Consider a bond selling at par with modified duration of 10.6 years and convexity of 210. A 2% decrease in yield would cause the price to increase by 21.2% according to the duration rule. What would be the percentage price change according to the duration-with-convexity rule?
A) 21.2%
B) 25.4%
C) 17.0%
D) 10.6%

Question

Quizplus · Accepted Answer

The duration-with-convexity adjustment formula for the percentage price change is: $\Delta P/P \approx -D \cdot \Delta y + \frac{1}{2} \cdot C \cdot (\Delta y)^2$, where $D$ is the modified duration, $C$ is the convexity, and $\Delta y$ is the yield change in decimal form. Substituting the given values: $-10.6 \cdot (-0.02) + \frac{1}{2} \cdot 210 \cdot (0.02)^2 = 0.212 + 0.042 = 0.254$ or 25.4%.

Consider a Bond Selling at Par with Modified Duration of 10.6