Understanding the standard deviation

The standard deviation can show the consistency of an investment's performance over time.

A fund with a high standard deviation shows price volatility.

A fund with a low standard deviation tends to be more predictable.

The standard deviation is calculated by taking the square root of the variance, which is itself the average of the squared differences from the mean.

Understanding the standard deviation

One reason for the great popularity of the standard deviation measurement is its consistency.

The standard deviation of the mean represents the same, whether you look at gross domestic product (GDP), crop yield, or height of various dog breeds. Also, it is always calculated in the same units as the data set. You do not need to interpret an additional unit of measure resulting from the formula.

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Standard deviation measurement example

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, or average, value is 4.9%. The standard deviation is 2.46%. That means each individual annual value is on average 2.46% of the mean.

Each value is expressed as a percentage, making it easy to compare the relative volatility of various mutual funds.

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Due to its consistent mathematical properties, 68% of the values in any data set are within one standard deviation of the mean and 95% are within two standard deviations of the mean. Alternatively, you can estimate with 95% certainty that annual returns do not exceed the range created within two standard deviations of the mean.1

Bollinger Bands

When reversing, standard deviations are generally demonstrated with the use of Bollinger bands. Developed by technical trader John Bollinger in the 1980s, Bollinger bands are a series of lines that can help identify trends in a given value.2

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In the center is the exponential moving average (EMA), which reflects the average price of the security over a set period of time. On both sides of this line are bands established one to three standard deviations from the mean. These outer bands oscillate with the moving average according to changes in price.

In addition to their many useful applications, Bollinger Bands are used as an indicator of market volatility. When a security has experienced a period of high volatility, the bands are widely separated. As volatility decreases, the bands narrow, hugging the EMA.

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Standard deviation measures consistency. Consistency is good, but it is not the only measure of the quality of a fund.

Even the most limited range charts experience short bouts of volatility from time to time, often after earnings reports or product announcements. In these charts, the normally narrow Bollinger bands appear suddenly to accommodate increased activity. Once things settle down again, the bands tighten.

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Since many investment techniques depend on changing trends, being able to identify highly volatile stocks at a glance can be especially helpful.

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Other data to consider

While important, standard deviations should not be taken as a final measure of the value of an individual investment or portfolio. For example, a mutual fund that returns between 5% and 7% each year has a lower standard deviation than a competitor fund that returns between 6% and 16% each year, but that does not make it a Better option.

It is important to note that the standard deviation can only show the dispersion of a mutual fund's annual returns, which does not necessarily imply future consistency with this measurement. Economic factors, such as changes in interest rates, can always affect the performance of a mutual fund.

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Disadvantages of measuring standard deviation

Even as an assessment of the risks associated with a mutual fund, the standard deviation is not an independent answer. For example, the standard deviation only shows the consistency (or inconsistency) of the fund's returns. It does not show the fund's performance against its benchmark, which is measured as beta.

Another potential drawback to relying on the standard deviation is that it assumes a bell-shaped distribution of data values.1 This means that the equation indicates that there is an equal probability of achieving values above or below the mean. Many portfolios do not show this trend, and hedge funds especially tend to lean one way or the other.

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