Sortino Ratio
The Sortino ratio is a risk-adjusted performance measure that improves upon the Sharpe ratio by penalizing only downside volatility (returns below a minimum acceptable return or target) rather than total volatility, making it more appropriate for evaluating investment strategies with asymmetric return distributions — particularly those targeting capital preservation or that exhibit positive skewness. A higher Sortino ratio indicates better risk-adjusted performance on a downside-risk basis.
Key takeaways
- The Sortino ratio divides excess return above the minimum acceptable return (MAR) by the downside deviation — only negative deviations from the MAR enter the denominator, unlike the Sharpe ratio which uses total standard deviation.
- The Sortino ratio is preferred over the Sharpe ratio when comparing strategies with asymmetric return distributions; a strategy that has high upside volatility will appear worse under Sharpe but more accurately valued under Sortino.
- Common choices for the MAR include zero (capital preservation target), the risk-free rate, or a target return based on liability objectives (e.g., an actuarial return rate for a pension fund).
- Sortino ratios above 1.0 are generally considered acceptable; ratios above 2.0 indicate strong performance relative to downside risk.
- The downside deviation (or semi-deviation) in the Sortino ratio's denominator is calculated as the square root of the average squared negative deviations below the MAR, effectively the downside analog of standard deviation.
Explanation
The Sharpe ratio, while universally used, has a well-recognized flaw: it treats upside volatility (returns above the mean) as equally undesirable as downside volatility (returns below the mean). For a normally distributed return series, this symmetry is mathematically appropriate. But most interesting investment strategies — particularly hedge funds, private equity, options strategies, and anything with non-normal return distributions — have asymmetric payoff profiles where upside volatility is a feature rather than a flaw. The Sortino ratio addresses this by using downside deviation in its denominator, penalizing only the 'bad' volatility.
The concept was developed by Frank Sortino and Robert van der Meer in 1991, drawing on earlier work in downside risk measurement by Harry Markowitz and Roy's safety-first criterion. The downside deviation (also called the downside semi-standard deviation) is calculated relative to a Minimum Acceptable Return (MAR), which the investor specifies based on their objectives. For a pension fund with a 7% actuarial return target, the MAR might be 7% annually. For a capital-preservation mandate, the MAR might be 0%.
The computation of downside deviation is analogous to standard deviation but restricted to below-MAR observations. For each return period, if the return exceeds the MAR, the deviation is set to zero; only negative deviations (returns below MAR) contribute to the squared sum. The result is divided by the total number of periods (not just those with negative deviations) before taking the square root — this convention, introduced by Sortino and Price, ensures the measure is comparable across strategies with different frequencies of below-MAR returns.
In practice, the Sortino ratio is particularly useful for evaluating hedge fund strategies with optional-like payoffs. A strategy that writes call options (capping upside but with defined downside) and a strategy that buys calls (limited downside with unlimited upside) can have similar Sharpe ratios if their total volatility is similar — but their Sortino ratios will differ substantially, correctly reflecting the asymmetric risk-reward profiles. Similarly, a trend-following CTA that has high volatility during bull runs (desirable) but limited downside (stops and risk limits) will show a superior Sortino ratio compared to a strategy with equivalent total volatility but more symmetric distribution.
When comparing multiple managers or strategies, investors should be aware that both the Sharpe and Sortino ratios are sample estimates subject to estimation error. The sampling variability of the Sortino ratio can be substantial for short track records (fewer than three years), since downside deviation estimates are based on a subset of the already-small return sample. For this reason, sophisticated allocators use the Sortino ratio as one of several performance metrics — alongside maximum drawdown, Calmar ratio, omega ratio, and skewness — rather than relying on any single measure.
Formula
Sortino Ratio = (R_p - MAR) / Downside Deviation, where Downside Deviation = √[(1/N) × Σ min(R_i - MAR, 0)²]
Example
A hedge fund of funds evaluates two managers over a 36-month period. Manager A returns an average of 12% annually with total standard deviation of 10% and downside deviation (below 0% MAR) of 4%. Manager B returns 11% annually with total standard deviation of 9% and downside deviation of 7%. Sharpe ratios (assuming 4% risk-free): Manager A = (12-4)/10 = 0.80; Manager B = (11-4)/9 = 0.78 — nearly identical. Sortino ratios (MAR = 0%): Manager A = 12/4 = 3.0; Manager B = 11/7 = 1.57 — vastly different. Manager A's high total volatility comes predominantly from upside returns, while Manager B's risk is concentrated on the downside. The Sortino ratio correctly identifies Manager A as the superior risk-adjusted performer from the perspective of an investor concerned primarily with avoiding losses.
Related terms
Basis Black Litterman Model Calmar Ratio Downside Risk Drawdown Dynamic Asset Allocation Equity Factor Model Fund Of Funds Hedge Fund Kelly Criterion Maximum Drawdown