Answer: 2.59%

## Explanation The expected percentage price change for a bond considering both duration and convexity effects is calculated using the formula: **%ΔP ≈ -Modified Duration × Δy + (1/2) × Convexity × (Δy)²** Where: - Modified Duration = 5 - Convexity = 75 - Δy = -0.0050 (50 basis points decrease, expressed as a decimal) **Step 1: Calculate the duration effect** - Duration effect = -Modified Duration × Δy = -5 × (-0.0050) = 0.0250 or 2.50% **Step 2: Calculate the convexity effect** - Convexity effect = (1/2) × Convexity × (Δy)² = (1/2) × 75 × (-0.0050)² - Convexity effect = 0.5 × 75 × 0.000025 = 0.5 × 0.001875 = 0.0009375 or 0.09375% **Step 3: Total percentage price change** - Total %ΔP = Duration effect + Convexity effect = 2.50% + 0.09375% = 2.59375% **Step 4: Round to the nearest option** - 2.59375% rounds to approximately 2.59% **Why this is correct:** - When yields decrease, bond prices increase - The duration effect alone gives 2.50% increase - Convexity adds a positive adjustment because convexity is positive for bonds (prices increase more when yields fall than they decrease when yields rise) - Option B (2.59%) is closest to the calculated value of 2.59375% **Verification of other options:** - Option A (2.41%): This would be too low, possibly from subtracting convexity instead of adding it - Option C (2.69%): This is too high, possibly from miscalculating the convexity effect

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