Kurtosis

Kurtosis measures the 'tailedness' of a return distribution - how often extreme outcomes (very large gains or losses) occur compared to a normal distribution. High kurtosis means fatter tails and more frequent shocks.

Interpretation: Normal distribution has kurtosis = 3 (or 'excess kurtosis' = 0). Excess kurtosis > 0 (leptokurtic) means fatter tails; < 0 (platykurtic) means thinner tails. Most financial returns are leptokurtic - 'six-sigma' events happen far more than theory predicts.

Example: Daily Nifty returns over 20 years show excess kurtosis around 5-8, meaning ±5% daily moves happen roughly 10x more often than a normal distribution would predict. This is why VaR models routinely fail in crises.

When to use: Validating whether Sharpe Ratio and standard deviation are meaningful (high kurtosis = they understate risk), pricing options where tail probabilities matter, and selecting strategies for portfolios that cannot tolerate gap-down events (e.g., retirees in withdrawal phase).

SEBI caveat: Like skewness, kurtosis is not in retail factsheets. Any quantitative claim that a strategy is 'low risk' based on standard deviation alone should be questioned if returns have high kurtosis - the real-world drawdown will be worse than the metric implies.

Related: Skewness, Standard Deviation, Value at Risk, Maximum Drawdown.