# Standard Deviation Explained

Standard deviation is a measure of volatility. When applied to investments, it can help investors determine a stock's riskiness.
Apr 12, 2022

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In investing, standard deviation is a way to measure the volatility of a stock, bond, fund or other financial instrument. Sometimes referred to as “volatility,” it’s one of the most commonly used metrics to project potential returns or losses from an investment.

In order to use it effectively, though, it’s important to understand how it works.

## What is standard deviation?

In a more technical sense, standard deviation is the square root of the variance of a group of numbers. Variance measures the average difference between a given number in a group of numbers, and that group’s average value

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If a group of numbers has a high standard deviation, you could assume the numbers in that group vary quite a bit from one another. On the flip side, if a group of numbers has a low standard deviation, then the numbers in that group don’t vary significantly from one another

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To illustrate this point, consider two groups of numbers with starkly different standard deviations.

Let’s pretend this first group of numbers — 12, 14, 13, 11 and 15 — represents the different values of a stock on five given days. So, across five days, the stock’s average trading price was \$12 per share, \$14 per share, \$13 per share, \$11 per share and \$15 per share. These values have a standard deviation of 1.41 and are graphed below.

As another example, let’s pretend this second group of numbers — 3, 19, 15, 7 and 24 — represents the values of a different stock across five days. This group of numbers has a standard deviation of 7.7, and are also graphed below.

As you can see, the numbers in the second group vary more from one another than the numbers in the first group. This variance is reflected in each group’s standard deviation.

According to Morningstar, a leading financial services and research firm, you can expect monthly returns for most funds to land in the range of one standard deviation of its average return 68% of the time. Roughly 95% of the time, you can expect future returns to fall within two standard deviations of its average return

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## How do you calculate standard deviation?

As stated above, the standard deviation is the square root of a group of numbers' variance.

In order to first find the group's variance, though, you must first find the group's average number. Then, you subtract that average number from each number in the group and square each new value. Finally, you'll need to find the average of those new values. That's your variance

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From there, find the square root of your variance. That's your standard deviation.

## What does standard deviation tell you about an investment’s riskiness?

When applied to investing, standard deviation tells you how often you can expect the price of a given stock or other financial instrument to vary from its average value.

For example, let’s say that a share of a company’s stock is usually trading at \$10 per share, with a standard deviation of two. This tells us that, on average, we can expect the value of that company’s stock to be trading at a value between \$8 and \$12 per share.

Here’s why:

• Low value: \$10 - 2 = \$8

• High value: \$10 + 2 = \$12

An even more detailed use of standard deviation tells us the company’s stock will likely trade at a value between \$8 and \$12 per share 68% of the time. We could also assume its stock would trade at a value between \$6 and \$14 per share 95% of the time.

Here’s why:

• Low value: \$8 (one standard deviation below \$10) - 2 = \$6

• High value: \$12 (one standard deviation above the mean) + 2 = \$14

## What is a good standard deviation?

There is no good or average standard deviation, says Maciej Kowara, associate director of manager research-quantitative research for Morningstar.

“It’s all related to what asset class you’re dealing with,” says Kowara. “You have to have some kind of a benchmark to compare against. There is no point in saying that a standard deviation of 5 is better than 15.”

To use standard deviation as a tool in investing, you should first determine the standard deviation of the stock you’re interested in buying. Most financial services websites, such as Morningstar and Yahoo Finance, list the standard deviation of a given stock or fund over several periods of time, in most cases, over the course of one year, five years and 15 years.

Once you know the standard deviation of the investment you’re interested in, look at the standard deviations of similar funds or stocks. For example, if you’re looking to invest in Facebook, consider the standard deviations of other large companies in tech or social media. As another example, if you’re considering investing in a fund focused on real estate development, take a look at the standard deviations of other similarly focused funds.

An investment is more volatile and risky if it has a higher standard deviation than similar funds. Conversely, a lower standard deviation would tell you that your investment’s returns will likely be more predictable than other similar stocks.

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