Problem 3 (25 marks)

Consider a pension plan that pays beneficiaries in the following manner: at the end of the retirement year of a beneficiary the value of all benefits are transferred to his or her personal account. This means that at the end of every year the pension plan makes lump-sum payments of pension benefits to its beneficiaries. The pension plan's actuarial team concluded that the pension's obligation stream could not be estimated beyond an 80-year horizon. They further estimate that the plan will have to make annual pension payments of $10 million per year throughout this 80-year horizon. The first payment will take place in exactly one year. Assume the current yield curve is flat at 6%.

Note: In your calculations, use dollar figures rather than millions of dollars.

1)What is the duration of the plan's expected obligation stream?

2)Assume that the pension plan hired a new actuarial team that revised the calculations in (1) and found that the present value of expected pension obligations in the next century is $150 million with a 22-year duration. You decide to utilize an immunization strategy for this obligation that exclusively involves two bonds J and K. Bond J is a 7-year bond paying a 5% annual coupon (annually). Bond K is a consol (perpetual) bond paying 10% annual coupon rate (annually). Both bonds have a 1,000 face value. How much money should the pension plan invest in each of the two bonds? Indicate the position the plan takes in each bond (long or short).

3)A different pension plan calculates a 16-year duration for its expected future obligations. It also calculates that its obligations have a convexity of 29. You were hired by this pension plan and you want to utilize an immunization strategy for its obligations, which exclusively involves three bonds: E, F and G. You calculated the following information for the three bonds: