Question

1. a) Calculate the percentage change in price on a 10 percent coupon (annual coupons), $1,000 face value 3-year bond if the discount rate rises from 5 percent to 10 percent. Calculate the percentage change in price on a 3-year zero coupon bond, face value $1,000, for the same interest rate change. Based on your answer, which of these bonds has a higher duration.

b) Suppose the term structure of interest rates for U.S. government bonds is “flat” meaning that short (1-year maturity) and long (20-year maturity) term rates have the same expected actual return, say 3 percent. (This was the case a few years ago.) What would that mean about the market’s expectations for interest rate changes?

Answer 1

1
=(100/0.1*(1-1/1.1^3)+1000/1.1^3)/(100/0.05*(1-1/1.05^3)+1000/1.05^3)-1=-11.9844136095799%

2
=(1000/1.1^3)/(1000/1.05^3)-1=-13.0259203606311%

3.
Zero coupon bond as it has higher change

4.
Market expects the rates would not change at stay at the current level