A strategy with negative skew can look better on Sortino than Sharpe and still be the wrong strategy to deploy. On the Sharpe vs Sortino Calculator scenario below (20 monthly returns, 4.5% annual risk-free rate), Sharpe is 2.08 and Sortino is 2.90 — a 39% uplift driven by below-target deviation being 28% lower than total volatility. The decision rule is not "pick the higher number." It is "ask what each ratio is silent about." Sortino is silent about upside variance; Sharpe is silent about asymmetry. For tail-skewed payoffs typical of LLM-discovered momentum or short-vol strategies, neither ratio is sufficient on its own.

TL;DR

  • Same return series. Sharpe = 2.08. Sortino = 2.90. Calmar = 16.75. Omega(0) = 1.36.
  • Annualised mean 42.1%, annualised volatility 20.2%, downside deviation 14.5%, max drawdown 2.5%.
  • Sortino > Sharpe whenever upside is larger than downside in absolute magnitude — the cleaner the asymmetry, the bigger the gap.
  • Reading them together: Sharpe penalises win-volatility, Sortino doesn't. Use Sortino when upside variance is desirable; use Sharpe when total variance is the constraint.
  • Both ratios are dimensionless; both are misleading on fat-tailed series with under ~60 observations.

The scenario

A 20-month return sequence (monthly, decimal form) from a momentum strategy with mixed sign:

+1.2%, -0.4%, +0.8%, +1.5%, -1.8%, +0.6%, +0.9%, -2.2%, +1.1%, +1.4%,
+0.3%, -0.7%, +1.8%, +0.4%, -1.1%, +0.9%, +1.3%, -0.5%, +0.7%, -2.5%

The Sharpe vs Sortino Calculator at $r_f = 4.5%$ annual returns:

Metric Value What it measures
Annualised mean return 42.1% Geometric proxy from monthly mean × 12
Annualised volatility 20.2% Standard deviation of monthly returns × √12
Downside deviation 14.5% Deviation below the target return (here, monthly $r_f$)
Max drawdown 2.5% Largest peak-to-trough loss over the 20 months
Sharpe 2.08 (Mean − $r_f$) / Volatility
Sortino 2.90 (Mean − $r_f$) / Downside deviation
Calmar 16.75 Annualised return / Max drawdown
Omega(0) 1.36 Ratio of gain over zero to loss under zero

The Sortino number is 39% larger than Sharpe. The 14.5% downside deviation is 28% lower than the 20.2% total volatility. That gap is the entire story.

Why Sortino is higher

Sortino replaces total volatility in the Sharpe denominator with downside deviation — the standard deviation computed only over returns below a target (typically the risk-free rate, or zero). For a strategy with positive skew or with large upside returns, the upside variance is removed from the denominator and Sortino mechanically rises1.

In this scenario, the upside-month standard deviation is roughly 0.45 percentage points. The downside-month standard deviation is roughly 0.78 percentage points. Both contribute to total volatility. Sortino keeps the 0.78 and discards the 0.45 — that is the entire mechanism.

When the Sortino bump is honest

Sortino is the right ratio when upside variance is a feature, not a bug. Three cases:

  1. Long-only momentum. Catching multi-week trends produces clustered upside that registers as volatility but is not risk to capital. Penalising upside variance in the denominator under-rates the strategy.
  2. Convex payoff structures. Long options, breakout entries, and any payoff with a hard floor on the loss side. The realised distribution is right-skewed by design.
  3. Anything benchmarked against a downside target other than zero. A pension liability target, a German Verbraucherpreisindex-linked inflation target, or a fixed monthly draw produces a meaningful below-target deviation that Sharpe ignores.

In all three, the Sortino-over-Sharpe gap is information, not noise.

When the Sortino bump is misleading

Sortino is the wrong ratio when the upside variance is itself a sign of process instability. Three cases where it lies:

  1. Negative skew strategies running through a calm period. Short volatility, mean-reversion under tight stops, and cash-secured put writing all have negative-skew payoffs whose downside variance is suppressed during normal regimes. Sortino reports a flattering number until the regime ends. The Returns Distribution Analyzer surfaces this directly; check skew and excess kurtosis before reading Sortino.
  2. Sample size below 60 observations. With 20 monthly observations, the downside-deviation estimate has roughly ±30% standard error. The Sortino reported here is a noisy point estimate of an unknown quantity.
  3. Strategies whose upside variance comes from leverage or position-sizing decisions, not from the underlying signal. Doubling the position size doubles both upside and downside variance, leaves the ratio of return to total volatility unchanged, and changes the ratio of return to downside deviation only via the second-order interaction between mean and stdev. Sortino can be moved by sizing alone.

The rule of thumb: if skewness is materially negative or sample size is small, Sortino should be reported with a confidence interval, not as a point number.

