What Is a Fat Tail? Definition and Examples

A fat tail is a probability distribution where extreme events occur more frequently than a normal (bell-curve) distribution would predict.

In a normal distribution, extreme outliers are very rare (roughly 1 in 22 million for 6 standard deviations from the mean).

In fat-tailed distributions, extreme events are relatively more likely. Wealth distribution is fat-tailed: extreme wealth concentrations happen regularly. Financial returns are fat-tailed: market crashes are more frequent and larger than normal distribution models predict.

The Problem

Risk models built on normal distributions catastrophically underestimate risk in fat-tailed domains.

Before 2008, financial models assumed returns were normally distributed. They calculated that a market crash as severe as what happened would occur once every million years.

It happened anyway, because financial returns have fat tails. The models were built on false assumptions.

Where Fat Tails Occur

Extremistan Property

Fat tails are the defining statistical property of Extremistan domains.

In Mediocristan (height, daily weather), tails are thin. Extremistan (wealth, markets) has fat tails.

This is why strategies that work in Mediocristan fail in Extremistan.

Go deeper:

For the full breakdown of fat tails and their implications, read Mediocristan vs. Extremistan: Two Types of Randomness.