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:
- Duration measures the linear relationship between bond prices and interest rates (negative relationship)
- Convexity accounts for the curvature in the price-yield relationship
- For interest rate increases, duration effect is negative, but convexity adjustment is positive (mitigates the price decline)
- The formula uses Δy in decimal form (0.5% = 0.005)
- The convexity adjustment is divided by 2 in the formula
The correct answer is C. -2.20%
