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Answer: C
**Modified Duration and Convexity for Discrete Compounding:** For bonds with discrete compounding (annual coupon payments in this case), we use: - **Modified Duration** for the first-order approximation - **Modified Convexity** for the second-order adjustment **The formula used:** ``` ΔP ≈ -Modified Duration × P × Δy + ½ × Modified Convexity × P × (Δy)² ``` **Given values:** - Modified Duration = 3.8653 - Modified Convexity = 21.8945 - Bond Price (P) = 94.3138 - Yield change (Δy) = 0.005 (50 basis points) **Calculation:** ``` First term: -3.8653 × 94.3138 × 0.005 = -1.823 Second term: ½ × 21.8945 × 94.3138 × (0.005)² = 0.258 Total ΔP ≈ -1.823 + 0.258 = -1.565 ``` **Key Points:** - Modified duration/convexity are appropriate for discrete compounding - The convexity adjustment improves the accuracy of the duration-only estimate - Without convexity, the estimate would be more negative (-1.823 vs -1.565)
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C is correct. Under discrete compounding frequency (in this case, the compounding frequency is annual since we have assumed annual coupon payment), modified duration and modified convexity should be used to perform analysis. Based on the formula, we have:
ΔP ≈ –Mod. D × P × Δy + ½ Mod. C × P × (Δy)²
= –3.8653 × 94.3138 × 0.005 + ½ × 21.8945 × 94.3138 × 0.005²
A
A
B
B
C
C
D
D
E
E
F
F
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