Bonita Singer is a hedge fund manager specializing in futures arbitrage involving stock index contracts. She is investigating potential trading opportunities in S&P 500 stock index futures to see if there are any inefficiencies that she can exploit. She knows that the S&P 500 stock index is currently trading at 1,100.

a. Assume that the Treasury yield curve is flat at 3.2 percent and the annualized dividend yield on the S&P index is 1.8 percent. Using the cost of carry model, demonstrate what the theoretical contract price should be for a futures position expiring six months from now.

b. Describe the set of transactions that Bonita would have to undertake to take advantage of an actual futures contract price that was (1) substantially higher or (2) substantially lower than the theoretical value you established in Part a.

c. Assuming that total round-trip arbitrage transaction costs are $20 for the set trades described in Part b, calculate the upper and lower bounds for the theoretical contract price such that arbitrage trading would not be profitable.