5 Steps to Calculating Standard Deviation

  • An asset’s standard deviation tells you how much its particular and average returns vary.
  • You can quickly calculate or look up the standard deviation of different assets.
  • A high standard deviation can indicate the asset’s returns will be more volatile.

Investors need to consider different types of risk when they’re choosing which investments to buy and sell. One of these risks is related to an investment or a portfolio’s volatility. Higher


volatility

may be riskier as big price swings can be hard to stomach and may make predicting an investment’s returns more difficult.

Standard deviation is used in many fields and situations to help determine a data point’s distance from a data set’s average. Within investing, which is what we’ll focus on, an asset or portfolio’s standard deviation is one way to assess its potential volatility.

What is a standard deviation?

Standard deviation — also referred to by the Greek letter sigma (σ) — measures how far an asset’s returns have been from its average return in a specific period. Investments that have a higher standard deviation may be more volatile, and could be prone to larger price swings.

“It’s like when you’re meeting a friend, and you tell him you’ll arrive at 1 pm, plus or minus 15 minutes,” says Alvin Carlos, a financial planner at District Capital Management. “The 15 minutes is your standard deviation.”

However, the standard deviation isn’t predictive. Instead, it tells you how volatile the asset has been in the past.

5 steps to calculate standard deviation

To find an asset’s standard deviation for a certain period of time, you’ll need to compare its returns at different points to its average return. Specifically, you’ll find the square root of the variance, and the formula looks like this:

Standard deviation formula


Rachel Mendelson/Insider


If you break down the equation step-by-step, you’ll find it’s not too difficult to calculate on your own. As an example, we can find the standard deviation for the S&P 500 during the first six months of 2021.

Step 1. Calculate the average return (the mean) for the period

Start by finding the average return, or mean, of the data points within the period. Here, we looked up historical returns to find how well the S&P 500 performed each month.

S&P 500 returns for Jan. 2021 to June 2021

To find the average, add up the six monthly returns and divide by six.

(-1.11 + 2.61 + 4.24 + 5.24 + 0.55 + 2.22) / 6 = 2.29

Step 2. Find the square of the difference between the return and the mean

Once you have the mean, you can find the square of the difference between the actual rate of return (ri ) and the average rate of return (ravg) for each month.

For example, in January, it would be (-1.11 – 2.29)2 = 11.56

February is (2.61 – 2.29)2 = 0.10

Repeat the process for all six months.

Step 3. Add the results

Now, add the results from step two to find the numerator (the number above the line) in the equation.

In this case, the result is 27.2

Step 4. Divide the result by the number of data points minus one

Next, divide the amount from step three by the number of data points (ie, months) minus one.

So, 27.2 / (6 – 1) = 5.44

Step 5. Take the square root

Finally, take the square root of the result — √5.44 — to find the standard deviation, which is 2.33%.

Don’t worry if that seems like a lot of math. There are plenty of online calculators you can use, and spreadsheet programs like Excel and Google Sheets have a built-in formula:

=STDEV(point, [point2, …])

Because it’s a commonly used financial metric, some investment analysis websites and programs will show you an asset’s standard deviations over different periods.

How to use standard deviation

Investors may use the standard deviation for an asset, whether that’s a specific stock or an index fund, as part of technical analysis. It can also be an indicator of an asset’s potential volatility and rate of return.

Within a normal distribution — an inverted bell-shaped curve — an asset’s returns may fall within one standard deviation of the average 68% of the time, within two standard deviations 95% of the time, and within three standard deviations 99% of the time .

“In investing, you may have read that the stock market has historically returned 10%,” says Carlos. “That doesn’t mean you’ll get a 10% return each year.” Instead, Carlos explains, you might expect a return of 10% plus or minus one standard deviation.

For example, over the last 10 years, the S&P 500’s average annual return was 9.2%, and it had an annual standard deviation of about 13%. So, you might conclude that there’s a 68% chance the next year’s returns will fall within the -3.8% to 22.2% range.

The financial takeaway

An asset’s standard deviation isn’t enough to tell you whether or not investing is a good idea. It’s also not predictive, as an asset’s historical price changes don’t necessarily align with its future returns. Still, it can be informative.

Carlos points to emerging market and US small-cap stocks, which have a higher standard deviation than US investment-grade bonds. “The higher your investment’s standard deviation, the wilder the price swings you’ll experience,” he says.

More volatility investments may be desirable in some cases, particularly if you have a long time horizon. But it can also be risky to hold volatile assets if you’re actively trading or may need the money soon.

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