Definition, calculation, example of investment

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  • Standard deviation is a measure of how much an asset’s return has changed relative to its average return over a period of time.
  • Standard deviation is a commonly used indicator of the volatility of securities, funds and markets.
  • A high standard deviation indicates an asset with larger price fluctuations and higher risk.
  • Visit Insider’s Investment Reference Library for more stories.

Standard deviation is a measure of the dispersion of values ​​in a particular data set from the sample mean. The concept is applied in everything from ranking on a curve to weather forecasts and opinion polls.

In investment, the standard deviation is used to measure the


volatility

of an asset, portfolio or market. This gives an indication of the level of risk for a particular investment and helps determine the required rate of return.

Why is the standard deviation important?

Standard deviation provides a measure of the volatility of a particular asset. This metric can be used to predict price performance trends and how much an investment may fluctuate from its expected return over a period of time.

“A higher standard deviation means that the investment has a potential for higher volatility with higher highs and lower lows,” says Brian Stivers, investment advisor and founder of Stivers Financial Services.

As an investor, you can consider the standard deviation of a particular asset to assess what rate of return is acceptable for the risks you take. 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. Everyone has different expectations for their return to stock investors.

“For a very active investor, who trades regularly, to try to keep up with trends or market dynamics, he may prefer a higher standard deviation if he thinks the market is going up in order to reallocate his investment. it reaches an acceptable high before the market starts to fall, ”says Stivers.

On the other hand, investors with a lower tolerance for risk may look to securities with a lower standard deviation, which tend to vary less from their average rate of return.

How to find the standard deviation

At first glance, the formula for the standard deviation seems quite complicated. But like any other mathematical equation, it can be broken down into its separate variables to help keep things straight.

This is how it works:

Standard deviation formula


Rachel Mendelson / Insider


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

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

Returns for the 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 the average rate of return, we can fit the numbers into the formula.

This process begins by 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. This gives us 3.8% as the standard deviation for the S&P 500 for the six month period.

The good news is that you probably won’t need to manually calculate the standard deviation of an investment. Instead, you can take advantage of formulas already built into spreadsheets like Excel or Google Sheets. If you have the historical data, it will only take a few clicks to find the standard deviation.

What are the limits of the standard deviation?

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

With a normal distribution, the values ​​will be within one standard deviation of the mean 68% of the time. And the values ​​will be within two standard deviations of the mean 95% of the time. Thus, any asset that does not follow a normal distribution pattern cannot be accurately measured through its standard deviation.

With that in mind, the standard deviation can serve as a starting point to help you assess the volatility of a particular investment. But this step should not make or break your decision to undertake an investment.

Stivers cautions against making an investment decision based solely on its standard deviation.

“An investor must accept that the standard deviation is no guarantee that an investment will be more or less volatile,” he says. “History doesn’t always repeat itself, so it is essential that every investor fully assesses their risk tolerance, time horizon, return expectations and ability to weather financial losses before choosing an investment.”

The financial report

Standard deviation is an important way to measure the volatility of a particular asset. It indicates how far the price of the asset has fluctuated historically. The higher the number, the more volatility you can expect.

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

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