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.