Lesson 5 of 7 · 15 min
Skewness and kurtosis
Skewness shows whether big surprises lean toward gains or losses; kurtosis shows how often big surprises occur compared with a normal distribution.
In short
- A normal distribution is symmetric, has mean = median = mode, and is fully described by its mean and variance.
- Positive skew: long right tail, frequent small losses and a few extreme gains; mode < median < mean.
- Negative skew: long left tail, frequent small gains and a few extreme losses; mean < median < mode.
- Kurtosis measures the weight of the tails. A normal distribution has kurtosis 3, so excess kurtosis = kurtosis − 3.
- Excess kurtosis above 0 = fat-tailed (leptokurtic); 0 = mesokurtic; below 0 = thin-tailed (platykurtic). Most equity return series are fat-tailed.
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