Thursday, May 14, 2009

Another Failure for Standard Deviation

Carl Noble, one of our excellent Pinnacle analysts, just passed around a chart from Ned Davis Research showing the short-term standard deviation of the change in price between the Financial SPDR, (ticker XLF), an exchange-traded fund that owns a diversified basket of financial stocks, and the rest of the market as measured by the S&P 500 Index. The chart shows that for the past 44 days the relative out performance of the XLF versus the broad market has been a 13 standard deviation event. In other words, the odds of this relative price move, using the common measure of risk in the industry, is somewhere around (give or take) once per 6,117,160,000,000,000,000,000,000,000,000,000,000,000 times. That’s a little less than once per trillion trillions. To put it mildly, this price move, as measured by standard deviation, is statistically impossible. Yet here it is, just another failure for using standard deviation as a measure of risk in financial models.

There are two lessons to be learned from the chart. One is that standard deviation can severely understate the probability of events in the world of finance, and investors need to take care when using financial models that use standard deviation to measure risk. Internally, we use standard deviation when we build our risk models that predict portfolio volatility. Externally, we use standard deviation as the measure of risk in the portfolio policy statements signed by our clients, and in the scatter charts we use to demonstrate portfolio performance. In each case, the user must beware. The models communicate a level of certainty about portfolio risk and volatility that can be invalidated by the misbehavior of markets. The past year has reminded us that our caution in using this risk measure is justified.

The second lesson is that after a 13 standard deviation move to the upside, it certainly pays to think about selling. I don’t know if we will ultimately execute the transaction in our managed accounts, but it sure has our attention.