Explanation

Modified duration measures the percentage change in bond price for a 100 basis point (1%) change in yield. The formula for approximate modified duration is:

$\text{Modified Duration} \approx \frac{V_- - V_+}{2 \times V_0 \times \Delta y}$

Where:

• $V_-$ = bond price when yield decreases
• $V_+$ = bond price when yield increases
• $V_0$ = initial bond price
• $\Delta y$ = change in yield (in decimal form)

Given:

• $V_0 = 92.733$
• $V_- = 94.474$ (for 60 bps decrease, or -0.0060)
• $V_+ = 91.041$ (for 60 bps increase, or +0.0060)
• $\Delta y = 0.0060$ (60 basis points)

Calculation:

$\text{Modified Duration} \approx \frac{94.474 - 91.041}{2 \times 92.733 \times 0.0060}$

$= \frac{3.433}{2 \times 92.733 \times 0.0060}$

$= \frac{3.433}{1.112796}$

$= 3.084$

This rounds to approximately 3.09.

Why this is correct:

1. Modified duration is calculated using the price change for a given yield change
2. The formula uses the average of price changes for both yield increases and decreases
3. 60 bps = 0.0060 in decimal form
4. The result of 3.084 is closest to 3.09 (Option B)

Why other options are incorrect:

• Option A (1.85): This might result from using only one-sided price change or incorrect decimal conversion
• Option C (6.17): This is approximately double the correct answer, which might result from forgetting to divide by 2 in the formula or using 1% instead of 60 bps