Assume that you are a fund manager holding an equity portfolio worth $20 million with an estimated beta of 1.2 and you are concerned about the performance of the market over the next 3 months. You plan to use 3-month futures contracts on the S&P 500 to hedge the portfolio risk over the next 3 months. The current level of the index is 4,300, the dividend yield on the index is 3% per annum, and the risk-free rate is 4% per annum. The current 3-month futures price is 4,400 and each index futures contract is on $250 times the index.

(1) What position should you take to hedge all exposure to the market movements over the next 3 months?

(2) Calculate and discuss the effect of your strategy if the index in 3 months is: (i) 4,100 and (ii) 4,500. Assume that the 3-month futures price is 0.5% higher than the index level at this time. Comment on the effectiveness of the hedging

(3) What would be your intention if you change your mind and decide to increase the beta of the position from 1.2 to 1.5 over the next 3 months, to hedge or to speculate? What position in futures contracts should you take?