
Explanation:
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:
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:
Solving for W gives:
Now, we calculate the value of the 1.5-year maturity bond using the weight W:
This is the amount the portfolio manager should purchase to achieve the desired duration on the combined position.
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To effectively adjust the portfolio's duration to 3 years, considering an anticipated rise in interest rates, the portfolio manager plans to sell a portion of their 5-year zero-coupon bond holdings and reinvest the proceeds into 1.5-year zero-coupon bonds. Currently, the portfolio manager holds USD 88 million face value of 5-year zero-coupon bonds, yielding 4% with continuous compounding. The 1.5-year bonds yield 3% under similar continuous compounding assumptions. What market value of 1.5-year zero-coupon bonds should the portfolio manager purchase to achieve the desired duration adjustment?
A
USD 31.00 million
B
USD 37.72 million
C
USD 41.17 million
D
USD 50.28 million