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

Rashad Morley · Accepted Answer

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

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