You are managing a portfolio of $2.3 million. Your target duration is 10 years,

Question

You are managing a portfolio of $2.3 million. Your target duration is 10 years, and you can choose from two bonds: a zero-coupon bond with maturity 8 years, and a perpetuity, each currently yielding 8%.

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 $2.3 million. Your target duration is 10 years, and you can choose from two bonds: a zero-coupon bond with maturity 8 years, and a perpetuity, each currently yielding 8%.

Explanation / Answer

Answer:a. Let x=wt of zero coupon bonds and 1-x = wt of perpetuities. Then of duration of perpetuity is given by

(1+y)/y =1.08/0.08=13.5 years

10=2x + (1-x)13.5=0.3043

Thus $2.3 M(0.3043)=0.69989M in zeros.

and $ 2.3M(0.6957)=$1.60011 M in perpetuities.

b. 9=x+(1-x)13.5=0.36

Thus $2.3 M(0.36)=0.828 M in zeros.

and $ 2.3 M(0.64)=$1.472 M in perpetuities.

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