You are managing a portfolio of $2.4 million. Your target duration is 10 years,

Question

You are managing a portfolio of $2.4 million. Your target duration is 10 years, and you can choose from two bonds: a zero-coupon bond with maturity 5 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.)

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

You are managing a portfolio of $2.4 million. Your target duration is 10 years, and you can choose from two bonds: a zero-coupon bond with maturity 5 years, and a perpetuity, each currently yielding 5%.

Explanation / Answer

(a) Zero coupan bond .69%

Perpetuity bond .31%

(b) Zero coupan bond .71

Peepetuity bond .29

Explanation

The weighed averages of durations of bonds should be equal to desired duration

Duration of a zero coupon bond =remaining maturity of bonds

Duration of a Perpetuity bond = 1+current yield/yields

(a) Duration of Zero coupon bond =5

  Duration of Perpetuity bond =1+.05/.05

=21

lets take weight of Duration of Zero coupon bond =W1

weight of Duration of Perpetuity bond =1-W1

10=W1*5+(1-W1)21

(b) 9=W1*4+(1-W1)21

by solving these equation above answers will be calculated

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