Question

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. What would that mean about the market’s expectations for interest rate changes?

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.

Answer 1

1.

Market expects no change in interest rates

2.

=(10%*1000/10%*(1-1/1.1^3)+1000/1.1^3)/(10%*1000/5%*(1-1/1.05^3)+1000/1.05^3)-1=-11.984%

3.

=(0%*1000/10%*(1-1/1.1^3)+1000/1.1^3)/(0%*1000/5%*(1-1/1.05^3)+1000/1.05^3)-1=--13.026%

4.

Zero coupon bond as it has higher % change