Answer: 13.46%

## Explanation To estimate the percentage price change of a bond given a change in yield, we use the duration-convexity approximation formula: **Percentage Price Change ≈ -Modified Duration × Δy + (1/2) × Convexity × (Δy)²** Where: - Modified Duration = 15.213 - Convexity = 350.32 - Δy = 100 bps = 0.01 (as a decimal) **Step 1: Calculate the duration effect** - Duration effect = -Modified Duration × Δy = -15.213 × 0.01 = -0.15213 or -15.213% **Step 2: Calculate the convexity effect** - Convexity effect = (1/2) × Convexity × (Δy)² = 0.5 × 350.32 × (0.01)² - = 0.5 × 350.32 × 0.0001 = 0.5 × 0.035032 = 0.017516 or 1.7516% **Step 3: Combine the effects** - Total percentage price change = -15.213% + 1.7516% = -13.4614% **Step 4: Interpret the result** Since the yield increases by 100 bps, the bond price declines by approximately 13.46%. **Why other options are incorrect:** - **A. 0.15%**: This is far too small and represents only the convexity effect without considering duration. - **B. 8.21%**: This might be the result if only duration was considered without convexity adjustment, or if the convexity effect was subtracted instead of added. **Key Concept**: When yields increase, bond prices decrease. The duration effect is negative (price decline), while the convexity effect is always positive (mitigating the price decline). The combined effect gives a more accurate estimate than using duration alone.

Author: LeetQuiz .