You manage a pension fund, which provides retired workers with lifetime annuities. The fund must pay out $1 million per year to cover these annuities. Assume for simplicity that these payments continue for 20 years and then cease. The interest rate is 4% (flat term structure). You plan to cover this obligation by investing in 5- and 20-year maturity Treasury strips.
(a) What is the duration of the funds 20-year payout obligation?
(b) You decide to minimize the funds exposure to changes in interest rates. How much should you invest in the 5- and 20- year strips? What will be the par value of your holdings of each strip?
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(c) After three months, you reexamine the pension funds investment strategy. Interest rates have increased. You still want to minimize exposure to interest rate risk. Will you invest more in 20-year strips and less in 5-year strips? Explain briefly.