Answer: 3.09.

## 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

Author: LeetQuiz .