Glossary

Sortino Ratio — Definition, Formula, and Limitations

The Sortino ratio is excess return divided by downside deviation. Definition, formula, worked example, and the threshold-choice problem that makes it gameable.

By NakedPnL Research·May 7, 2026·4 min read

TL;DR

Sortino is a Sharpe-like ratio that replaces total volatility with downside-only deviation.
The result depends heavily on the choice of minimum acceptable return (MAR) threshold.
NakedPnL doesn't display Sortino on profile pages because the threshold choice is itself a tunable knob a public-figure trader can optimise.

Definition

The Sortino ratio, attributed to Frank A. Sortino, is a modification of the Sharpe ratio that replaces total return volatility with downside deviation — the standard deviation of returns falling below a chosen minimum acceptable return (MAR), often called the target return. The motivation is that upside variance is not, in any practical sense, a risk; only returns below the target are.

Formula

Sortino = (mean(R_p) - MAR) / DownsideDeviation

DownsideDeviation = sqrt( (1/N) * sum( min(R_t - MAR, 0)^2 ) )

where:
  R_t = periodic portfolio return
  MAR = minimum acceptable return (often 0 or the risk-free rate)
  N   = number of periods (some authors divide only by the count of below-target periods)

Different vendors disagree on whether to divide by N or by the count of below-target periods. The choice can swing the result substantially.

Worked example

Over 252 daily returns a portfolio has a mean of 0.07% and a downside deviation against MAR = 0% of 0.45%. Daily Sortino is 0.07 / 0.45 ≈ 0.156, which annualises (×√252) to roughly 2.47. Switch the MAR from 0% to the daily risk-free rate of 0.015% and the numerator drops to 0.055%; the denominator also shifts because more or fewer periods now qualify as 'below target'. The reported Sortino can move by 30% or more between equally defensible MAR choices.

Why NakedPnL doesn't display this on profile pages

Sortino solves one well-known weakness of Sharpe — the symmetric treatment of upside and downside variance — but it introduces another: the result is a function of the MAR threshold, the lookback window, and the divisor convention. A trader who knows the public Sortino number is computed against MAR = 0 over a trailing 90 days can deliberately structure positions whose negative-skew tail falls outside that window. Because NakedPnL is a public registry of verified performance, every metric we surface becomes a target for that kind of optimisation. We therefore restrict profile-level metrics to TWR, total PnL, and trade count — quantities whose meaning does not depend on a tunable threshold. Sortino can still be computed by allocators against the daily-return series exposed via the API, with their own MAR and window choices declared explicitly.

Sharpe ratio — uses total volatility instead of downside deviation
Calmar ratio — uses maximum drawdown as the denominator
Maximum drawdown
Volatility (standard deviation of returns)

Frequently asked questions

What MAR should I use?

Common choices are 0% (any loss is undesirable), the periodic risk-free rate (an opportunity-cost benchmark), or a strategic target return. There is no universally correct answer; honest reporting requires that the MAR is disclosed alongside the ratio.

Is a higher Sortino always better than a higher Sharpe?

Not necessarily. Sortino discards information about upside variance, which can matter for capital-allocation decisions if the upside is itself unstable. The two ratios answer slightly different questions and are best read together rather than as substitutes.

Can Sortino be infinite?

If a return series has no observations below the MAR, downside deviation is zero and the ratio is mathematically undefined. Reporting tools usually show this as 'n/a' or, less helpfully, as an inflated finite number based on a tiny non-zero floor.

References