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 1.5 . Hunter Investment is concerned about a bear market and would like to reduce its portfolio beta to one. Currently, the S\&P 500 spot index is trading at 2,000 and a June S\&P 500 futures contract is trading at 2,000, with a \(\$ 250\) multiplier.

a. Using the price-sensitivity model, determine how many S\&P 500 futures contracts the Hunter Investment Company would need in order to reduce its portfolio beta from 1.5 to 1.0 in June.

b. Show in a table the values of the portfolio, futures cash flows, and the futures-adjusted 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.

c. Calculate the futures-adjusted portfolio values as a proportion of the initial \(\$ 100\) million portfolio value and the unadjusted portfolio values as a proportion of \(\$ 100\) million value for possible spot index values of \(1,500,2,000\), and 2,500 .

d. Calculate the proportional return for the futures-adjusted portfolio to the proportion changes in S\&P from its initial value of 2,000 . Calculate the proportional return for the unadjusted portfolio to the proportion changes in S\&P from its initial value of 2,000. Comment on how the futures lower the portfolio's beta.