Skewness — Return

Asymmetry of daily returns on the Return curve (low-to-low). Negative = left-tail risk, more large losses than gains.

Computed from: Equity curve
Scope: Single report
Range: Any real number
Direction: Higher is better

Basis

Computed on the low-to-low Return Series (money-weighted) — measured day-worst-point to day-worst-point, not close-to-close.

Skewness measures which side the daily results lean — whether the rare, outsized days are gains or losses. Positive skew means the rare big days are wins (many small losses, the occasional large gain). Negative skew means the rare big days are losses (many small wins, the occasional large hit — the dangerous one). The sign is what you read first.

Key takeaways

What it is — the lopsidedness of the spread of your daily results: which side has the rare, extreme days, the winning side or the losing side. (Mathematically it's the "third standardized moment," but you only need the sign.)
Read it as — positive (> 0) is preferred: your worst days are bounded, your best days are not. Negative (< 0) is the dangerous shape — but with a catch (below).
Why it matters — negative skew is the picking-up-pennies-in-front-of-a-steamroller profile: frequent small gains, a rare catastrophic loss. It hides behind a high win-days % and a flattering Sharpe (the headline risk-adjusted-return score) right up until the steamroller arrives — LTCM, Madoff (steady ~1%/month until zero), the 2018 short-volatility blowup.
The catch — the sign describes the sample you have. A negative-skew strategy that hasn't hit its tail event yet can read neutral or even positive. Read skew together with record length and whether a real drawdown has been survived.

How it's calculated

The "tail" of a distribution is its stretched-out far end — the rare extreme days. Skewness asks which tail is longer: cube each day's standardized result (so the far-out days dominate and the sign survives), and average. A long right tail pushes it positive; a long left tail pushes it negative.

Skewness = ( n / ((n−1)(n−2)) ) · Σ ( (rᵢ − r̄) / σ )³

rᵢ: each day's return
r̄, σ: the mean and standard deviation (typical spread) of those returns
n: the number of days

In this product: Conceptually it's the average cubed standardized return — cubing keeps the sign, so right-tail outliers push positive and left-tail outliers push negative. EquityTruth uses the bias-corrected sample form shown (the n/((n−1)(n−2)) Fisher-Pearson adjustment, σ with ddof=1) so short records aren't systematically off. It's computed on the daily low-to-low returns — one value per trading day, each day's lowest equity to the next day's lowest — the same series as [Sharpe](/glossary/sharpe-ratio), Sortino, and [volatility](/glossary/volatility).

On the Return and TWR curves skewness is computed on the equity curve's returns. Because it's a standardized, unitless number, it's comparable across accounts. Return is money-weighted (deposits/withdrawals move it); TWR strips cashflows out for the purest read of the strategy's own asymmetry.

What it tells you

Daily-return skewness is noisy — a single large day can swing it, and on a short record the number means little. Treat ±0.5 as the inconclusive zone, and only believe a strong reading on a record long enough to have actually seen tail days (roughly 250+).

Value	Reading	Notes
< −1.5	Strongly negative — dangerous	A pronounced long left tail: rare large losses fund many small gains. The grid / martingale / short-vol danger zone — smooth now, catastrophic later. Inspect leverage and the worst day.
−1.5 – −0.5	Negative	A real lean toward bigger losers than winners — worth a hard look, on a long-enough record.
−0.5 – +0.5	Inconclusive	Roughly symmetric, or too noisy/short to tell. Cross-check with tail ratio rather than trusting the sign.
> +0.5	Positive — healthy shape	A long right tail: rare large gains, frequent small losses. The trend-following / convex profile; worst days are bounded.

A negatively skewed account: most days are small gains hugging zero (right), but a handful of large losses stretch far into the left tail. The long tail is on the loss side, so skewness is negative — the 'picking up pennies in front of a steamroller' shape. A positively skewed account is the mirror image: small losses near zero, the long tail on the winning side.

Worked example

Two accounts both average a small daily gain. Account A posts steady +0.3% days and, once a quarter, a brutal −6% day — its results pile up just right of zero with a lone bar far to the left, giving a negative skew (on a multi-year record, roughly −1 to −2, though the exact value is unstable). Account B loses a small −0.2% most days but occasionally catches a +5% runner — its long tail is on the right, giving a positive skew. A risk-blind glance favors A's smooth curve, but A's asymmetry is the one that ends careers; B's bounded losses and unbounded wins are the survivable shape.

The price of B's shape, though, is real: positive-skew strategies win infrequently — many small losing days punctuated by rare large gains, so they endure long, demoralizing droughts between winners. The math is favorable but the experience is punishing, which is why traders abandon them at the worst possible time.

Pitfalls

Pitfalls & caveats

The sign describes the past, not the future. The most dangerous negative-skew strategy is the one currently showing benign or positive skew — the tail just hasn't printed yet (the turkey is fine right up to Thanksgiving). Always read skew with record length and whether the strategy has survived a real shock.
Negative skew hides in smooth curves. The calmest-looking strategies — high win-days %, flattering Sharpe — are often the most negatively skewed, because the loss is a rare tail event. The very metrics that look best are the ones the structure inflates.
Noisy on short records, and one outlier dominates. Skew is sample-hungry, and because deviations are cubed, a single huge day can set the whole estimate. Trust it only on a long record; cross-check with tail ratio, which is steadier.
Daily, not per-trade. This measures the shape of daily returns, not individual trades — and the two can differ in sign. A strategy with positive trade-level skew can still produce negatively-skewed days, and it's the daily/aggregate tail that empties the account.
Blind to magnitude. Skew says nothing about whether the account makes money. A positively skewed strategy can still be a net loser, and a skewed losing strategy is still losing.

Skewness and the short-vol trap

Negative skew is the mathematical fingerprint of selling insurance to the market: grid and martingale systems that average down, carry trades that collect a steady premium, option-writing that pockets small credits. All share a payoff that is frequently, mildly positive and rarely, severely negative. They print a high win-days %, low realized volatility between blowups (a flattering Sharpe), and a smooth equity curve for long stretches — and then one move erases months in a day. The famous failures (LTCM, Madoff, the short-vol funds of February 2018) all wore this shape. When you see a strongly negative skew on a leveraged account, the action is concrete: size down, demand a longer record, and check the max drawdown and tail ratio.

Skew pairs with kurtosis: skew tells you which tail is fatter, kurtosis tells you how fat both tails are, and tail ratio gives a steadier empirical cross-check than either. A strategy with negative skew and high kurtosis has a rare loss that is both one-sided and extreme — the worst combination.

Kurtosis measures tail fatness, Tail Ratio the right-vs-left tail ratio (a steadier read than raw skew), Win Days % the consistency that negative skew can mask, and the Sharpe ratio sets return against its dispersion.

Compare withKurtosis