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