Problem
A 13.55-year maturity zero-coupon bond selling at a yield to maturity of 8% (effective annual yield) has convexity of 169.0 and modified duration of 12.55 years. A 40-year maturity 6% coupon bond making annual coupon payments also selling at a yield to maturity of 8% has nearly identical modified duration-12.30 years-but considerably higher convexity of 272.9.
Task
Suppose the yield to maturity on both bonds increases to 9%.
a) What will be the actual percentage capital loss on each bond?
b) What percentage capital loss would be predicted by the duration-with-convexity rule?