Kurtosis - Explained
What is Kurtosis?
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Table of ContentsWhat is Kurtosis?How is Kurtosis Used?Types of KurtosisAcademic Research on Kurtosis
What is Kurtosis?
This is a statistical procedure used in reporting the distribution. Unlike skewness which differentiates extreme values between one tail and another, kurtosis computes the absolute values in each tail. Large kurtosis is present in the distributions that possess tail data surpassing the tails of the normal distribution. Conversely, the distributions that exhibit less extreme tail data in comparison to the tails of the normal distribution have low kurtosis. Investors interpret high kurtosis of the return distribution as a signal that they will face frequent and more extreme returns than the typical + or - three standard deviations from the mean that the normal distribution of returns predicts. This is called kurtosis risk.
How is Kurtosis Used?
Kurtosis is computed from the combination of the tails of a distribution relative to the center of the distribution. Graphing a set of approximately normal data through a histogram displays a bell peak and a majority of data within + or three standard deviations of the mean. These tails, however, go beyond the + or 3 standard deviations of the normal bell-curved distribution in the presence of high kurtosis. Kurtosis doesn't measure the peakedness of distribution but instead describes the shape of the distribution's tail in relation to its form. This means that distribution can have an infinite peak and a low kurtosis and an infinite kurtosis but a perfectly flat top. It measures only tailedness.
Types of Kurtosis
A set of data can display up to three categories of kurtosis whose measures are compared against a bell curve. These categories are as follows:
Mesokurtic distribution. In this distribution, the kurtosis statistic is the same as that of the bell curve, and so the distribution's extreme value characteristic is the same as the one belonging to a normal distribution.
Leptokurtic distribution. This has a higher kurtosis than that of a mesokurtic distribution. It has elongated tails and is skinny because of the outliers stretching the horizontal axis of the histogram graph causing the most of the data to result in a narrow vertical range. This has led to the leptokurtic distribution being viewed as a concentrated towards the mean. However, some extreme outliers lead to concentration appearance.
Platykurtic distribution. These distributions possess short tails. Uniform distributions have broad peaks although the beta (.5, 1) has an infinitely pointy peak. These two distributions are platykurtic since their extreme values are lower than that of the bell curve. Investors view these distributions as stable and predictable because they don't often become extreme returns.