Question

Problem 11-17

You are managing a portfolio of $1.7 million. Your target duration is 15 years, and you can choose from two bonds: a zero-coupon bond with maturity 4 years, and a perpetuity, each currently yielding 4%.

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

Duration of Zero Coupon Bond = Time to Maturity

Duration of Zero Coupon Bond = 4 years

Duration of Perpetuity = (1 + i)/i

Duration of Perpetuity = 1.04/0.04

Duration of Perpetuity = 26 years

a.

Target Duration = 15 years

So,

15 = w(4) + (1 - w)26

w = 0.50

So,

Value of Zero Coupon Bond = $0.85 million

Value of Perpetual Bond = $0.85 million

b.

After 1 year

Duration of Zero Coupon Bond = 3 years

So,

14 = w(3) + (1 - w)26

w = 0.5217

Value of Zero Coupon Bond = 0.5217(1.7) = $0.887 million

Value of Perpetual Bond = 1.7 - 0.887 = $0.813 million