Question

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

Year	Forward Rate
1	6$
2	8
3	9

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.)

Price=

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

Yield to maturity= %

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.)

Realized compound yield= %

d. If you forecast that the yield curve in 1 year will be flat at 9.0%, 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.)

Holding period return= %

Answer 1

As per the question

Year	Forward Rate
1	6
2	8
3	9

   

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

  

Price = 50/(1+6%)+50/((1+6%)*(1+8%))+1050/((1+6%)*(1+8%)*(1+9%))

Price = 932.31

.

B. What is the yield to maturity of the coupon bond

Yield to maturity = ((1+6%)*(1+8%)*(1+9%))^(1/3)-1

Yield to maturity = 0.076594

Yield to maturity = 7.66%

.

C . Under the expectations hypothesis, what is the expected realized compound yield of the coupon bond?

realized compound yield = ((50*1.08*1.09+50*1.09+1050)/932.31)^(1/3)-1

realized compound yield = 0.07659

realized compound yield = 7.65%

.

D . If you forecast that the yield curve in 1 year will be flat at 9.0%, what is your forecast for the expected rate of return on the coupon bond for the 1-year holding period

Next year bond price = 50/(1+8%)+1050/(1+8%)^2

Next year bond price = 946.502

Holding period return = (946.502-932.31+50)/932.31

Holding period return = 0.06885

Holding period return = 6.88%