The Keynes Investment Company is expecting a \(\$ 100\) million inflow of cash in June and is planning to invest the cash in a portfolio of stocks with a \(\beta=1.5\). Keynes Investments is concerned there will be a strong bull market and would like to cap its June portfolio investment cost with June S\&P 500 spot call options with an exercise price of 2,250 , multiplier of \(\$ 100\), and premium of 35 . Currently, the S\&P 500 index is at 2,250 .

a. Using the price-sensitivity model, determine how many S\&P 500 spot call contracts the Keynes Investment Trust Company would need in order to set a \(\$ 100\) million cap on the purchase of its portfolio in June. What is the cost of the call?

b. Show in a table the proportional changes in the S\&P 500 from its current level of 2,250 , the proportional changes in the portfolio, the values of the portfolio corresponding to the spot index, the call option values, the call position's cash flow, and the call-hedged portfolio cost on the June expiration date for possible spot index values of index values for possible spot index values starting at 1,900 with 25 point steps to 2,500 .