5. Stock Index Futures Arbitrage On February 26, 1986, Jim Lucey, a program trader at a New York Stock Exchange member firm, studied the pricing of futures contracts written on the Major Market Index (MMI). The MMI, a price-weighted stock index designed to measure the market performance of major U.S. industrial corporations, tracked movements in the prices of 20 blue chip stocks (see Exhibit 1). Unlike the Standard & Poor's 500 and other market capitalization-weighted indices, the MMI was affected equally by a price change in any one of its component stocks. Jim regularly monitored the values of major stock indices and stock index futures in search of index-futures arbitrage opportunities. Although the efficiency of index futures pricing had improved since the initiation of trading in stock index futures contracts in 1982, index futures prices at times diverged significantly from their theoretical values. Such pricing anomalies were usually attributed to the activities of speculators using the futures markets to anticipate major moves in the stock market. As Jim considered his strategy, he estimated the transaction costs associated with an MMI arbitrage. Transacting for his firm's account, Jim would incur no commission expenses but would be exposed to the market impact of buying/selling the MMI. Although the round-trip market impact of implementing an S&P 500 index-futures arbitrage often totaled 0.5%, Jim believed that transactions in the 20 large-capitalization stocks included in the MMI could be executed with less than 0.25% market impact. Jim's stock purchases would be subject to 10% margin restrictions, and his firm's cost of borrowing was approximately 8.0%. At mid-morning on February 26 the March 86 MMI futures, which were to expire on March 21, were priced at 313.55, while the cash index stood at 311.74. One-month Treasuries were yielding 6.8%. 1. What is the theoretical price of the MMI March '86 futures contract? 2. Assume that Jim is subject to a $5,000,000 position limit. What position should he take to exploit the mispricing of the March '86 MMI futures? 3. What rate of return can Jim expect to earn on his position? 4. Who, in addition to securities dealers, would you expect to engage in index-futures arbitrage? 5. Why do index futures often trade at a premium or discount to their theoretical values? How do you expect the pricing efficiency of broader market index futures, like the S&P 500, to compare to the pricing of MMI futures?