DEFINITION of Excess Kurtosis

Excess kurtosis is a statistical term describing that a probability, or return distribution, has a kurtosis coefficient that is larger than the coefficient associated with a normal distribution, which is around 3. This signals that the probability of obtaining an extreme outcome or value from the event in question is higher than would be found in a probabilistically normal distribution of outcomes.

BREAKING DOWN Excess Kurtosis

Kurtosis refers to the size of the tails on a distribution. The tails of a distribution measure the number of events that have occurred that are outside of the normal range. Excess kurtosis means the distribution of event outcomes have lots of instances of outlier results, causing "fat tails" on the bell-shaped distribution curve. This means the event in question is prone to extreme outcomes. It is an important consideration to take when examining historical returns from a stock or portfolio, for example. The higher the kurtosis coefficient is above the "normal level," or the fatter the tails on the return distribution graph, the more likely that future returns will be either extremely large or extremely small.

Example of Excess Kurtosis

For example, if you track the closing value of stock ABC every day for a year, you will have a record of how often the stock closed at a given value. If you build a graph with the closing values along the "X" axis and the number of instances of that closing value that occurred along the "Y" axis of a graph, you will create a bell-shaped curve showing the distribution of the stock's closing values. If there are a high number of occurrences for just a few closing prices, the graph will have a very slender and steep bell-shaped curve. If the closing values vary widely, the bell will have a wider shape with less steep sides. The "tails" of this bell will show you how often heavily deviated closing prices occurred, as graphs with lots of outliers will have thicker tails coming off each side of the bell. 

Stock prices that have a higher likelihood of outliers either on the positive or negative side of the mean closing price can be said to have either positive or negative skewness, which can be related to kurtosis.