Answer: -2.20%

## Explanation To calculate the percentage change in bond price given duration and convexity, we use the following formula: **Percentage Price Change ≈ -Duration × Δy + (1/2) × Convexity × (Δy)^2** Where: - Duration = 4.50 - Convexity = 39.20 - Δy = 0.5% = 0.005 (in decimal form) **Step 1: Calculate the duration effect** - Duration effect = -Duration × Δy = -4.50 × 0.005 = -0.0225 = -2.25% **Step 2: Calculate the convexity adjustment** - Convexity adjustment = (1/2) × Convexity × (Δy)^2 = (1/2) × 39.20 × (0.005)^2 - (0.005)^2 = 0.000025 - Convexity adjustment = 0.5 × 39.20 × 0.000025 = 0.5 × 0.00098 = 0.00049 = 0.049% **Step 3: Combine both effects** - Total price change = Duration effect + Convexity adjustment = -2.25% + 0.049% = -2.201% **Step 4: Round to nearest option** - -2.201% is closest to -2.20% **Key Points:** 1. Duration measures the linear relationship between bond prices and interest rates (negative relationship) 2. Convexity accounts for the curvature in the price-yield relationship 3. For interest rate increases, duration effect is negative, but convexity adjustment is positive (mitigates the price decline) 4. The formula uses Δy in decimal form (0.5% = 0.005) 5. The convexity adjustment is divided by 2 in the formula The correct answer is **C. -2.20%**

Author: LeetQuiz .