Standard Deviation

What Is Standard Deviation?

Standard deviation is a statistical measure of how spread out a set of values is around their arithmetic mean. In investing, it is most often used to describe how much an investment's returns have varied over time. A low standard deviation means returns stayed close to the average, while a high one means they swung more widely. It is usually represented by the Greek letter sigma (σ).

How It Is Calculated

The calculation takes a few steps. First, find the average of the values. Next, subtract that average from each value and square the result, so that negative and positive differences do not cancel out. Average those squared differences, which gives the variance, then take the square root to return to the original units.

For a complete population of values, the formula is:

σ = √[ Σ(xᵢ − μ)² / N ]

Here xᵢ is each value, μ is the mean, and N is the number of values. When working from a sample instead, analysts divide by N − 1, which gives a slightly larger estimate.

An Example

Suppose one fund returned 2%, 4%, 6%, 8% and 10% in five successive years. Its average is 6%. Using the sample method, its standard deviation is about 3.2%. A second fund returned 5%, 6%, 6%, 6% and 7%. It has the same average, but its standard deviation is about 0.7%, showing much more consistent results.

Why It Matters to Investors

Standard deviation is a common way to measure volatility, which is one part of investment risk. It is often read alongside average return, because two investments with similar averages can look very different once their variability is considered. Some analysts also use it in ratios such as the Sharpe ratio.

The measure has limits. It treats upward and downward swings alike, so it does not distinguish between gains and losses. It also assumes returns are roughly bell-shaped, following a normal distribution, which real market returns often do not. Past standard deviation does not guarantee future variability.