Download Chapter 5 PowerPoint

Power Point Slides for:
Financial Institutions, Markets, and
Money, 9th Edition
Authors: Kidwell, Blackwell, Whidbee &
Peterson
Prepared by: Babu G. Baradwaj, Towson University
And
Lanny R. Martindale, Texas A&M University
Copyright© 2006 John Wiley & Sons, Inc.
1
CHAPTER 5
BOND PRICES AND
INTEREST RATE RISK
The Time Value of Money:
Investing—in financial assets or in real assets—means
giving up consumption until later.
Positive time preference for consumption must be offset
by adequate return. Opportunity cost of deferring
consumption determines minimum rate of return required
on a risk-free investment—
Present sums are theoretically invested at not less than this rate;
Future cash flows are discounted by at least this rate.
Time value of money has nothing primarily to do with
inflation.
Inflation expectations affect discount rate, but
Deferred consumption has opportunity cost by definition.
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Future Value or Compound Value
The future value (FV) of a sum (PV) is
FV = PV (1+i)n
where
i is the periodic interest rate and
n is the number of compounding
periods.
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Present Value
The value now of a sum expected at a future
time is given by
1
PV = FV
n
(1 + i)
With risk present, a premium may be added to the riskfree rate. The higher the discount rate, the lower the
present value.
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Bond Pricing: What is a bond?
A form of loan—a debt security obligating
a borrower to pay a lender principal and interest.
Borrower (issuer) promises contractually to make periodic
payments to lender (investor or bondholder) over given
number of years
At maturity, holder receives principal (or face value or par
value).
Periodically before maturity, holder receives interest
(coupon) payments determined by coupon rate, original
interest rate promised as percentage of par on face of bond.
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What is a bond? Example
Par value
Coupon Rate
Issued
Matures
$1,000
5%
Today
30 years from today
Scheduled
Payments: $50/year interest for 30 years
$1,000 par at end of year 30
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Bond Pricing: bond cash flows
Bondholder thus owns right to a stream of
cash flows:
Ordinary annuity of interest payments and
Future lump sum in return of par value,
Discountable to a present value at any time
while bond is outstanding.
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Bond Pricing: Present Value
The value (price) of a bond is the present
value of the future cash flows promised,
discounted at the market rate of interest
(the required rate of return on this risk
class in today’s market)
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PV of bond cash flows
C1
C2
CN + F N
PB =
+
+
...
1
2
N
(1 + i) (1 + i)
(1 + i)
Where PB = price of bond or present value of promised payments;
Ct = coupon payment in period t, where t = 1, 2, 3,…, n;
Fn = par value (principal amount) due at maturity;
i = market interest rate (discount rate or market yield); and
n = number of periods to maturity.
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Bond pricing: principles
Cash flows are assumed to flow at end of the period and to
be reinvested at i. Bonds typically pay interest
semiannually.
Increasing i decreases price (PB); decreasing i increases
price; thus bond prices and interest rates move inversely.
If market rate equals coupon rate, bond trades at par.
If coupon rate exceeds market rate, the bond trades above
par—at a premium.
If market rate exceeds coupon rate, bond trades below
par—at a discount.
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Zero coupon bonds are “pure discount” instruments.
No periodic coupon payments.
Issued at discount from par.
Single payment of par value at maturity.
PB is simply PV of FV represented by par value,
discounted at market rate.
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Bond yields: risks rewarded
Yield rewards investor for at least 3 risks:
Credit or default risk: chance that issuer may be
unable or unwilling to pay as agreed.
Reinvestment risk: potential effect of variability
of market interest rates on return at which
payments can be reinvested when received.
Price risk: Inverse relationship between bond
prices and interest rates.
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Bond yields: set by market
Discount rate at which bond price equals
discounted PV of expected payments.
Measure of return ideally capturing impact
of
Coupon payments
Income from reinvestment of coupons
Any capital gain or loss
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Common yield measures
Yield to maturity
Realized yield
Expected yield
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Yield to maturity
Investor's expected yield if bond is held to
maturity and all payments are reinvested at same
yield.
Normally determined by iteration—try different
discount rates until PB=present value of future
payments.
The longer until maturity, the less valid the
reinvestment assumption.
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Computing yield to maturity
Investor buys 5% percent coupon
(semiannual payments) bond for $951.90;
bond matures in 3 years. Solve the bond
pricing equation for the interest rate (i) such
that price paid for the bond equals PV of
remaining payments due under the bond.
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Computing yield to maturity, cont.
25
25
1,025
951.90 =
+
+ ...
1
2
6
(1 + (i / 2) ) (1 + (i / 2) )
(1 + (i / 2) )
Solving either by trial and error or with a financial calculator
results in yield to maturity of 3.4% semiannually, or 6.8%
annually.
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Realized yield
Investor’s ex post or “hindsight” actual rate of
return, given the cash flows actually received and
their timing. May differ from YTM due to—
change in the amount or timing of promised payments
(e.g. default).
change in market interest rates affecting
reinvestment rate.
sale of bond before maturity at premium or discount.
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Computing Realized Yield
Investor pays $1,000 for 10-year 8% coupon
bond; sells bond 3 years later for $902.63.
Solve for i such that $1,000 (the original
investment) equals PV of 2 annual payments
of $80 followed by a 3rd annual payment of
$982.63 (the actual cash flows this investor
received).
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Computing realized yield, cont.
80
80
982.63
1000 =
+
+
...
1
2
3
(1 + i) (1 + i)
(1 + i)
Solving either by trial and error or with a financial calculator
results in a realized yield of 4.91%.
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Expected yield
Predicted yield for a given holding period.
Must forecast—
Expected interest rate(s)
Bond price at end of holding period
Plug forecast results into bond pricing
formula
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Bond price volatility (price risk)
Percentage change in price for given change in interest
rates:
Pt  Pt 1
%PB 
 100
Pt 1
where %∆PB = percentage change in price
Pt = new price in period t
P t – 1 = bond’s price one period earlier
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Bond theorems
Bond prices are inversely related to bond yields.
The price volatility of a long-term bond is greater than
that of a short-term bond, holding the coupon rate
constant.
The price volatility of a low-coupon bond is greater
than that of a high-coupon, bond, holding maturity
constant
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Interest Rate Risk and Duration
Price Risk
Reinvestment Risk
Duration as a risk management tool
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Interest rate risk comprises price risk and reinvestment risk.
Price risk is the variability in bond prices caused by their
inverse relationship with interest rates.
Reinvestment risk is the variability in realized yield caused
by changing market rates at which coupons can be
reinvested.
Price risk and reinvestment risk work against each other.
As interest rates fall —
• Bond prices rise but
• Coupons are reinvested at lower return.
As interest rates rise—
• Bond prices fall but
• Coupons are reinvested at higher return.
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Duration - a measure of interest rate risk
Macaulay’s Duration
CFt * t

