Question

You are managing a portfolio of $1 million. Your target duration is 3 years, and you can choose from two bonds: a zero-coupon bond with time to maturity of 5 years, and a bond with an annual coupon rate of 8% and time to maturity of 2 years, both with yield to maturity of 5%. Assume both bonds have a face value of $1000. a. How much of each bond will you hold in your portfolio? b. How will these fractions change next year if target duration is now 2 years and the interest rates do not change?

Answer 1

N	CF	PVF	PVF x CF	PVF x CF x N
1	80	0.952381	76.19	76.19
2	1080	0.907029	979.59	1959.18
		Sum	1055.78	2035.37
			Duration	1.93

Firstly, we need to calculate the duration of coupon bond.

Duration of coupon bond = Sum of PVF x N x CF / Sum of PVF x CF = 1.93

Duration of zero coupn = 5

Assume you invest y% in zero coupon and 1 - y% in coupon bond such that you get target duration = 3

=> 3 = 5 x y + 1.93 x (1 - y)

=> y = 34.85% invest in zero coupon bond

and 1 - 34.85% = 65.15% invest in coupon bond.