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# Expiration

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Today's opening marked the expiration of the December S&P futures contract. There has been buying the last few days that culminated at the opening print this morning. Here is why.

There are massive portfolios built around stock and futures positions. This is an arbitrage strategy where long (short) stock is offset by short (long) futures. Everything is based on the price of the futures. Let's look at an example.

Sheryl runs the index arbitrage desk at BS Securities. Her cost of carry is the risk free rate of 1.17% annualized: this means that when she buys stock her finance department, who must borrow the funds to buy the stock, charges her 1.17% annualized on the notional amount (The fed funds rate is 1% so a broker like BS Securities can borrow a lot at a small premium to this rate. It is no wonder there is a lot of liquidity in the system). She then calculates the dividend yield on a basket of S&P stocks and determines precisely that it is \$4.53for the next 90 days for a yield of .42% (4.53/1087.39).

If Sheryl buys every stock in the index to replicate the futures contract, she winds up paying 1087.39. She is charged on this notional amount \$3.137 in index points (1.17% x 90/365 x 1087.39) for the next 90 days. Since dividends over the next 90 days are 4.53 and since she receives dividends by being long stocks (and doesn't have to pay dividends being short futures), she actually comes out ahead by -\$3.137 + \$4.53 = \$1.39 by being long stocks and short futures. This means that the futures should be trading \$1.39 less in price than the cash level. If Sheryl can buy the stocks at 1087.39 and sell futures at 1086.39, only \$1 less than the cash index, she can profit.

Because she can do this on borrowed money she will do this in large quantities.

Another way to affect this trade is to buy December futures contracts and sell March futures contracts at a spread. When the December futures contracts expire as they did this morning, Sheryl will on the opening buy all the stocks in the index to replace her expiring December contracts. If she buys all the stocks at the opening prices, which wholly determines the closing price of her December contracts, she has effectively entered into a long stock short March futures position.

This is what happened this morning. There was buying on the opening to replace the expiring December futures contract. There was a fairly heavy amount of selling into this.

Program trading now comprises almost half of all trading in equities. Many participants enter the market through futures: this is what causes futures to either become rich or cheap relative to the underlying cash index. When a participant starts buying large amounts of futures, initially at least the price becomes rich relative to cash. Sheryl notices this, calculates her execution costs and begins buying stock and selling futures.
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No positions in stocks mentioned.

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