A pension plan is obligated to make disbursements of $1 million, $2 million, and

Question

A pension plan is obligated to make disbursements of $1 million, $2 million, and $1 million at the end of each of the next three years, respectively. The annual interest rate is 10%. If the plan wants to fully fund and immunize its position, how much of its portfolio should it allocate to one-year zero-coupon bonds and perpetuities, respectively, if these are the only two assets funding the plan? (Do not round intermediate calculations. Round your answers to 2 decimal places.) Portfolio Investment in one-year zero-coupon bonds Investment in perpetuity /o

Explanation / Answer

Let us first find the duration of plan's obligation

Duration of perpetuity is = (1+r)/r = 1.1/0.1 =11 years

Let W be weight of zero coupen bond

(W*1) + [(1-W)*11] = 1.9524

W+[11-11W] = 1.9524

11-10W=1.9524

10W=9.0476

W=0.90476 i.e. 90.476%

Therefor portfolio should be 90.476% in zero coupen bond and 9.524% in Perpetuity

Year Payment PVIF @ 10% PV Weight Duration = Weight*year 1 1 0.9091 0.90909 0.2744 0.2744 2 2 0.8264 1.65289 0.4989 0.9977 3 1 0.7513 0.75131 0.2268 0.6803 3 1.9524

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