(2) An equity portfolio manager wants to reduce the market exposure of her portfolio (with the value of $45,000,000) by reducing its beta from 1.5 to 1.2 over the next 3 months using S&P 500 futures contract with 4-month to maturity. Currently, spot index price is 2,600 and the index futures price maturing in 4 months is 2,640. The risk-free interest rate is 3% per annum and index dividend yield is 2% per annum. Assume the futures contract multiplier is 250. (a) What is the optimal number of contracts to reduce portfolio beta to 1.2? Is this a short hedge or a long hedge? (b) If in 3-month the index spot price will be 2,620 and the index futures price will be $2,650, what is the gain/loss on the futures contracts? c) What is the gain/loss of the equity portfolio (keep four decimal points)? (2) An equity portfolio manager wants to reduce the market exposure of her portfolio (with the value of $45,000,000) by reducing its beta from 1.5 to 1.2 over the next 3 months using S&P 500 futures contract with 4-month to maturity. Currently, spot index price is 2,600 and the index futures price maturing in 4 months is 2,640. The risk-free interest rate is 3% per annum and index dividend yield is 2% per annum. Assume the futures contract multiplier is 250. (a) What is the optimal number of contracts to reduce portfolio beta to 1.2? Is this a short hedge or a long hedge? (b) If in 3-month the index spot price will be 2,620 and the index futures price will be $2,650, what is the gain/loss on the futures contracts? c) What is the gain/loss of the equity portfolio (keep four decimal points)