Investors who believe that financial markets have evolved into “quants” versus “traditionalists” have forgotten the admonition that the investment industry is built on disagreement. There is ample disagreement as to the motivations to trade among quants and traditional investors alike. Therefore, it is a fiction to say that quants are on one side of trades and traditional investors are on the other. The investors in this case still could not, on average, beat the market. They were, however, able to avoid large negative variations through diversification. Because the concept of a standard deviation plays an important role in modern finance, it is useful to understand the basics of this popular statistical measure.
A standard deviation is a measure of variability around a mean. If it is assumed that the observations of a given characteristic, or value, cluster around the mean in a normal fashion, the computed standard deviation has a very convenient property: 68.0 percent of the values fall within plus or minus one standard deviation from the mean; 95.5 percent of the values fall within plus or minus two standard deviations from the mean; and 99.7 percent of the values fall within plus or minus three standard deviations from the mean.
Because 68.0 percent is very close to two-thirds (66.7 percent), a convenient rule of thumb is that the chances are two out of three that an expected value will fall within one standard deviation (plus or minus) of the mean. The key point to remember is that the smaller the standard deviation, the smaller the probability of a result that is far from the mean.