2
3
4
5
6
7
8
Risks Associated with Investing in Bonds
Fixed-Income Valuation
Term Structure of Interest Rates
Yield Measures
Interest Rate Risk: Duration and Convexity
Credit Risk: Fundamentals of Credit Analysis
Managing Bond Portfolio
Relative-Value Methodologies for Global
Corporate Bond Portfolio Management
9
10
11
12
Exchange Rate Risk: International Bond Investing
Managing Interest Rate Risk with Derivatives
Managing Credit Risk with Derivatives
Currency Risk Management
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Exchange Rate Risk
International Bond Investing
Potential Sources of Excess Return
Foreign bonds offer several potential sources of excess return for the fixed-income portfolio manager:
–
–
–
Country market selection: This strategy identifies those countries that are going to produce above-average
returns and overweights the portfolio in the assets of those countries. – The economic cycles of countries are not
synchronized. A portfolio manager can still earn a return advantage over treasuries by moving his credit allocation
from one country to another country.
Currency selection: This strategy identifies and overweights those currencies that will appreciate relative
to the domestic currency and underweights the portfolio in those currencies that will depreciate.
Duration/yield curve management: This can be executed within each country, based on expectations
for interest rates in each country.
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International Bond Investing
–
–
–
Sector selection: Opportunities are generally limited outside the U.S. because non-government bonds make up
only a small fraction of those markets. For example, the securitized mortgage market in Europe is less developed
compared to the U.S. market. A European portfolio manager wishing to take a view on convexity would be more
constrained if the were not allowed to invest in U.S. mortgages.
Security selection: International bond investing gives the portfolio manager access to a much broader set of
names to consider for the portfolio. In addition, a manager can take advantage of any mispricing of a given issuer
across markets
“Core-Plus” strategies: Some managers have domestic currency benchmarks but are sometimes given
permission to invest in “non-benchmark” securities. – This strategy identifies a market or bonds that are not
included in the benchmark index that will outperform the index and add it to the portfolio to enhance relative
performance.
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International Bond Investing
Change in Bond Value
Portfolios that contain foreign bonds make duration difficult to compute and interpret
Yield changes are not consistent across countries, so the duration of a portfolio including foreign bonds would be
subject to differing yield changes for each respective country represented in the portfolio
It is important to focus on the correlation between domestic interest rates and rates in each foreign country
Change in value of foreign bond = Duration x Country beta x i
The change in foreign yield given a change in domestic yield is estimated via regression analysis. The result
is country beta, which measures the change in foreign yield per unit change in domestic yield.
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International Bond Investing
To measure the contribution of a foreign bond to a domestic portfolio’s duration, simply multiply the country beta
by the bond’s duration
Example:
The duration of a Swedish bond is 8 and the country beta for Sweden is 0.85 (compared to the U.S). Compute
the duration contribution to a USD denominated portfolio!
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International Bond Investing
The duration of each country’s bond is adjusted by the country beta that takes into account the less then perfect
correlation of interest rates across countries
Example:
A portfolio consists of a domestic and a foreign bond. The domestic bond has a weight of 60% and a duration of 6 years,
while the foreign bond with a duration of 7 years has a country beta of 1.1. Compute the duration of the portfolio!
It is difficult to assess the duration impact of a foreign bond to a domestic portfolio. It requires knowing the bond’s
duration measured against foreign interest rates and the correlation between domestic and foreign rates.
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Hedge or not Hedge Currency Risk in a Bond Portfolio
Example:
A U.S. investor purchases a U.K. stock selling at 10 pounds sterling when the British pound is USD 1.70. One year later,
the stock is sold for 12 pounds sterling in the U.K. market, but the British pound exchange rate has changed to USD 1.50.
– What is the return to a U.K. investor measured in British pounds? What is the return in U.S. dollars to a U.S. investor?
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The unhedged return to domestic investor from a foreign security can be calculated in the following way:
RH = (1 + ri) x (1 + eH,i) – 1  ri + eH,I
where:
RH
ri
eH,i
return to the domestic investor, in the home currency
local market return of country i in its own currency
% return of currency i relative to the domestic home currency where currency units are expressed as H/i
Example:
Same data as previous example. Calculate the return to the U.S. investor with the above stated equation.
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Exchange Rate Risk
International Bond Investing
Managers of international portfolios can avoid the currency risk by hedging the currency. Hedging is normally done by
using currency futures or forward contracts.
To hedge the currency risk, the manager will sell the currency forward using a contract with an expiration date
comparable to the time period over which the manager desires to hedge the currency risk
Example:
Same data as previous example. The U.S. investor has sold the British pound forward at USD 1.55/GBP. What would be
the currency return and total return on the investment to the U.S. investor?
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International Bond Investing
The forward premium is defined as the differential between the forward and spot currency exchange rates. It can be
expressed as a price difference or a percentage difference though the percentage price difference is more useful in the
following analysis.
Forward premium = FY/X – SY/X
Forward premium (%) =
FY / X
1
SY / X
Thus the forward premium could be either positive or negative. Frequently, if the premium is a negative value it is
referred as a forward discount.
