Kurtosis and fat tails

What kurtosis measures, why stock returns have fat tails, what excess kurtosis means, and why extreme days happen far more often than a bell curve predicts.

What it measures

Kurtosis measures how heavy the tails of a return distribution are, in other words how often very large moves happen compared with a bell curve. Most tools report excess kurtosis, where a normal bell curve scores 0.

Fat tails in markets

Daily stock market returns have high excess kurtosis. On a bell curve with the S&P 500's volatility, a one-day fall of 20% like October 1987 would essentially never happen. It did. Days of 5% moves occur many times more often than a normal curve predicts.

Why it matters

Reading it

Excess kurtosis above about 3 means tails well beyond normal. Look at the worst 1% of days directly rather than trusting averages.

See also

Pages that link here: Sharpe ratio

Last updated September 30, 2026. Education only, not investment advice.