Answer: -1.71%.

## 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.

Author: LeetQuiz .