Example in definition, calculation, investment

  • Standard deviation is a measure of how much the return of an asset differs from its average return over a period of time.
  • Standard deviation is a commonly used gauge of volatility in securities, funds, and markets.
  • A high standard deviation indicates an asset in which there is greater volatility in prices and greater risk.
  • See Insider’s Investing Reference Library for more stories.

Standard deviation is a measure of how well the values ​​in a particular dataset are dispersed from the sample average. The concept applies to everything from curve ratings to weather forecasts and polls.

In investing, standard deviation is used to measure.


Up and down

An asset, portfolio, or market. It provides an indication of the level of risk for a particular investment and helps determine the desired rate of return.

Why is standard deviation important?

Standard deviation offers a measure of fluctuations for a particular asset. This measure can be used to estimate price performance trends and how much the investment can fluctuate over its expected return over a period of time.

“High standard deviations mean that investments have the potential to fluctuate with higher and lower levels,” says Brian Stevers, investment advisor and founder of Stevers Financial Services.

As an investor, you may want to consider the standard deviation of a particular asset in order to estimate the acceptable rate of return for the risks you are taking. For example, a stable blue chip company has less standard deviation in its stock, while fast-growing tech startups are more likely to have a standard deviation. Each stock has different expectations of investors for its return.

“For a very active investor, who trades on a regular basis, to test and follow market trends or momentum, he may prefer a high standard deviation if he thinks the market is his capital. Carrie is moving upwards with the goal of redistributing if it touches an acceptable height before the market starts trending downwards, “says Stevers.

On the other hand, investors with low risk tolerance may move to securities with low standard deviation, which is less different than their average rate of return.

How to find the standard deviation.

At first glance, the formula for standard deviation seems quite complex. But like every other mathematical equation, it can be divided into its variables so that you can keep things straight.

Here’s how it works:

Standard deviation formula


Rachel Mendelson / Inside


In mathematical terms, the standard deviation is equal to the square root of the variable.

Using this formula, let’s take a look at the standard deviation of the S&P 500 Index on a six-month basis from October 2021.

Return to S&P 500, May 2021-October 2021

First, determine the average rate of return.

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

With an average rate of return, we can put numbers into formulas.

The process begins with finding the change.

((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, square root of this number to find the standard deviation. This gives us a standard deviation of 3.8% for the S&P 500 for a period of six months.

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

What are the limits of standard deviation?

The standard deviation is based on a basic assumption that the data in question follows a general distribution pattern.

With a simple distribution, the values ​​will fall within a standard deviation of 68% of the time average. And values ​​will fall within two standard deviations of an average of 95% of the time. Therefore, any asset that does not follow the general pattern of distribution cannot be accurately estimated by standard deviation.

With that in mind, standard deviations can serve as a starting point to help you estimate the volatility of a particular investment. But with that measure, you should not decide to invest or break.

Stivers warns against making investment decisions based solely on its standard deviation.

“An investor needs to accept that standard deviation does not in any way guarantee that the investment will be more or less volatile,” he says. “History does not always repeat itself, so it is important for every investor to have a thorough assessment of their risk tolerance, time horizon, return expectations and ability to manage financial losses before choosing an investment. Take it. “

Take financial advantage

Standard deviation serves as an important way of measuring the volatility of a particular asset. This indicates how much the value of the asset has risen historically. The higher the number, the more fluctuations you can expect.

For investors, standard deviation can be used as a starting point for assessing the risks involved in a particular investment. While standard deviations can only shed light on past performance, investors can use the measurement as an indication of how much risk an asset can add to their portfolio.

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