You are managing a portfolio of $2.9 million. Your target duration is 14 years,

Question

You are managing a portfolio of $2.9 million. Your target duration is 14 years, and you can choose from two bonds: a zero-coupon bond with maturity 5 years, and a perpetuity, each currently yielding 5%.

a. 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 thirteen years? (Do not round intermediate calculations. Round your answers to 2 decimal places.)

Explanation / Answer

a) Duration of perpetuity = (1 + i) / i = (1 + 5%) / 5% = 21 years

Assume y - weight of zero coupon bond and 1 - y is the weight of perpetuity

=> 14 = y x 5 + (1 - y) x 21

=> y = 43.75% is the weight of zero coupon bond and 1 - y = 56.25% is the weight of perpetuity

b) A year later

13 = y x 4 + (1 - y) x 21

=> y = 47.06% and 1 - y = 52.94%

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