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You are managing a portfolio of $1 million. Your target duration is 10 years and you can choose from two bonds: a zero-coupon bond with maturity of seven years and a perpetuity, each currently yielding 5%.a. how much of each bond will you hold in your portfolio?

Question

You are managing a portfolio of $1 million. Your target duration is 10 years and you can choose from two bonds: a zero-coupon bond with maturity of seven years and a perpetuity, each currently yielding 5%.a. how much of each bond will you hold in your portfolio?

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Solution

To solve this problem, we need to understand that the duration of a portfolio is the weighted average of the durations of the individual bonds in the portfolio.

The duration of a zero-coupon bond is equal to its time to maturity, which in this case is 7 years. The duration of a perpetuity is (1 + yield) / yield, which in this case is (1 + 0.05) / 0.05 = 21 years.

Let's denote the proportion of the portfolio invested in the zero-coupon bond as x and the proportion invested in the perpetuity as 1 - x.

We can set up the following equation to solve for x:

10 = x * 7 + (1 - x) * 21

Solving for x gives us x = 0.55. Therefore, you would invest 55% of your portfolio in the zero-coupon bond and the remaining 45% in the perpetuity.

In terms of dollar amounts, this would be 550,000inthezerocouponbondand550,000 in the zero-coupon bond and 450,000 in the perpetuity.

This problem has been solved

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