The normal distribution (bell curve) predicts that a six-sigma event should happen about once every 1.5 million days, or roughly once every 6,000 years. In actual financial markets, moves of six standard deviations or more happen multiple times per decade. The Black Monday crash of 1987 was a roughly 20-sigma event under normal assumptions, meaning it should never have happened in the lifetime of the universe. It happened on a Monday afternoon.
Fat tails mean that the probability of extreme outcomes is much higher than normal distributions assume. Mathematically, this means the distribution of returns has higher kurtosis (fatter tails and a sharper peak) than the normal distribution. Leptokurtic distributions capture this property. The Student-t distribution, power law distributions, and stable Levy distributions are all candidates that better fit observed financial returns.
For risk management, the implications are severe. If you calculate your position sizes, stop losses, and margin requirements based on normal distribution assumptions, you are systematically underestimating the probability of large losses. A position that has a 1% chance of a catastrophic loss under normal assumptions might have a 5-10% chance under a fat-tailed distribution. That difference is the gap between thinking you are safe and actually being safe.
Crypto exhibits even fatter tails than traditional financial assets. The daily return distribution of Bitcoin has significantly higher kurtosis than the S&P 500, which itself has fatter tails than the normal distribution. Single-day moves of 20-30% have occurred in major crypto assets, events that would be essentially impossible under normal assumptions but are observed features of the asset class.
Nassim Taleb's concept of fragility versus antifragility is built on the recognition of fat tails. Fragile strategies are those that perform well most of the time but blow up during tail events. Antifragile strategies sacrifice average performance for the ability to profit from extreme events. Most trading strategies fall somewhere in between, and knowing where yours sits on that spectrum is essential.
Options pricing using the Black-Scholes model implicitly assumes normal distributions, which is why out-of-the-money options tend to be more expensive than the model predicts. The volatility smile (or skew) reflects the market's recognition that fat tails exist and that tail protection is worth more than the normal distribution would suggest.
Practical adaptations for fat tails include using wider stop losses than standard deviation would suggest, sizing positions smaller than optimal under normal assumptions, stress testing against historical tail events, and maintaining a portfolio structure that can survive moves that are 3-5x larger than your expected maximum loss. The gap between what you think can happen and what actually can happen is where ruin lives.
The most dangerous version of fat tail risk is correlation breakdown. During normal times, diversification reduces risk because assets move somewhat independently. During tail events, correlations spike toward one, and the portfolio loss can be much larger than the sum of individual position risks would suggest. Planning for correlated tail events rather than independent ones produces portfolios that actually survive stress.