Fat tails
Why do extreme market moves actually happen more often than a bell curve would predict?
In plain words
A fat-tailed distribution is one where very large moves occur far more often than a bell curve, the smooth symmetric normal distribution, would suggest. In markets, this means the worst and best weeks are both bigger and more frequent than standard statistics assume.
Why it matters
Much of risk management relies on models that assume normal returns. When returns are fat-tailed, those models understate the true chance of a ruinous week, so stop levels, position sizes and margin buffers calibrated to them can be badly too small.
In a real week: BTC, week of 18 November 2019
In the week of 18 November 2019, BTC fell 18.81% and traded within a 25.24% range, its largest one-hour move being -4.36%. That weekly return ranked in the 3.0 percentile of 92 weeks of history, and annualised realised volatility was 61.0%. A bell curve fitted to that volatility would place a week this extreme far lower in probability than it actually occurred.
A common mistake
Assuming returns follow a normal distribution because most weeks are small. The typical weeks look normal, but the rare weeks are so much larger that they dominate total risk.