You are managing a portfolio of $2.7 million. Your target duration is 15 years,

Question

You are managing a portfolio of $2.7 million. Your target duration is 15 years, and you can choose from two bonds: a zero-coupon bond with maturity 10 years, and a perpetuity, each currently yielding 5%.

How much of each bond will you hold in your portfolio? (Do not round intermediate calculations. Round your answers to 2 decimal places.)

b.

How will these fractions change next year if target duration is now fourteen years? (Do not round intermediate calculations. Round your answers to 2 decimal places.)

How much of each bond will you hold in your portfolio? (Do not round intermediate calculations. Round your answers to 2 decimal places.)

b.

How will these fractions change next year if target duration is now fourteen years? (Do not round intermediate calculations. Round your answers to 2 decimal places.)

Explanation / Answer

Duration of a zero coupon bond = time to maturity = 10

Duration of a perpetuity = (1 + yield) / yield = (1.05/0.05) = 21

Weight of zero coupon bond in portfolio = x

Weight of perpetuity in portfolio = 1-x

1. Total duration of portfolio = weighted average of the durations of the bonds

15 = 10*x + (21 *(1-x)) = 21 - 11x

x = 6/11

Amount invested in zero coupon bond = (6/11) * 2.7 million = 1.47million

Amount invested in perpetuity = (2.7 - 1.47)million = 1.23million

2.

Total duration of portfolio = weighted average of the durations of the bonds

14 = 10*x + (21 *(1-x)) = 21 - 11x

x = 7/11

Amount invested in zero coupon bond = (7/11) * 2.7 million = 1.72million

Amount invested in perpetuity = (2.7 - 1.72)million = 0.98million

Hope this helps, regards

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