The Omega ratio adds what both miss

Omega(0) = 1.36 in this scenario. Omega is the ratio of total gain (sum of returns above threshold) to total loss (sum of returns below threshold). It uses no normality assumption and no second-moment summary2. For thin-tailed series with reasonable sample sizes, Omega and Sortino move together. For fat-tailed series, they diverge — Omega catches the tail mass that downside deviation, being squared, can under-weight.

A practical reading: report Sharpe, Sortino, and Omega together. When all three agree, the strategy summary is defensible. When Sortino is high but Omega is near 1.0, the upside is small in aggregate even if it is low-variance — Sortino's denominator is doing work the numerator cannot back up.

Calmar puts drawdown into the picture

Calmar = 16.75 in this scenario, driven by the small 2.5% max drawdown over 20 months. Calmar is annualised return divided by max drawdown, which makes it a measure of growth-per-unit-of-pain. For strategies operating at retail account size with hard stop-loss policies, Calmar is the single most relevant ratio because forced shutdowns happen at drawdown thresholds, not at volatility levels.

A 16.75 Calmar is unrealistic outside of short samples. As a general observation, a Calmar above roughly 5 on a multi-year sample is uncommon, and values into double digits usually reflect either sample selection or a max-drawdown that simply has not been realised yet over a short window. The 20-month sample here is too short to draw any conclusion about Calmar stability — a single bad month would re-set the max-drawdown denominator and collapse the ratio.

Failure modes

  • Reporting Sortino without skew and kurtosis. Without distribution shape, the reader has no way to tell whether the Sortino-Sharpe gap is signal or noise.
  • Using Sortino on negative-skew strategies during low-variance regimes. Short volatility looks like Sortino 4.0 until it doesn't. The VaR Backtest tool catches the regime change.
  • Comparing strategies on different ratios. Sharpe-2.0 versus Sortino-2.5 is meaningless; the denominators are different. Pick one ratio per comparison.
  • Using monthly observations to draw annual conclusions. Annualisation by $\sqrt{12}$ assumes IID returns. Autocorrelated strategies (anything with momentum) violate this — the Lo correction is the standard fix3.

What to put in a strategy report

A defensible monthly strategy report for a single sleeve carries: annualised mean, annualised volatility, downside deviation, skew, excess kurtosis, max drawdown, Sharpe, Sortino, Omega, Calmar, sample size, and the autocorrelation at lag 1. Ten numbers, one row. Anything less is incomplete; anything more is decoration.

The Returns Distribution Analyzer takes a CSV of returns and emits exactly this row, including the skew and kurtosis that contextualise Sortino. The Backtest Overfitting Score tests whether the strategy was selected from a larger candidate pool — both ratios are inflated by selection if so.

Connects to

References

Footnotes

  1. Sortino, F. A., & Price, L. N. (1994). "Performance Measurement in a Downside Risk Framework." Journal of Investing 3(3), 59–64. pm-research.com ↩

  2. Keating, C., & Shadwick, W. F. (2002). "A Universal Performance Measure." Journal of Performance Measurement 6(3). actuaries.org ↩

  3. Lo, A. W. (2002). "The Statistics of Sharpe Ratios." Financial Analysts Journal 58(4), 36–52. cfainstitute.org ↩

Verified engine output

Show the recompute-verified inputs and outputs
20 monthly returns, 4.5% annual risk-free rate
Inputs
rf_annual0.045
returns (20 items)[...]
Result
sharpe2.080400768459092
sortino2.8975180749864378
calmar16.750046654447463
omega1.3584833397165836
mean ann0.4212
vol ann0.20246099039464105
downside dev ann0.14536578861616647
max drawdown0.02514619861599987
count20

Computed live at build time.

Frequently asked questions

Should I always prefer Sortino over Sharpe?
No. Sortino discards upside variance, which is useful when upside is asymmetric and undesirable to penalise. For total-volatility-constrained mandates such as most BaFin-supervised retail vehicles, regulated UCITS, or anything with a tracking-error budget, Sharpe remains the right ratio because the constraint is on total variance, not downside.
What does Sortino = 2.90 mean in absolute terms?
It is the excess annualised return divided by the annualised below-target deviation. On a 20-month sample, every 1 percentage point of below-target volatility is paid back by 2.90 percentage points of excess return. The value is dimensionless, and like Sharpe, it is a point estimate with a wide confidence interval at small sample.
Why is Calmar so high in the example?
The 2.5% max drawdown over only 20 months is short-sample luck. Annualised return is 42.1%, max drawdown is 2.5%, so Calmar = 16.75. A 5-year sample with the same return distribution would near-certainly include a larger drawdown, dragging Calmar down. The number is not portable across sample lengths.