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Sortino Ratio

Like Sharpe, but the denominator uses only downside deviation (volatility of returns below the risk-free rate), not total volatility. Penalizes losses but not upside swings.

When to use: Use when upside volatility shouldn't count as risk — e.g. for asymmetric strategies (long-options, momentum) where high upside variance is the goal. Sortino is the more honest measure for any strategy where you welcome positive surprises.

Calculator

Formula

Sortino=RpRfσdown,σdown=Ri<Rf(RiRf)2n1\text{Sortino} = \frac{\overline{R_p} - R_f}{\sigma_{down}}, \quad \sigma_{down} = \sqrt{\frac{\sum_{R_i < R_f}(R_i - R_f)^2}{n - 1}}

Variables

SymbolNameDescriptionUnit
SortinoSortino RatioExcess return per unit of downside volatilityinteger
ReturnsPeriodic ReturnsSequence of periodic returns as decimals (e.g. 0.05 for 5%)%
RfRisk-Free RatePer-period risk-free rate as a decimal (use the same period as the returns)%

Real-Life Examples

Example 1: Mixed Returns

Returns: 10%, −5%, 8%, −3%, 12%, 4%. Rf = 3%.

Given

Returns = Rf = 0.03

Step-by-Step

1.Mean = (10 − 5 + 8 − 3 + 12 + 4)/6 = 4.33%
2.Returns below 3%: −5%, −3% → deviations −8%, −6%
3.Downside dev = √((0.08² + 0.06²)/5) = √(0.01/5) = 0.0447
4.Sortino = (0.0433 − 0.03) / 0.0447 ≈ 0.299
Result:0.30

Sortino of 0.30 — modest. Compare against this portfolio's Sharpe ratio: a meaningful gap between Sharpe and Sortino indicates that some of the volatility is upside-favorable.

Frequently Asked Questions

Both are useful. Sharpe penalizes all volatility; Sortino penalizes only downside. For symmetric return distributions they often tell similar stories. For asymmetric strategies (option-buying, momentum, equity long-only) Sortino is more representative because the upside variance is the point.

Most commonly the risk-free rate (this calculator). Some practitioners use 0% (any negative return) or a minimum acceptable return (MAR) specific to their objective. The choice doesn't change the conceptual interpretation, only the magnitudes.

When the sample has zero or one observation below the threshold — the denominator collapses or becomes unstable. Use longer return histories (≥ 30 observations) for a stable Sortino.

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