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Exchange Rate Risk
International Bond Investing
Alternatively, by combining the forward premium calculation with the interest rate parity relationship it can be shown that
the forward premium can be calculated directly from the interest rate differentials between the two countries.
Forward Premium (%) =
FY / X
1  rY
1
 1  rY  rX
SY / X
1  rX
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Exchange Rate Risk
International Bond Investing
Example:
Calculate the forward premium or discount (in %) of the U.S. dollar to the Euro for the 6-month currency contract
if the following information is given:
U.S. interest rate
Euro interest rate
Spot exchange rate
Forward exchange rate
3%
5%
USD 1.00/EUR
USD 0.99024/EUR
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International Bond Investing
Calculating returns for an international portfolio
For an international portfolio with allocations in a number of countries, the return to the investor in the investor’s home
currency will be:
RH  w1  (r1  eH,1 )  w 2  (r2  eH,2 )  ....  w n  (rn  eH,n )
where:
wi
ri
eH,i
H/i
percentage portfolio weighting by each country
local market return of country i in its own currency
percent return of currency i relative to the domestic home currency where currency units are expressed as
More properly, (r1 + eH,1) would be ((1 + r1) x (1 + eH,1) – 1), but simple addition of returns provides a close
approximation, and is used in the primary readings to simplify the equations and demonstrate the core concepts.
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International Bond Investing
1. Invest in the domestic market:
The return of the portfolio is the local market return rH of the home market
RH = rH
2. Invest in the foreign market (i) without hedging currency (i):
The return of the portfolio is the return of the local foreign market (ri) and the return of the foreign currency (eH,i)
RH,i  (1 ri )(1 eH,i )  1
or approx.
RH,i  ri + eH,i
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International Bond Investing
3. Invest in the foreign market and hedge the currency back to the home currency by selling the foreign
currency forward
The return of the portfolio is the return of the local foreign market ri and the forward premium, or discount. The forward
premium or discount can be assumed to be the periodic interest rate differential in the two countries.
Hedged return (HRH,i) =
or approx.



 (1  ri ) 1  cH    1
 1 c  

i 


HRH,i  ri + cH – ci
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Exchange Rate Risk
International Bond Investing
A bond’s hedged return equals the investor’s domestic interest rate plus the bond’s risk premium (local bond currency
return – foreign interest rate):
HRH,i  cH + (ri – ci)
Hedged Return = Domestic Interest Rate + Bond’s Local Risk Premium
The investor can simply compare expected risk premia across markets. The investor should invest (on a hedged basis)
in those markets that offer the highest risk premia.
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Exchange Rate Risk
International Bond Investing
Example:
Short-term interest rates are 4% in the U.S. and 1% in Japan. The U.S. manager expects the Japanese yen to appreciate
by 2.5% versus the U.S. dollar over the next year. Assuming that interest rate parity holds, should the investor hedge or not
hedge his Japanese government bond holdings?
The decision to hedge or not hedge depends on the investor’s ability to forecast the unexpected component
of the currency return: forex return – forward forex discount or premium
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International Bond Investing
Breakeven Spread Analysis
Although foreign yields can sometimes look very enticing, the investor needs to be aware of the risk that any spread
advantage can evaporate through spread widening (ignoring any currency impacts). Breakeven analysis addresses
the conditions under which two investments will produce the same return over some time horizon.
Example:
YTM
Effective Duration
Risk-free rate
10-year British bond
5%
8-year U.S. bond
4%
9.6%
6.7
7.2%
5.4
How much can the spread widen over one quarter before the British bond underperforms?
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Exchange Rate Risk
International Bond Investing
Example:
Same data as previous example. Let’s assume that the pound will decline by 25 bps over the next 3 months. What is the
break even spread change?
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International Bond Investing
Risks of Investing in Emerging Market Debt
Emerging market debt refers to public and private bonds issued by governments and corporations located in developing
countries. This is a very large market of approx. more than USD 3 trillion.
Many of these countries have relatively high credit ratings. – In fact, some emerging market debt is rated
investment grade. However, investors are attracted to the wider spread offered by many bonds.
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The issues are:
Although there are many issuers, a large portion of debt is concentrated in just a handful of countries such as Mexico
and Brazil. This can pose a concentration risk.
Emerging market bonds may not be as liquid as other international bonds, especially in periods of higher than usual
market volatility
Emerging market debt shares some characteristics with high-yield debt: higher negative skewness, implying higher
tail risk due to the possibility of large negative returns
Sovereign emerging market debt also contains sovereign risk. This is the risk that the issuing government can
repudiate its debt. – Measuring and monitoring sovereign risk requires different skills than the usual credit risk analysis
that is familiar to most portfolio managers.
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Content
1
2
3
4
5
6
7
8
Risks Associated with Investing in Bonds
Fixed-Income Valuation
Term Structure of Interest Rates
Yield Measures
Interest Rate Risk: Duration and Convexity
Credit Risk: Fundamentals of Credit Analysis
Managing Bond Portfolio
Relative-Value Methodologies for Global
Corporate Bond Portfolio Management
9
10
11
12
Exchange Rate Risk: International Bond Investing
Managing Interest Rate Risk with Derivatives
Managing Credit Risk with Derivatives
Currency Risk Management
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10
Managing Interest Rate Risk with Derivatives
Interest Rate Futures
Managers generally find the interest rate futures market to be an efficient and lower cost way to manage their interest
rate risk. Interest rate futures used are Treasury bond futures.
