Consider the futures contract written on the S&P 500 index and maturing in six months. The interest rate is 3 percent per six-month period, and the future value of dividends expected to be paid over the next six months is $15. The current index level is 1425. Assume that you can short sell the S&P 500 index. 4. a) Suppose the expected rate of return on the market is 6% per six-month period. What is the expected level of the index in six months? b) What is the theoretical no-arbitrage price for a six- month futures contract on the S&P 500 stock index? c) Suppose the futures price is 1422. Is there an arbitrage opportunity here? If so, how would you exploit it and what is the risk-free profit