The market timing strategy of Example 23.3 also can be achieved by an investor who holds an indexed stock portfolio and “synthetically exits” the position using futures if and when he turns pessimistic concerning the market. Suppose the investor holds $100 million of stock (which is 50,000 times the current value of the index).

What futures position added to the stock holdings would create a synthetic T-bill exposure when he is bearish on the market? Confirm that the profits are effectively risk-free using a table like that in Example 23.3.

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Example 23.3 Synthetic Positions Using Stock-Index Futures Suppose that an institutional investor wants to invest $100 million in the market for one month and, to minimize trading costs, chooses to buy the S&P 500 E-mini futures contracts as a substitute for actual stock holdings. If the index is now at 2,000, the 1-month delivery futures price is 2,020, and the T-bill rate is 1% per month, it would buy 1,000 contracts. (Each contract controls $50 x 2,000 = $100,000 worth of stock, and $100 million/$100,000 = 1,000.) The institution thus has a long position on $50,000 times the S&P 500 index (1,000 contracts times the contract multiplier of $50). To cover payment of the futures price, it must buy bills worth 50,000 times the present value of the futures price. This equals 50,000 x (2,020/1.01) = $100 million market value of bills. Notice that the $100 million outlay in bills is precisely equal to the amount that would have been needed to buy the stock directly. (The face value of the bills will be 50,000 x 2,020 = $101 million.) This is an artificial, or synthetic, stock position. What is the value of this portfolio at the maturity date? Call S, the value of the stock index on the maturity date T and, as usual, let Fo be the original futures price: In General (Per Unit of the Index) Our Numbers 1. Profits from contract 2. Face value of T-bills ST-Fo Fo $50,000 (S-2,020) 101,000,000 Total ST 50,000ST The total payoff on the contract maturity date is exactly proportional to the value of the stock index. In other words, adopting this portfolio strategy is equivalent to holding the stock index itself, aside from the issue of interim dividend distributions and tax treatment.