Dollar Duration per $100,000  CTD Duration  CTD Price

Futures Contract
Conversion Factor
Number of
Duration Target  Duration Portfolio  Market Value of Bond Portfolio

Futures Contract
Dollar Duration of Futures Contract
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Managing Interest Rate Risk with Derivatives
Example:
A bond manager owns a USD 100 million market value bond portfolio with an effective duration of 4. The manager would
like to increase the duration to 5.0. The price of the cheapest-to-deliver bond (CTD) is 107 with a duration of 8.4 and a
conversion factor of 1.1787. What is the number of futures contracts to buy or sell to raise the portfolio’s duration from 4
to 5?
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Managing Interest Rate Risk with Derivatives
Using futures to adjust a portfolio’s duration is fast, easy, and cheap. However, one potential drawback is basis risk. –
Basis risk is defined as the risk that changes in the futures price may not track changes in the cash price of the
portfolio.
Basis risk arises from several sources, including:
–
–
Futures-CTD basis risk: Changes in the price of the futures contract may not track changes in the price of the
underlying CTD bond
Cash-Futures basis risk: Changes in the value of the manager’s portfolio may not track changes in the value of
the futures position
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Managing Interest Rate Risk with Derivatives
The manager is holding corporate bonds and he decides to immunize the portfolio to a schedule of liabilities provided by
the client. In order to change the duration of the bond portfolio the manager will use Treasury bond futures. – Despite
this duration hedge the manager will be exposed to basis risk because the yield of the corporate bond portfolio will
change more or less than the yield of the cheapest-to-deliver bond.
One way to deal with this potential basis risk is to use regression to estimate a yield beta. A yield beta measures how
much the portfolio’s yield changes per basis point change in the CTD bond’s yield.
Yield on Bond (Portfolio) to be Hedged = α + ß x Yield on CTD Bond + Error Term
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Managing Interest Rate Risk with Derivatives
Example:
A bond manager owns a USD 35 million market value corporate bond portfolio with an effective duration of 10. The
manager decides to immunize the portfolio to a schedule of liabilities provided by his client. The duration of the liabilities is
9. In order to immunize the portfolio the manager will use Treasury bond futures. The price of the cheapest-to-deliver bond
(CTD) is 107 with a duration of 8.4 and a conversion factor of 1.1787. The yield beta is 1.08. What is the number of
futures contracts to buy or sell to immunize the portfolio?
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Managing Interest Rate Risk with Derivatives
Interest rate swaps
Another quick and inexpensive way to adjust portfolio duration is to execute an interest rate swap
Unlike futures, an interest rate swap is an OTC derivative contract. Swaps are very liquid and are common interest rate
risk management tool.
Dollar Duration of a Receiver Swap = Dollar Duration of Fixed-Rate Bond – Dollar Duration of Floating-Rate Bond > 0
Dollar Duration of a Payer Swap = Dollar Duration of Floating-Rate Bond – Dollar Duration of Fixed-Rate Bond < 0
The advantage of interest rate swaps is that they can be customized to the manager’s specific requirements whereas
the manager is limited to just a handful of available futures contracts
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Managing Interest Rate Risk with Derivatives
Interest rate options
There are options on physical Treasury bonds and on Treasury bond futures contracts
To use options in interest rate risk management, the portfolio manager must measure the duration of the option
contract
–
–
First the manager must identify the underlying instrument
The manager must measure how much the option price will change as the underlying price changes – delta
Duration of Option = Duration of Underlying Instrument x Delta
Not only can options be used to adjust a portfolio’s duration, but they can be used to create asymmetric returns, using
a protective put or a covered call strategy
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Content
1
2
3
4
5
6
7
8
Risks Associated with Investing in Bonds
Fixed-Income Valuation
Term Structure of Interest Rates
Yield Measures
Interest Rate Risk: Duration and Convexity
Credit Risk: Fundamentals of Credit Analysis
Managing Bond Portfolio
Relative-Value Methodologies for Global
Corporate Bond Portfolio Management
9
10
11
12
Exchange Rate Risk: International Bond Investing
Managing Interest Rate Risk with Derivatives
Managing Credit Risk with Derivatives
Currency Risk Management
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11
Managing Credit Risk with Derivatives
In recent years, bond dealers have begun to offer a variety of derivative instruments designed specifically to manage
the credit risk of fixed-income portfolios. – In many cases, these derivatives are designed to protect the portfolio
against the effects in changes in the interest-rate spread between the portfolio and assets that do not have credit risk
such as Treasury securities.
All of the credit derivatives discussed in the primary readings are OTC contracts. – Thus, they have counterparty risk.
