Question

You are managing a portfolio of $2 million. Your target duration is 15 years, and you can choose from two bonds: a zero-coupon bond with maturity 5 years, and a perpetuity, each currently yielding 5%.

Required:

(a)	How much of each bond will you hold in your portfolio? (Round your answers to 4 decimal places.)

Zero-coupon bond
Perpetuity bond

(b)	How will these fractions change next year if target duration is now fourteen years? (Round your answers to 4 decimal places.)

Zero-coupon bond
Perpetuity bond

Answer 1

a.

Duration of Zero Coupon Bond = 5 years

Duration of Perpetual Bond = 1.05/0.05 = 21 years

Target Duration = 15 years

So,

15 = 5w + (1 - w)21

w = 0.3750

Amount in Zero Coupon Bond = (0.3750)2,000,000 = $750,000

Amount in Perpetual Bond = (1 - 0.3750)(2,000,000) = $1,250,000

b.

Target Duration = 14 years

Duration of Zero Coupon Bond = 3 years

14 = 3w + (1 - w)21

w = 0.3889

Amount in Zero Coupon Bond = (0.3889)2,000,000 = $777,800

Amount in Perpetual Bond = (1 - 0.3889)2,000,000 = $1,222,200