Explanation

To calculate the expected percentage price change of a bond when yields change, we use the duration-convexity approximation formula:

Formula: $\Delta P/P \approx -MD \times \Delta y + \frac{1}{2} \times C \times (\Delta y)^2$

Where:

• $MD$ = Modified Duration = 6.2
• $C$ = Convexity = 328
• $\Delta y$ = Change in yield = 30 bps = 0.0030 (as a decimal)

Step 1: Calculate the duration effect $-MD \times \Delta y = -6.2 \times 0.0030 = -0.0186$ This equals -1.86%

Step 2: Calculate the convexity effect $\frac{1}{2} \times C \times (\Delta y)^2 = 0.5 \times 328 \times (0.0030)^2$ $= 0.5 \times 328 \times 0.000009$ $= 0.5 \times 0.002952$ $= 0.001476$ This equals +0.1476%

Step 3: Combine both effects $\Delta P/P \approx -1.86\% + 0.1476\% = -1.7124\%$

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 only the duration effect was considered (-1.86%), but it's too negative.
• Option C (-1.56%): This would be the result if the convexity effect was subtracted instead of added, or if there was a calculation error.

Key Concept: When yields increase, bond prices decrease. The duration effect (negative) is partially offset by the convexity effect (positive), making the actual price decline less severe than what duration alone would predict.