Consider the futures contract written on the S&P 500 index and maturing in one year. The interest rate is 6.2%, and the future value of dividends expected to be paid over the next year is $90. The current index level is 3,000. Assume that you can short sell the S&P index.

Required:

Suppose the expected rate of return on the market is 12.4%. What is the expected level of the index in one year?

What is the theoretical no-arbitrage price for a 1-year futures contract on the S&P 500 stock index?

Suppose the actual futures price is 3,080. Is there an arbitrage opportunity here?