Question

a pension fund anticipates needing to pay out $2.5 million dollars in benefits in 2027 (seven years from today). assume the yield curve is a flat 5%. it has two options for bonds in which to invest: a zero coupon treasury bond with a time to maturity of 10 years and a YTM of 3%, and a zero coupon bond Johnson&Johnson bond with 3 years to maturity and a 6% YTM. they want zero interest rate risk. how much should they invest in the treasury?

Answer 1

Answer :

Pension fund has a single liability 7 years from now therefore duration of the liability is 7

To minimize interest rate risk portfolio of the two bonds must have durtion of 7

We know that duration of ZCB is its time to maturity

Therefore ZCB (Treasury) duration = 10

ZCB (J&J) = 3

Let ZCB (Treasury) weight = X

ZCB (J&J) Weight = 1 -X

So we have the following equation

(X*10) + (1-X)*3 = 7

10X + 3 - 3X = 7

7X = 4

X = 57.14%

Therfore money required to be invested in treasury = 2.3*0.5714 = $1.31 million or $1,314,285.71