You are the manager of a pension fund that is index to the S&P 500 and has a beta of 1.00. You will receive $20 million from the fund sponsor next month, which you plan to invest in the funds portfolio and buy S&P 500 shares. The current beta of this contribution is zero. You expect that the stock prices will increase substantially until then. There exist futures contracts on the S&P 500 Index. The contract size is $50 times the value of the index, and its beta is 1.00. The current futures price is $4000.

a) Design the optimal hedge of this contribution.

b) Suppose that everything behaved the way you estimated (including your portfolios beta). Both the spot and futures S&P 500 prices rose by 10%. Calculate: The increase in your cost of buying the S&P shares, the gain or loss on your futures position, and your total gain or loss on the hedge (that is, on your spot purchase and futures position).