## Thursday, September 14, 2006

### The Most Common Mistake Traders Make

What is the trader's most common mistake? Candidates abound: failing to diversify capital, adding to losing positions, trading through stop-loss levels, trading on hot tips and news items, revenge trading to recover losses, overtrading during slow periods: the list goes on and on.

I'd like to suggest, however, an even more fundamental error that gets traders into hot water: They confuse descriptive statistics with inferential ones.

Allow me to explain.

A descriptive statistic summarizes some characteristic of a sample of a population. Lets say I go out on the sidewalk and survey passers-by as to their political leanings. I find that 65% of the people in my survey support the mayor and plan to vote for him. That is a descriptive statistic. If I conduct the survey several times in a row and find that the percentage stays steady at 65%, this, too, provides a description of my sample.

Much of the information that traders work with is descriptive in nature. Consider these statements:

* The market trendline is up;
* We are making new weekly highs in the market;
* Volatility is at a new monthly low;

All of these are descriptive. They take a sample from a price or indicator series and describe characteristics of that sample.

All good science begins with observation and description. Such qualitative, descriptive analysis allows us to notice regularities--or patterns--in our data and frame meaningful hypotheses based upon these.

Descriptive statistics can lead us to the formulation of hypotheses, but they cannot provide tests of those hypotheses. That is the role of inferential statistics. To test a hypothesis, we must evaluate multiple samples and verify the existence of suspected patterns. My hypothesis, for instance, in the above example might be that the mayor will win the upcoming election. To test that hypothesis, however, I would have to conduct multiple surveys in different neighborhoods at different times.

It would be a mistake to assume that a description of a sample necessarily reflects the properties of the entire population. The sample of voters on my sidewalk may not reflect the composition of voters in the entire city. Generalizing from a single sample to an entire population is dangerous: it confuses a hypothesis with a conclusion.

But that is the mistake that many traders make: They proceed directly from descriptions of recent markets to assumptions about future ones. They assume that the sample of recent price changes can be generalized to the population of all price changes. Thus, they'll conclude that the market is going to rise because the trendline is rising; that we have a bull market because stocks have been advancing.

The only way to know that, however, is to test a number of rising periods and see whether indeed rising prices in the past lead to future rises significantly more often than not. That's the role of inferential statistics, such as tests of significance.

Jeffrey Miller, Ph.D., in his blog A Dash of Insight, neatly frames the issue: We need ways of deciding whether or not market moves (or trader P/L) are due to luck.

That is the most common mistake traders make. We assume that strings of events are meaningful, when--much of the time--they reflect the luck of chance. The patterns perceived by our minds are not necessarily patterns that exist in nature.

The quantitative, system trader trades patterns that have been tested with inferential statistics. The discretionary trader trades descriptive hypotheses that he/she validates with updated, real-time readings of market conditions. Is the discretionary trader justified in doing that? The same inferential tests that inform us of the validity of trading systems, when applied to the trader's trading results, will answer that question.

That is why I find programs that establish and evaluate trader performance metrics, such as Trader DNA, to be so important. Only by evaluating results can discretionary traders know whether or not their judgments are adding skill to luck. Of the discretionary traders I know personally who have made more than a million dollars a year for multiple years, one characteristic stands out: they obsessively keep score. They track their results carefully, figure out what they're doing right or wrong, and make periodic adjustments. As Bill Rempel perceptively noted, they, too, are trading systems.