Excess Kurtosis

What Is Excess Kurtosis?

The term excess kurtosis alludes to a measurement utilized in statistics and likelihood theory looking at the kurtosis coefficient with that of a normal distribution. Kurtosis is a statistical measure that is utilized to portray the size of the tails on a distribution. Excess kurtosis decides how much risk is engaged with a specific investment. It flags that the likelihood of getting an extreme outcome or value from the event being referred to is higher than would be found in a probabilistically normal distribution of outcomes.

Grasping Excess Kurtosis

Kurtosis measures how fat a distribution's tail is when compared to the center of the distribution. The tails of a distribution measure the number of events that happened outside of the normal reach. Not at all like skewness, kurtosis measures either tail's extreme values. Excess kurtosis means the distribution of event outcomes have heaps of occurrences of anomaly results, causing fat tails on the bell-molded distribution curve. Normal distributions have a kurtosis of three. Excess kurtosis can, consequently, be calculated by deducting kurtosis by three.

Since normal distributions have a kurtosis of three, excess kurtosis can be calculated by deducting kurtosis by three.

Excess kurtosis is an important apparatus in finance and, all the more specifically, in risk management. With excess kurtosis, any event being referred to is inclined to extreme outcomes. It is an important consideration to take while inspecting historical returns from a specific stock or portfolio. The higher the kurtosis coefficient is over the normal level — or the fatter the tails on the return distribution graph — the almost certain that future returns will be either extremely large or extremely small. Stock prices with a higher probability of exceptions on either the positive or negative side of the mean closing price can be said to have either positive or negative skewness, which can be connected with kurtosis.

Types of Excess Kurtosis

The values of excess kurtosis can be either negative or positive. At the point when the value of an excess kurtosis is negative, the distribution is called platykurtic. This sort of distribution has a tail that is more slender than a normal distribution. When applied to investment returns, platykurtic distributions — those with negative excess kurtosis — by and large produce results that will not be exceptionally extreme, which are great for investors who would rather not face a ton of challenge.

At the point when excess kurtosis is positive, it has a leptokurtic distribution. The tails on this distribution is heavier than that of a normal distribution, demonstrating a heavy degree of risk. The returns on an investment with a leptokurtic distribution or positive excess kurtosis will probably have extreme values. Investors who are willing and able to face a great deal of challenge will most likely need to invest in a vehicle with a positive excess kurtosis.

Excess kurtosis can be at or close to zero too, so the chance of an extreme outcome is rare. This is known as a mesokurtic distribution. The tails of this sort of distribution is like that of a normal distribution.

Illustration of Excess Kurtosis

We should utilize a speculative illustration of excess kurtosis. In the event that you track the closing value of stock ABC consistently for a year, you will have a record of how frequently the stock closed at a given value. On the off chance that you build a graph with the closing values along the X-hub and the number of examples of that closing value that happened along the Y-pivot of a graph, you will make a bell-formed curve showing the distribution of the stock's closing values. On the off chance that there are a high number of events for just a couple closing prices, the graph will have an extremely thin and soak bell-molded curve. In the event that the closing values differ widely, the bell will have a more extensive shape with less steep sides. The tails of this bell will show you how frequently vigorously veered off closing prices happened, as graphs with heaps of exceptions will have thicker tails falling off each side of the bell.

Highlights

• Excess kurtosis can be positive (leptokurtic distribution), negative (platykurtic distribution), and at or close to zero (mesokurtic distribution).
• Excess kurtosis is a valuable device in risk management since it shows whether an investment is inclined to extreme outcomes.
• Excess kurtosis compares the kurtosis coefficient with that of a normal distribution.