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Managing Credit Risk with Derivatives
Credit risk type
Derivative instrument for hedging
Default: the borrower cannot
meet interest and principal
payments when due
– Binary credit options
– Credit swaps
Credit spread: yield differences
between risky and riskless debt
widen (after purchase)
– Credit spread options
– Credit forwards
Downgrade: the rating agency
reduces the credit rating on an
issuer – it would likely cause the
the spread to widen and liquidity
to deteriorate (many investors are
not permitted to hold bonds below
a certain rating category)
– Binary credit options based on a credit rating
– Credit swaps
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Managing Credit Risk with Derivatives
If a portfolio’s credit exposure is not at the manager’s desired level, the manager will need to make an adjustment. The
manager can reduce credit exposure in a number of ways:
Selling cash bonds with greater credit risk sensitivity and buying bonds with lower credit sensitivity
Credit swaps
Credit options
Credit forwards
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Managing Credit Risk with Derivatives
(1) Cash Market
For example, if the portfolio’s credit exposure is too low, the manager can sell a bond with a spread duration of 2 and
use the proceeds to buy a bond with a spread duration of 5
Adjusting a portfolio’s duration using cash bond transactions can be difficult and costly. Especially for credit bonds, it
can take considerable time to find willing sellers and buyers.
In addition, cash market transactions can be expensive in terms of the bid-ask spread
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Managing Credit Risk with Derivatives
(2) Total Return Swap
Capital Markets
LIBOR
LIBOR +
1%
Investor
(Credit Protection
Seller)
Cash
Cash to buy
Asset
Dealer
(Credit Protection
Buyer)
Referenced
Asset
Asset Total
Return
Asset Total
Return
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Managing Credit Risk with Derivatives
Total return swap transfer all of the economic exposure of a referenced asset to the credit swap purchaser. In return
for receiving this exposure to an underlying asset, the credit swap purchaser pays a floating rate plus a spread
(i.e., 1%) to the credit swap seller.
If the reference obligation is a sector of a bond index, the swap is called a total return index swap. – The total return in
the swap includes both periodic cash flows received from the reference asset as well as any capital appreciation or
depreciation.
The party who is selling the credit protection gains exposure to the reference obligations without financing the
exposure. – In addition, the party can gain exposure to a diversified basket of assets without incurring the cost of
several cash market transaction (just using the total return swap). Finally, a total return swap allows a manager to short
one or more corporate bonds efficiently.
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Managing Credit Risk with Derivatives
(3) Credit default swaps are similar to credit options and allow to hedge credit exposure
The investor returns from investing in a risky asset. At the same time, the investor pays a swap premium to a
counterparty and receives a cash payment if the risky asset defaults or some other trigger event occurs.
Total
Return
Swap
Premium
Investor
(Credit Protection
Buyer)
Risky
Asset
Counterparty
(Credit Protection
Seller)
Cash Payment
if default occurs
Investment
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Managing Credit Risk with Derivatives
If there is only one reference obligation, the swap is called a single-name credit default swap, while a swap
involving a portfolio of reference obligations is called a basket default swap
The protection buyer can pay the swap premium over several settlement dates and can receive payments at
intermediate settlement dates as compared to only one payment under a credit option contract
Credit default swaps may be settled in cash or by physical delivery of the reference obligation by the buyer to the
protection seller in exchange for the seller’s cash payment (most common settlement method for single-name credit
default swaps)
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Managing Credit Risk with Derivatives
(4) Credit Options (Binary Credit Options)
A standard bond option’s payoff would be based on change in the bond’s price which is basically due to a general
change in the level of interest rates. – In contrast, a credit option is designed to respond specifically to credit risk and
changes in interest rate spreads.
Credit option structures include:
–
Binary credit options:
They pay a single predetermined amount if some trigger event occurs, or nothing if it does not
–
Credit spread options:
They have a payout determined by a formula based on a change in credit spread
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Managing Credit Risk with Derivatives
Binary credit option: (put option)
Such an option allows investors to put the bonds back to the issuer at face value if a certain condition exists like the
credit rating falls below investment grade
The put option protects the bondholder from any decrease in value due to a widening credit spread (caused by a
downgrading)
The value of a credit put can be computed as:
Value of Put = (St – Vt) x (Notional Principal)
where:
St
Vt
strike price of the option at time t (normally at par)
value of the bond at time t
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Managing Credit Risk with Derivatives
Example:
An investor buys a binary credit put option on USD 40,000,000 par value of XYZ bond with a two-year-term. The investor
paid an option premium of USD 400,000. The trigger event is defined as a bond rating below BBB-.
Calculate the net payoff if the credit rating falls to BB+ and if the price of the bond is 89.12
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Managing Credit Risk with Derivatives
Credit spread option (call option written on credit spread)
Credit spread options are designed to compensate the buyer for any price deterioration in the bond due to the spread
widening to a level greater than some strike spread
The value of a credit spread call can be computed as:
Value of Call = Max ((RSt – SSt) x (Notional Principal) x (RF)), 0)
where:
RSt
SSt
RF
actual spread over the benchmark rate at time t
specified strike spread over the benchmark
risk factor, or an adjustment for interest rate sensitivity
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Managing Credit Risk with Derivatives
Example:
The 10-year 8.25% annual coupon bonds were issued with a credit spread option with a strike price of 250 basis points
over LIBOR. Let assume that LIBOR is 5.0% today. The actual spread amounts to 325 basis points. The face value of the
bond is USD 5 million and we assume a risk factor of 2.5. Calculate the option payoff of the credit spread call!
