FMI7e_ch08

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Chapter 8

Bond Valuation and Risk

Financial Markets and Institutions, 7e, Jeff MaduraCopyright ©2006 by South-Western, a division of Thomson Learning. All rights reserved.

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Chapter Outline

Bond valuation process Relationships between coupon rate, required

return, and bond price Explaining bond price movements Sensitivity of bond prices to interest rate

movements Bond investment strategies used by investors Return and risk of international bonds

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Bond Valuation Process

Bonds: Are debt obligations with long-term maturities issued by

government or corporations to obtain long-term funds Are commonly purchased by financial institutions that wish to

invest for long-term periods

The appropriate bond price reflects the present value of the cash flows generated by the bond (i.e., interest payments and repayment of principal):

nk

C

k

C

k

CPV

)1(

Par....

)1()1(bond of

21

4

Computing the Current Price of A BondA 2-year bond has a par value of $1,000 and a coupon rate of 5 percent. The prevailing annualized yield on other bonds with similar characteristics is 7 percent. What is the appropriate market price of the bond?

84.96307.1

050,1

07.1

50

)1(

Par....

)1()1(bond of

2

21

nk

C

k

C

k

CPV

5

Bond Valuation Process (cont’d)

Bond valuation with a present value table Present value interest factors in Exhibit 8A.3 can be

multiplied by coupon payments and the par value to determine the present value of the bond

Impact of the discount rate on bond valuation The appropriate discount rate for valuing any asset is the yield

that could be earned on alternative investments with similar risk and maturity

Investors use higher discount rates to discount the future cash flows of riskier securities

The value of a high-risk security will be lower than the value of a low-risk security

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Computing the Current Price of A Bond Using PVIFsA 2-year bond has a par value of $1,000 and a coupon rate of 5 percent. The prevailing annualized yield on other bonds is 7 percent. What is the appropriate market price of the bond using PVIFs?

80.963$

07.917$73.46$

)8734(.050,1$)9346(.50$

)(050,1$)(50$bond of 2%,71%,7

nknk PVIFPVIFPV

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Impact of the timing of payments on bond valuation Funds received sooner can be reinvested to earn additional

returns A dollar to be received soon has a higher present value than

one to be received later

Valuation of bonds with semiannual payments First, divide the annual coupon by two Second, divide the annual discount rate by two Third, double the number of years

nk

C

k

C

k

CPV

221 )2/1(

Par2/....

)2/1(

2/

)2/1(

2/bond of

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Computing the Current Price of A Bond With Semiannual Coupons

A 2-year bond has a par value of $1,000 and a semiannual coupon rate of 5 percent. The prevailing annualized yield on other bonds with similar characteristics is 7 percent. What is the appropriate market price of the bond?

27.963035.1

025,1

035.1

25

035.1

25

035.1

25

)2/1(

Par2/....

)2/1(

2/

)2/1(

2/bond of

4321

221

nk

C

k

C

k

CPV

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Use the annuity tables for valuation A bond can be valued by separating its payments

into two components:PV of bond = PV of coupon payments + PV of principal

The bond’s coupon payments represent an annuity (an even stream of payments over a given period of time)

The present value can be computed using PVIFAs

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Computing the Current Price of A Bond Using PVIFs and PVIFAsA 30-year bond has a par value of $1,000 and an annual coupon rate of 10 percent. The prevailing annualized yield on other bonds with similar characteristics is 9 percent. What is the appropriate market price of the bond?

1,102.80$$75.40$1,027.40bond of

40.75$)0754(.000,1$

)(000,1$principal of

40.027,1$)274.10(100$

)(payments coupon of

30%,9

30%,9

PV

PVIFPV

PVIFACPV

nk

nk

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Relationship between Coupon Rate, Required Return, and Price If the coupon rate of a bond is below the

investor’s required rate of return, the present value of the bond should be below par value (discount bond)

If the coupon rate equals the required rate of return, the price of the bond should be equal to par value

If the coupon rate of a bond is above the required rate of return, the price of the bond should be above par value

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Relationship between Coupon Rate, Required Return, and Price

$0.00

$200.00

$400.00

$600.00

$800.00

$1,000.00

$1,200.00

$1,400.00

$1,600.00

$1,800.00

0.05 0.08 0.1 0.12 0.15

Required Return

Pres

ent V

alue 5-Year Bond

10-Year Bond

20-Year Bond

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Relationship between Coupon Rate, Required Return, and Price (cont’d) Implications for financial institutions

