Answer: 7.38

## Explanation To calculate effective duration, we use the formula: \[ \text{Effective Duration} = \frac{V_- - V_+}{2 \times V_0 \times \Delta y} \] Where: - \( V_- \) = value when rates fall (USD 127.723 million) - \( V_+ \) = value when rates rise (USD 122.164 million) - \( V_0 \) = initial value (not given, but we can calculate it) - \( \Delta y \) = change in yield (30 basis points = 0.003) First, we need to find \( V_0 \). Since the portfolio value changes symmetrically around the initial value: \[ V_0 = \frac{V_- + V_+}{2} = \frac{127.723 + 122.164}{2} = \frac{249.887}{2} = 124.9435 \text{ million} \] Now calculate duration: \[ \text{Effective Duration} = \frac{127.723 - 122.164}{2 \times 124.9435 \times 0.003} = \frac{5.559}{2 \times 124.9435 \times 0.003} \] \[ = \frac{5.559}{0.749661} = 7.414 \] The closest answer is **7.38** (Option A).

Author: LeetQuiz Editorial Team