Kurtosis

Definition of Kurtosis

Like skewness, kurtosis is a statistical measure that is utilized to describe distribution. While skewness separates extreme values in one versus the other tail, kurtosis measures extreme values in one or the other tail. Distributions with large kurtosis show tail data surpassing the tails of the normal distribution (e.g., at least five standard deviations from the mean). Distributions with low kurtosis show tail data that are generally less extreme than the tails of the normal distribution.

For investors, high kurtosis of the return distribution infers the investor will experience intermittent extreme returns (either positive or negative), more extreme than the typical + or - three standard deviations from the mean that is anticipated by the normal distribution of returns. This phenomenon is known as kurtosis risk.

Breaking Down Kurtosis

Kurtosis is a measure of the combined weight of a distribution's tails relative to the center of the distribution. At the point when a set of roughly normal data is graphed through a histogram, it shows a bell top and most data inside three standard deviations (plus or minus) of the mean. Be that as it may, when high kurtosis is available, the tails broaden farther than the three standard deviations of the normal bell-curved distribution.

Kurtosis is in some cases mistook for a measure of the peakedness of a distribution. In any case, kurtosis is a measure that portrays the state of a distribution's tails comparable to its overall shape. A distribution can be boundlessly crested with low kurtosis, and a distribution can be entirely level finished off with endless kurtosis. Consequently, kurtosis measures "tailedness," not "peakedness."

Types of Kurtosis

There are three categories of kurtosis that can be shown by a set of data. All measures of kurtosis are compared against a standard normal distribution, or bell curve.

The primary category of kurtosis is a mesokurtic distribution. This distribution has a kurtosis statistic like that of the normal distribution, meaning the extreme value characteristic of the distribution is like that of a normal distribution.

The subsequent category is a leptokurtic distribution. Any distribution that is leptokurtic shows greater kurtosis than a mesokurtic distribution. Characteristics of this distribution is unified with long tails (exceptions.) The prefix of "lepto-" means "thin," making the state of a leptokurtic distribution simpler to recollect. The "thinness" of a leptokurtic distribution is a result of the exceptions, which stretch the horizontal hub of the histogram graph, causing the bulk of the data to show up in a narrow ("thin") vertical reach. Accordingly leptokurtic distributions are once in a while portrayed as "concentrated toward the mean," however the more pertinent issue (particularly for investors) is there are periodic extreme exceptions that cause this "focus" appearance. Instances of leptokurtic distributions are the T-distributions with small degrees of freedom.

The last type of distribution is a platykurtic distribution. These types of distributions have short tails (lack of exceptions.) The prefix of "platy-" means "broad," and it is meant to depict a short and broad-looking pinnacle, yet this is a historical blunder. Uniform distributions are platykurtic and have broad pinnacles, yet the beta (.5,1) distribution is likewise platykurtic and has a boundlessly sharp pinnacle. The explanation both these distributions are platykurtic is their extreme values are not exactly that of the normal distribution. For investors, platykurtic return distributions are stable and unsurprising, as in there will rarely (if at any time) be extreme (exception) returns.