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 modified duration, 11.79 years, but considerably higher convexity of 231.2.
a. Suppose the yield to maturity on both bonds increases to 8.5%.
1. What will be the actual percentage capital loss on each bond?
2. What percentage capital loss would be predicted by the duration-with-convexity rule?