Consider a bond selling at par with modified duration of 12 years and convexity of 265. A 1% decrease in yield would cause the price to increase by 12%, 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) 13.3%

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 (expressed as a decimal). For a 1% decrease in yield ($\Delta y = -0.01$), the calculation is: $-12 \cdot (-0.01) + \frac{1}{2} \cdot 265 \cdot (-0.01)^2 = 0.12 + 0.01325 = 0.13325$, or 13.325%, which rounds to 13.3%.

Consider a Bond Selling at Par with Modified Duration of 12