The January 2023 S&P 500 cash index is 3950 points while the S&P 500 futures March 2023 index is 4000 and the contract value of each index point is $150. You are convinced the futures market will fall 20% by expiry. You are only prepared to buy or sell one futures contract. (i) Will you buy or sell a contract in the futures market? (ii) What is your profit (+) in dollars if you are correct? (iii) What is your profit (+)/loss (-) if the futures price on expiry is 4400? (iv) What is your profit (+)/loss (-) if the futures price on expiry is 3700? (v) Explain how a fund manager that is manging $100 million pension fund that track the S&P 500 index who is concerned the spot index will be 3200 on date of expiration of the futures contract in March 2023 can hedge the risk to the pension fund. Explain the net position if on the March expiration the index reads 3000 or 4500.