Sigma is another of the Greeks, important statistical measures commonly referenced in the world of alternative investments. Sigma refers to the volatility of an asset or fund. Statistically speaking Sigma is the standard deviation of that asset or fund’s returns, and is therefor an important measure of risk.
Q. So, another one of those wonderful Greek letters we need to know to evaluate hedge fund performance. What’s this one about?
A. This is one of the more important statistics. Sigma refers to the standard deviation, or volatility, of a fund. As we know, we always want to check not just the total returns that a manager has generated, but how much risk he took to get there. The most basic was to see that is to look at the Sigma.
Q. So exactly how does Standard Deviation tell us about the risk? What is it exactly that makes Sigma so helpful?
A. Standard deviation is a measure of how well clustered a data set is around its mean. If most of the numbers in a series – say, monthly investment returns –are close to the average of those numbers, the standard deviation is low. But if there’s a very wide band into which those results fall, if the numbers are widely dispersed as compared to the average, the standard deviation is high. So Sigma is telling us, essentially, how erratic the returns have been. The higher the Sigma, the greater the variation in the returns over time has been. In theory, that means more risk was taken.
Q. So how about a very simple example of how we’d use this?
A. One fund returns an average of 5% with a sigma of 5; another one returns 6 with a sigma of 10. Nearly all professionals would tell you the first one is a better investment, because the extra 1% the second fund provides is not worth the additional risk: odds are that his future returns will involve more downside than the first fund.
Q. OK. And what kind of Sigma should someone be looking for, then?
A. Very tough to answer by itself, which is why we use the other measures, like Alpha and Sharpe, to consider at the same time. For example, a skilled momentum trader who uses leverage might have high volatility, but still outperform the market and be generating both Alpha and a good Sharpe ratio. So, overall, you’d like to be under a 6 or maybe 8 number for the Sigma…it’s a very important number, but still just one of the factors to consider.