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Answer: USD 41.17 million
C is correct. In order to find the proper amount, we first need to calculate the current market value of the portfolio (P). Assuming continuous compounding, the current value of the portfolio is: \[ P = 88 \times e^{-0.04 \times 5} = USD 72.05 million \] The desired portfolio duration (after the sale of the 5-year bond and purchase of the 1.5-year bond) can be expressed as \( 1.5 \times W + 5 \times (1 - W) \), where \( W \) is the weight of the 1.5-year maturity bond and \( (1 - W) \) is the weight of the 5-year maturity zero-coupon bond. Thus, the weighted duration of the new bond portfolio should be equal to 3 years: \[ 1.5 \times W + 5 \times (1 - W) = 3 \] which gives \( W = 0.5714 \) and \( (1 - W) = 0.4286 \). Therefore, the value of the 1.5-year maturity bond = \( 0.5714 \times 72.05 = USD 41.17 million \).
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An investment manager currently holds zero-coupon bonds with a nominal value of USD 88 million, a 5-year maturity, and a 4% yield. Anticipating an increase in interest rates, the manager plans to sell a part of these 5-year bonds and reinvest the resulting capital into zero-coupon bonds maturing in 1.5 years with a 3% yield. Using continuous compounding, determine the amount that should be reinvested in the 1.5-year bonds to ensure the overall portfolio achieves a duration of 3 years.
A
USD 30.88 million
B
USD37.72 million
C
USD 41.17 million
D
USD 50.28 million
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