Tail Ratio — Return
95th percentile / |5th percentile| of daily returns on the Return curve (low-to-low). >1 = upside outliers dominate.
- Computed from
- Equity curve
- Scope
- Single report
- Range
- ≥ 0
- Direction
- Higher is better
Tail Ratio measures how big your best days are versus your worst days. The "tails" are the extreme days — your biggest wins (the right tail of a chart of your results) and your biggest losses (the left tail). Tail ratio divides the size of one by the other: 1.0 means they match, above 1.0 means your best days are bigger than your worst (the healthy shape), below 1.0 means your worst days are bigger than your best (the dangerous one).
How it's calculated
Tail ratio takes the 95th percentile of your daily returns (a really good day — only your top 5% of days beat it) and the 5th percentile (a really bad day — only your worst 5% are worse), and divides the size of the first by the size of the second.
Tail Ratio = | 95th percentile of returns | / | 5th percentile of returns |
- p95
- a really good day — only your best 5% of days beat it (the right-tail threshold)
- p5
- a really bad day — only your worst 5% of days are worse (the left-tail threshold)
- | · |
- the size, ignoring the minus sign — so a −3% day counts as 3
abs(p95) / abs(p5). It's percentile-based, so unlike the cubed [skewness](/glossary/skewness) calculation a single outlier can't dominate it. 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 [skewness](/glossary/skewness), [kurtosis](/glossary/kurtosis), and [Sharpe](/glossary/sharpe-ratio).On the Return and TWR curves tail ratio is computed on the equity curve's percentage returns. As a ratio of two magnitudes it's already unitless and comparable across accounts. Return is money-weighted (deposits/withdrawals move it); TWR strips cashflows out for the purest read of the strategy's own tail asymmetry.
What it tells you
Read it around 1.0. But note: losses tend to cluster (gaps, stop cascades, volatility spikes), so a slightly heavier left tail is normal for many perfectly sound strategies — a reading around 0.8–0.9 is unremarkable, not a red flag. Only a pronounced lean is a real signal.
| Value | Reading | Notes |
|---|---|---|
| < 0.6 | Left tail dominates — flag | Worst days much bigger than best. With a smooth curve, the short-vol / martingale signature — check leverage, the worst day, and max drawdown. |
| 0.6 – 0.9 | Mildly left-heavy — normal | Worst days edge out best days. Common and usually fine, because losses cluster. Watch it, don't alarm. |
| 0.9 – 1.3 | Balanced to right-leaning | Best days match or beat worst days — the bounded-loss shape you want. |
| > 1.3 | Strong right tail | Best days much bigger than worst — pronounced upside asymmetry, typical of trend-following (which pairs it with a low win rate). |
Worked example
An account's best 5% of days clear +2% (its 95th percentile), while its worst 5% fall below −3% (its 5th percentile). The tail ratio is |2| / |3| ≈ 0.67 — below 1, so the left tail leans heavier: the big losing days are half again as large as the big winning days. (At 0.67 this is still inside the "normal" band — a lean to watch, not yet an alarm.) Flip the figures (+3% best, −2% worst) and the ratio is 1.5 — the same curve shape, the opposite, survivable tail.
Pitfalls
- It cannot see the tail that kills you. This is the headline limitation. p95 and p5 are the thresholds where the tails begin, not the extremes beyond them. A −30% day sitting past the 5th percentile doesn't move the ratio at all. So a healthy 1.2 tail ratio is silent about a lurking catastrophic day — by construction. Pair it with the worst single day and max drawdown, which capture exactly what it discards. (The metric that averages the severity past the threshold is expected shortfall / CVaR, not this.)
- The wins-vs-losses reading assumes the worst days are losses. On a strongly trending account even the 5th-percentile day can be a small gain, and then the ratio compares two gains — a value below 1 no longer means "losses bigger than wins." Check that the worst-5% day is actually negative before trusting the bands.
- Sample-hungry. The 5th percentile is roughly the 12th-worst day in a year of daily data — a wobbly estimate. It needs multiple years of daily returns before p5/p95 are stable.
- > 1 doesn't mean profitable. It's purely about the size of big days, not how often you win or your edge. A right-leaning tail ratio can still belong to a net loser. Pair with win-days % and expectancy.
- Daily, not per-trade. Measured on daily returns, which capture overnight gaps and intraday aggregation that per-trade returns miss.
Tail Ratio vs Skewness
Both measure which tail is bigger, but they cut it differently — and the difference is the lesson. Tail ratio is robust because it reads the 5%/95% cutoffs and ignores everything past them. Skewness is sensitive because it cubes deviations, so one extreme day dominates it. So when the two disagree, that's information: a tail ratio near 1 (typical days look symmetric) plus a strongly negative skewness (a rare, huge left-tail day) is the most dangerous and most common short-volatility signature — small steady gains hiding a fat-left-tail bomb. Trust tail ratio for the typical asymmetry; let skewness, the worst day, and max drawdown flag the extreme one tail ratio is built to ignore.
Related
Skewness measures which tail is fatter (the sensitive read), Kurtosis how fat both tails are, Win Days % the consistency a low tail ratio can mask, and Max drawdown the worst-case the far tail can hide.