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Key Takeaways
- Sortino measures mean return above a chosen target per unit of target downside deviation.
- The target is the minimum acceptable return (MAR), which can be zero, the risk-free rate, an index return, or an absolute goal, and it appears in both the numerator and the denominator.
- Returns at or above the target contribute zero squared shortfall while remaining in the total observation count.
- Compare two Sortino ratios only when both use the same MAR, the same return frequency and the same downside deviation method.
- Read the mean, target and downside deviation together, and calculate drawdown separately from the ordered return path.
What is the Sortino ratio?
The Sortino ratio is a risk-adjusted return measure that divides arithmetic mean return above a target by target downside deviation. Unlike the Sharpe ratio, it counts only returns below the target, called the minimum acceptable return, as risk. Periods that meet or beat the target add zero shortfall but still count in the average.
How is the Sortino ratio calculated?
Choose the target at the same frequency as the observed returns. For each observation, calculate the amount below target. Square that shortfall, assigning zero to periods that meet or exceed the target. Average across all observations and take the square root.
Formula
Sortino ratio = (R − MAR) / Downside deviation; Downside deviation = square root of the average of min(0, Ri − MAR) squared- R is the arithmetic mean return at the same observation frequency as the target and downside deviation.
- MAR is the minimum acceptable return, the target the investor requires. It can be zero, the risk-free rate, an index return, or an absolute goal.
- Downside deviation squares only the returns that fall below the MAR, sums them, divides by the total number of periods, then takes the square root. Returns at or above the MAR contribute zero.
- Two Sortino ratios are comparable only when they use the same MAR and the same return frequency.
Sortino ratio example: eight quarterly returns
Use eight quarterly returns of +6%, +4%, −3%, +8%, −5%, +2%, +7% and −1%. Set the quarterly target and comparison risk-free return to 0%.
- Mean quarterly return: (6 + 4 − 3 + 8 − 5 + 2 + 7 − 1) / 8 = 2.25%
- Downside deviation: square root of ((3² + 5² + 1²) / 8) = square root of (35 / 8) = 2.09%
- Sortino ratio: (2.25% − 0%) / 2.09% = 1.08
- Sample standard deviation of all eight returns (n minus 1 divisor): square root of (163.5 / 7) = 4.83%, giving a total-volatility ratio of 2.25% / 4.83% = 0.47
Mean quarterly return is 2.25% and target downside deviation is 2.09%, a quarterly Sortino ratio of 1.08. Against total volatility of 4.83%, the same returns score a Sharpe ratio of 0.47, because Sharpe counts the swings up to +8% as risk too.
The eight returns sum to 18 percentage points, giving a 2.25% mean quarterly return. Against a zero target, the three shortfalls are −3%, −5% and −1%.
Their squared percentage-point values sum to 35. Dividing by all eight quarters gives 4.375, and its square root is 2.09 percentage points. The quarterly Sortino ratio is 2.25 ÷ 2.09 = 1.08.
The sample standard deviation of all eight returns is 4.83%, so with a zero risk-free baseline the quarterly Sharpe ratio is 0.47.
How the downside deviation definition changes the ratio
Dividing the same 35 by only the three below-target quarters gives 3.42% after the square root, which measures how deep the losing quarters run when they happen. The all-period 2.09% also counts how rarely they happen, so name the divisor before you compare.
A zero target measures shortfalls from breakeven, and the position’s stop sets its maximum loss. If the target equals the mean, downside deviation matches below-mean semideviation under the same divisor convention, whether or not the return distribution is symmetric.
Sortino ratio vs Sharpe ratio
Sharpe and Sortino use different denominators and can use different return baselines. With a zero target and a positive mean, downside deviation always comes in below standard deviation, so a Sortino above Sharpe is the expected result; the size of the gap still needs the return distribution to explain it.
Compare the actual return distribution, downside observations and ordered account path. Drawdown adds the depth and duration of declines to the review.
How to choose the target and compare Sortino ratios
Choose a target that fits the return record, such as 0% for capital preservation or the risk-free rate for a cash benchmark, and compare strategies on the same basis. Keep a quarterly result labeled quarterly, and rebuild the ratio from annual returns before you quote an annual figure.
Limitations of the Sortino ratio
- Match the target, frequency and divisor before you compare. Change any one of them and the ratio changes.
- Demand a long record. Only below-target observations set downside deviation, three quarters in the example, so one more bad quarter moves the ratio sharply, and a record with no misses divides by zero.
- Check Sharpe beside it. Sortino ignores upside variability, so a strategy whose gains swing wildly scores the same as a steady one with the same mean and the same misses.
- Pull drawdown from the equity curve. Its depth and duration depend on the order of returns, which the ratio ignores.
- Refresh it as the record grows. The ratio summarizes the quarters you have, and each new quarter below the target moves the downside deviation.
Bottom line
The Sortino ratio measures return above a target per unit of downside risk, which suits a review focused on shortfalls rather than total volatility. Compare it only with ratios built on the same target, frequency and divisor, and read it with drawdown and the full return distribution.
Clear answers
Frequently Asked Questions
Sources and Further Reading
- CFA Institute: The Sortino Ratio, Is Downside Risk the Only Risk that Matters?
- CFA Institute: Risk-Adjusted Performance Measures
How entries are sourced, calculated and updated: editorial methodology.