Definition
Financial returns exhibit fat tails—extreme positive and negative returns occur far more often than the bell curve suggests. Kurtosis measures this "tailedness." Normal distribution predicts a 4+ sigma event roughly once every 31,560 years; in financial markets, they occur every few years. Risk models based on normal distributions systematically underestimate extreme risk.
lightbulb Example
The normal distribution predicts a daily loss of 5%+ should occur once every 14,000 years for the S&P 500. In reality, it has happened dozens of times in the last century—demonstrating extreme fat tails in equity returns.
verified_user Key Points
- Extreme events occur far more often than normal distribution predicts
- Kurtosis > 3 indicates fat tails (excess kurtosis > 0)
- VaR models underestimate risk due to thin-tail assumptions
- Student's t-distribution better captures fat tails