A company is considering hedging a portfolio of stocks using a futures contract. The current value of the portfolio is $500,000 and the beta of the portfolio is 1.5. The stock index futures contract has a multiplier of $250 and the current index level is 3,000. The risk-free rate is 2% per annum and the futures price is $3,100.

(a) Calculate the number of futures contracts the company needs to hedge the portfolio. (b) If the index level increases to 3,200, calculate the profit or loss on the futures contract. (c) If the index level decreases to 2,800, calculate the profit or loss on the futures contract. (d) Explain how the company can adjust the hedge to maintain the portfolio's beta at 1.5.

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