Definition

Sortino ratio

The Sortino ratio is the Sharpe ratio with downside deviation in the denominator, so upside swings are not penalised. Formula, the √2 benchmark against Sharpe, and why it is noisy.

Updated

The Sortino ratio is the Sharpe ratio with the denominator replaced by downside deviation: excess return over a minimum acceptable return (MAR, usually 0 or the risk-free rate) divided by the root-mean-square of the shortfalls below that MAR, so volatility on the upside is not penalised. For returns symmetric around the MAR the Sortino is about √2 times the Sharpe, so a Sharpe of 1.0 implies a Sortino near 1.4 with no skew at all; a Sortino well above that multiple signals positive skew, well below it negative skew.

Also known as
downside-risk ratio · Sortino index · reward-to-downside-risk ratio

How it is calculated

            Sortino = (R − MAR) ÷ DD
DD = √( Σ min(rᵢ − MAR, 0)² ÷ n )   — n is ALL periods, not only the losing ones
MAR = minimum acceptable return, usually 0 or the risk-free rate

Annualise: numerator × 252 (× 365 for crypto), DD × √252 (√365)
Symmetric returns: Sortino ≈ √2 × Sharpe

Worked example: Daily mean excess return 0.05%, downside deviation 0.6% over all 252 days → annualised 12.6% ÷ (0.6% × √252 = 9.5%) = Sortino 1.32; with daily volatility of 1.0% the Sharpe is 0.79, a ratio of 1.67 — above √2, so the losses were smaller than the gains.

The √2 benchmark is the only useful comparison

Downside deviation squares only the shortfalls below the MAR but divides by every period, so for a symmetric return stream it equals volatility divided by √2 and the Sortino lands at √2 × Sharpe, roughly 1.41. A ratio far above that — say 2.5 on a Sharpe of 1.0 — means losses were smaller and gains larger than symmetry predicts, the signature of trend-following. A ratio far below it means many small gains and a few large losses, the signature of short-volatility and martingale-like systems, and it is the case in which the Sortino is quietly diagnosing the strategy its owner prefers to judge by Sharpe.

The MAR, the sample and the convention set the number

Moving the MAR from 0 to a 4% risk-free rate lowers the numerator and raises the downside deviation at once, so the same series produces two different ratios. The denominator is estimated from the losing periods alone: a three-year monthly track record has around fifteen of them, and a single month losing three times the typical shortfall raises the downside deviation by roughly a quarter on its own. Bailey and López de Prado show that the sampling error of a Sharpe estimate grows with the fat tails and negative skew of the returns, and that picking the best of many trials inflates whichever ratio was used to pick; both effects hit the Sortino at least as hard, because it is built for skewed series and its denominator uses fewer observations. Annualise by multiplying the numerator by 252 (365 for crypto) and the downside deviation by √252 (√365), and only compare figures built the same way.

How it gets misread

"Sortino above Sharpe" is routinely presented as evidence of a favourable return profile, but for any series whose mean sits above the MAR the downside deviation is smaller than the standard deviation, so the Sortino exceeds the Sharpe by construction; the informative comparison is against √2 × Sharpe, not against Sharpe. The second error is comparing Sortinos built on different conventions: a MAR of 0 versus the risk-free rate, monthly versus daily data, or a downside deviation that divides by the number of losing periods rather than all periods, which alone inflates the denominator by about 40% when roughly half the periods lose.

Calculate it

See also

Sources

Definitions are educational. Nothing here is investment advice, and no metric described on this page predicts future results.

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