Definition
Downside deviation measures the risk and price fluctuations of investments by comparing returns that fall below the average annual return with the minimum investment threshold.
What is Downside Deviation?
Although there is no guaranteed way to predict investment performance accurately, you can study past returns to gain an idea of how much profit you are likely to achieve over time.
In addition to considering the monthly and annual average returns on stocks, it is helpful to review how much their performance deviates from that average, especially when performance is below average. This measurement is called “downside deviation.”
How Does Downside Deviation Work?
The goal of most investors is to direct their money into assets that yield positive and consistent returns rather than assets that swing wildly. Downside deviation can help calculate the risks associated with returns that fall below the required minimum.
Stocks with a high downside deviation may be considered less valuable than those with a normal deviation, even if their average annual returns are identical. This is because when a stock’s value declines, you will need higher future returns to get back to its previous level.
How to Calculate Downside Deviation
Downside deviation can be determined using a simple formula. For example, let’s study the performance of a fictional company.
If you would like to see that company’s stock achieve an average annual return of 5%, this is called the “minimum acceptable return” or MAR. The annual returns for the company over the past 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 below your MAR of 5%.
To calculate 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 returns are positive. This leaves:
2022: -9% 2021: -2% 2020: -6% 2015: -7%
The next step is to square the deviations. This results in:
8143649
Then add these numbers to get a total of 170.
Divide this number by the total number of periods studied (in this case, 10), and calculate the square root of the absolute value: 179 divided by 10 equals 17.9, and the square root of 17.9 is approximately 4.23.
The downside deviation for this investment is about 4.23%.
How to Use Downside Deviation
Numbers mean nothing in isolation. Downside deviation is most useful when comparing two potential investments.
Let’s take a look at a second fictional company. This company achieves an identical average annual return over the same 10-year period as the first company, but there is a difference in annual 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 below MAR by 5%, with a difference of -2% in each case. The total of the squares of these three cases is -12%, and when we divide by the total of 10 periods, we get -1.2%. The square root of 1.2 is approximately 1.1, giving a downside deviation of about 1.1%.
Thus, the downside deviation of the second company is much lower than that of the first company, even though both show the same average annual return.
These differences matter to you as an investor because you prefer to invest in stocks that yield positive and consistent returns rather than in stocks with high volatility. This is especially important for short-term investors, who will be affected by any sharp declines in the value of their equity portfolios.
Comparing Investments Using the Sortino Ratio
You can also use downside deviation to determine the Sortino ratio, which is a measure of whether the risks associated with downside are worth achieving a certain return. The higher the ratio, the better it is for the investor.
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Calculating the Sortino ratio involves subtracting the average annual return and the risk-free rate, then dividing the total by the downside deviation. The risk-free interest rate is typically the U.S. Treasury bond rate; for example, 2.5%.
For the first company mentioned 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 can be considered a better investment, even though it shows the same annual returns.
Source: https://www.thebalancemoney.com/what-is-downside-deviation-4590379
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