1 Chapter 8 Bond Valuation and Risk Financial Markets and Institutions, 7e, Jeff Madura Copyright ©2006 by South-Western, a division of Thomson Learning. All rights reserved.

2 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

3 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):

4 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?

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

6 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?

7 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

8 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?

9 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

10 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 bond?

11 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

12 Relationship between Coupon Rate, Required Return, and Price

13 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

14 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

15 Explaining Bond Price Movements (cont’d) Factors that affect the risk-free rate  Inflationary expectations  Economic growth  Money supply  Budget deficit

16 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

17 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

18 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

19 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

20 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

21 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

22 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

23 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

24 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

25 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, If the yield to maturity increases to 9 percent, the new price of the bond is $1, What is this bond’s bond price elasticity?

26 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

27 Computing the 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 duration of this bond?

28 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:

29 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 change in yield is:

30 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.

31 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?

32 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

33 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

34 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

35 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

36 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 bond  Changes in the perceived credit risk of the bond  Exchange rate risk

37 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

38 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