Explanation

To calculate the percentage change in bond price using both duration and convexity, we use the following formula:

Percentage price change ≈ -Modified Duration × Δy + (1/2) × Convexity × (Δy)^2

Where:

• Modified Duration = 8
• Convexity = 150
• Δy = -1.40% = -0.0140 (since yield decreases by 140 bps)

Step 1: Calculate the duration effect Duration effect = -Modified Duration × Δy = -8 × (-0.0140) = 0.1120 = 11.20%

Step 2: Calculate the convexity effect Convexity effect = (1/2) × Convexity × (Δy)^2 = (1/2) × 150 × (-0.0140)^2 = (1/2) × 150 × 0.000196 = 0.5 × 150 × 0.000196 = 75 × 0.000196 = 0.0147 = 1.47%

Step 3: Total price change Total price change = Duration effect + Convexity effect = 11.20% + 1.47% = 12.67%

Step 4: Compare to options 12.67% is closest to 12.7% (Option B).

Why not the other options?

• 9.7% (Option A): This would be the result if you only used duration (11.20%) but forgot to convert bps to decimal properly or made a sign error.
• 14.1% (Option C): This would be the result if you added the convexity effect incorrectly (11.20% + 2.94% = 14.14%) by forgetting to multiply convexity by 1/2.

Key Concepts:

1. Modified duration measures the sensitivity of bond price to yield changes.
2. Convexity accounts for the curvature in the price-yield relationship.
3. For yield decreases, both duration and convexity effects are positive (price increases).
4. The convexity adjustment is always positive regardless of the direction of yield change.
5. 100 basis points = 1% = 0.01 in decimal form.