Question

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

Year	Forward Rate
1	6%
2	7
3	8

   

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. Omit the "$" sign in your response.)

  

Price

$

  

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

  

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. Omit the "%" sign in your response.)

  

Realized compound yield

%

   

d.	If you forecast that the yield curve in 1 year will be flat at 8.0%, 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. Omit the "%" sign in your response.)

  

Holding period return

%

Answer 1

a. The price of the coupon bond as of now is: $793.83

Price = Maturity Value/ (1 + return) ^ time period

=$1000/ (1+0.06)^3, where 0.06 i.e. 6% as per the $60 annual payments for 3 years.

=$793.83

b. Yield to Maturity of the Coupon Bond: 8%

Yield to Maturity = (Face Value / Current Price of Bond) ^ (1 / Years to Maturity) - 1

= (1000/793.83) ^ (1/3) - 1

= 0.08 i.e. 8%

c. Under the expectations hypothesis, the expected realized compound rate of the coupon bond is: 14.56%

For Compound Realized Return, we need to indentify the future value of the bond.

Interest received for year 1: $60

Interest received for year 2: 60 (1+ 7%) = $64.2

Interest received for year 3: 64.2 (1+ 8%) = $69.34

Total Interest: $193.54

Face Value of the Bond: $1000

Total Future Value of the amounts to be received: $1193.54

To calculate the Compound Realized Return:

r = (Future Value / Current Value) ^ (1/3) - 1

=(1193.54/793.83)^(1/3)-1

=14.56%

d. For a 1 year holding period, the yield on the bond is the expected rate of return since it includes coupon payments and interest. Hence, 8%.