Consider a bond selling at par with modified duration of 22 years and convexity of 415. A 2% decrease in yield would cause the price to increase by 44% 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) 52.3%

Question

Quizplus · Accepted Answer

The duration-with-convexity rule for estimating the percentage price change of a bond is given by the formula: $\Delta P/P \approx -D \cdot \Delta y + \frac{1}{2} \cdot C \cdot (\Delta y)^2$, where $\Delta P/P$ is the percentage change in price, $D$ is the modified duration, $\Delta y$ is the change in yield (in decimal form), and $C$ is the convexity. Given a 2% (or 0.02) decrease in yield, the formula becomes: $\Delta P/P \approx -22 \cdot (-0.02) + \frac{1}{2} \cdot 415 \cdot (0.02)^2 = 0.44 + 0.083 = 0.523$ or 52.3%.

Consider a Bond Selling at Par with Modified Duration of 22