Question

1. A 12.75-year maturity zero-coupon bond selling at a yield to maturity of 8% (effective annual yield) has convexity of 150.3 and modified duration of 11.81 years. A 30-year maturity 6% coupon bond making annual coupon payments also selling at a yield to maturity of 8% has nearly identical duration—11.79 years—but considerably higher convexity of 231.2.

1. Suppose the yield to maturity on both bonds increases to 9%. What will be the actual percentage capital loss on each bond? What percentage capital loss would be predicted by the duration-with-convexity rule? Actual: -11.09%, -10.72%; duration with convexity: -11.06%, -10.63%)
2. Repeat part (a), but this time assume the yield to maturity decreases to 7%. (Actual: 12.59%, 13.04%; duration with convexity: 12.56%, 12.95%)
3. Compare the performance of the two bonds in the two scenarios, one involving an increase in rates, the other a decrease. Based on the comparative investment performance, explain the attraction of convexity.

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Answer 1

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