The impact of interest rate movements depends on how the institution’s asset and liability portfolios are structured

Institutions with interest rate-sensitive liabilities that invest heavily in bonds are exposed to interest rate risk

Many institutions adjust the size of their bond portfolio according to interest rate expectations

When rates are expected to rise, bonds can be sold and the proceeds used to purchase short-term securities

When rates are expected to fall, the bond portfolio can be expanded in order to capitalize on the expectations

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Explaining Bond Price Movements

The price of a bond should reflect the present value of future cash flows based on a required rate of return:

An increase in either the risk-free rate or the general level of the risk premium results in a decrease in bond prices

- - -

),()( RPRfkfP fb

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Explaining Bond Price Movements (cont’d) Factors that affect the risk-free rate

Inflationary expectations Economic growth Money supply Budget deficit

-

),,,( DEFMSECONINFfRf

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Explaining Bond Price Movements (cont’d) Factors that affect the risk-free rate (cont’d)

Impact of inflationary expectations An increase in expected inflation will increase the

required rate of return on bonds Indicators of inflation are closely monitored

Consumer price index Producer price index Oil prices A weak dollar

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Impact of economic growth Strong economic growth places upward pressure on the

required rate of return Signals about future economic conditions affect bond

prices immediately Employment GDP Retail sales Industrial production Consumer confidence

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Impact of money supply growth If there is no simultaneous increase in the demand for

loanable funds, an increase in money supply growth should place downward pressure on interest rates

In high inflation environments, an increased money supply may increase the demand for loanable funds and place upward pressure on interest rates

Impact of budget deficit An increase in the budget deficit places upward

pressure on interest rates

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Explaining Bond Price Movements (cont’d) Factors that affect the credit (default) risk

premium The general level of credit risk on corporate or

municipal bonds can change in response to a change in economic growth:

Strong economic growth tends to improve a firm’s cash flows and reduce the probability that the firm will default on its debt payments

-

)( ECONfRP

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Explaining Bond Price Movements (cont’d) Summary of factors affecting bond prices

Other factors are also changing, making the precise impact of each factor on bond prices uncertain

Impact of bond-specific characteristics Changes in the issuing firm’s capital structure and factors such

as call features can affect individual bond prices

- ?

),,,(

),(

DEFMSECONINFfR

RPRfP

f

fb

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Explaining Bond Price Movements (cont’d) Bond market efficiency

In an efficient market, bond prices should fully reflect all available information

In general bond prices should reflect information that is publicly available

Prices may not reflect information about firms that is known only by managers of the firms

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Sensitivity of Bond Prices to Interest Rate Movements If bonds are not held to maturity, future

prices are most sensitive to changes in the risk-free rate

A measurement of bond price sensitivity can indicate the degree to which the market value of bond holdings may decline in response to an increase in interest rates

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Sensitivity of Bond Prices to Interest Rate Movements (cont’d) Bond price elasticity

Measures the sensitivity of bond prices to changes in the required rate of return:

The price sensitivity is greater for declining interest rates than rising interest rates

Bond price elasticity is always negative

k

Ppe

in change percent

in change percent

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Sensitivity of Bond Prices to Interest Rate Movements (cont’d) Bond price elasticity (cont’d)

Influence of coupon rate on bond price sensitivity The relationship between bond price elasticity and coupon rates

is inverse Zero-coupon bonds have the greatest price sensitivity Bonds yielding only coupon payments are least sensitive Financial institutions may restructure their bond portfolios to

contain higher-coupon bonds when they are concerned about a possible increase in interest rates

Influence of maturity on bond price sensitivity As interest rates decrease, long-term bond prices increase by a

greater degree than short-term bond prices

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Computing Bond Price Elasticity

A 15-year bond has a yield to maturity of 7 percent and a coupon rate of 10 percent. The current price of this bond is $1,273.24. If the yield to maturity increases to 9 percent, the new price of the bond is $1,080.61. What is this bond’s bond price elasticity?

