Reading the Return Distribution with Skewness and Kurtosis
Judging an asset by the mean and standard deviation alone is seeing only half. We look at skewness and kurtosis, which measure which way the distribution is tilted and how fat its tails are.
Skewness — which way the distribution is tilted
Skewness is a value that measures the 'asymmetry' of a distribution.
- If skewness is 0, it's left-right symmetric (like a normal distribution). - If skewness is negative (-), the left tail is long. That is, big losses appear more rarely but more extremely than big gains. - If skewness is positive (+), the right tail is long. Lottery-like assets that occasionally deliver a windfall fall here.
Stock-market returns generally show negative skewness. In some older studies, the average skewness of annual stock returns came out strongly negative. It's a property that resonates with the market adage 'rise slowly, collapse suddenly.'
Kurtosis — how fat the tails are
Kurtosis measures the tail thickness (the frequency of extreme values) of a distribution.
A normal distribution has a kurtosis of 3, and if it's larger than this (excess kurtosis > 0), it's a 'fat tail' where extreme values appear more often than a normal distribution.
Stock returns usually have a kurtosis greater than 3. So crashes and surges that 'should almost never happen' arrive more often than you'd think. If skewness is about 'which way it's tilted,' kurtosis tells you 'how dangerous the ends are.'
Skewness and kurtosis wobble greatly in value when the sample is small. View skewness and kurtosis calculated from just a few years of data as reference only, and it's best not to over-trust them.
Looking at an asset with four eyes
A proper risk diagnosis looks at four things together.
(1) The mean (the center of returns), (2) the standard deviation (the size of swings), (3) skewness (the tilt), and (4) kurtosis (the tail thickness).
For example, even if two assets both have 'a high average return and a moderate standard deviation,' if one has strongly negative skewness and high kurtosis, there's a hidden risk of an occasional big collapse. Looking only at the mean and standard deviation, you'd miss this difference.
Skewness and kurtosis let you look beyond 'the story near the mean' to 'what happens at the extremes.' That's why, viewed together with the maximum drawdown (MDD), an asset's true character is revealed.
Frequently Asked Questions
Q. Is 'excess kurtosis' different from kurtosis?
Excess kurtosis is kurtosis minus 3 (the normal-distribution value). So a normal distribution's excess kurtosis is 0. If excess kurtosis is greater than 0, it means the tails are fatter than a normal distribution, which is convenient for comparison, so in practice excess kurtosis is often used. In many software packages, the value labeled 'kurtosis' is actually excess kurtosis.
Q. Is a positively skewed asset always better?
Not necessarily. Positive skewness (an occasional windfall) looks attractive, but such assets often have a structure of small frequent losses that are occasionally made up for by a large gain. You have to endure the periods when the windfall doesn't come. You can't judge good or bad by skewness alone; you have to view it together with other measures.
Related pages
📋 Results are based on historical data; past returns do not guarantee future returns.
📋 This service is provided for educational purposes to help you understand investing, not as investment advice.