How do I interpret skewness and kurtosis in return distributions?

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AcadiFi · Accepted Answer

Skewness measures asymmetry. A normal distribution has skewness = 0. Positive skew means the right tail is longer (rare large gains, like lottery tickets); negative skew means the left tail is longer (rare large losses, like corporate bonds or short-volatility strategies).

Kurtosis measures tail heaviness. A normal distribution has kurtosis = 3, or 'excess kurtosis' = 0. High (leptokurtic) kurtosis — like 6 or 8 — means fatter tails, implying more extreme outcomes than a normal distribution predicts. Hedge funds, emerging-market debt, and currency carry trades typically show leptokurtic returns.

Example: Moss Creek Hedge Fund reports monthly return mean of 0.8%, standard deviation of 2.5%, skewness of -1.2, excess kurtosis of 4.5. The negative skew plus fat tails is a classic blow-up profile — lots of small positive months punctuated by rare big losses. Sharpe ratio alone would flatter the strategy; skewness and kurtosis reveal the hidden tail risk.

CFA application: when skewness and excess kurtosis are both near zero, normal-distribution-based metrics (VaR, Sharpe) are reasonable. When either deviates meaningfully, use Sortino ratio, CVaR, or historical simulation. The Jarque-Bera test formalizes this: JB = (n/6)(S² + K²/4), with a chi-squared distribution under the null of normality. Rejecting the null implies you need non-parametric or heavy-tailed models.

How do I interpret skewness and kurtosis in return distributions?

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