Question

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

Year	Forward Rate
1	6	%
2	7
3	9

In addition to the zero-coupon bond, investors also may purchase a 3-year bond making annual payments of $60 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 7.0%, 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

Price of the coupon bond = Present value of the future cashflows

= 60 / 1.06 + 60 / 1.07*1.06 + 1060 / 1.09*1.07*1.06

= 56.6038 + 52.9007 + 857.412

= $966.917

ytm is given by the below approximate formula,

ytm = [C + ( F - P) / N ] / ( F + P ) / 2

C = Coupon

F = Face value

P = Price

N = No of years till maturity

ytm = [60 +(1000 - 966.917 )/3] / ( 1000 + 966.917 ) /2

= (60 + 11.0277 ) / 983.458

= 7.22%

Under the expectations hypothesis expected realized compound yield =(1.06 *1.07*1.09) ^1/3

= 1.07326 - 1

=7.326%

Price after 1 year = 60 /1.07 + 1060/1.07^2

= 56.0748 + 925.8451

= 981.9198

Holding period return =(Ending price - beginning price + coupon ) / beginning price

=(981.9198 - 966.917 + 60)/ 966.917

= 75.0028 / 966.917

=7.76%