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Financial Risk Manager Part 1

Financial Risk Manager Part 1

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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.

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Explanation:

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×e−0.04×5=USD72.05millionP = 88 \times e^{-0.04 \times 5} = USD 72.05 millionP=88×e−0.04×5=USD72.05million 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×W+5×(1−W)1.5 \times W + 5 \times (1 - W)1.5×W+5×(1−W), where WWW is the weight of the 1.5-year maturity bond and (1−W)(1 - W)(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×W+5×(1−W)=31.5 \times W + 5 \times (1 - W) = 31.5×W+5×(1−W)=3 which gives W=0.5714W = 0.5714W=0.5714 and (1−W)=0.4286(1 - W) = 0.4286(1−W)=0.4286. Therefore, the value of the 1.5-year maturity bond = 0.5714×72.05=USD41.17million0.5714 \times 72.05 = USD 41.17 million0.5714×72.05=USD41.17million.

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