The Hunter Investment Company manages a well-diversified equity fund. The current value of the portfolio it manages is \(\$ 100\) million and the portfolio has a beta of 1.0. Hunter Investment is bullish about the market and would like to increase its portfolio beta to 1.5 if the market is 2,250 or greater in June, while keeping its beta at one if the market is less than 2,250. Currently, the S\&P 500 spot index is trading at 2,250 and a June S\&P 500 spot call contract with an exercise price of 2,250 and \(\$ 100\) multiplier is trading at 50 .

a. Using the price-sensitivity model, determine how many S\&P 500 call contracts the Hunter Investment Company would need in order to increase its portfolio beta to 1.5 in June if the market is 2,250 or greater while keeping its portfolio at one if the market is 2,250 or less.

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 long call option values, the long call position's cash flow, the call-enhanced portfolio values, and the proportion changes in the call-enhanced portfolio from its \(\$ 100\) million current value, proportion changes in the call-enhanced portfolio value to the proportional changes in S\&P 500. Evaluate for possible spot index values on the June expiration date starting at 2,000 with 25 point steps to 2,600 .

c. Comment on the convexity of the call-enhanced portfolio's beta.