Consider the futures contract written on the S&P 500 index and maturing in 6 months. The interest rate is 3% per 6-month period, and the future value of dividends expected to be paid over the next 6 months is $15. The current index level is 1,425. Assume that you can short sell the S&P index.

a. Suppose the expected rate of return on the market is 6% per 6-month period. What is the expected level of the index in 6 months?

b. What is the theoretical no-arbitrage price for a 6-month futures contract on the S&P 500 stock index?

c. Suppose the futures price is 1,422. Is there an arbitrage opportunity here? If so, how would you exploit it?