How you can profit from a simple 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
my research blog, large cap
stocks in the Major Market Index
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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
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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

Now, however, let’s add a third factor:
the performance of small cap stocks
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. When the large caps have been up
strongly and the small caps have been strong, the S&P 500 actually modestly
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 and author of

The Psychology of Trading
(Wiley, 2003). As Director of Trader
Development for Kingstree Trading, LLC in Chicago, he has mentored numerous
professional traders and coordinated a training program for traders. An active
trader of the stock indexes, Brett utilizes statistically-based pattern
recognition for intraday trading. Brett does not offer commercial services to
traders, but maintains an archive of articles and a trading blog at and a
blog of market analytics at
. He is currently writing a book on the topics
of trader development and the enhancement of trader performance due for
publication this fall (Wiley).