Skewness & Kurtosis

Trading Intelligence

9 min read

skewnesskurtosis

Go beyond mean and variance to examine the asymmetry and tail thickness of return distributions and why they matter for risk.

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Distribution of Trade Returns

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Nash Equilibrium and No Arbitrage

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Bayesian Thinking

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The Kelly Criterion

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Skewness & Kurtosis

Not all trading results follow a normal distribution — and ignoring this fact can ruin even statistically sound strategies.

Introduction

You’ve built a system.

You’ve measured EV
You understand variance
You’ve even applied Kelly sizing

But then:

One massive trade completely distorts your equity curve
Or one rare loss is so large it wipes out a month of progress

What happened?

It’s not randomness. It’s skewness and kurtosis — critical statistical traits of your trade distribution that tell you how your edge plays out over time.

What Is Skewness?

Skewness measures the asymmetry of your trade outcome distribution.

In trading terms:

Positive skew: lots of small losses, a few big wins
Negative skew: lots of small wins, occasional large losses

Most retail systems are negatively skewed — they feel good (frequent wins), but blow up occasionally.

Examples:

Type	Skew	Example
Scalping	Negative	80% win rate, but one –5R loss ruins a week
Trend-following	Positive	30% win rate, but occasional +6R or +10R wins
Martingale	Very Negative	Many small wins, occasional total wipeout

What Is Kurtosis?

Kurtosis measures the fatness of the tails — how common extreme outcomes are.

In trading:

High kurtosis: more outliers than expected
Low kurtosis: outcomes cluster close to the mean

Strategies with high kurtosis carry tail risk — rare, extreme outcomes that matter more than they should.

Why This Matters to Traders

1. Your PnL Isn’t Normally Distributed

Most trading books assume a bell curve (Gaussian distribution) — where:

Most outcomes are near the average
Big winners/losers are rare

But in reality:

Markets have fat tails
Black swan events are more common
Your system might be quietly carrying hidden risk

2. Skew Affects How You Perceive a Strategy

A system that wins 80% of the time feels amazing… until one –6R loss shows up
A system that wins 30% of the time feels brutal… until a +10R trade launches your equity curve

If you only evaluate based on short-term win rate, you will misjudge the system.

3. Kurtosis Affects How You Size Risk

High-kurtosis = expect extreme volatility → size small
Low-kurtosis = smoother curve → size more aggressively

Don’t use the same risk model across all strategies — match sizing to distribution shape, not just EV.

How to Check Your Skew/Kurtosis

Journaling tools like:

Edgewonk
TradeZella
Custom Notion dashboards → Can track distribution shape and outliers

Manually:

Sort trades by R
Plot a histogram
Look for:
Frequent small gains or losses
Rare outliers
Long “tails” of performance

Using This in Strategy Design

If your strategy is negatively skewed, focus on cutting losses quickly
If positively skewed, be ready for long drawdowns before the big win
For high kurtosis, reduce size and increase sampling window
If low kurtosis, consider scaling harder with compounding

Know what game you’re playing — and whether it fits your psychology and capital constraints.

Final Thought

Your edge doesn’t just live in the average. It lives in the shape of your results — and how you handle the extremes.

Ignoring skew and kurtosis is like flying without knowing your plane's stall speed.

Understand the profile of your trades. Respect the tails. Size and evaluate your system based on distribution, not hope.