Thị trường tài chính và các định chế tài chính_ Chapter 08

Chapter Outline Bond valuation process  Relationships between coupon rate, required return, and bond price  Explaining bond price movements  Sensitivity of bond prices to interest r

Chapter 8

Bond Valuation and Risk

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

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):

C C

C

PV of bond  Par

Computing the Current Price of

A Bond

A 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

?

84 963

07 1

050 ,

1 07

1 50

) 1

(

Par

) 1

( )

1 (

bond of

2

2 1

C k

C PV

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

Computing the Current Price of

A Bond Using PVIFs

A 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

Bond Valuation Process (cont’d)

 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

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

?

035 1

025 , 1 035

1

25 035

1

25 035

1 25

) 2 / 1

(

Par 2

/

) 2 / 1

(

2 / )

2 / 1

(

2 / bond

of

4 3

2 1

2 2

C k

C PV

Bond Valuation Process (cont’d)

 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

Computing the Current Price of

A Bond Using PVIFs and PVIFAs

A 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

of

40 75

$ )

0754 (.

000 ,

1

$

) (

000 ,

1

$ principal of

40 027 ,

1

$ )

274

10 ( 100

$

) (

payments coupon

of

30

%, 9

30

%, 9

PVIFA C

PV

n k

n k

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

Relationship between Coupon

Rate, Required Return, and Price

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

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

-

-

) ,

( )

( k f R RP f

Pb     f 



Explaining Bond Price Movements (cont’d)

 Factors that affect the risk-free rate

) ,

, ,

f

Rf

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

Explaining Bond Price Movements (cont’d)

 Factors that affect the risk-free rate (cont’d)

 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

Explaining Bond Price Movements (cont’d)

 Factors that affect the risk-free rate (cont’d)

 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

Explaining Bond Price Movements (cont’d)

 Factors that affect the credit (default) risk

premium

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

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

?

) ,

, ,

(

) ,

(

DEF MS

ECON INF

f R

RP R

f P

f

f b

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

Sensitivity of Bond Prices to

Interest Rate Movements

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

can indicate the degree to which the

market value of bond holdings may decline

in response to an increase in interest rates

Sensitivity of Bond Prices to

Interest Rate Movements (cont’d)

in the required rate of return:

rates than rising interest rates

k

P

pe

in change percent

in change percent



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

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

?

24 273 ,

1

$

24 273 ,

1

$ 61 080 ,

1

$

in change percent

in change percent





k P

pe

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

t C

1

1

) 1

(

) 1

(

) ( DUR

Computing the Duration of A

)2(090,1

$)

10.1(

90

$

)1

(

)1

(

)(DUR

2 1

1 1

Sensitivity of Bond Prices to

Interest Rate Movements (cont’d)







m j

j j

1

DUR DUR

Sensitivity of Bond Prices to

Interest Rate Movements (cont’d)

 Duration (cont’d)

 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

) 1

(

DUR DUR*

k





Computing the Modified Duration

of A Bond

A 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*

Computing the Price Change of

003

075.1

*-DUR

Sensitivity of Bond Prices to

Interest Rate Movements (cont’d)

 Duration (cont’d)

 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

Sensitivity of Bond Prices to

Interest Rate Movements (cont’d)

 Duration (cont’d)

 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

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

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

Return and Risk of International

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

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