Sortino fixes Sharpe's biggest flaw — it only punishes downside moves. But before it can do that, it needs one number nobody talks about: the target return, or MAR. Change that one setting and the exact same trade data produces a different Sortino ratio. Here's the worked math showing by how much.
Risk-adjusted returns look different depending who's measuring.Negocie no Bybit — grande liquidez, taxas baixas, bônus de boas-vindas de até US$ 30.000.Abra a conta Bybit →Sharpe penalizes volatility in both directions — a huge winning streak inflates its denominator exactly like a huge losing streak would. Sortino fixes this by only counting deviations below a target as risk. Anything above the target, including explosive upside, contributes nothing to the risk measure.
Sortino = (annualized return − risk-free rate) ÷ downside deviation
The part that trips people up is downside deviation from what? That threshold — called MAR, the minimum acceptable return — is a free parameter. The formula's name doesn't tell you its value, and most calculators don't display it. Three choices are common in the wild: 0% (literally any loss is downside), the risk-free rate (only underperforming cash is downside), and the strategy's own mean return (only below-average trades are downside). Each produces a different number from identical data.
Take a 55% win-rate strategy: +2.5% average win, −2% average loss, 120 trades/year, 4% risk-free rate. Per-trade mean = 0.55×2.5 − 0.45×2 = 0.475%, annualized to 57.0%. The numerator of Sortino (57.0 − 4.0 = 53.0) never changes — only the downside-deviation denominator moves, because only the threshold below which a trade counts as "downside" changes:
| MAR used | What counts as downside | Per-trade downside variance | Annualized downside dev. | Sortino |
|---|---|---|---|---|
| 0% | Only the −2% losses | 0.45×(−2−0)² = 1.80 | √1.80×√120 = 14.70% | 3.61 |
| Risk-free (0.033%/trade) | Losses vs. the cash hurdle | 0.45×(−2−0.033)² = 1.86 | √1.86×√120 = 14.95% | 3.55 |
| Mean (0.475%/trade) | Losses e their gap to the average | 0.45×(−2−0.475)² = 2.76 | √2.76×√120 = 18.19% | 2.91 |
Same 50 trades, same win rate, same payoff — Sortino ranges from 2.91 to 3.61, a 24% spread, purely from which MAR a calculator silently picked. Under MAR=mean, the shortfall being measured isn't "−2% vs. zero," it's "−2% vs. the 0.475% you were supposed to average" — a bigger gap, so a bigger downside deviation, so a lower Sortino.
Now the trend-style setup from our Proporção de Sharpe breakdown: 35% win rate, +5% average win, −1.5% average loss, 150 trades/year — the exact profile that scores a strong 7.58 Sortino at MAR=0%. Annualized return is 116.25%, numerator is 112.25 at every MAR:
| MAR used | Annualized downside dev. | Sortino |
|---|---|---|
| 0% | 14.81% | 7.58 |
| Risk-free (0.027%/trade) | 15.07% | 7.45 |
| Mean (0.775%/trade) | 22.46% | 5.00 |
Here the spread is 34% — far wider than the symmetric example. The reason: this strategy's losses (−1.5%) are small relative to its 0.775% mean, so measuring the gap to the mean (−1.5 − 0.775 = −2.275%) inflates the shortfall by more, proportionally, than it did in the symmetric case. The more asymmetric a strategy's win/loss profile, the more its reported Sortino depends on which MAR was used — which matters most exactly for the trend-following and options-selling systems that Sortino was invented to flatter.
All three columns above are mathematically correct Sortino ratios — for their own definition of "downside." None of them made an arithmetic mistake. The academic Sortino & Price (1994) formulation leaves MAR as an explicit, user-chosen input for exactly this reason: it's meant to answer "how much risk did I take relative to my own goal," and different traders have different goals — beat zero, beat cash, or beat your own track record. The practical failure mode isn't using the "wrong" MAR, it's comparing two Sortino numbers without checking they used the same one. A 3.0 reported by one tool and a 3.0 reported by another can describe meaningfully different risk profiles.
Downside deviation is only ever estimated from the losing trades in the sample. A strategy with a 90% win rate over 50 trades has just 5 losing trades feeding the entire downside-deviation estimate — one unusually large or small loss among those 5 swings the Sortino ratio dramatically, in a way that a 500-trade sample with 50 losers would smooth out. A high Sortino built on a handful of losses is a much noisier estimate than the same number built on a few hundred. Cross-check any eye-catching Sortino against the raw trade count before trusting it, the same way you'd distrust a Proporção de Sharpe above 2.5 on a small backtest.
MAR is the threshold return below which a result counts as "downside" for the purpose of computing downside deviation. Returns above MAR contribute zero to the risk measure; only shortfalls below it are squared and averaged. Common choices are 0% (any loss counts), the risk-free rate (only underperforming cash counts), or the strategy's own mean return (only below-average results count). The Sortino ratio's formula never specifies which one to use — each calculator or platform picks for you, usually without saying so.
On a symmetric 55% win-rate strategy (+2.5%/−2% payoff, 120 trades/year) the Sortino ratio was 3.61 with MAR=0%, 3.55 with MAR=risk-free rate, and 2.91 with MAR=mean return — a 24% spread on identical trade data. On an asymmetric trend strategy (35% win rate, +5%/−1.5%, 150 trades/year) the spread was far wider: 7.58 at MAR=0% down to 5.00 at MAR=mean — a 34% difference. The more asymmetric the return profile, the more the MAR choice matters.
Almost always because they assume different MAR values, not because either one made an arithmetic error. A tool using MAR=0% only penalizes outright losing trades; a tool using MAR=mean penalizes every trade that underperforms the strategy's own average, including small wins. Before comparing two reported Sortino numbers, confirm both used the same target return — otherwise the comparison is meaningless even if both calculations are individually correct.
As a rough guide — holding MAR fixed — above 1 is respectable, above 2 is strong, and above 3 on a real (non-overfit) sample is excellent. But because Sortino is MAR-dependent, these thresholds only apply when comparing ratios computed the same way. A 3.0 at MAR=mean reflects a meaningfully better downside profile than a 3.0 at MAR=0%, since the mean-return version is a strictly harder bar to clear.
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