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The fat-tailedness of your returns. Why "100-year events" keep happening every decade.
Kurtosis measures the "fat-tailedness" of a return distribution. Normal distributions have kurtosis = 3 (excess kurtosis = 0). Equity returns typically have excess kurtosis of 3–10, meaning extreme moves happen far more often than a normal distribution would predict. Higher kurtosis = more black-swan tail risk.
Kurt = E[(R − μ)⁴] / σ⁴Kurt = E[(R − μ)4] / σ4Raise each deviation from mean to the fourth power, average, divide by σ⁴. Larger numbers indicate fatter tails.
Higher kurtosis = more "black swan" tail risk. The 1987 crash, 2008 collapse, and March 2020 sell-off were all 5+ sigma events under a normal distribution, meaning they should happen roughly once every 10,000+ years. Real markets produce them every decade.
Practical implication: any risk model assuming normal distributions (basic VaR, basic Sharpe statistical tests) underestimates real-world tail risk. Use PSR, fat-tailed VaR, and CVaR to compensate.
S&P 500 daily returns since 1926 have excess kurtosis of approximately +15. Highly fat-tailed.
BTC daily returns have excess kurtosis around +25. Even fatter tails — extreme moves are common.
Excess kurtosis levels by asset:
| Asset | Excess Kurtosis |
|---|---|
| Normal distribution | 0 (reference) |
| Diversified equity | 3–10 |
| Single stocks | 5–20 |
| BTC | 15–30 |
| Altcoins | 30–100+ |
| Short volatility strategies | 50–200+ (extreme) |
Skewness · Value at Risk (VaR) · CVaR (Conditional Value at Risk) · Standard Deviation
Extreme moves (both up and down) happen more often than a normal-distribution model would predict. Tail risk is higher than naive VaR suggests.
Foliolytic shows excess kurtosis (kurtosis − 3). 0 means normal-distribution-like; positive means fatter tails.
High kurtosis means Sharpe statistics are noisy. Use Probabilistic Sharpe Ratio, which adjusts for kurtosis.
Yes — excess kurtosis in the tail risk section.
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