Any time you invest, you have to accept risk. Even the most successful, dividend-paying, blue-chip companies will experience fluctuations in value, known in the market as volatility.
Investors often attempt to measure volatility as a measure of risk prior to making an investment. Although there are multiple ways of doing so, one of the most common metrics used to measure volatility is the standard deviation.
What Is Standard Deviation in Investing?
Standard deviation is a statistical measure designed to show how far away the furthest points in a data set are from the mean, or the average within the set. When it comes to investing, the data being analyzed is a set of the high and low points in a financial asset’s price over the course of a year, with the annual rate of return acting as the mean.
A low standard deviation shows that the asset doesn’t experience much volatility. A high standard deviation suggests high levels of volatility are the norm.
When applying the standard deviation to mutual funds, the mean is slightly different.
Mutual funds often attempt to track market benchmarks, with a focus on avoiding variability from the benchmark’s returns. These funds show the deviation from the benchmark’s returns by using the benchmark as the mean rather than the fund’s performance itself. This shows investors how far the fund return tends to deviate from expected returns.
What Does Standard Deviation Measure?
Take a look at this image:
You’ll notice that the data set forms a line with a hump in the middle, with the Greek letter mu (the u-like symbol) for the mean. Standard deviation measures how far a set of data points are spread out from this mean.
Data points farther from the center of this distribution curve occur less frequently. More than two-thirds (68.26%) of the time, the value stays within one standard deviation of the mean. The vast majority of the time (95.44%), it remains within two standard deviations. It almost always (99.72% of the time) stays within three standard deviations.
In investing, this dispersion reflects how far the price of an asset typically deviates from the average price.
For example, a stock with a 10% standard deviation will generally fluctuate 10% up or down in a typical year (one standard deviation). It will rarely move 20% up or down (two standard deviations) and only very rarely fluctuate 30% up or down (three standard deviations).
Note: Standard deviation measures all volatility as risk, regardless of direction. This means that even when the movement is in the investor’s favor, anything above average gains is considered heightened volatility, and therefore risk.
How to Calculate the Standard Deviation
The standard deviation is calculated as the square root of the variance from the mean in a data set. This may sound confusing at first, but read on, and you’ll find that it’s quite simple to calculate, especially with Excel or Google Sheets.
The Standard Deviation Formula
Don’t let the formula above fool you — there are only a few steps to calculating the standard deviation, and the process is relatively simple. Here’s how it’s done:
- Step #1: Find the Mean. The mean is calculated by adding all your data points together and dividing your total by the number of data points. Essentially, you’re finding an average for your data. Most investors use historical data of the stock’s closing price over the past five years as their data set to determine the standard deviation of a stock.
- Step #2: Subtract the Mean. Subtract the mean from each data point.
- Step #3: Square the Results. Once the mean has been subtracted from each data point, square the results (multiply each number by itself).
- Step #4: Calculate the Variance. Add all squared results together and subtract 1. This gives you the variance.
- Step #5: Find the Standard Deviation. Finally, calculate the square root of the variance calculated in Step #4 to determine the standard deviation of the data set.
Using Excel & Google Sheets to Calculate Standard Deviation
Done by hand, this can involve a lot of math, especially for large data sets. To make it simpler, you can use the power of spreadsheets to find the standard deviation of any data set, including stock price changes, using either Microsoft Excel or Google Sheets.
In either software, use one row for all data in your data set. In an empty cell, type =STDEV( to call up the standard deviation function. Now, click the first data point and drag the mouse to the last data point before typing ) and hitting enter. Excel or Google Sheets will handle all the math for you.
Example of Standard Deviation
In investing, standard deviation is generally calculated using percentages gained or lost.
For example, say ABC stock gained 25% in year one, 10% in year two, 2% in year three, and 17% in year four.
Step #1: Find the Mean
To find the standard deviation in this example, you’ll start by finding the average (mean) of all of these values by adding them together and dividing by 4. This yields a mean return, or average annual return, of 13.5%.
Now, it’s time to figure out how much annual returns tend to deviate from the average return of ABC stock.
Step #2: Subtract the Mean
Start by subtracting the mean you calculated (13.5%) from each of the values. Doing so gives you 11.5, -3.5, -11.5, and 3.5.
Step #3: Square the Results
Next, square each of these values by multiplying them by themselves. When you do, you’ll end up with the values 132.25, 12.25, 132.25, and 12.25.
Step #4: Calculate the Variance
Add these together and divide the total by one less than the number of data points. This data set has 4 data points, so you’d divide by 3. In this case, you get a variance of 96.34.
Step #5: Find the Standard Deviation
Finally, to find the standard deviation, simply find the square root of the variance, or the square root of 96.34. In this case, the standard deviation is 9.815%.
What the Standard Deviation Tells You About an Investment
The standard deviation was designed to show investors how far an investment might be expected to stray from its average annual returns. A lower standard deviation suggests that the financial asset tends to provide reliable, easy-to-predict returns. A higher standard deviation suggests the financial asset’s annual returns tend to vary wildly from one year to the next.
Standard Deviation FAQs
With the standard deviation being one of the most common measures of volatility in the stock market, it only makes sense that there’s quite a few frequently asked questions about this statistical measure. Some of the most common include:
What Is a Good Standard Deviation?
What qualifies as a “good” deviation to shoot for is a relatively objective measure. Everyone’s goals and risk appetite are different.
However, if you’re a risk-averse investor, you’ll want to shoot for a standard deviation of 10% or less. This means during any given year, the returns generated by the asset may be 10% higher or lower than the average returns generated on an annual basis.
If you’re an investor with a healthy risk appetite, you’ll want to shoot for a higher deviation, ultimately looking for stocks that have the potential to generate dramatic returns. In this case, a deviation of 35%, 40%, or higher is perfectly acceptable.
Just keep in mind that a higher deviation might suggest the potential for larger returns, but it also suggests that there’s potential for equally significant declines.
What Does a High Standard Deviation Mean?
An investment opportunity with a higher standard deviation is considered to be a riskier investment because the returns on the investment are known to vary wildly from one year to the next.
What Is One Standard Deviation From the Mean?
This means that the data set has moved in the amount of the standard deviation.
For example, if XYZ is known for producing 10% gains with a 10% standard deviation, and the returns on the stock last year were 9%, it produced returns that were one standard deviation lower than average.
What Is Two Standard Deviations From the Mean?
Using the XYZ stock example above, if the stock produced returns of 12%, it would mean the stock produced returns two standard deviations above the mean, or two times the average standard deviation it’s known to experience.
When the standard deviation was developed in 1893, it would have been relatively difficult for the average investor to find any use for it due to the complex calculations involved in finding square roots. However, thanks to widely available software, finding the deviation of a stock from its average return is as simple as launching a spreadsheet and punching in a few figures.
Considering the simplicity of access to this data these days, there’s no reason to leave it out of your investment research. By paying close attention to this data, you’ll be able to find stocks that produce similar returns and choose the best option based on the amount of risk you must accept. All told, the standard deviation is a powerful tool.