Answer: 7.3.

## Explanation Effective duration measures the sensitivity of a bond's price to changes in interest rates. The formula for effective duration is: \[ \text{Effective Duration} = \frac{P_- - P_+}{2 \times P_0 \times \Delta y} \] Where: - \( P_- \) = Price when yield decreases - \( P_+ \) = Price when yield increases - \( P_0 \) = Current price - \( \Delta y \) = Change in yield (in decimal form) Given: - \( P_- = 132.41 \) (price when yield decreases by 25 bps) - \( P_+ = 127.66 \) (price when yield increases by 25 bps) - \( P_0 = 130.00 \) (current price) - \( \Delta y = 0.0025 \) (25 basis points = 0.25% = 0.0025) Plugging in the values: \[ \text{Effective Duration} = \frac{132.41 - 127.66}{2 \times 130.00 \times 0.0025} \] \[ = \frac{4.75}{2 \times 130.00 \times 0.0025} \] \[ = \frac{4.75}{0.65} \] \[ = 7.3077 \] Rounded to one decimal place, the effective duration is approximately 7.3. **Why this is correct:** - The calculation follows the standard formula for effective duration - 25 basis points = 0.25% = 0.0025 in decimal form - The result matches option A (7.3) **Common mistakes to avoid:** - Forgetting to convert basis points to decimal (25 bps = 0.0025, not 0.25) - Using the wrong denominator (should be \( 2 \times P_0 \times \Delta y \)) - Confusing effective duration with modified duration

Author: LeetQuiz .