Playing the Probabilities

Within that time frame, another pattern emerges. If the S&P 500 was up by the 10th day and finished the month up, it finished higher than its 10th-day level 76% of the time. Conversely, if it was down by the 10th day and finished the month down, it finished lower than day 10 about 61% of the time.

Also, the mean return of the absolute value of monthly returns is 3.5%. Even with slippage, if you could capture just a fraction of that return, you'd be better off than the buy-and-hold investor. The position can also be adjusted at the standard deviation levels above and below the mean, which would result in changing your risk profile at these important levels.

A Real-World Russell Example

For an example, let's look at the Russell 2000 last July, when the index dropped 15.2%. Considering the magnitude of the loss, it's not surprising that July started off lower from the very start. At this point, a short in the iShares Russell 2000 (IWM - commentary - Cramer's Take), the exchange-traded fund based on the index, could be initiated. As long as the index remains in negative territory, this short position is maintained, but it is adjusted at the standard deviations.

In order to find this information, you could import raw historical data from a Web site such as Yahoo! Finance into Microsoft Excel. Using very simple equations, the mean and standard deviation can then be determined.

On July 3, the Russell was already one standard deviation below its mean monthly return. At that point, you could have reduced your short position, because the market has a good chance of moving back toward its mean. In the next few days, the index bounced slightly, only to move back to the one standard deviation level on July 16. As the Russell moves through one standard deviation, keep in mind the important characteristic of equity-market returns: the distribution has fat tails.

Again, this means that the probability of an extreme event -- in this case, a huge down month -- is more likely than a normal distribution would imply. Therefore, as the Russell moves back through minus one standard deviation, you could reinitiate the full short position.

Sure enough, on July 23, the index traded two standard deviations below its mean monthly return, a pretty rare event. Again, at this point, you'd probably want to reduce your position size. However, you wouldn't want to close the position completely because of -- all together now -- fat tails.

Russell 2000 iShares (IWM) July 2002, Hourly Data

Source: GNI Capital

You could then hold the smaller position until the end of the month, when the trade is closed. In August the whole thing starts over.

As with Bollinger Bands, this strategy isn't one you should use in isolation. Rather, it's a simple approach to following the market's trend and is meant to be used in conjunction with other indicators.

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At time of publication, Norton's fund was long IWM calls and puts, though positions may change at any time.

Charles L. Norton, CFA, is a principal of GNI Capital, Inc., a registered investment adviser that manages a hedge fund, GNI Partners, L.P., as well as discretionary private client accounts. Norton had been a vice president in the equity research department of a New York-based hedge fund, where he was also a registered representative managing discretionary private client accounts. Prior to his experience on the buy side, Norton worked in the investment banking division of Salomon Smith Barney, where he was an analyst in the health care group, reporting directly to the head of the group. Under no circumstances does the information in this column represent a recommendation to buy or sell stocks. While Norton cannot provide investment advice or recommendations, he welcomes your feedback.