Benefiting From a Small Statistical Idea

In this article, I will give you a crash course in a couple of statistical ideas and show you how you can use them to your advantage. Before your eyes glaze over and traumatic stresses take you back to the dreaded math classes of your youth, let me assure you that no heavy mathematical lifting will be involved. All you'll need to do is juggle three things in your head instead of two.

Most of us think in terms of what statisticians call main effects. A main effect says: A is related to B. For instance, vigorous exercise is related to health. More vigorous exercise, more health; less vigorous exercise, less health. That's a main effect. You can think of it as a simple correlation.

Many relationships among things in the world are more complex, however. One slightly more complex relationship is called an interaction effect. Here we are saying: A is related to B, but only when C is present. For instance, vigorous exercise might bring more health for people below the age of 75, but not for people above age 75. You can see why interactions are important. If we assume a simple main effect, we might encourage everyone to exercise vigorously, putting older people at risk.

Many market relationships are interactions and not main effects. This means that when we adopt simple "A, therefore B" thinking, we can put our portfolios at risk.

Here's a simple example. As I noted on Traderfeed, large cap stocks in the Major Market Index have been up over 2-1/2 percent in the past six sessions. If we look at what typically happens after six-day periods of large cap strength going back to March, 2003 (N = 762), we find that the S&P 500 Index ) tends to underperform its historical norms over the next six days. That's our main effect: strong six days in XMI leads to subnormal S&P performance.

Now, however, let's add a third factor: the performance of small cap stocks. When the large caps have been up strongly and the small caps have been strong, the S&P 500 actually modestly outperforms its average six-day performance over the next six days. When the large caps have been strong and the small caps have been weak, the S&P 500 has actually had bearish expectations over the next six days. In other words, whether a strong six-day period in the large caps is bullish or bearish depends upon the relative performance of the small issues.

Now let's take the reverse scenario. When we have six-day strength in the small-cap stocks (a gain over 3%), the next six days in the small caps average a loss of -.003% (46 up, 36 down). That is weaker than the average six-day gain of .62% for the general sample (464 up, 298 down). Once again, that's our main effect: six days of strength in the small caps leads to small cap underperformance in the next six days.

Let's look at those strong days in the small caps, however, as a function of S&P 500 performance during those six days. When small caps are strong and the S&P is strong, the next six days in the small caps average a gain of .41% (28 up, 13 down). When small caps are strong and the S&P is weak, the next six days in the small caps average a decline of -.41% (15 up, 26 down). Clearly, the main effect is misleading. When the small caps and the S&P are strong, the next six days in the small caps tend to be bullish, in line with historical norms. When the small caps are strong and the S&P is weak, the next six days in the small caps tend to be bearish.

You need not be a statistician to benefit from the presence of interactions. The way I like to think of it is that rising tides will lift all boats, just as falling tides will drop them. If we see discrepancies between small stocks and large ones, it's time to question the market tide. I'll be keeping one eye on the big issues and one on the small ones this week to see how strong the current market tide really is.

Brett N. Steenbarger, Ph.D. is Associate Clinical Professor of Psychiatry and Behavioral Sciences at SUNY Upstate Medical University in Syracuse, NY.