t
t  1 (1  i)
D  n
CFt

t
t  1 (1  i)
n
where: D = duration of the bond
CFt = interest or principal payment at time t
t = time period in which payment is made
n = number of periods to maturity
i = the yield to maturity (interest rate)
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Duration concepts (all else equal):
Higher coupon rates mean shorter duration and
less price volatility.
Duration equals term to maturity for zero coupon
securities.
Longer maturities mean longer durations and
greater price volatility.
The higher the market rate of interest, the shorter
the duration.
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Duration can be calculated for an entire portfolio
i 1
Portfolio Duration   wi Di
n
where: wi = proportion of bond i in portfolio and
Di = duration of bond i.
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Using Duration to Measure & Manage Interest Rate
Risk
Duration is the holding period for which reinvestment risk just offsets price
risk: the holder obtains the original, promised yield to maturity.
Financial institutions use duration to manage interest rate risk and actually
achieve the desired yield for the desired holding period.
Zero-coupon approach: zero-coupon bonds have no reinvestment risk.
The duration of a “zero” equals its term to maturity.
Buy a “zero” with the desired holding period and lock in the YTM.
Must hold to maturity to evade price risk.
Duration matching: To realize yield to maturity, investors select bonds
with durations matching their desired holding periods.
Maturity matching: Selecting a term to maturity equal to the desired
holding period eliminates price risk, but not reinvestment risk.
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