The Keynes Investment Company is expecting a \(\$ 20\) million inflow of cash from one of its investment clients in June and is planning to invest the cash in a portfolio of stocks with a \(\beta=1\). Keynes Investments is concerned that there will be a strong bull market and would like to hedge its June investment with June S\&P 500 futures contracts currently trading at 2,000 with a \$250 multiplier. Currently, the S\&P 500 spot index is at 2,000.

a. Using the price-sensitivity model, determine how many S\&P 500 futures contracts the Keynes Investment Company would need in order to lock in the purchase price of the portfolio at \$20 million portfolio.

b. Show in a table the values of the portfolio, futures cash flows, and the hedged portfolio values on the June expiration date for possible spot index values of 1,500, 2,000, and 2,500. Assume no quantity, quality, or timing risks.