Consider a bond selling at par with modified duration of 10.6 years and convexity of 210.A 2 percent 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%
E) none of these.

Question

Quizplus · Accepted Answer

The duration-with-convexity rule takes into account the curvature of the bond's price-yield relationship, which the duration rule ignores. The percentage price change can be estimated using the following formula:

% Price Change = - Duration x Δy + 0.5 x Convexity x (Δy)^2

where: 
- Duration = 10.6 
- Convexity = 210 
- Δy = 2% = 0.02

% Price Change = -10.6 x 0.02 + 0.5 x 210 x (0.02)^2 = -0.212 + 0.021 = -0.191 
% Price Change = - 19.1%

Therefore, the percentage price change according to the duration-with-convexity rule is approximately 25.4% (21.2% + (-19.1%)). The best choice is B.

Consider a Bond Selling at Par with Modified Duration of 10.6