Question

1. You buy a 20-year bond with a coupon rate of 9.0% that has a yield to maturity of 10.1%. (Assume a face value of $1,000 and semiannual coupon payments.) Six months later, the yield to maturity is 11.1%. What is your return over the 6 months?

Rate of return:

2. Consider two 30-year maturity bonds. Bond A has a coupon rate of 4%, while bond B has a coupon rate of 12%. Both bonds pay their coupons semiannually.

a. Compute the prices of the two bonds at each interest rate. (Round the bond price to 2 decimal places.)

b. Suppose Bond A is currently priced to offer a yield to maturity of 8%. Calculate the (percentage) capital gain or loss on the bond if its yield immediately changes to each value of yield to maturity. (Enter your answers as a percent rounded to the nearest whole percent.)

c. Suppose Bond B is currently priced to offer a yield to maturity of 8%. Calculate the (percentage) capital gain or loss on the bond if its yield immediately changes to each value of yield to maturity. (Enter your answers as a percent rounded to the nearest whole percent.)

d. Which bond’s price exhibits greater proportional sensitivity to changes in its yield? In other words, which bond has greater interest rate risk?

e. Which bond pays a high coupon rate has lower “average” or “effective” maturity than a bond that pays a low coupon rate?

Answer 1

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Answer 1)

Value of Bond =

Where r is the discounting rate of a compounding period i.e. 10.1% /2 = 0.0505

And n is the no of Compounding periods 20 years * 2 = 40

Coupon 0.09 /2 = 0.045

=

= 906.27

Value after 6 months

Value of Bond =

Where r is the discounting rate of a compounding period i.e. 11.1% /2 = 0.0555

And n is the no of Compounding periods 20 years * 2 = 39

Coupon 0.09 /2 = 0.045

=

= 833.83

Return = Coupon + Capital Gain / Purchase Price

= 45 + (833.83 - 906.27) / 906.27

= -3.03%