Kurt -- Rolling Kurtosis

Contents

• Format
• Understanding Kurtosis Values
• Understanding Operators with Kurtosis
  • < Less Than
  • > Greater Than
  • cross_below
  • cross_above
  • = Equal
• TOML Examples
  • Low Kurtosis Safe Entry
  • High Kurtosis Exit
  • Full Distribution: Kurtosis + Skewness
  • Kurtosis Volatility Regime Filter
• Tips

Overview

Rolling Kurtosis measures how fat the tails of the return distribution are over a rolling window. It is computed on log returns using excess kurtosis (kurtosis relative to the normal distribution). Kurtosis answers a critical risk question: is the market producing more extreme moves than expected?

The formula computes the fourth moment of the return distribution, normalized by its variance, minus 3:

Kurtosis = E[(r - mean)^4] / std^4 - 3

The subtraction of 3 makes the result relative to the normal distribution (which has a kurtosis of 3). This means a reading of 0 indicates the tails match what you would expect from a normal distribution. Positive values mean the tails are fatter -- extreme moves are happening more often than a bell curve would predict.

• High kurtosis (fat tails) means the market is producing extreme moves -- both up and down -- more frequently than normal. This is the domain of gap opens, flash crashes, and "impossible" events. Stop-losses get blown through because price jumps past them.
• Low kurtosis (thin tails) means the market is behaving predictably. Returns cluster near the mean with few outliers. This is a safe, stable environment where systematic strategies perform well.
• Zero kurtosis means the tails match the normal distribution exactly. This is the theoretical baseline.

The key insight: kurtosis is a risk indicator. It does not tell you which direction the market will move -- it tells you how extreme the moves are likely to be. High kurtosis environments are dangerous because they produce the outsized moves that destroy positions. Low kurtosis environments are where systematic strategies thrive because price behavior is predictable and well-behaved.

Format

kurt_{period}

The period defines the rolling lookback window -- how many candles of log returns are included in the kurtosis calculation.

Period range: 20 to 500.

Value range: Typically -2.0 to +10.0. 0 = normal distribution tails. Positive = fat tails (more extremes than normal). Negative = thin tails (fewer extremes than normal). Values above 4 indicate a highly volatile, tail-heavy environment.

Understanding Kurtosis Values

Kurtosis values are standardized (excess kurtosis relative to the normal distribution), making them universal across assets and timeframes.

Understanding Operators with Kurtosis

Each operator behaves differently with kurtosis. Because kurtosis is a risk/environment indicator, it is almost always used as a filter to gate entries and exits, not as a standalone signal.

< (Less Than) -- State-Based

What it does: The trigger is true on every candle where kurtosis is below the threshold. This detects periods when the return distribution has thin or normal tails -- a safe, predictable trading environment.

On the chart: Returns are well-behaved. There are no extreme outliers in the recent lookback window. Price moves are consistent and predictable.

[[actions.triggers]]
indicator = "kurt_60"
operator = "<"
target = "2.0"
timeframe = "1h"

Typical use: Safety filter for entries. Only enter new positions when kurtosis is low -- the environment is predictable and stop-losses are likely to function as intended. This protects against opening positions right before extreme events.

> (Greater Than) -- State-Based

What it does: The trigger is true on every candle where kurtosis is above the threshold. This detects periods when the return distribution has fat tails -- extreme moves are happening more often than expected.

On the chart: Price has been making sharp, unexpected moves. The recent return history includes large outliers -- spikes, crashes, or violent reversals.

[[actions.triggers]]
indicator = "kurt_60"
operator = ">"
target = "4.0"
timeframe = "1h"

Typical use: Risk management exit. When kurtosis spikes above 4, the market is in a dangerous state. Existing positions may need to be closed or reduced. Can also be used as a negative filter -- "do NOT enter when kurtosis > 4."

cross_below -- Event-Based

What it does: Fires once, at the exact candle where kurtosis transitions from above the threshold to below it. The previous candle had kurtosis >= the target, and the current candle has kurtosis < the target.

[[actions.triggers]]
indicator = "kurt_60"
operator = "cross_below"
target = "2.0"
timeframe = "1h"

Typical use: Detect the moment the market transitions from a fat-tail regime to a normal regime. The volatility storm has passed. This can signal that it is safe to resume systematic trading.

cross_above -- Event-Based

What it does: Fires once, at the exact candle where kurtosis transitions from below the threshold to above it. The previous candle had kurtosis <= the target, and the current candle has kurtosis > the target.

[[actions.triggers]]
indicator = "kurt_60"
operator = "cross_above"
target = "4.0"
timeframe = "1h"

Typical use: Detect the moment the market enters a fat-tail regime. Kurtosis has just spiked -- extreme moves have started. This is an early warning signal to tighten stops, reduce exposure, or exit positions entirely.

= (Equal) -- Not Recommended for Kurtosis

Why: Kurtosis produces floating-point values that are rarely exactly equal to any specific number. Use < or > instead.

TOML Examples

Low Kurtosis Safe Entry

Enter long positions only when the market is in a predictable, low-kurtosis environment. Combined with a bullish trend filter, this ensures you are trading in calm conditions where systematic strategies perform best.

[[actions]]
type = "open_long"
amount = "100 USDC"

  [[actions.triggers]]
  indicator = "kurt_60"
  operator = "<"
  target = "2.0"
  timeframe = "1h"

  [[actions.triggers]]
  indicator = "ema_20"
  operator = ">"
  target = "ema_50"
  timeframe = "1h"

  [[actions.triggers]]
  indicator = "rsi_14"
  operator = "<"
  target = "40"
  timeframe = "1h"

High Kurtosis Exit

Exit existing positions when kurtosis spikes above 4. The market is producing extreme moves and the risk of a catastrophic loss increases dramatically. This is a defensive risk management action.

[[actions]]
type = "sell"
amount = "100%"

  [[actions.triggers]]
  indicator = "kurt_60"
  operator = "cross_above"
  target = "4.0"
  timeframe = "1h"

Full Distribution: Kurtosis + Skewness

The complete distribution picture. Buy when: (1) skewness is negative (crash has occurred), (2) kurtosis is low (extreme moves have stopped -- the storm has passed), and (3) RSI confirms recovery. This is the highest-conviction contrarian setup.

[[actions]]
type = "open_long"
amount = "100 USDC"

  [[actions.triggers]]
  indicator = "skew_60"
  operator = "<"
  target = "-0.8"
  timeframe = "1h"

  [[actions.triggers]]
  indicator = "kurt_60"
  operator = "<"
  target = "2.0"
  timeframe = "1h"

  [[actions.triggers]]
  indicator = "rsi_14"
  operator = "cross_above"
  target = "30"
  timeframe = "1h"

Kurtosis Volatility Regime Filter

Use kurtosis as a volatility regime gate. Only enter DCA positions when the market is calm (low kurtosis) and price is at a discount to VWAP. This avoids accumulating during chaotic markets where prices can gap unpredictably.

[[actions]]
type = "open_long"
amount = "50 USDC"

  [[actions.triggers]]
  indicator = "kurt_100"
  operator = "<"
  target = "2.5"
  timeframe = "4h"

  [[actions.triggers]]
  indicator = "price"
  operator = "<"
  target = "vwap"
  timeframe = "4h"

  [[actions.triggers]]
  indicator = "rsi_14"
  operator = "<"
  target = "45"
  timeframe = "4h"
  max_count = 5

Tips