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 five years and a perpetuity, each currently yielding 5%. (lo 11-4) a. how much of (i) the zero-coupon bond and (ii) the perpetuity will you hold in your portfolio? b. how will these fractions change next year if target duration is now nine years?

Answer 1

To calculate the proportion of the zero-coupon bond and the perpetuity in your portfolio, you need to calculate the duration of each bond. The proportion of the zero-coupon bond is given by the formula: proportion = target duration / duration of the bond. The proportion of the perpetuity is calculated in the same way.

Step-by-step explanation:

To calculate the proportion of the zero-coupon bond and the perpetuity in your portfolio, we first need to calculate the duration of each bond. The duration of a zero-coupon bond is its time to maturity, which in this case is 5 years. The duration of a perpetuity is calculated using the formula: duration = (1 + yield) / yield.

For the zero-coupon bond, the duration is 5 years. For the perpetuity with a yield of 5%, the duration is (1 + 0.05) / 0.05 = 21 years.

Now we can calculate the proportion of each bond in your portfolio. The proportion of the zero-coupon bond is given by the formula: proportion = target duration / duration of the bond. So, for the zero-coupon bond, the proportion is 10 years / 5 years = 2. For the perpetuity, the proportion is 10 years / 21 years ≈ 0.476.