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##### Q-11. 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 | Financial Risk Manager Part 1 Quiz - LeetQuiz

Explanation:

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

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

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)