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Managing Credit Risk with Derivatives
Example:
A manager owns USD 50,000,000 of XYZ bonds and buys the following credit spread call option to protect the portfolio
from an anticipated deterioration in XYZ’s credit quality and spread:
Notional
Strike spread
Term
Premium
Risk factor
USD 50,000,000
175 basis points
six months
75 basis points
4.2
The spread is calculated as the yield of XYZ bond, less the yield on the Treasury 8% with the same maturity of the bond.
a) Calculate the cost of the option
b) Calculate the option net payoff if the spread narrows to 125 bp.
c) Calculate the option net payoff if the spread widens to 225 bp.
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Managing Credit Risk with Derivatives
Credit spread option can be used to:
–
Protect against macroeconomic events such as an economic slowdown leading to a flight to quality (widening
spreads)
–
Protect against or speculate that the credit quality of an issuer will decline (a microeconomic event)
–
Enhance income through writing the option
Credit put options written on an underlying bond pay off when the bond rating falls or default occurs. The owner of
the put option can put (sell) the bond at an agreed upon price (the strike price).
Credit call options written on a credit spread gain value if the spread widens. These options have value
independent of the level of interest rates. Selling these options can be used to gain income when the writer believes
spreads will not widen enough to make the call valuable.
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Managing Credit Risk with Derivatives
(5) Credit forwards are written on a spread over benchmark Treasury bonds
If the credit spread widens, the long side of the contract will receive payments. If the credit spread declines, the long
must make payments to the short. – There is no option premium to enter the contract.
Credit options on the other hand, have one-sided payoffs where cash flows change hands only if the option is in the
money. They protect the buyer if spreads widen, while allowing the buyer to benefit from the relative appreciation in the
bond if spread narrows.
The forward payoff can be calculated as follows:
FV = (RSt – SSt) x (Notional Principal) x (Risk Factor)
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Managing Credit Risk with Derivatives
Example:
A bond portfolio manager holds USD 40 million of XYZ bonds and buys the following credit forward contract to protect the
portfolio against spread widening on the bonds:
Notional
Contracted spread
Risk factor
USD 40,000,000
175 bp
4.2
Calculate the payout of the credit forward contract if the spread narrows to 125 bp. and widens to 225 bp.
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Content
1
2
3
4
5
6
7
8
Risks Associated with Investing in Bonds
Fixed-Income Valuation
Term Structure of Interest Rates
Yield Measures
Interest Rate Risk: Duration and Convexity
Credit Risk: Fundamentals of Credit Analysis
Managing Bond Portfolio
Relative-Value Methodologies for Global
Corporate Bond Portfolio Management
9
10
11
12
Exchange Rate Risk: International Bond Investing
Managing Interest Rate Risk with Derivatives
Managing Credit Risk with Derivatives
Currency Risk Management
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Currency Risk Management
An investment priced in a foreign currency has two sources of risk and return:
–
–
Return on asset in the foreign currency (RFC)
Return on the foreign currency (RFX)
RDC  (1 RFC)(1 RFX)  1  RFC  RFX  (RFC)(RFX)
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Example
A US-based investor holds a portfolio of securities that trade in CHF. Over a one-year holding period, the value of the
portfolio increases by 10% (in CHF) and the CHF-USD exchange rate increases from 1.10 USD/CHF to 1.15 USD/CHF.
The investor’s return in domestic currency is closest to:
A.
B.
C.
5%
12%
15%
 The FX return calculation is based on the foreign currency as the base currency (denominator):
Return FX = EV / BV – 1
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Currency Risk Management
Domestic currency return on a portfolio of multiple foreign assets will be equal to:
RDC 
n
 w (1 R
i
FC,i )(1  RFX,i )  1
i 1
where:
RFC
RFX
wi
foreign currency return on the i-th foreign asset
appreciation/depreciation of the i-th foreign currency against the domestic currency
portfolio weights of the foreign-currency assets (defined as the percentage of the aggregate domestic
currency value of the portfolio); ∑wi = 1 (short positions have a negative weight)
RFX is defined with the domestic currency as the price currency and the foreign currency as the base currency.
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Example:
A portfolio consisting of two foreign assets denominated in GBP and EUR is held by an investor in India. Performance is
measured in terms of the Indian rupee (INR) and the weights of the two assets in the portfolio are 75% for the GBPdenominated asset and 25% for the EUR-denominated asset, respectively.
INR/GBP spot rate
INR/EUR spot rate
GBP-denominated asset value1
EUR-denominated asset value1
1 Millions
One year ago
Today
84.12
65.36
42.25
14.08
85.78
67.81
50.70
12.17
of units of foreign currency; today’s asset values are prior to rebalancing.
