Answer: 11.0

## Explanation Effective duration measures the sensitivity of a bond's price to changes in interest rates. The formula for effective duration is: \[ D = -\frac{\Delta P}{P \Delta r} \] Where: - \(\Delta P\) = Price change for a given rate change - \(P\) = Original price - \(\Delta r\) = Change in interest rates Given: - Original price \(P = 125.00\) million - Price if rates fall by 20 bps: \(127.70\) million - Price if rates rise by 20 bps: \(122.20\) million - Rate change \(\Delta r = 0.002\) (20 bps = 0.20% = 0.002) Calculation: \[ D = \frac{P_{-} - P_{+}}{P \times (2 \times \Delta r)} = \frac{127.70 - 122.20}{125.00 \times (2 \times 0.002)} = \frac{5.5}{125.00 \times 0.004} = \frac{5.5}{0.5} = 11.0 \] **Key points:** - The denominator uses \(2 \times \Delta r\) because we're calculating the duration for a 20 bps change but reporting it for a 100 bps (1%) change - The numerator uses the difference between the price when rates fall and the price when rates rise - The result of 11.0 means the portfolio's value would change by approximately 11% for a 100 bps (1%) change in interest rates **Why other options are incorrect:** - **A (5.5)**: Results from incorrectly switching the prices in the formula - **C (22.0)**: Results from omitting the "2" multiplier in the denominator - **D (44.0)**: Results from incorrectly applying the "2" multiplier to the numerator instead of the denominator

Author: LeetQuiz .