202601121642
Status: #reference
Tags: Financial Machine Learning, Statistics
State: #nascient

Kurtosis

The kurtosis can be understood as a measure of how likely a 6-sigma event (an event 6 standard deviations away) is. In a low kurtosis environment, say one that follows a Normal Distribution, such an event happens once every 1.38 million years (In daily trading terms, assuming 252 trading days/year.)

In a high kurtosis environment like financial markets, or pareto environments (say crypto), this might happen once a month.

Kurtosis is the standardized fourth moment about the mean. That is:

Note: There are TWO standard implementations of Kurtosis:

1. Pearson Kurtosis: Where the Normal Distribution has a kurtosis of 3.
2. Fisher Kurtosis (Excess Kurtosis): Where the Normal Distribution has a kurtosis of 0. That is Pearson Kurtosis minus 3.

You should be cognizant of which implementation you use, and be consistent!

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