Standard Deviation vs Downside Deviation: Measuring the Right Risk

Key Takeaways

• Standard deviation measures dispersion around the mean and treats an unusually large gain as just as "risky" as an equally large loss.
• Downside deviation measures dispersion below a minimum acceptable return (MAR), so only shortfalls count and upside swings are ignored.
• Downside deviation is always less than or equal to standard deviation for the same series whenever there is any upside variability.
• Use standard deviation for symmetric, roughly normal returns; use downside deviation when returns are skewed and you care about losses, not volatility itself.

What It Is

Standard deviation is the square root of variance: the average distance of each return from the mean of the series. It is symmetric by construction, so a return 10 points above the mean and a return 10 points below the mean contribute identically to the total.

Downside deviation keeps the same square-root-of-averaged-squares machinery but changes two things. It measures distance from a chosen target, the minimum acceptable return (MAR), rather than from the mean. And it includes only returns that fall below that target; every return at or above the MAR contributes zero. The result is a one-sided volatility number focused on the outcomes an investor wants to avoid.

The Intuition

No investor complains about a surprise gain. Yet standard deviation, by squaring both positive and negative deviations, penalizes a strategy for having big up-months exactly as much as for having big down-months. That is fine when returns are symmetric, because the two sides roughly balance. It is misleading when they are not.

Downside deviation encodes the plain-language idea of risk that most people carry: risk is falling short of what I needed. Set the MAR to the outcome you cannot accept slipping below, then measure only how far and how often returns dropped under it. Upside becomes free.

How It Works

Both statistics follow the same three steps: compute deviations, square them, average, and take the square root. They differ in what feeds the deviations.

• Standard deviation = square root of the average of (each return minus the mean) squared.
• Downside deviation = square root of the average of min(0, each return minus the MAR) squared.

The min(0, ...) term is the whole story. Any return above the MAR produces a positive value inside the parentheses, which min(0, ...) forces to zero, so it drops out of the sum. Because you are adding fewer (and never more) squared terms than standard deviation does, downside deviation cannot exceed standard deviation for the same series once there is any upside dispersion. Note the convention followed here: the sum is divided by the total number of periods, not by the count of losing periods only, which keeps the two measures on a comparable footing.

Worked Example

A strategy posts five annual returns: 10%, -6%, 14%, -4%, 8%. Set the MAR at 0%.

Standard deviation first. The mean is (10 - 6 + 14 - 4 + 8) / 5 = 22 / 5 = 4.4%. Squared deviations from that mean:

• (10 - 4.4)^2 = 5.6^2 = 31.36
• (-6 - 4.4)^2 = (-10.4)^2 = 108.16
• (14 - 4.4)^2 = 9.6^2 = 92.16
• (-4 - 4.4)^2 = (-8.4)^2 = 70.56
• (8 - 4.4)^2 = 3.6^2 = 12.96

The sum is 315.2, so variance = 315.2 / 5 = 63.04 and standard deviation = 7.94%.

Now downside deviation against the 0% MAR. Only the -6% and -4% years fall below zero; the three positive years contribute nothing. Their squared shortfalls are (-6)^2 = 36 and (-4)^2 = 16, summing to 52. Divide by the full five periods: 52 / 5 = 10.4, and downside deviation = 3.22%.

Same track record, two very different numbers: 7.94% of total volatility, but only 3.22% of it lives below the target. The gap is the upside the two positive-heavy years contributed, which standard deviation counts as risk and downside deviation discards.

Common Mistakes

1. Comparing the two numbers directly. Downside deviation is almost always smaller. A lower downside deviation is not the same fund "being safer" than one quoted with standard deviation; they are different measures.
2. Forgetting to state the MAR. Downside deviation is undefined until you pick a target. A 0%, risk-free-rate, and required-hurdle MAR give three different answers for the same returns.
3. Dividing by the count of losses only. Using only the number of downside periods in the denominator inflates the figure and breaks comparability with standard deviation. Divide by the total number of periods.
4. Assuming they disagree. For symmetric, roughly normal returns the two move together and rank strategies almost identically. The divergence only appears with skew.

Frequently Asked Questions

Q: What is the standard deviation vs downside deviation difference in plain terms? Standard deviation measures how far all returns scatter from the average, counting big gains and big losses alike. Downside deviation measures how far returns fall below a chosen target, so only shortfalls count and upside is ignored.

Q: Is downside deviation always lower than standard deviation? For the same return series it is less than or equal to standard deviation whenever there is any upside variability, because the upside deviations are set to zero rather than added in. If every return were below the MAR, the two could coincide.

Q: When should I use standard deviation vs downside deviation? Use standard deviation for broad, symmetric, roughly normal portfolios where up and down swings balance. Use downside deviation for skewed strategies, such as options or trend-following, where most volatility is upside and you care specifically about losses below a target.

Q: What minimum acceptable return should I choose? Common choices are 0% (avoid nominal losses), the risk-free rate, or a required hurdle rate. The right MAR is the return you cannot accept falling below; changing it changes the downside deviation, so always report the target you used.

Q: Which risk-adjusted ratios use each measure? The Sharpe ratio divides excess return by standard deviation, penalizing total volatility. The Sortino ratio divides by downside deviation, penalizing only shortfalls below the MAR. That single swap is the practical payoff of the standard deviation vs downside deviation distinction.

Sources

1. Investopedia. "Standard Deviation." https://www.investopedia.com/terms/s/standarddeviation.asp
2. Investopedia. "Downside Deviation." https://www.investopedia.com/terms/d/downside-deviation.asp
3. Investopedia. "Sortino Ratio." https://www.investopedia.com/terms/s/sortinoratio.asp
4. CFA Institute. "The Sortino Ratio Is More Relevant Than the Sharpe Ratio." https://blogs.cfainstitute.org/investor/2013/06/24/the-sortino-ratio-is-more-relevant-than-the-sharpe-ratio/

Disclaimer

This article is educational content only and is not financial advice. Nothing here is a recommendation to buy, sell, or hold any security. Consult a licensed advisor before making investment decisions.