Answer: USD 41.17 million

The correct answer is C, which is USD 41.17 million. To determine the market value of the 1.5-year bonds the portfolio manager should purchase, we start by calculating the current market value of the portfolio. Given the 88 million USD face value of zero-coupon bonds maturing in 5 years with a yield of 4%, and assuming continuous compounding, the current value is calculated as: \[ P = 88 \times e^{-0.04 \times 5} = USD 72.05 million \] The portfolio manager aims to reduce the duration of the combined position to 3 years. The duration of the new bond portfolio should be a weighted average of the durations of the 1.5-year and 5-year bonds. Let W be the weight of the 1.5-year bond, then (1 - W) is the weight of the 5-year bond. The equation for the desired duration is: \[ 1.5 \times W + 5 \times (1 - W) = 3 \] Solving for W gives: \[ W = \frac{3 - 5 \times (1 - W)}{1.5} \] \[ W = 0.5714 \] \[ 1 - W = 0.4286 \] Now, we calculate the value of the 1.5-year maturity bond using the weight W: \[ \text{Value of 1.5-year bond} = 0.5714 \times 72.05 = USD 41.17 million \] This is the amount the portfolio manager should purchase to achieve the desired duration on the combined position.

Author: LeetQuiz Editorial Team