Question

You are managing a portfolio of $1.0 million. Your target duration is 12 years, and you can choose from two bonds: a zero-coupon bond with maturity five years, and a perpetuity, each currently yielding 5%.

a. How much of (i) the zero-coupon bond and (ii) the perpetuity 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 eleven years? (Do not round intermediate calculations. Round your answers to 2 decimal places.)

Answer 1

a.

Duration of Zero Coupon Bond = 5 years

Duration of Perpetuity = 1.05/0.05 = 21 years

Let w be weight in Zero Coupon Bond

12 = 5w + (1 - w)(21)

w = 56.25%

So,

Amount in Zero Coupon Bond = $562,500

Amount in Perpetuity = $437,500

b.

11 = 4w + (1 - w)21

w = 0.5852

Amount in Zero Coupon Bond = $588,235.29

Amount in Zero Coupon Bond = $411,764.71