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**

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