Sortino Ratio
A refinement of the Sharpe Ratio that penalises only downside volatility.
Definition
The Sortino Ratio is a variant of the Sharpe Ratio that uses downside deviation instead of total standard deviation. The intuition is that investors do not actually dislike upside volatility, only downside surprises. By dividing excess return by downside risk, the Sortino Ratio gives a more intuitive view of how much pain you endured per unit of return. It is especially useful for evaluating strategies with asymmetric return profiles such as trend-following, options selling or convex strategies.
Formula
Sortino = (Rp - Rf) / sigma_d
sigma_d = sqrt( (1/N) * sum_{Ri < MAR} (Ri - MAR)^2 )
where:
Rp = portfolio return
Rf = risk-free rate
MAR = minimum acceptable return (often Rf or 0)
Ri = individual period returns
N = number of periodsWorked example
A momentum strategy returns 22% per year with 18% total volatility but only 9% downside deviation (most volatility comes from big up months). Sortino = (22% - 4%) / 9% = 2.0, while its Sharpe is (22% - 4%) / 18% = 1.0. The Sortino reveals that the strategy is much friendlier than Sharpe alone suggests.
How ARIA Analyst uses it
ARIA reports both Sharpe and Sortino on every backtest, and the Bull vs Bear debate engine cites Sortino when defending trend or momentum strategies.
Related terms
Sharpe Ratio
Risk-adjusted return measured as excess return per unit of total volatility.
Calmar Ratio
Annualised return divided by maximum drawdown, favouring strategies with shallow losses.
Maximum Drawdown
The largest peak-to-trough decline of equity over a given window.
Volatility (σ)
Standard deviation of returns — the most common dispersion-based risk measure.
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