What are Skewness and Excess Kurtosis?
Skewness and kurtosis describe the shape of the return distribution beyond what mean and standard deviation capture. They reveal asymmetry and tail thickness - critical for understanding risks that standard deviation alone misses.
Skewness
Negative skew = longer left tail (more extreme losses than gains)
Positive skew = longer right tail (more extreme gains than losses)
Zero = symmetric (like a normal distribution)
Most equity funds exhibit negative skewness - they have occasional large drawdowns that are more extreme than their best up days. This means the "average" return overstates how often you actually experience good outcomes.
Excess Kurtosis
Normal distribution = excess kurtosis of 0
Positive = fatter tails than normal (more extreme events in both directions)
Negative = thinner tails than normal (fewer extreme events)
Most equity funds show positive excess kurtosis - more crashes and rallies than a normal distribution would predict. This means standard deviation underestimates the probability of extreme moves.
Example
Interpreting Shape Metrics
Fund A: Skewness = −0.45, Excess Kurtosis = 2.1
Interpretation: Moderately left-skewed (losses are more extreme than gains) with fat tails
(extreme events happen more often than normal distribution predicts).
Fund B: Skewness = 0.10, Excess Kurtosis = 0.3
Interpretation: Nearly symmetric with tails close to normal - a "well-behaved" return distribution.
How to Interpret
- Skewness closer to zero is generally preferred - symmetric distributions have no directional tail bias.
- Negative skew is worse for investors - it means the downside surprises are larger than upside surprises.
- Higher kurtosis = more tail risk - extreme events (both good and bad) occur more frequently than standard deviation implies.
- A fund with high kurtosis and negative skew has the worst combination: fat tails biased toward losses.
Important Notes
- Both computed using DuckDB's built-in SKEWNESS() and KURTOSIS() functions on daily returns.
- DuckDB's KURTOSIS() returns excess kurtosis (already subtracts 3), so 0 = normal distribution.
- These metrics require a reasonable sample size (60+ observations) to be stable.
- Skewness and kurtosis complement VaR/CVaR - they explain why the tails look the way they do.
Related metrics
More Advanced Risk methodology from the MFPRO analytics tool: