Standard deviation is a mathematical measurement of average variance and features prominently in statistics, economics, accounting and finance. For a given data set, the standard deviation measures how spread out numbers are from an average value. Standard deviation can be calculated by taking the square root of the variance, which itself is the average of the squared differences of the mean.

When it comes to mutual fund or hedge fund investing, analysts look to standard deviation more than any other risk measurement. By taking the standard deviation of a portfolio's annual rate of return, you can better measure the consistency with which returns are generated. Mutual funds with a long track record of consistent returns display a low standard deviation. Growth-oriented or emerging market funds, however, likely see more volatility and have a higher standard deviation, and therefore a larger degree of risk.

### The Consistency of Standard Deviation

One of the reasons for the widespread popularity of standard deviation measurements is their consistency. Not only does "one standard deviation from the mean" represent the same thing whether you are talking about gross domestic product (GDP), crop yields or the height of dogs, but it is always calculated in the same units as the data set. You never have to interpret an additional unit of measurement resulting from the formula.

For example, suppose a mutual fund achieves the following annual rates of return over the course of five years: 4%, 6%, 8.5%, 2% and 4%. The mean value, or average, is 4.9%. The standard deviation is 2.46%, meaning each individual yearly value is an average of 2.46% away from the mean. Every value is expressed in a percentage, and now the relative volatility is easier to compare among similar mutual funds.

Due to its consistent mathematical properties, 68% of the values in any data set lie within one standard deviation of the mean, and 95% lie within two standard deviations of the mean. Put another way, you can estimate with 95% certainty that annual returns do not exceed the range created within two standard deviations of the mean.

### Bollinger Bands

In investing, standard deviations are chiefly used under the guise of Bollinger bands. Developed by John Bollinger in the 1980s, Bollinger bands are a series of lines that can help identify trends in a given security. At the center is the exponential moving average (EMA), which reflects the average price of the security over an established time frame. To either side of this line are bands set one to three standard deviations away from the mean. These outer bands oscillate with the moving average according to changing price action.

In addition to numerous other useful applications, Bollinger Bands are used as an indicator of market volatility. When a security has experienced a period of great volatility, the bands are quite wide. As volatility decreases, the bands narrow, hugging closer to the EMA. Even the most range-bound charts experience brief spurts of volatility from time to time, after earnings reports or product releases, for example. In these charts, normally narrow Bollinger bands suddenly bubble out to accommodate the spike in activity. Once things settle again, the bands narrow. Because many investment techniques are dependent on changing trends, being able to identify highly volatile stocks at a glance can be an especially useful tool.

### Other Data to Consider

While important, standard deviations should not be taken as an end-all measurement of the worth of an individual investment or a portfolio. For example, a mutual fund that returns between 5% and 7% every single year has a lower standard deviation than a competing fund that returns between 6% and 16% every year, but it is clearly an inferior choice with all other things being equal.

It is important to note that standard deviation only shows the dispersion of annual returns for a mutual fund, which does not necessarily imply future consistency with this measurement. Economic factors such as interest rate changes can always affect performance of a mutual fund. When assessing risk associated with a mutual fund, standard deviation is not a standalone answer. For example, standard deviation only shows consistency or inconsistency of returns but does not show how well the fund performs against its benchmark, which is measured as beta.

Another potential weakness of relying on standard deviation to measure risk for a portfolio is it assumes a bell-shaped distribution of data values. This means the equation indicates the same probability exists for achieving values above the mean or below the mean. Many portfolios do not display this tendency, and hedge funds especially tend to be skewed in one direction or another.

The more securities held in a portfolio, and the more different types of securities, the more likely standard deviation may not be appropriate. Also, as with any statistical model, large data sets are more reliable than small data sets. The 4.9% mean and 2.46% standard deviation in the example above is not as reliable as the same values produced from 50 different calculations instead of five.

(For related reading, see: *What is the difference between standard deviation and average deviation?*)