Question

15.7

Prices of zero-coupon bonds reveal the following pattern of forward rates:

Forward Rate For years 1-3, respectively.  5,6, and 7%.

In addition to the zero-coupon bond, investors also may purchase a 3-year bond making annual payments of $50 with par value $1,000.

a. What is the price of the coupon bond? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

b. What is the yield to maturity of the coupon bond? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

c. Under the expectations hypothesis, what is the expected realized compound yield of the coupon bond? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

d. If you forecast that the yield curve in 1 year will be flat at 6.0%, what is your forecast for the expected rate of return on the coupon bond for the 1-year holding period? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Answer 1

Forward rates: Year 1 rate = 5%; Year 2 rate = 6%; Year 3 rate = 7%

a). Price of the bond = sum of PV of all future cash flows

= 50/(1+5%) + 50/(1+5%)*(1+6%) + (1,000+50)/(1+5%)*(1+6%)*(1+7%) = 974.22

b). PV = 974.22; FV = 1,000; PMT = 50; N = 3, solve for rate. YTM = 5.96%

c). As per the expectations hypothesis, the forward rates are ubiased estimates of the future interest rates.

Then, FV of the total return of the bond = sum of FV of all cash flows

= 50*(1+6%)*(1+7%) + 50*(1+7%) + (1,000+50) = 1,160.21

The annual return of the bond will be

Price*(1+r)^3 = 1,160.21

r = [(1,160.21/974.22)^(1/3)] -1 = 6.00%

d). If the yield curve is flat at 6% for 1 year then next year, the price of the bond will be

50/(1+6%) + (1,000+50)/(1+6%)^2 = 981.67

Gain = selling price - purchase price = 981.67 - 974.22 = 7.44

Holding period return = Total gain/price = (7.44 + 50)/974.22 = 5.90%