Question

You are managing a portfolio of $1.9 million. Your target duration is 11 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 ten 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 Perpetuity = 1.05/0.05 = 21 years

Let weight of Zero Coupon BOnd is w

11(1,900,000) = 5(w) + (1,900,000 - w)(21)

20,900,000 = 5w + 39,900,000 - 21w

w = $1,187,500

Amount in Zero Coupon BOnd = $1,187,500.0000

Amount in Perpetuity = $712,500.0000

b.

Target Duration = 10 years

Duration of Zero Coupon Bond = 4 years

Duration of Perpetuity = 1.05/0.05 = 21 years

Let weight of Zero Coupon BOnd is w

10(1,900,000) = w(4) + (1,900,000 - w)21

19,000,000 = 4w + 39,900,000 - 21w

w = $1,229,411.7647

Amount in Zero Couon Bond = $1,229,411.7647

Amount in Perpetuity = $670,588.2353