Kurtosis

What is Kurtosis?

Kurtosis in statistics is used to describe the distribution of the data set and depicts to what extent the data set points of a particular distribution differ from the data of a normal distribution. It is used to determine whether a distribution contains extreme values.

Explanation

In the area of finance, this is used to measure the volume of financial riskFinancial RiskFinancial risk refers to the risk of losing funds and assets with the possibility of not being able to pay off the debt taken from creditors, banks and financial institutions. A firm may face this due to incompetent business decisions and practices, eventually leading to bankruptcy.read more associated with any instrument or transaction. The more the kurtosis more is the financial risk associated with the concerned data set. SkewnessSkewnessSkewness is the deviation or degree of asymmetry shown by a bell curve or the normal distribution within a given data set. If the curve shifts to the right, it is considered positive skewness, while a curve shifted to the left represents negative skewness.read more is a measure of symmetry in distribution, whereas the kurtosis is the measure of heaviness or the density of distribution tails.

Types of Kurtosis

Below is the pictorial representation of the kurtosis (all three types, each one is explained in detail in the subsequent paragraph)

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For eg:
Source: Kurtosis (wallstreetmojo.com)

#1 – Mesokurtic

If the kurtosis of data falls close to zero or equal to zero, it is referred to as Mesokurtic. This means that the data set follows a normal distributionNormal DistributionNormal Distribution is a bell-shaped frequency distribution curve which helps describe all the possible values a random variable can take within a given range with most of the distribution area is in the middle and few are in the tails, at the extremes. This distribution has two key parameters: the mean (µ) and the standard deviation (σ) which plays a key role in assets return calculation and in risk management strategy.read more. The blue line in the above picture represents a Mesokurtic distribution. In finance, such a pattern depicts risk at a moderate level.

#2 – Leptokurtic

When kurtosis is positive on in other terms, more than zero, the data falls under leptokurtic. Leptokurtic has heavy steep curves on both sides, indicating the heavy population of outliers in the data set. In terms of finance, a leptokurtic distribution shows that the return on investment may be highly volatile on a huge scale on either side. An investment following leptokurtic distribution is said to be a risky investment, but it can also generate hefty returns to compensate for the risk. The green curve on the above picture represents the leptokurtic distribution.

#3 – Platykurtic

Whenever the kurtosis is less than zero or negative, it refers to Platykurtic. The distribution set follows the subtle or pale curve, and that curve indicates the small number of outliers in a distribution. An investment falling under platykurtic is usually demanded by investors because of a small probability of generating an extreme return. Also, the small outliers and flat tail indicate the less risk involved in such investments. The red line in the above graphical representation depicts a platykurtic distribution or a safe investment.

Significance

• From the perspective of investors, high kurtosis of the return distribution implies that an investment will yield occasional extreme returns. This can swing both the ways that are either positive returns of extreme negative returns. Thus such an investment carried high risk. Such a phenomenon is known as kurtosis risk. The skewness measures the combined size of the two tails; the kurtosis measures the distribution among the values in these tails.
• When the kurtosis distribution is calculated on any data set of a particular investment, the risk of the investment against the probability of generating returns, depending on its value and type it belongs to; the investment predictions can be made by the investment advisors. Based on the predictions, advisors will advise the strategy and investment agenda to the investor, and they will choose to go about the investment. To calculate kurtosis in excel, there is a built-in function Kurt in excel.

Advantages

• This is calculated on the data set of the investment; the value obtained can be used to depict the nature of the investment. Greater the deviation from the mean means the returns are also high for that particular investment.
• When the excess kurtosis in flat, it means the probability of generating a high return from the investment is low and will generate high returns in only a few scenarios, regularly the return is not so high on the investment.
• High excess kurtosis means that the return on the investment can swing both ways. It means the generated returns can either be very high or very low as per the outliers in the distribution. When it is negative, it indicates that the deviation of the data set from the mean is flat.

Conclusion

• Kurtosis is used as a measure to define the risk an investment carries. The nature of the investment to generate higher returns can also be predicted from the value of the calculated kurtosis. The greater the excess for any investment data set, the greater will be its deviation from the mean.
• This means such an investment has the potential to generate higher returns or to deplete the investment value to a greater extent. Excess kurtosis closer to zero or a flat deviation from the mean depicts that the investment will have a lesser probability of generating high returns. This can be used to define the financial risk of the investment. For investment advisors, kurtosis is a crucial factor in defining the investment risk associated with the portfolio of the fund.

Recommended Articles

This has been a guide to What is Kurtosis & its Definition. Here we discuss the types of kurtosis along with its significance, advantages, and applications in Finance. You can learn more about from the following article –

• Log-Normal Distribution
• Uniform Distribution
• Probability Distribution
• Frequency Distribution