Answer: USD 41.17 million

To hedge against the expected increase in interest rates, the portfolio manager needs to reduce the duration of their bond portfolio. The duration measures the sensitivity of a bond's price to changes in interest rates, and a lower duration indicates lower sensitivity. The current market value of the portfolio is calculated using the formula for the present value of a zero-coupon bond with continuous compounding: \[ P = \text{Face Value} \times e^{-\text{Yield} \times \text{Time to Maturity}} \] For the 5-year zero-coupon bond, this calculation is: \[ P = 88 \text{ million} \times e^{-0.04 \times 5} = 88 \text{ million} \times e^{-0.2} = 72.05 \text{ million USD} \] The desired duration of the new portfolio is 3 years. Let \( W \) be the weight of the 1.5-year maturity bond in the new portfolio, and \( (1 - W) \) be the weight of the remaining 5-year maturity bond. The weighted duration can be expressed as: \[ 1.5 \times W + 5 \times (1 - W) = 3 \] Solving for \( W \) gives: \[ 1.5W + 5 - 5W = 3 \] \[ -3.5W = -2 \] \[ W = \frac{2}{3.5} = 0.5714 \] This means that approximately 57.14% of the portfolio should be invested in the 1.5-year bonds, and the remaining 42.86% in the 5-year bonds. The value of the 1.5-year maturity bond to be purchased is then: \[ \text{Value of 1.5-year bond} = W \times P = 0.5714 \times 72.05 \text{ million USD} = 41.17 \text{ million USD} \] Thus, the portfolio manager should purchase USD 41.17 million of the 1.5-year bonds to achieve the desired duration of 3 years on the combined position. The correct answer is C. USD 41.17 million.

Author: LeetQuiz Editorial Team