Consider the futures contract written on the S&P 500 index and maturing in one year. The interest rate is 3%, and the future value of dividends expected to be paid over the next year is $35. The...

Consider the futures contract written on the S&P 500 index and maturing in one year. The interest rate is 3%, and the future value of dividends expected to be paid over the next year is $35.

The current index level is 2,000. Assume that you can short sell the S&P index.
a. Suppose the expected rate of return on the market is 8%. What is the expected level of the index in one year?
b. What is the theoretical no-arbitrage price for a 1-year futures contract on the S&P 500 stock index?
c. Suppose the actual futures price is 2,012. Is there an arbitrage opportunity here? If so, how would you exploit it?