1. Consider a pension fund at 01/01/2023 that requires a payout of $100, 000, 000 at the end on 31/12/2025. The fund would like to invest into a portfolio that delivers this payout for sure. The yield curve is flat at y = 10% across maturities, so that the net present value of the liability is given by $68, 301,-345.54. The fund considers two bonds. Bond A is a one year pure discount bond, while Bond B is a 5 year bond with coupons paid annually at the rate of 5%. All payouts and investment decisions take place at the start of each year. (a) Construct a portfolio using the two bonds that immunizes the investment to market movements when funds need to be reinvested on 01/01/2024. (b) Show that if any cash flow received at the end of 2023 and 2024 can be invested for two years at a yield of 8%, the pension fund will receive $100, 000, 000 at the on 31/12/2025. c) Suppose now that the pension fund can invest in Bond B again and Bond O which is a one year pure discount bond on 01/01/2024. Find the investments in Bond B and Bond C that immunize the portfolio against market movements when funds need to be reinvested on 01/01/2025. (d) Show that the new portfolio yields $100, 000, 000 at the end of 2024 given that yields in 2024 increase to 9%. (e) How would your reinvestment strategy change on 01/01/2024 if there was a Bond D available which is a two year pure discount bond maturing on 31/12/2025