Answer: 7.38

## Explanation Effective duration measures the sensitivity of a bond's price to changes in interest rates. The formula for effective duration is: \[ \text{Effective Duration} = \frac{V_- - V_+}{2 \times V_0 \times \Delta y} \] Where: - \( V_- \) = portfolio value when rates decrease (USD 127.723 million) - \( V_+ \) = portfolio value when rates increase (USD 122.164 million) - \( V_0 \) = initial portfolio value - \( \Delta y \) = change in yield (30 basis points = 0.0030) First, we need to find the initial portfolio value \( V_0 \). Since the portfolio changes symmetrically with rate changes, we can estimate: \[ V_0 \approx \frac{V_- + V_+}{2} = \frac{127.723 + 122.164}{2} = \frac{249.887}{2} = 124.9435 \text{ million} \] Now calculate effective duration: \[ \text{Effective Duration} = \frac{127.723 - 122.164}{2 \times 124.9435 \times 0.0030} \] \[ = \frac{5.559}{2 \times 124.9435 \times 0.0030} \] \[ = \frac{5.559}{0.749661} \] \[ = 7.414 \] The effective duration is approximately 7.414, which is closest to **7.38** (Option A).

Author: LeetQuiz .