On this page
Kurtosis — Volatility, in its own panel below the chart.
What Kurtosis measures
Returns over the window are standardised by their population standard deviation, computed with a divisor of N rather than N−1, and the mean of their fourth powers is taken; subtracting 3 recentres the Gaussian case on zero. The fourth power is what makes this a tail statistic: a return twice the typical size contributes sixteen times more than a typical one, so a single outlier dominates the reading. The default window is 50 returns, deliberately the same convention and default as the skewness indicator so that the two can be read together. A window whose standard deviation is zero produces no value.
The formula, as implemented
This is not how the indicator is usually defined elsewhere — it is what the shipped code computes, documented next to the implementation:
Kurtosis EXCÈS des N derniers rendements (−3, convention de Fisher) — moment d'ordre 4 standardisé, population (÷N) : g2 = m4 / σ⁴ − 3 Le −3 recentre la gaussienne sur 0 : g2 > 0 = queues épaisses (risque de barre extrême), g2 < 0 = distribution aplatie. σ = 0 → null. Mêmes conventions et même défaut N=50 que `skewness` (les deux se lisent ensemble).
How to read it
- Positive readings mean the window contains returns far larger than its own typical return, so the chance of an outsized bar is elevated relative to a normal model.
- Negative readings describe a flatter distribution, where returns cluster at a similar magnitude without extremes.
- A jump in kurtosis usually traces back to one or two specific bars — find them on the chart before drawing any conclusion about the regime.
- The measure is blind to sign: a large up bar and a large down bar of the same size affect it identically. Read it next to skewness to see which tail is doing the work.
- The value drops sharply when an outlier leaves the window, which is a mechanical consequence of the window length, not a change in the market.
Parameters and defaults
Period defaults to 50 and accepts 3 to 1000. A short window lets a single extreme bar dominate and produces large swings; a long one dilutes genuine tail events into the average. Because the statistic is normalised by the window's own standard deviation, changing the period changes both the sample and the yardstick it is measured against.
| Parameter | Type | Default | Range |
|---|---|---|---|
| Period | number | 50 | 3 – 1000 |
What it does not show
Excess kurtosis describes the shape of a past window and carries no forecast — a high value says extremes have happened, not that another is due. It is extremely sensitive to individual observations, so one bad print or one data gap can move it materially. It ignores order and direction entirely: the same returns in any sequence give the same number. And it is computed on returns alone, so a market where size is arriving without price movement, which order flow would reveal, is invisible to it.
Related indicators
- True Range — Volatility
- Std Dev — Volatility
- Squeeze — Volatility
- Chaikin Volatility — Volatility
- Realized Vol — Volatility
- Skewness — Volatility
This page in other languages
Frequently asked questions
- What is a normal kurtosis value?
- Zero. This indicator reports excess kurtosis under Fisher's convention, which subtracts 3 so that a normal distribution sits at 0. Positive values indicate fatter tails than a normal distribution and negative values a flatter shape. Raw kurtosis, which some tools report instead, would place the normal case at 3.
- Why did kurtosis drop suddenly without a large move?
- Because the outlier that was inflating it left the rolling window. With a 50-return default, a single extreme bar stops being counted exactly fifty returns after it printed, and the statistic falls back sharply. The drop reflects the window rolling forward, not a change in current conditions.
- Should kurtosis be read together with skewness?
- They complement each other, and in Senzoukria they share the same conventions and the same default window of 50 returns so the pair can be read side by side. Kurtosis tells you the tails are heavy but not which side; skewness tells you which tail is longer. Together they describe the asymmetry and the extremity of the same return distribution.