## Wednesday, April 28, 2010

### Risk is not the same as uncertainty

For many people semantic distinctions are niceties that are the stock in trade of rigid English teachers and zealous copy editors. They are ever so quickly glossed over by the infamous word “whatever.” But in the financial world a semantic distinction can sometimes differentiate profit from loss, innocence from culpability. We may care less about semantic precision in everyday conversation with our coworkers or neighbors, but when we’re building models or writing contracts we need not only a grasp of mathematics or the law but also of the subtleties of language. (And, no, I’m not going down the slippery slope of the meaning of “is.”)

In financial literature risk is often equated with uncertainty. But Terje Aven argues in Misconceptions of Risk that this equation fails to take consequences into account. He gives the extreme example of a case where there are only two possible outcomes, 0 and 1, corresponding to no and one fatality. “[T]he decision alternatives are A and B, having uncertainty (probability) distributions (0.5, 0.5) and (0.0001 and 0.9999), respectively. Hence, for alternative A there is a higher degree of uncertainty than for alternative B, meaning that risk according to this definition is higher for alternative A than for B. However, considering both dimensions, both uncertainty and the consequences, we would, of course, judge alternative B to have the highest risk as the negative outcome 1 is nearly certain to occur.” (p. 52)

Continuing on the fatality theme, Aven writes that we can predict the number of traffic fatalities in a given country over the course of the coming year with a high level of precision since there are rather small variations in traffic deaths from year to year. “The variance is small. Hence, seeing risk as uncertainty means that we have to conclude that the risk is small, even though the number of fatalities are many thousands each year. Again we see that this perspective leads to a non-intuitive language.” (p. 52)

For traders the distinction between risk and uncertainty should be apparent. All trades have uncertain outcomes; there is no way to measure this uncertainty. It matters not how good your trading strategy is, the fact remains that the outcome of each and every trade is uncertain. The trader hopes that he has devised a winning strategy that will pay off over a number of trades, but he can never know whether it will. The future may not resemble the past sufficiently to make his backtested system pay off, and outliers may (indeed, will) occur that will skew the results of his strategy dramatically, positively or negatively.

Trading risk, however, can and must be managed. Risk management is neither a perfect nor a precise science; the uncertainty inherent in the marketplace can bedevil even the best designed risk management scheme. But risk management is nonetheless the line in the sand between winners and losers. A mediocre trading strategy with great risk management will almost always beat a great trading strategy with poor risk management. (Note the lack of symmetry here; I didn’t say a poor trading strategy with great risk management would outperform.) Why is it, then, that traders are so lazy about devising risk management guidelines? I really don’t know. I’m a risk manager by temperament and I think it’s terrific fun to try to figure out ways to manage trades. (I’m not so great when it comes to portfolio management, but just give me another ten years or so!)