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Currency Risk Management
An investor investing in a foreign currency denominated asset has two sources of risk:
–
–
Fluctuation of the foreign currency
Fluctuation in foreign currency price of the foreign asset
The variance of RDC can be calculated as follows:
2(RDC)  w 2 (RFC)2 (RFC)  w 2 (RFX)2 (RFX)  2w (RFC)w (RFX)(RFC)(RFX)(RFC, RFX)
This basic two asset variance equation can be simplified when a domestic investor holds a single foreign currency
denominated asset. The exposures (weights) to RFC and RFX are each 100%:
2 (RDC)  2 (RFC)  2 (RFX)  2(RFC)(RFX)(RFC, RFX)
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Currency Risk Management
If RFC is a risk-free return: the standard deviation of the risk-free asset is 0 and the correlation coefficient with the
RFX is 0 as well. Thus, RFX is the only source of risk for the domestic investor in the foreign asset and the risk can be
calculated as follows:
(RDC)  (RFX)
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Arguments made for not hedging currency risk are:
–
–
–
It is best to avoid the time and cost of hedging or trading currencies.
In the long-run, unhedged currency effects are a “zero-sum game”; if one currency appreciates, another must
depreciate.
In the long-run, currencies revert to a theoretical fair value.
The argument for active management of currency risk are:
–
–
In the short-run, currency movements can be extreme.
Inefficient pricing of currencies can be exploited to add to portfolio return. Many foreign exchange trades are
dictated by international trade transactions or central bank policies. These are not motivated by consideration of fair
value and may drive currency prices away from their fair value.
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Currency Risk Management
Currency management strategies include:
–
Passive hedging: typically matches the portfolio’s currency exposure to that of the benchmark used to evaluate
the portfolio’s performance. It will require periodic rebalancing to maintain the match. The objective is to eliminate
currency risk relative to the benchmark.
–
Discretionary hedging: deviates modestly (e.g. 5%) from passive hedging (benchmark) by a specified
percentage. The objective is to reduce currency risk while allowing the manager to pursue modest incremental
currency returns relative to the benchmark.
–
Active currency management: greater deviations from benchmark currency exposures. The objective is to
generate incremental return (alpha), not to lower risk.
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Currency overlay: outsourcing currency management. At the extreme, currency will be treated as an asset class and
may take positions independent of other portfolio assets. For example, a manager who is bullish Yen for a portfolio with
no exposure to Yen would go long the Yen. The manager is purely seeking alpha (incremental return), not risk
reduction.
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Active Currency Trading Strategies
1) Economic fundamentals
–
This approach assumes that, in the long term, currency value will converge to fair value (i.e., purchasing power
parity will determine long-run exchange rates).
–
Several factors will impact the eventual path of convergence over the short and intermediate terms. Increases in
the value of a currency occur because of:
Currencies are more undervalued relative to their fundamentals.
Currencies have the greatest rate of increase in their fundamental value.
Currencies with higher real or nominal interest rates.
Currencies with lower inflation relative to other countries.
Currencies of countries with decreasing risk premiums.
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Currency Risk Management
2) Technical Analysis
– The underlying assumptions are:
Past price data can predict future price movement and because those prices reflect fundamental and other
relevant information, there is no need to analyze such information.
Fallible human beings react to similar events in similar ways and therefore past price patterns tend to repeat.
It is unnecessary to know what the currency should be worth (based on fundamental value); it is only important
to know where it will trade.
–
Typical patterns to be exploited are:
Overbought or oversold market has gone up or down too far and the price is likely to revert.
Support level (a price that falls to that level is likely to reverse).
Resistance level (a price that rises to that level is likely to reverse).
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Currency Risk Management
3) Carry Trade
–
A carry trade refers to borrowing in a lower interest rate currency and investing the proceeds in a higher interest
rate currency.
Covered interest rate arbitrage: difference between spot (S0) and forward (F0) exchange rates equals the
difference in the interest rates of the two currencies. Thus, forward exchange rate is an unbiased estimate of
the spot exchange rate that will occur in the future.
–
–
Currency with the higher interest rate trades at a forward discount (F0 < S0).
Currency with a lower interest rate trades at a forward premium (F0 > S0).
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Currency Risk Management
The carry trade is based on a violation of uncovered interest rate parity.
–
The currency with the higher interest rate will decrease in value by the amount of the initial interest rate differential
and vice versa. If these expectation do hold, a carry trade would earn a return of 0%.
With a carry trade the forward rate bias is traded. Historical evidence indicates:
–
–
On average, higher interest rate currency has depreciated less than predicted by IRP or even appreciated (profit
with a carry trade).
A few times, the higher interest currency has depreciated substantially more than predicted by IRP (loss with a
carry trade).
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Currency Risk Management
Covered interest rate parity is stated as:
FP / B

 Actual
 1  ip 
 360
 SP / B 

 Actual
 1  iB 
 360


 


 

Assuming a one-year time horizon (360 days), the forward premium or discount (expressed as a percentage of the
spot rate): is:
FP / B  SP / B  iP  iB 

 
SP / B
 1  iB 
Being low-yield currency and trading at a forward premium or being high-yield currency and trading at a forward
discount. Borrowing in the low-yield currency and investing in the high-yield currency (carry trade) is hence equivalent
to selling currencies that have a forward premium and buying currencies that have a forward discount – trading the
forward rate bias.
