1. You manage a pension fund that will provide retired workers with lifetime annuities. You determine that the payouts of the fund are (approximately) level perpetuities of $1 million per year. The interest rate is 10%. You plan to fully fund the obligation using 5-year maturity and 20- year maturity zero-coupon bonds.

(a) How much market value of each of the zeros will be necessary to fund the plan if you desire an immunized position?

(b) What must be the face value (FV) of the two zeros to fund the plan?

(c) If interest rate increases to 11% right after you constructing your portfolio, what actions are needed to rebalance your portfolio?