What Is Downside Deviation?

Definition & Examples of Downside Deviation

Woman sitting in front of a laptop and using a calculator

 mapodile / Getty Images

Downside deviation measures risk and price volatility of investments by comparing returns that fall below the average annual return to minimum investment thresholds. It can be used to compare multiple potential investments, even when they have similar average annual returns.

Learn how downside deviation is calculated and used to compare investments.

What Is Downside Deviation?

While there is no surefire way to predict the future performance of investments, 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, particularly when it falls short of the average. This measure is called downside deviation.

Investors can also examine instances of when the stock falls short or exceeds the average to determine its standard deviation.

Downside deviation is a measure of price volatility. 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 experience significant losses in short periods of time.

How Downside Deviation Works

As an investor, you generally want an investment that has consistent, positive returns instead of one that has wild swings up and down. 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 relatively simple formula. To illustrate this, 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, this is called your minimal acceptable return, or MAR. The annual returns over 10 years are:

  • 2019: 6%
  • 2018: 10%
  • 2017: 7%
  • 2016: -2%
  • 2015: 8%
  • 2014: 9%
  • 2013: -4%
  • 2012: 3%
  • 2011: -1%
  • 2010: 10%

The average annual return was 4.6%, and there were four periods were 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:

  • 2019: 1%
  • 2018: 5%
  • 2017: 2%
  • 2016: -7%
  • 2015: 3%
  • 2014: 4%
  • 2013: -9%
  • 2012: -2%
  • 2011: -6%
  • 2010: 5%

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

  • 2016: -7%
  • 2013: -9%
  • 2012: -2%
  • 2011: -6%

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

  • -49
  • -81
  • -4
  • -36

Then add these figures for a total of -170.

Divide this figure by the total number the 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 17.9 of this is about 4.23.

This investment has a downside deviation of 4.23%.

How to Use Downside Deviation

Numbers don’t mean anything in a vacuum. Downside deviation is most useful when it's used to compare two potential investments.

Another company may have an identical average annual return over the same 10-year period but different yearly returns, such as:

  • 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 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 1.1%.

Thus, the downside deviation of the second company is significantly lower than that of the first, despite showing the same average annual returns.

This matters to you as an investor, because it’s preferable to invest in a stock with consistent, positive returns, rather than one with high volatility. This is especially important for short-term investors who would be hurt by any sharp downturn in the value of their stock portfolio.

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 worth it to achieve a certain return. The higher the ratio, the better 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 this case, the second company could be considered a better investment, despite having the same annual returns.

Key Takeaways

  • Downside deviation is a value that can help investors calculate the price volatility of an investment.
  • Unlike standard deviation, this measures only downside returns that fall below minimum investment thresholds.
  • Comparing the downside deviation of different investments can help you determine which is more likely to experience significant losses and which is a safer investment, even if their average annual returns are similar.

Article Sources

  1. Morningstar. "Downside Deviation." Accessed Aug. 21, 2020.