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Inc has a pension liability that obligates it to pay out $3 million per year for the next 20 years. The term structure of interest rates is flat and the current interest rate is 3%. You intend to invest in 5- and 20-year STRIPS (with face value of $100) to cover the obligation.

(a) What is the value of the pension obligation?
(b) What is the duration of the pension obligation?
(c) If you want to hedge the interest rate risk, specify the number of bonds (using thousands) you should invest in the
(i) 5-year STRIP?
(ii) 20-year STRIP?
(d) Is this a perfect hedge? Yes, No?

1 Answer

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Final answer:

The value, duration, and hedging strategy for a pension obligation require the calculation of the present value of annuities, the weighted average time of payments, and the matching of durations of STRIPS. Hedging with STRIPS entails purchasing bonds with durations to match the obligation, but a perfect hedge is impractical due to differences in durations and the assumption of a constant interest rate.

Step-by-step explanation:

The student asks about calculating the value, duration, and hedging strategy for a pension obligation using STIPS. The obligation is to pay out $3 million per year for the next 20 years with a flat interest rate of 3%.

The value of the pension obligation is calculated using the present value (PV) formula for annuities, considering the flat interest rate and the stream of payments:

PV = Payment / Interest Rate * (1 - (1 + Interest Rate) -Number of Payments)

The duration is the weighted average time to receive the pension payments. It can be calculated using the formula:

Duration = Σ (PV of Payment * Time) / Total PV of Payments

To hedge the interest rate risk, the investor would match the duration of the pension obligation with the duration of the STRIPS investments. The numbers of bonds to invest in the 5-year and 20-year STRIPS would depend on their respective durations and the PV of each STRIP. A perfect hedge would be difficult since the duration of the pension payments might not match the duration of the bonds exactly, and it assumes the interest rate remains flat.

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