Question

To create a portfolio with a duration of 4 years using a 5 year zero-coupon bond and a 3 year zero-coupon bond, one would have to invest of the portfolio value in the 5 year zero-coupon bond.

A. 50%

B. 55%

C. 60%

D. 75%

Answer 1

Given about a portfolio,

Duration = 4 years

it consist of a 5 year zero-coupon bond and a 3 year zero-coupon bond.

duration of the portfolio is weighted average duration of its bonds.

Duration of a zero-coupon bond is equal to its years to maturity

So, duration of 5 years zero-coupon bond = 5 years

and duration of 3 year zero-coupon bond = 3 years

let weight of 5 year bond be w, then weight of 3 year bond is (1-w)

So, duration of portfolio = Wa*Da + Wb*Db

=> 4 = w*5 + (1-w)*3

=> w = 0.5 or 50%

So, weight of 5 year bond in portfolio is 50%

Option A is correct.