Fat-Tailed Distribution

A fat-tailed distribution is a probability distribution that exhibits extremely large skewness or kurtosis. This is relative to the normal distribution, which itself is an example of an exceptionally thin tail distribution. 

Fat-Tailed Distribution

A fat-tailed distribution is a probability distribution that exhibits extremely large skewness or kurtosis. This is relative to the normal distribution, which itself is an example of an exceptionally thin tail distribution. 

 

Fat-Tailed Distribution Identification

Fat- tailed distributions have power law decay in the tail of the distribution, but do not necessarily follow a power law everywhere.

Graph comparing fat-tailed distribution versus normal distribution.
Graph comparing fat-tailed distribution versus normal distribution.


Fat-Tailed Distribution Interpretation

Fat-tailed distributions have been empirically encountered in a fair number of areas: economics, physics, and earth sciences.

In finance, fat tails are considered undesirable because they imply additional risk beyond what would be seen from a normal distribution.  For example, an investment strategy may have an expected return that is five times its standard deviation.  The likelihood of its failure (negative return) is less than one in a million based on a normal distribution.  However, factors influencing an asset's price,such as an earthquake, war, corporate bankruptcy or financial crisis, are not so mathematically "well-behaved".  Such factors cause additional risk resulting in a fat-tailed distribution.



Fat tails in market return distributions also have some behavioral origins (investor excessive optimism or pessimism leading to large market moves) and are therefore studied in behavioral finance.  In marketing, the familiar 80-20 rule frequently found (e.g. "20% of customers account for 80% of the revenue") is a manifestation of a fat tail distribution underlying the data.

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