Suppose that a pension fund has committed to pay 200 million to retirees at the end of year 10 and another 100 million at the end of year 12. The yield curve is flat and all bonds currently have a yield to maturity of 5%.

a) How much money does the pension fund need to raise from the prospective retirees today in the form of premiums ?

b) What is the Duration of the Pension funds liabilities?

c) Suppose that you can invest in a five-year zero-coupon bond and in a fifteen-year zero- coupon bond. Suppose also that you are uncertain about the level of interest rates going forward. Specifically, you believe that immediately after you invest the proceeds from the premiums, all yields could decrease to 4% (permanently), or they could increase to 6% (permanently). What dollar amounts would you invest in each of the two bonds to ensure that you can meet your obligation to the retirees in 10 and 12 years, irrespective of how the yield curve moves?

d) Immediately after raising the amount of funds implied by (a), but before investing it, you become convinced that all yields will increase tomorrow to 6% and will stay there permanently. Suppose that you can invest in the five-year or the fifteen-year zero coupon bond, or you can leave the money in a bank account where it will be earning the pre- vailing one-year yield each year. However, you cannot short any of the two bonds, nor can you borrow. Assume that your objective is to maximize the net worth (i.e., present value of assets minus present value of liabilities) in year 10. (That way you can give some extra money to the retirees.) How would you invest the money now? How large would the net worth (i.e., the value of assets net of liabilities) of the fund in year 10 be, assuming you are right and you follow the optimal policy?