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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.
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
=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.
Guy: The kurtosis for the
distribution is 1.15, and I think it's fair to assume that that's
Bud: It's also fair to assume this whole discussion about kurtosis, to me, is excess.
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Click box for answer.
False. Stock returns tend to have fatter tails and higher kurtosis.
False, kurtosis is the result of raising to the fourth power.
Still unclear on Kurtosis? Check out our free Excel financial modeling course called Quant 101.
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