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:
Bond.                Duration                          Convexity
E                            9.00                                29.00
F                           21.00                             35.00
G                          28.00                              56.00

Use both duration and convexity in your immunization strategy, to determine the weights of investment in each of the three bonds.