What Is Downside Deviation?

What Is Downside Deviation?

While there is no surefire way to predict the how well an investment will perform, you can examine past returns to get a sense of how much you’ll likely earn over time.

In addition to looking at a stock's average monthly and annual returns, it’s helpful to review how often, and to what degree, its performance deviates from that average, especially when it falls short of the average. This measure is called "downside deviation."

Downside deviation is a measure of price volatility, or how stable it is over a certain amount of time. It looks at the returns over time and calculates how likely they are to fall below the average return. Comparing the downside deviation of different stocks can help you avoid highly volatile stocks that may suffer from severe losses in short amounts of time.

How Downside Deviation Works

Most investors' goal is to focus their money into assets that have consistent, positive returns, instead of assets that have wild swings up and down. (Of course, there are some investors who deal in riskier methods, but here, we'll assume a more modest approach.) Downside deviation can help you calculate the downside risk on returns that fall below your minimum threshold.

A stock with a high downside deviation can be considered less valuable than one with a normal deviation, even if their average returns over time are identical. That’s because when a stock dips, it will require higher returns in the future to get back to where it was.

How To Calculate Downside Deviation

Downside deviation can be determined through a simple formula. By way of example, we’ll examine the performance of a fictional company.

If you’d like to see that company's stock earn an average of 5% annually, that is called your "minimal acceptable return," or MAR. The company's annual returns over 10 years are:

• 2022: -4%
• 2021: 3%
• 2020: -1%
• 2019: 10%
• 2018: 6%
• 2017: 10%
• 2016: 7%
• 2015: -2%
• 2014: 8%
• 2013: 9%
  

The average annual return was 4.6%, and there were four periods when the annual performance was lower than your MAR of 5%.

To determine downside deviation, start by subtracting your MAR of 5% from these annual totals. The results are:

• 2022: -9%
• 2021: -2%
• 2020: -6%
• 2019: 5%
• 2018: 1%
• 2017: 5%
• 2016: 2%
• 2015: -7%
• 2014: 3%
• 2013: 4%

Then remove any instance where the return is positive. That leaves:

• 2022: -9%
• 2021: -2%
• 2020: -6%
• 2015: -7%

The next step is to square the differences. This results in:

• 81
• 4
• 36
• 49

Then add these figures for a total of 170.

Divide this figure by the total number of periods being examined (in this case, 10), and calculate the square root of that number's absolute value: 179 divided by 10 is 17.9, and the square root of 17.9 is about 4.23.

This investment has a downside deviation of about 4.23%.

How To Use Downside Deviation

Numbers don’t mean anything in a vacuum. Downside deviation is most useful in comparing two potential investments.

Let's look at a second fictional company. This one has an identical average annual return over the same 10-year period as the first, but different yearly returns:

• 2019: 5%
• 2018: 5%
• 2017: 6%
• 2016: 5%
• 2015: 3%
• 2014: 3%
• 2013: 3%
• 2012: 5%
• 2011: 6%
• 2010: 5%

This stock shows three periods where returns were lower than the MAR of 5%, with a difference of -2% in each instance. The total of the squares of these three instances is -12%, and when we divide by the total of 10 periods, we come up with -1.2%. The square root of 1.2 is about 1.1, for a downside deviation of about 1.1%.

Thus, the downside deviation of the second company is much lower than that of the first, even though both showed the same average annual returns.

This distinction matters to you as an investor because you'd much prefer to invest in a stock with consistent, positive returns rather than one with high volatility. This priority is especially important for short-term investors, who would be hurt by any sharp downturn in the value of their stock portfolios.

Comparing Investments With the Sortino Ratio

You also can use downside deviation to determine the Sortino Ratio, which is a measure of whether the downside risk is worthwhile to achieve a certain return. The higher the ratio, the better it is for the investor.

The Sortino Ratio can be calculated by taking the average annual return and subtracting a risk-free rate, then dividing that total by the downside deviation figure. The risk-free rate is usually that of U.S. Treasury Bills, for example, 2.5%.

For the first company above, subtract 2.5% from 4.6% to get 2.1%, then divide that by the downside deviation of 4.23. The result is 0.496.

Using the same formula with the second set of returns, the result is 1.909. In that case, the second company could be considered a better investment, even though it shows the same annual returns.