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Currency Risk Management
The carry trade can also be implemented by borrowing in the lower interest rate currency of developed economies
(funding currencies) and investing in the higher interest rate currencies of emerging economies (investing
currencies).  significant losses in periods of financial distress.
Buy/Invest
Sell/Borrow
Implement the carry trade
high-yield currency
low-yield currency
Trading the forward bias
forward discount
currency
forward premium
currency
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Currency Risk Management
Example
The spot exchange rate is CHF/USD 0.90. The interest rates in the two countries are 1% and 5%, respectively.
1. What is the 1-year forward exchange rate for the CHF?
2. State the steps to initiate the carry trade?
3. What is the profit on the trade if the spot exchange rate is unchanged and the trade is initiated by borrowing 100
currency units (over 1 year)?
4. What is the primary risk of this trade?
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Currency Risk Management
4) Volatility Trading
–
Volatility trading permits managers to profit from predicting changes in currency volatility.
–
Delta hedging: small changes in the price of the underlying asset are eliminated, but will be exposed to changes
in implied volatility.
–
Long straddle (at-the-money long call and long put): expectation is that volatility goes up – positive vega and
delta-neutral.
–
Short straddle (at-the-money short call and short put): expectation is that volatility goes down – negative vega,
delta-neutral, negative gamma.
–
Long strangle (out-of-the-money long call and long put with same absolute delta); initial costs are lower
compared to a straddle; expectation is that volatility goes up.
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Currency Risk Management
Relative currency:
Expectations
Action
Appreciation
Reduce the hedge on or
increase the long position in the currency
Increase the hedge on or
decrease the long position in the currency
Depreciation
Volatility
Increase
Decrease
Long straddle (or strangle)
Short straddle (or strangle)
Market conditions
Stable
Crisis
Carry trade
Discontinue carry trade
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A hedge can be static (held until expiration) or dynamic (periodically rebalanced). The choice of hedging approach
should consider:
–
–
–
Shorter term contracts or dynamic hedges with more frequent rebalancing tend to increase transaction costs but
improve the hedge result.
Higher risk aversion suggests more frequent rebalancing.
Lower risk aversion and strong manager views suggest allowing the manager greater discretion around the
strategic hedging policy.
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Currency Risk Management
Hedging also exposes the portfolio to roll yield or roll return. Roll yield is a return from the movement of the forward
price over time toward the spot price of an asset. The roll yield is determined as follows:
Roll Yield 
Forward Price  Spot Price
Spot Price
Roll yield is a cost of hedging. Positive roll yield will shift the analysis toward hedging and negative roll yield will shift the
analysis away from hedging.
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Currency Risk Management
If the hedge requires:
FP/B > SP/B; iP > iB
forward price curve
is upward-sloping
FP/B < SP/B; iP < iB
forward price curve
is downward-sloping
A long forward position in
Currency B, the hedge earns:
Negative roll yield,
which increases
hedging costs and
discourages hedging.
Positive roll yield,
which decreases
hedging costs and
encourages hedging.
A short forward position in
Currency B, the hedge earns:
Positive roll yield,
which decreases
hedging costs and
encourages hedging.
Negative roll yield,
which increases
hedging costs and
discourages hedging.
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Trading Strategies to Reduce Hedging Costs
To lower hedging costs, the manager can increase the size of trades that earn positive roll yield and reduce the size of
trades that earn negative roll yield.
Forward hedging also incurs opportunity costs. With a forward contract the downside risk as well as the upside
opportunity is eliminated. – Opportunity costs can be reduced with discretionary or option-based hedging strategies.
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Selection of Currency Management Strategies
Forward contracts
Over-/under-hedging
Profit from market view
Risk reversals
Put/call spreads
Seagull spreads
Cheaper than ATM
Sell options to earn premiums
Sell options to earn premiums
Sell options to earn premiums
Knock-in/out features
Digital options
Reduced downside/upside exposure
Extreme payoff strategies
Option contracts OTM options
Exotic options
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Currency Risk Management
1) Over- or under-hedge with forward contracts based on the manager’s view. If the manager expects the
EUR to appreciate, he can reduce the hedge ratio, hedging less than the full exposure to EUR. If the EUR is expected
to depreciate, he can increase the hedge ratio, hedging more than the full exposure to EUR risk. If successful, this
strategy creates “positive convexity”; gains will be increased and losses will be reduced. This is a relatively low cost
strategy.
2) Buy at-the-money put options (protective put strategy). All downside risk is eliminated and all upside potential
is retained (reduced by the option premium paid). The strategy is relatively expensive and the put option has only time
value (no intrinsic value). This strategy has the highest initial cost but no opportunity cost.
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Currency Risk Management
3) Buy out-of-the-money put options. Puts are less expensive the further they are out-of-the-money, but also offer
less downside protection. The manger will have downside exposure down to the exercise price of the puts. The initial
costs are lower compared to the strategy with the at-the-money puts but does not eliminate all downside risk.
