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# Kurtosis

## Definition

Kurtosis is a statistical measure used in finance to describe the distribution of observed data around the mean, specifically its tails and sharpness. High kurtosis indicates a high level of risk because data has heavy tails or outliers, meaning significant values are extreme from the average. Conversely, low kurtosis implies a low degree of risk, with smaller tails or fewer outliers.

### Phonetic

The phonetic spelling of the word “Kurtosis” is: kur-toh-sis.

## Key Takeaways

• Kurtosis is a statistical measure that describes the distribution of observed data around the mean. It specifically measures the “tailedness” of the data distribution.
• A high kurtosis indicates that the data has heavy tails or outliers, meaning there are extreme values. In contrast, a low kurtosis suggests that the data lacks extreme values and has light tails.
• There are three types of kurtosis: leptokurtic (high kurtosis), platykurtic (low kurtosis), and mesokurtic (kurtosis similar to a normal distribution). These classifications help in understanding the characteristics of a given distribution.

## Importance

Kurtosis is a crucial statistical measure used in finance and business to describe the distribution of observed data around the mean. It provides information about the tails and sharpness of the distribution, highlighting the level of risk or volatility associated with a particular investment or portfolio. High kurtosis signifies a higher probability of extreme values or outliers, indicating a heavy-tailed or a more volatile and risky investment. Conversely, low kurtosis implies lighter tails with fewer extreme values, suggesting less risk or volatility. Therefore, understanding kurtosis can assist investors and business professionals to make educated decisions and manage risk strategically.

## Explanation

Kurtosis is a statistical measure that is used assess the ‘peakedness’ or ‘tailedness’ of the distribution of a data set. Essentially, it provides deeper insight into the characteristics of the distribution of a set of data beyond what standard deviation or variance can offer. This allows for a more comprehensive understanding of the distribution, where one can discern whether the distribution is heavy-tailed (or fat tailed) or light-tailed (thin tailed) compared to a normal distribution. It’s essential for risk assessment and management, wherein rare events could lead to significant deviations from the mean.

In the world of finance and business, Kurtosis is used mainly to identify and assess risk. For instance, stocks returns which are characterized by high kurtosis tend to have heavy tails, suggesting that these stocks are likely to produce outcomes that are extremely far from the mean value. This could be either severe losses or exceptional gains. As such, understanding the Kurtosis of business or financial data is valuable in predicting and preparing for potential outcomes that could have a large impact on business or investment strategy. It is a valuable tool that goes hand-in-hand with other statistical measures in risk assessment utilised to make informed financial decisions.

## Examples

1. Stock Market: When analyzing returns on a specific stock or overall market, kurtosis may be used to understand the distribution of returns. For instance, if a stock’s return possesses a high kurtosis, this indicates that the stock had more extreme price deviations than expected under a normal distribution, which can imply the stock bears a higher risk.

2. Real Estate Pricing: The variability of house prices in a certain area can also be studied with kurtosis. A high kurtosis would suggest that the data has heavy tails or outliers, which means there are many homes that sold for unusually higher or lower prices than the average. This might indicate volatility in that real estate market makes it more challenging for investors or homeowners to predict and budget for property prices.

3. Credit Risk Analysis: Financial institutions use kurtosis to assess the risk level of credit defaults. If a borrower’s credit score dataset exhibits high kurtosis, it means there are more extreme deviations in the data set than a regular distribution would possess. These extreme values could potentially be customers who are highly likely to default, which would help the institution to create more effective credit policies and risk management strategies.

What is Kurtosis in finance?

In finance, Kurtosis is a statistical measurement that describes the shape of a probability distribution, specifically its tails and sharpness. It helps quantify the extreme return outliers possibility within an investment’s return distribution.

What does a high Kurtosis mean?

A high Kurtosis implies a large occurrence of extreme outcomes. In other words, a risky investment or financial market is likely to produce occasional extreme outliers. It may indicate a higher risk associated with an investment.

How is Kurtosis calculated?

Kurtosis is calculated using the fourth moment about the mean, which involves finding the difference between each data point and the average, raising this difference to the fourth power, and then finding the average of these values.

What are the different types of Kurtosis?

The two types of Kurtosis are leptokurtic and platykurtic. Leptokurtic distributions, with a Kurtosis greater than 3, have heavy tails, meaning more frequent extreme returns. Platykurtic distributions, with a Kurtosis less than 3, have light tails, indicating less frequent extreme returns.

What is Excess Kurtosis?

Excess Kurtosis refers to the Kurtosis of a given distribution compared to that of a normal distribution. In finance, a positive excess Kurtosis is a sign of high risk in an investment.

How does Kurtosis affect portfolio management?

Kurtosis is an essential measure in portfolio management as it helps portfolio managers quantify the risk of extreme returns. High Kurtosis indicates a higher probability for extreme returns which therefore impacts the risk management strategy.

What’s the difference between Kurtosis and Skewness?

While Kurtosis measures the tailedness and the extreme values in the outcome, skewness is a measure of the asymmetry of the probability distribution. In other words, Kurtosis focuses on the tails of the distribution while skewness looks at its tilt.

Why is Kurtosis important in finance?

Kurtosis is crucial in finance because it allows investors and analysts to perceive the likelihood of extreme market moves. Understanding the potential for such outliers can guide investment decision-making and risk analysis.

## Related Finance Terms

• Leptokurtic
• Platykurtic
• Normal Distribution
• Statistical Moments
• Excess Kurtosis

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