Koryu · 黄龍
Koryu
← Research library
Research · 研究 · 45 · Foundations

Risk is losing money, not making it irregularly.

12 Aug 20264 min readFoundationsKoryu Research

This article explains a downside-risk metric. The worked relationships are arithmetic under stated assumptions, not performance claims. Nothing here is investment advice. Decisions are yours.

The Sortino ratio is the Sharpe ratio with a fairer denominator: excess return divided by downside deviation only, the volatility of returns below a target, usually zero. It exists because standard deviation punishes violent gains and violent losses identically, and in a market built on violent gains, that symmetry misjudges exactly the strategies worth judging.

The definition and the motivating flaw

Frank Sortino's refinement keeps Sharpe's numerator and replaces the denominator with downside deviation: compute the shortfall of each period's return below a minimum acceptable target, square, average, root. Periods above the target contribute zero risk. The motivating flaw in Sharpe is real and easy to state, and the Sharpe explainer states it: a strategy that returns +40% in its best months carries a huge standard deviation because of those months, and Sharpe books them as risk. No holder of that strategy experiences the +40% months as risk. Sortino formalizes the asymmetry every practitioner already feels: risk is losing money, not making it irregularly.

Why the asymmetric market is Sortino's home turf

Momentum and breakout systems, the family this site studies, aim at right-skewed return profiles by construction, and the breakout base rates show the shape: many small losses from failed breaks, occasional outsized wins when one runs. Crypto amplifies the shape, because the winners here do not rally, they detonate. Judged by Sharpe, that profile pays a volatility tax on its own successes; judged by Sortino, the detonations count only in the numerator. The pair of ratios together therefore carries information neither holds alone: Sortino sitting far above Sharpe flags right skew, the shape a trend follower wants, while Sortino sitting close to or below the normal-case relationship flags left skew, the quiet-grind-then-catastrophe shape of carry trades, sold volatility, and most funding-harvest strategies. As an anchor: for symmetric, normally distributed returns measured against their own mean, downside deviation is the full deviation shrunk by the square root of two, so Sortino lands near 1.4 times Sharpe. Ratios far from that anchor are the skew speaking.

The smoothing lesson from our equity work

A concrete episode from our own research, and the audit story tells it in full: a partial-exit overlay on our equity system raised its Sharpe substantially, and part of that improvement came from trimming positions into strength, which removes upside volatility. Sharpe rewarded the overlay twice, once for genuinely softening drawdowns, once for merely deleting good months from the variance. A Sortino comparison separates those two effects, because only the drawdown softening moves downside deviation. The general lesson travels to every smoothed track record a seller shows you: ask which half of the volatility the smoothing removed. Products engineered to maximize quoted Sharpe have a documented tendency to sand off the upside, and Sortino is the cheapest detector of that trade.

The estimation pitfalls

Three, and they bind harder in crypto. Thin downside samples: only below-target periods enter the denominator, so a two-year daily track might rest its entire risk estimate on a few hundred observations, and a bull-phase track on far fewer. Run the significance arithmetic over that count and Sortino comes out noisier than Sharpe exactly when the history is short. Target sensitivity: zero, the risk-free rate, and a return objective produce different rankings from the same data, so any published Sortino should name its target, and comparisons across products rarely share one. And the same survivorship and regime inflations that game Sharpe game Sortino identically, the graveyard problem chief among them: a denominator-only fix cures none of the numerator's diseases.

How to use the pair

Practical synthesis. Read Sharpe first as the conservative common denominator, then Sortino as the asymmetry report, and treat the ratio between them as the third statistic: near 1.4 means roughly symmetric, well above means right skew earned or luck enjoyed, well below means a left tail is hiding in the average. Demand the same footnotes for both: day-count convention, track length, trial count, target. And remember what neither ratio sees: path. Two strategies with identical Sortinos can differ by years of underwater time, which is why drawdown and its duration stay on the scorecard next to any ratio. One number never judges a strategy; a small honest panel of them, stated with their assumptions, gets close enough to act on. Decisions are yours.

Related reading
FoundationsPerpetuals vs spot: what you actually own4 min readFoundationsToken unlocks and emissions: supply schedules that move prices4 min readFoundationsThe Kelly criterion in crypto: why fractional is the only way5 min read
Frequently asked

What is the Sortino ratio?

Excess return divided by DOWNSIDE deviation: the volatility of returns below a target, usually zero, with above-target periods contributing no risk. It keeps Sharpe's numerator and replaces the denominator that punishes gains and losses identically.

When is Sortino better than Sharpe?

For asymmetric return profiles. Momentum and breakout systems aim at many small losses and occasional outsized wins; Sharpe books the explosive wins as risk, Sortino counts them only as return. For symmetric strategies the two rank things similarly and Sharpe's larger sample makes it steadier.

What does the gap between Sortino and Sharpe mean?

For symmetric normal returns measured against their mean, Sortino lands near 1.4 times Sharpe. A much larger gap flags right skew (the trend-follower shape); a smaller or inverted gap flags a hidden left tail, the quiet-grind-then-catastrophe shape of carry and funding-harvest strategies.

What are Sortino's estimation problems?

Only below-target periods enter the denominator, so short or bull-heavy tracks rest the risk estimate on very few observations, making Sortino noisier exactly when history is thin. The target choice changes rankings, and survivorship or regime inflation game it just like Sharpe.

Can smoothing a track record game Sharpe?

Yes: trimming positions into strength removes upside volatility, which raises Sharpe without touching drawdowns. Our equity research saw part of an overlay's Sharpe gain come from exactly that. Sortino separates the effects, because only genuine downside softening moves downside deviation.