4) Risk reversal or collar: buying calls and selling puts with the same delta. The out-of-the money puts provide some
downside protection while costing less than at-the-money puts. The sale of out-of-the-money calls remove some
upside potential (increasing opportunity costs) but generates premium income to further reduce initial cost. This
strategy further reduces initial cost but also limits upside potential compared to a put only strategy.
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Currency Risk Management
5) Put spread: Buy out-of-the-money puts and sell puts that are further out-of-the-money. There is downside
protection, which begins at the exercise price of the bought put, but if the currency falls below the lower exercise price
of the sold put, that downside protection is lost. This strategies reduces initial cost and also reduces downside
protection compared to a long put only strategy.
6) Seagull spread: Put spread combined with a short call. Compared to put spread, this hedge has less initial costs
and the same downside protection, but limits upside potential.
7) Exotic options: A knock-in option comes only into existence if the underlying first reaches some pre-specified
level. A knock-out option ceases to exist if the underlying reaches some pre-specified level. A binary or digital
option pay a fixed amount that does not vary with the difference in price between the exercise price and underlying
price.
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Cross hedges, Macro hedges, and Minimum-Variance-Hedge Ratios
A cross hedge (or proxy hedge) refers to hedging with an instrument that is note perfectly correlated wit the
currency exposure being hedged. Such a hedge can also introduce additional risk – when the correlation of returns
between the hedging instrument and the position being hedged is imperfect, the residual risk increases.
A macro hedge is a type of cross hedge that addresses portfolio-wide risk factors rather than the risk of individual
portfolio assets. One type of currency macro hedges uses a derivative contract based on a fixed basket of currencies to
modify currency exposure at a macro (portfolio) level.
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A mathematical approach to determining the optimal cross-hedging ratio is known as the minimum-variance hedge
ratio. It is a regression of the past changes in value of the portfolio (RDC) to the past changes in value of the hedging
instrument (RF) to minimize the value of the tracking error between these two variables. The hedge ratio is the beta
(slope coefficient) of that regression.
Cov RDC,RF
 RDC 



RDC,RF
2

 RDC,RF
 RF 
Because the hedge ratio is based on historical returns, if the correlation between the returns on the portfolio and the
returns on the hedging instrument change, the hedge will not perform as well as expected.
The minimum-variance hedge ratio can be used to jointly optimize over changes in value of RFX and RDC to minimize
the volatility of RDC.
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Currency Risk Management
For example, a foreign country where the economy is heavily dependent on imported oil. Appreciation of the currency
(+RFX) would make imports less expensive, which is likely to decrease production costs, increasing profits and asset
values (+RFC). Strong positive correlation between RFX and RFC increases the volatility of RDC. A hedge ratio greater
than 1 would lower the volatility of RDC.
For example, a foreign country where the economy is heavily dependent on exports. Appreciation of the currency
(+RFC) would make its exports more expensive, likely reducing sales, profits, and asset values (–RFC). Strong
negative correlation between RFX and RFC naturally decreases the volatility of RDC. A hedge ratio less than 1 would
lower the volatility of RDC.
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A portfolio manager who is long the base currency in the P/B quote and wants to hedge that price risk needs to
understand the following:
–
Because the portfolio has a long exposure to base currency, to neutralize this risk the hedge will attempt to build a
short exposure out of that currency’s derivatives using some combination of forward and/or option contracts.
–
A currency hedge is not a free good. The hedge cost, real or implied, will consist of some combination of lost
upside potential, potentially negative roll yield (forward points at a discount or time decay on long option positions),
and upfront payments of option premiums.
–
The cost of any given hedge structure will vary depending on market conditions (i.e., forward points and implied
volatility).
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For a manager with a long exposure to a currency, the cost of this “core” hedge will be the implicit costs of a short
position in a forward contract (no upside potential, possible negative roll yield) or the upfront premium on a long position
in a put option. Either of these two forms of insurance can be expensive. However, there are various cost mitigation
methods that can be used alone or in combination to reduce these core hedging costs:
–
–
–
–
Write options to gain upfront premiums.
Varying exercise prices of the options written or bought.
Varying notional amounts of the derivative contracts.
Using various “exotic” features, such as knock-ins or knock-outs.
These cost mitigations approaches involve some combination of reduced upside and/or reduced downside protection.
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There are often “natural” hedges within the portfolio, in which some residual risk exposures are uncorrelated with each
other and offer portfolio diversification effects. Cross hedges and macro hedges bring basis risk into the portfolio,
which will have to be monitored and managed.
There is no single or best way to hedge currency risk. The portfolio manager will have to perform a due diligence
examination of potential hedge structures and make a rational decision on a cost/benefit basis.
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The majority of investable asset value and FX transactions are in the six largest developed market currencies.
Transactions in other currencies pose additional challenges because of:
–
–
higher transaction costs, “high markups” and
increased probability of extreme events.
Non-deliverable forwards: Emerging markets governments (i.e., Brazil, China, Russia) frequently restrict movement
of their currency into or out of the country to settle normal derivative transactions. They are an alternative to deliverable
forwards and require a cash settlement of gains or losses in a developed market currency at settlement rather than a
currency exchange.
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