You work for a pension fund that has an obligation that must be paid in 10 years. Currently, this obligation, which has a present value of $200 million, is exactly funded (i.e., the market value of the funds assets equals the present value of its obligation; net equity is exactly zero). The duration of the funds assets is currently 8. The yield-to-maturity on zero coupon bonds of all maturities is currently 6%.

(a) Using the duration information, what would be the approximate change in the equity of the fund if interest rates decrease to 5% at all maturities?

(b) Your boss tells you that she would like you to shift all of the funds assets into a combination of 5-year and 20-year zero-coupon bonds. How would you structure your investment to immunize the fund against interest rate risk? That is, how much should you invest in the 5-year zero, and how much in the 20-year zero?