Kurtosis Definition and Quiz for Investment Modeling

Understanding Kurtosis in Finance

Intermediate

Kurtosis is a measure of the weight in the tails of a distribution, often described as how peaked a distribution appears. A standard normal distribution has a kurtosis of 3, so many times kurtosis is reported as excess kurtosis, or the difference from 3. It is often called the fourth moment because it is generated from calculations to the fourth power.

Synonym: excess kurtosis, fourth mathematical moment

For context, in the preliminary analysis of risk measures in the context of distributions in Finance, kurtosis usually ranks behind the mean, standard deviation and skewness. In fact, these also correspond with the mathematical moments we learned about in high school.

As a reminder, these moments mathematically describe the shape of the distribution of a function. And if you've used programming languages to model investments then this is clear to you.

zeroth - total distribution
first - mean or average (first power)
second - variance (second power, square)
third - skew (third power, cube)
fourth - kurtosis (fourth power)

So it stands to reason that the interpretation of kurtosis is less common than others and its calculation is complicated and best left to Excel with the =KURT() function or a statistical programming language like Python, R or MatLab.

The resulting kurtosis figure is typically related to a normal distribution which has a reading of 3.0. So some programs report kurtosis as a raw kurtosis like 3.2, or the equivalent excess kurtosis of 0.2. This represents the difference from 3.0. Excel for example reports excess kurtosis.

To interpret, higher numbers indicate more extreme observations in the tails of the distribution.

In a Sentence

Guy: The kurtosis for the distribution is 1.15, and I think it's fair to assume that that's excess.
Bud: It's also fair to assume this whole discussion about kurtosis, to me, is excess.

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Quiz

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The kurtosis for stock returns tends to be less than 3. | True or False

False. Stock returns tend to have fatter tails and higher kurtosis.

The kurtosis calculation is the result of cubing. | True or False

False, kurtosis is the result of raising to the fourth power.

Questions or Comments?

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Kurtosis Definition and Quiz