# Standard deviation: A measure of risk based on how widely an asset's price fluctuates over a given period of time Knowing an investment's historical volatility helps determine a required rate of return.SeventyFour/Getty
• Standard deviation is a measure of how much an asset's return varies from its average return over a set period of time.
• Standard deviation is a commonly used gauge of volatility in securities, funds, and markets.
• A high standard deviation indicates an asset with larger price swings and greater risk.

Standard deviation is a measure of how dispersed the values in a particular data set are from the average of the sample. The concept is applied in everything from grading on a curve, to weather forecasting, and opinion polling.

In investing, standard deviation is used to measure the volatility of an asset, portfolio, or market. This provides an indication of the level of risk for a particular investment and helps to determine the required rate of return.

## Why does standard deviation matter?

Standard deviation offers a measurement of the volatility for a particular asset. That measurement can be used to predict price performance trends and how much an investment might fluctuate from its expected return over a given period of time.

"A higher standard deviation means the investment has more volatility potential with higher highs and lower lows," says Brian Stivers, an investment advisor and founder of Stivers Financial Services.

As an investor, you can consider the standard deviation of a particular asset to evaluate what rate of return is acceptable for the risks you are taking on. For example, the stock of a stable blue-chip company tends to have a lower standard deviation, while a fast-growing tech startup is more likely to have a higher standard deviation. Each carries different expectations for its return to stock investors.

Note: If a stock has a high standard deviation it means the price swings widely, which is a greater risk for investors.

"For a very active investor, who trades on a regular basis, to try and follow the trends or momentum in the marketplace, they may prefer a higher standard deviation if they believe the market is heading upward with the goal of reallocating their investment if it hits an acceptable high before the market begins to trend downward," Stivers says.

On the flip side, investors with a lower risk tolerance may steer toward securities with a lower standard deviation, which tend to vary less from their average rate of return.

## How to find standard deviation

At first glance, the formula for standard deviation appears rather complicated. But like every other mathematical equation, it can be broken down into its distinct variables to help you keep things straight.

Here's how it works:

In mathematical terms, the standard deviation equals the square root of the variance.

Using this formula, let's take a look at the standard deviation for the S&P 500 Index based on the six months through October 2021.

### Returns for S&P 500, May 2021-October 2021

 Month Return October 2021 6.9% September 2021 -4.8% August 2021 2.9% July 2021 2.3% June 2021 2.2% May 2021 0.6%

First, determine the average rate of return.

(6.9 - 4.8 + 2.9 + 2.3 + 2.2 + 0.6) / 6= 1.68

With the average rate of return, we can plug the numbers into the formula.

That process starts with finding the variance

((6.9 - 1.68)2 + (-4.8 - 1.68)2 + (2.90 - 1.68)2 + (2.3 - 1.68)2 + (2.2 - 1.68)2 +(0.6 - 1.68)2) / (6-1) = 14.509667

Now, take the square root of that number to find the standard deviation. That gives us 3.8% as a standard deviation for the S&P 500 for the six-month period.

The good news is that you probably won't need to calculate the standard deviation for an investment manually. Instead, you can take advantage of the formulas already built into spreadsheet programs like Excel or Google Sheets. If you have the historical data available, it should take just a few clicks to find the standard deviation.

## What are the limits of standard deviation?

Standard deviation is based on an underlying assumption that the data set in question follows a pattern of normal distribution.

With a normal distribution, the values will fall within one standard deviation of the mean 68% of the time. And values will fall within two standard deviations of the mean 95% of the time. So, any asset that doesn't follow a normal pattern of distribution cannot be accurately evaluated through its standard deviation.

With that in mind, the standard deviation can serve as a starting point to help you evaluate the volatility of a particular investment. But this measurement shouldn't make or break your decision to take on an investment.

Quick Tip: Standard deviation is based on historical data, which provides insight into the past. But past performance doesn't always line up with future results.

Stivers warns against making an investment decision solely on the basis of its standard deviation.

"An investor needs to accept that standard deviation in no way guarantees an investment will be more or less volatile," he says. "History doesn't always repeat itself, so it is essential for each investor to fully evaluate their risk tolerance, time horizon, return expectations and ability to overcome financial losses before choosing an investment."