Question

You are managing a bond portfolio of $10 million. Your target duration is 8 years and you can choose from two bonds: a zero-coupon bond with a maturity of 7 years and a zero-coupon bond with a maturity of 12 years each yielding 5%. How much should you hold of each bond in your portfolio?

A) 55% of the 7-year bond and 45% of the 12 years bond
B) 45% of the 7-year bond and 55% of the 12 years bond
C) 40% of the 7-year bond and 60% of the 12 years bond
D) 60% of the 7-year bond and 40% of the 12 years bond
E) 80% of the 7-year bond and 20% of the 12 years bond

Answer 1

Given about a portfolio.

investment in portfolio is today's term = $1000000

duration of the portfolio = 8 year

the portfolio is made from a 7 year zero coupon bond and a 12 year zero coupon

So, duration of a zero coupon bond is equals to its years to maturity

So, duration of 7 year zero coupon bond D1 = 7

Similarly, duration of 12 year zero coupon bond D2 = 12

For a portfolio be duration Dt = 8 years, duration is weighted average duration of its assets

let weight of 7-year zero-coupon bond be W, then weight of 12-year zero coupon bond will be (1-W)

=> Dt = D1*W + D2*(1-W)

=> 8 = 7W + 12*(1-W)

=> W = 0.8 & 1-W = 0.2

So, weight of 7-year bond is 80% and weight of 12-year bond is 20%

Option E is correct.