Explanation

To calculate the expected 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 = 6.2
• Convexity = 328
• Δy = 0.0030 (30 basis points = 0.30% = 0.0030)

Step 1: Calculate the duration effect

• Duration effect = -Modified Duration × Δy = -6.2 × 0.0030 = -0.0186 = -1.86%

Step 2: Calculate the convexity effect

• Convexity effect = (1/2) × Convexity × (Δy)² = 0.5 × 328 × (0.0030)²
• (0.0030)² = 0.000009
• Convexity effect = 0.5 × 328 × 0.000009 = 164 × 0.000009 = 0.001476 = 0.1476%

Step 3: Combine both effects

• Total percentage price change = -1.86% + 0.1476% = -1.7124%

Step 4: Compare with options

• -1.7124% is closest to -1.71% (Option B)

Why not the other options?

• Option A (-2.01%): This would be the result if you only used the duration effect (-1.86%) and didn't account for convexity, or if you used a larger yield change.
• Option C (-1.56%): This would be the result if you subtracted the convexity effect instead of adding it, or if you used a smaller convexity value.

Key Concept: Convexity provides a positive adjustment to the price change estimate when yields change. For a given yield increase, convexity reduces the magnitude of the price decline predicted by duration alone, making the bond's price decline less severe than what duration alone would suggest.