Consider the futures contract written on the S&P $500$ index and maturing in one year. The interest rate is $4\mathrm{.}6\%,$ and the

future value of dividends expected to be paid over the next year is $$85.$ The current index level is $5,000.$ Assume that

you can short sell the S&P index.

Required:

a$.$ Suppose the expected rate of return on the market is $9\mathrm{.}2\%.$ 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 $5,108.$ Is there an arbitrage opportunity here?

a$.$ Expected level of the index

b$.$ Price

c$.$ Is there an arbitrage opportunity here?