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 YTM of 3%, and a zero coupon Johnson & Johnson bond with 3 years to maturity and a 6% YTM. They want zero interest rate risk. How much money should they invest in the Treasury? Note: Answer in dollars, rounding to the nearest cent.

Answer 1

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

To immunize interest rate risk portfolio of the two bonds must have duration 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 %

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