What Is Kurtosis?
Kurtosis measures the “tailedness” of the return distribution—how often extreme outcomes (large gains or losses) occur compared to a normal distribution.
Quick Answer
Kurtosis measures the “tailedness” of the return distribution—how often extreme outcomes (large gains or losses) occur compared to a normal distribution.
What Does Kurtosis Measure?
Kurtosis is the fourth moment of the return distribution. Excess kurtosis (often reported by software) is kurtosis minus 3, so that a normal distribution has excess kurtosis 0. Positive excess kurtosis means fatter tails (more extreme events than normal); negative means thinner tails. For trading and backtesting, high kurtosis often indicates tail risk: rare but large drawdowns or spikes.
Excess Kurtosis = E[(R - μ)^4] / σ^4 - 3 (μ = mean, σ = std dev)Typical range: Excess kurtosis: -1 to +5+; financial returns often positive
How to Interpret Kurtosis
- 1Excess kurtosis > 0: more extreme returns than normal (fat tails)
- 2Excess kurtosis < 0: fewer extremes than normal (thin tails)
- 3High kurtosis strategies may have “quiet” periods then large moves
- 4Combine with skewness to understand full shape of return distribution
How to Use Kurtosis in Backtesting & Portfolio Analysis
Common Mistakes to Avoid
Backtest with Kurtosis in VaultCharts
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