What is Kurtosis?

Explanation

In finance, this measures 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 is, the more financial risk is 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 Kurtosis measures heaviness or the density of distribution tails.

Types of Kurtosis

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

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#1 – Mesokurtic

If the Kurtosis of data falls close to zero or equals zero, it is referred to as Mesokurtic. It 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. For example, 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 in other terms, more than zero, the data falls under leptokurtic. Leptokurtic has steep curves on both sides, indicating the large population of outliers in the data set. In 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 risky, but it can also generate hefty returns to compensate for the risk. The green curve in 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 in demand by investors because of a small probability of generating an extreme return. Also, the small outliers and flat tails 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 investors’ perspective, high Kurtosis of the return distribution implies that an investment will yield occasional extreme returns. It can swing both ways, which are either positive returns or extreme negative returns. Thus, such investment carries high risk. Such a phenomenon is known as Kurtosis risk. The skewness measures the combined size of the two tails. In addition, it measures the distribution among the values in these tails.When one calculates the Kurtosis distribution 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 advisors can make the investment predictions. Based on the predictions, advisors will advise the strategy and investment plan to the investor, and they will choose to go about the investment. There is a built-in function called Kurt in Excel To calculate Kurtosis in Excel.

Advantages

  • One may calculate it on the data set of the investment. The value obtained can be used to depict the nature of the investment. Greater deviation from the mean means the returns are also high for that particular investment.When the excess Kurtosis is flat, the probability of generating a high return from the investment is low and will generate high returns in only a few scenarios. This is because the return is not so high on the investment so regularly.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 negative, it indicates that the deviation of the mean data set from the mean is flat.

Conclusion

  • One may use Kurtosis as a measure to define the risk an investment carries. One can also predict the nature of the investment to generate higher returns from the value of the calculated Kurtosis. The greater the excess for any investment data set, the greater its deviation from the mean.It 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. One can use it to define the financial risk of the investment. For investment advisors, Kurtosis is crucial in defining the investment risk associated with the fund’s portfolio.

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

  • Log-Normal DistributionUniform DistributionProbability DistributionFrequency Distribution