53.0%7

%7%924.273,1$

24.273,1$61.080,1$

in change percent

in change percent

k

Ppe

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Sensitivity of Bond Prices to Interest Rate Movements (cont’d) Duration

Duration measures the life of a bond on a present value basis

The longer the bond’s duration, the greater its sensitivity to interest rates

n

tt

t

n

tt

t

k

C

k

tC

1

1

)1(

)1(

)(

DUR

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Computing the Duration of A BondA bond has two years remaining to maturity, a $1,000 par value, a 9 percent coupon rate, and a 10 percent yield to maturity. What is the duration of this bond?

years92.1

)10.1(

090,1$

)10.1(

90$)10.1(

)2(090,1$

)10.1(

90$

)1(

)1(

)(

DUR

21

21

1

1

n

tt

t

n

tt

t

k

C

k

tC

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Sensitivity of Bond Prices to Interest Rate Movements (cont’d) Duration (cont’d)

Duration of a portfolio Bond portfolio managers commonly immunize their

portfolio from the effects of interest rate movements A bond portfolio’s duration is the weighted average of

bond durations, weighted according to relative market value:

m

jjjp w

1

DURDUR

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Modified duration Duration can be used to estimate the percentage change in a

bond’s price in response to a 1 percentage point change in bond yields:

The estimate of modified duration should be applied such that the bond price moves in the opposite direction from the change in bond yields

The percentage change in a bond’s price in response to a change in yield is:

)1(

DURDUR*

k

yP *-DUR%

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Computing the Modified Duration of A BondA bond has two years remaining to maturity, a $1,000 par value, a 9 percent coupon rate, and a 10 percent yield to maturity. What is the modified duration of this bond? Interpret the modified duration for this bond.

A 1 percent increase in bond yields leads to a 1.75 percent decline in the price of the bond.

75.110.1

92.1

)1(

DURDUR*

k

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Computing the Price Change of A Bond in Response to A Change in Yield

In the previous example, assume that bond yields rise by 0.30%. What is an estimate of the percentage drop in the bond’s price?

%53.

003.075.1

*-DUR%

yP

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Estimation errors from using modified duration If investors rely only on modified duration to estimate

percentage price changes in bonds, they will tend to overestimate price declines and underestimate price increases

To accurately estimate the percentage change in price, bond convexity must also be considered

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Bond convexity Modified duration estimates assume a linear relationship

between bond prices and yields The actual relationship between bond prices and yields is convex

How the estimation errors from modified duration can vary For high-coupon, short-maturity bonds, price change estimates

based on modified duration will be very close to actual price changes

For low-coupon, long-maturity bonds, price change estimates based on modified duration can give large estimation errors

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Bond Investment Strategies Used by Investors Matching strategy

The bond portfolio generates periodic income that can match expected periodic expenses

Involves estimating future cash outflows and developing a bond portfolio that can generate sufficient payments to cover those outflows

Laddered strategy Funds are evenly allocated to bonds in each of

several different maturity classes Achieves diversified maturities and different

sensitivities to interest rate risk

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Bond Investment Strategies Used by Investors (cont’d) Barbell strategy

Funds are allocated to bonds with a short term to maturity and bonds with a long term to maturity

Allocates some funds to achieving relatively high returns and other funds to cover liquidity needs

Interest rate strategy Funds are allocated to capitalize on interest rate

forecasts Requires frequent adjustment in the bond portfolio to

reflect current forecasts

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Return and Risk of International Bonds The value of an international bond is

influenced by:Changes in the risk-free rate of the currency

denominating the bondChanges in the perceived credit risk of the

bondExchange rate risk

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Return and Risk of International Bonds (cont’d) Influence of foreign interest rate movements

An increase in the risk-free rate of the foreign currency results in a lower value for bonds denominated in that currency

Influence of credit risk An increase in risk causes a higher required rate of return on the

bond and lowers the present value of the bond Influence of exchange rate fluctuations

The most attractive foreign bonds offer a high coupon rate and are denominated in a currency that strengthens over the investment horizon

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Return and Risk of International Bonds (cont’d) International bond diversification

Reduction of interest rate risk International diversification of bonds reduces the sensitivity of the

overall bond portfolio to any single country’s interest rate movements

Reduction of credit risk Because economic cycles differ across countries, there is less

chance of a systematic increase in the credit risk of internationally diversified bonds

Reduction of exchange rate risk Financial institutions attempt to reduce their exchange rate risk by

diversifying among foreign securities denominated in various foreign currencies

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