Playing the Probabilities

Markets generally revert to the mean. When stretched too far in one direction, stocks will eventually snap back in the opposite direction like a rubber band. This phenomenon has happened repeatedly throughout history and most recently can be seen in the bubble of the late '90s and the collapse in its aftermath. "What goes up must come down," the old saying goes, and the opposite is true as well.

An important point, however, is that markets can remain in a trend for long periods of time, stretching much further than expected before they snap back. You can profit from the market's mean-reverting nature in a number of different ways.

For example, Bollinger bands, a frequently used indicator in technical analysis, are based on this basic premise. They are bands that surround the price bars on a chart, usually two standard deviations from a moving average (typically a 20-day moving average, but it can be customized for the user) on either side. When the price hits the lower band -- dipping two standard deviations below its moving average -- odds favor a bounce back to the moving average. Conversely, if the price extends to the upper band, the stock will likely correct back to the moving average. Bollinger bands are generally used not in isolation to generate buy and sell signals but in conjunction with other indicators.

At my firm, GNI Capital, we attempt to capitalize on the market's mean-reverting tendency by using another method that's based on the distribution of the market's returns. We use monthly data for this exercise, but any time frame will work similarly, as long as it's consistent with the time horizon for the trade.

Talking Fat Tails

Take a look at the distribution of the S&P 500's monthly returns. It looks similar to a normal distribution, but it's extremely important to note that equity market returns have "fatter tails" than a normal distribution. That means that the probability of an extreme event occurring is greater than implied by a normal distribution.

Distribution of S&P 500 Monthly Returns

Source: GNI Capital

The S&P 500's mean monthly return from December 1970 through September 2003 is 0.71%, indicating that over very, very long periods of time, equities have earned, on average, about 71 basis points per month. This average is made up of some months in which the index gained and others in which it lost, averaging out to a slightly positive return for the buy-and-hold investor.

But what happens if, instead of holding a long position forever, you were able to capture the absolute value of the monthly change? In other words, when the index was up for the month, you were long; when it was down for the month, you were short. After all, every huge up month started unchanged on the month at some point before moving higher. The same is true for down months: They all were flat at one time during the month, even if only briefly.

The distribution of the absolute value of the monthly change looks much different: It has a mean of 3.5% and is skewed right. In order to capture this, you'd initiate a long position as soon as the market moved higher on the month, using the unchanged level for the month as a stop. If the market were down for the month, you'd short the market at unchanged and use this level as a stop.

Distribution of Absolute Value of S&P 500 Monthly Returns

Source: GNI Capital

Now, what about months when the market flips back and forth on either side of unchanged? This is certainly a trending strategy that doesn't work well in choppy markets. But the direction of most months is determined by the 10th day. In fact, in the 393 months from January 1971 to September 2003, the S&P 500 had a monthly return that was the same direction as its return for the first 10 days of the month about 73% of the time.

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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.