Question

A 30-year maturity bond making annual coupon payments with a coupon rate of 12% has a duration of 11 years and convexity of 100. The bond currently sells at a yield to maturity of 8%. The actual price of the bond as a function of yield to maturity is:

Yield to maturity           Price

7%                             $1,620.45

8%                             $1,450.31

9%                             $1,308.21

1. What prices for the bond would be predicted by the duration rule if the yield falls to 7%? What is the percentage error for the duration rule compared to the actual change?
2. What prices for the bond would be predicted by the duration-convexity rule if yield increases to 9%? What is the percentage error for the duration-convexity rule compared to the actual change?

The duration-convexity formula is given by

∆P/P=-Modified Duration×∆y+0.5×Convexity×(∆y)2

Answer 1

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