Consider the futures contract written on the S&P $500$ index and maturing in one year. The interest rate is $6\mathrm{.}2\%,$ 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.Suppose the expected rate of return on the market is $12\mathrm{.}4\%.$ 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?