## 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 signalsÂ that the probability of obtaining an extreme outcome or value from the event in questionÂ is higher than would be found inÂ a probabilisticallyÂ normal distribution of outcomes.

Next Up

## 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 which 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.Â This means the event in question is prone to extreme outcomes. It isÂ 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,Â the more likely that future returns will be either extremely large or extremely small.

## Example ofÂ Excess Kurtosis

For example, if you trackÂ 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 occurredÂ 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 sides that are less steep. 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.Â

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 beÂ related to kurtosis.

RELATED TERMS
1. ### Normal Distribution

A probability distribution that plots all of its values in a ...
2. ### Tail Risk

A form of portfolio risk that arises when the possibility that ...
3. ### Platykurtosis

Platykurtosis is a statistical term that refers to the relative ...
4. ### Probability Distribution

A statistical function that describes all the possible values ...
5. ### Bell Curve

A bell curve is the most common type of distribution for a variable.
6. ### Platykurtic

A type of statistical distribution where the points along the ...
Related Articles
1. Investing

### Find the right fit with probability distributions

Discover a few of the most popular probability distributions and how to calculate them.
2. Investing

### Optimize your portfolio using normal distribution

Normal or bell curve distribution can be used in portfolio theory to help portfolio managers maximize return and minimize risk.
3. Investing

### Scenario Analysis Provides Glimpse Of Portfolio Potential

This statistical method estimates how far a stock might fall in a worst-case scenario.
4. Insights

### SKEW Index Suggests a Market Downturn is Possible

The CBOE SKEW Index is at record highs. Does that mean a crash is coming?
5. Investing

### Multivariate Models: The Monte Carlo Analysis

This decision-making tool integrates the idea that every decision has an impact on overall risk.
6. Personal Finance

### Average Investors and Average Financial Advisors

Does an average investor gain value from an average financial advisor? It appears so.
7. Investing

### Understanding the Probabilities of Investing

Safe but underperforming investments will lose you money in the long-run.

### How to Save Clients from RMD Aggregation Mistakes

Advisors can help clients avoid required minimum distribution mistakes in their retirement plans.
9. Investing

### Redefining Investor Risk

Changing the way you think about time and risk can change the way you invest.
RELATED FAQS
1. ### What does Value at Risk (VaR) say about the "tail" of the loss distribution?

Learn about value at risk and conditional value at risk and how both models interpret the tail ends of an investment portfolio's ... Read Answer >>
2. ### What is a "non linear" exposure in Value at Risk (VaR)?

Learn about nonlinearity and value at risk and what a nonlinear exposure is in the value at risk of a portfolio of nonlinear ... Read Answer >>
Hot Definitions
1. ### Return On Equity - ROE

The profitability returned in direct relation to shareholders' investments is called the return on equity.
2. ### Working Capital

Working capital, also known as net working capital is a measure of a company's liquidity and operational efficiency.
3. ### Bond

A bond is a fixed income investment in which an investor loans money to an entity (corporate or governmental) that borrows ...
4. ### Compound Annual Growth Rate - CAGR

The Compound Annual Growth Rate (CAGR) is the mean annual growth rate of an investment over a specified period of time longer ...
5. ### Net Present Value - NPV

Net Present Value (NPV) is the difference between the present value of cash inflows and the present value of cash outflows ...
6. ### Price-Earnings Ratio - P/E Ratio

The Price-to-Earnings Ratio or P/E ratio is a ratio for valuing a company that measures its current share price relative ...