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 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: