Consider a pension fund at 01/01/2017 that requires a payout of $100; 000; 000 at the end on 31/12/2019. The fund would like to invest into a portfolio that delivers this payout for sure. The yield curve is at 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 01/01/2018.

(b) Show that if any cash ow received at the end of 2017 and 2018 can be invested for two years at a yield of 8%, the pension fund will receive $100; 000; 000 at the on 31/12/2019.

(c) Suppose now that the pension fund can invest in Bond B again and Bond C which is a one year pure discount bond on 01/01/2018. Find the investments in Bond B and Bond C that immunize the portfolio against market movements when funds need to be reinvested on 01/01/2019.

(d) Show that the new portfolio yields $100; 000; 000 at the end of 2019 given that yields in 2019 increase to 9%.

(e) How would your reinvestment strategy change on 01/01/2018 if there was a Bond D available which is a two year pure discount bond maturing on 31/12/2019?