You are managing a portfolio of $1.2 million. Your target duration is 10 years,

Question

You are managing a portfolio of $1.2 million. Your target duration is 10 years, and you can choose from two bonds: a zero-coupon bond with maturity 7 years, and a perpetuity, each currently yielding 10%. a. How much of each bond will you hold in your portfolio? (Do not round intermediate calculations. Round your answers to 2 decimal places.) Zero-coupon bond % Perpetuity bond % b. 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.) Zero-coupon bond % Perpetuity bond %

Explanation / Answer

a)

Let x be in 7 year zero coupon bond and 1.2-x in perpetuity

Duration of zero coupon bond=maturity=7 years

Durtion of a perpetuity=1/y+1=1/0.1+1=11 years

So, Total duration of portfolio=(x*7+(1.2-x)*11)/1.2

This should equal 10

So, 10=(x*7+(1.2-x)*11)/1.2

12=-4x+13.2

x=0.3 million

7 year zero coupon bond=0.3 million

perpetuity=1.2-0.3=0.9 million

b)

9=(x*7+(1.2-x)*11)/1.2

=>2.4-4x=0

=>x=0.6

So,

7 year zero coupon bond=0.6 million

perpetuity=1.2-0.6=0.6 million

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