Fat Tail Distribution

Fat tail distributions have a higher probability of extreme outcomes than the normal (Gaussian) bell curve predicts. In finance, this means market crashes and booms happen more often and more severely than standard risk models assume.

Normal vs. Fat Tail Distribution:

Event Size	Normal Distribution	Fat Tail (Actual Markets)
1σ move (daily)	31.7% of days	~31% of days
2σ move	4.6% of days	~6-8% of days
3σ move	0.27% of days	~1-2% of days
4σ move	0.006% (once in 63 years)	Several times per decade
5σ+ move	Virtually impossible	Happens every few years

Real Market Examples:

• Black Monday (1987): -22.6% in one day = ~25σ event (impossible under normal distribution)
• 2008 Financial Crisis: Multiple 4-5σ daily moves
• Flash Crash (2010): -9% intraday = ~8σ event

Why This Matters for Investors:

• Risk models based on normal distributions dramatically underestimate tail risk
• Options pricing (Black-Scholes) assumes normal distribution — misprices tail protection
• Portfolio VaR calculations may be too optimistic
• "Once in a century" events happen every decade or two

Implications for Risk Management:

• Don't trust risk models that assume normality
• Allocate more to tail protection than models suggest
• Keep more cash/liquidity than seems "optimal"
• Consider barbell strategies (safe + speculative, nothing in between)