The Sortino ratio formula itself is just one line: (average return - target return) / downside deviation. What really causes different people to get different results, or even wrong conclusions, is the denominator. The most common mistake is throwing away positive returns and calculating the standard deviation only of negative returns. The correct approach is to keep all observations, set returns above the target to 0, and then calculate the root mean square of all the data. These two methods differ significantly when the return distribution is asymmetric, and the whole point of the Sortino ratio is to handle asymmetric distributions.
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Formula and Denominator: Target Downside Deviation, Not the "Standard Deviation of Negative Returns"
The Sortino ratio is defined as:
S = (Average Return - Target Return) / Target Downside Deviation
The "target return" in the numerator was called MAR (Minimum Acceptable Return) in early literature. Later, Frank Sortino himself renamed it "Desired Target Return." You can set it to 0%, or use the risk-free rate, or a performance benchmark that a strategy must achieve. The key is that once you choose a target, you must use the same value when comparing different strategies.
The denominator is calculated in four steps, and the order matters:
For each observation, calculate the difference between it and the target return. If the difference is above the target, record it as 0, not delete it.
Square each difference.
Add up all the squared values and divide by the total number of observations N (including those recorded as 0).
Take the square root of the result.
Let's illustrate with a simple example. Suppose eight annual returns are 17%, 15%, 23%, -5%, 12%, 9%, 13%, and -4%, with a target of 0%. Two periods are below the target: -5% and -4%. Their squares are 0.25% and 0.16% respectively (in decimal form). Adding them gives 0.41%. Dividing by the total number of observations, 8 (not 2), gives 0.05125%. Taking the square root gives approximately 2.26%. The average return is 10%, so Sortino = 10% / 2.26% ≈ 4.42.
If you incorrectly calculate the standard deviation of only -5% and -4% (dividing by 2 instead of 8), the denominator becomes about 0.5%, and the Sortino ratio will be severely overstated. An even more subtle mistake is failing to divide by 2 correctly and simply averaging the two negative returns, which produces yet another result.
Why "Throwing Away Positive Returns" Is Wrong
Deleting positive returns and calculating the standard deviation only of negative returns loses more than just precision. It loses the "frequency" information of downside risk. A paper from Red Rock Capital gives a clear comparison:
Return series A: [0, 0, 0, -10]
Return series B: [-10, -10, -10, -10]
If you discard the zeros, the "standard deviation of negative returns" is the same for both groups (both are 0, because the values within each group are identical). But obviously A is far less risky than B, because A only loses money one quarter of the time. The correct target downside deviation method keeps the zeros in the denominator N. A's denominator is pulled down by the zeros, so its Sortino is higher. B's denominator is larger, so its Sortino is lower. This matches intuition.
A CFA Institute article points out the same problem: the discrete method (looking only at historical returns below the MAR) significantly understates downside risk. They use the Japanese stock market in the 1980s as an example: ten years of annual returns were all positive, but in 1990 the market crashed 39%. Looking only at in-sample negative returns cannot predict such tail events. This does not mean the Sortino ratio can predict the future, but rather that using the wrong denominator will systematically cause you to underestimate a strategy's downside risk.
Three Practical Judgments When Comparing Strategies
First, the target return must be consistent. If you compare Strategy A and Strategy B, and A uses 0% while B uses 5%, the two Sortino values are not comparable. The choice of target should come from your actual constraints: if this is your own money, 0% is the "don't lose money" bottom line. If you manage a fund with an 8% performance benchmark, use 8%. R's PerformanceAnalytics package uses MAR by default and reminds users: if MAR is too low, it won't capture the risk you really care about; if it is too high, it may reject otherwise reasonable strategies.
Second, a high Sortino ratio does not mean good absolute returns. A strategy may have very low returns but almost never lose money, giving it a very high Sortino. If the two strategies you are comparing have very different return levels, look at returns first, then use Sortino to judge "whether this return is worth the corresponding downside volatility." Sortino is a risk-adjusted efficiency measure, not a return measure.
Third, when return distributions are symmetric, Sortino and Sharpe rankings agree. Research shows that if returns follow a normal distribution, the Sortino ratio and the Sharpe ratio have a monotonic relationship and produce exactly the same ranking of investment options. Sortino's advantage appears when the distribution is negatively skewed or has extreme downside: it can identify strategies that Sharpe misjudges because Sharpe penalizes upside volatility. If you are comparing trend following, option selling, or any strategy that "wins big when it wins and loses small or occasionally loses big," Sortino is more informative than Sharpe. If the return distribution is roughly symmetric with no obvious skew, either measure works; no need to agonize over the choice.
Practical Takeaways
If you are calculating it yourself, follow the four steps strictly: difference → square → divide by total N → square root. Do not take the shortcut of "only calculating the standard deviation of negative returns." In Excel, you can use SQRT(SUMPRODUCT((returns
If you are looking at a Sortino ratio reported by someone else, clarify two things: what the target return is, and how the denominator was calculated. Many fund pages and third-party data sources use the simplified "standard deviation of negative returns" method, and the value will differ from the correct method. It is not necessarily wrong, but you need to know what it is measuring.
If you are comparing two strategies, first check whether the return distributions are symmetric. If they are symmetric, Sharpe is enough; Sortino will not give you additional ranking information. If they are asymmetric, Sortino is more useful, but remember to use the same target return and be aware of how the denominator is calculated.
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References
- CFA Institute·Investment Performance Measurement: The Sortino Ratio, no update date indicated; checked on: 2026-10-21.
- CME Group·Sortino: A 'Sharper' Ratio, no update date indicated; checked on: 2026-10-21.
- Red Rock Capital·Sortino: A 'Sharper' Ratio (PDF), no update date indicated; checked on: 2026-10-21.
- IASG·Sortino: A 'Sharper' Ratio – What are the Differences?, published on: 2014-05-22; checked on: 2026-10-21.
- R Project·PerformanceAnalytics: SortinoRatio, no update date indicated; checked on: 2026-10-21.
- Wiley Online Library·A note on the relationships between some risk-adjusted performance measures, published on: 2002-03-06; checked on: 2026-10-21.
