The kurtosis of a normal distribution equals 3. All measures of kurtosis are compared against a standard normal distribution, or bell curve. is desirable for investors because there is a small probability that the investment would experience extreme returns. For one example, the beta(.5,1) has an infinite peak and has negative excess kurtosis. 1) Platykurtic - negative kurtosis value indicating a flatter distribution that normal bell curve. Here we discuss the types of kurtosis along with its significance, advantages, and applications in Finance. An investment falling under platykurtic is usually demanded by investors because of a small probability of generating an extreme return. Therefore, an investment whose returns follow a leptokurtic distribution is considered to be risky. Leptokurtic has heavy steep curves on both sides, indicating the heavy population of outliers in the data set. The prefix of "platy-" means "broad," and it is meant to describe a short and broad-looking peak, but this is an historical error. Learn risk analysis. Kurtosis is sometimes confused with a measure of the peakedness of a distribution. There are three categories of kurtosis that can be displayed by a set of data. Mesokurtic is a statistical term describing the shape of a probability distribution. Distributions with low kurtosis exhibit tail data that are generally less extreme than the tails of the normal distribution. When a set of approximately normal data is graphed via a histogram, it shows a bell peak and most data within + or - three standard deviations of the mean. A probability distribution is a statistical function that describes possible values and likelihoods that a random variable can take within a given range. How Probability Distribution Works. CFA Institute Does Not Endorse, Promote, Or Warrant The Accuracy Or Quality Of WallStreetMojo. From the perspective of investors, high kurtosis of the return distribution implies that an investment will yield occasional extreme returns. It is usually done with, Certified Banking & Credit Analyst (CBCA)™, Capital Markets & Securities Analyst (CMSA)™, Financial Modeling & Valuation Analyst (FMVA)™, Financial Modeling and Valuation Analyst (FMVA)®, Financial Modeling & Valuation Analyst (FMVA)®. When used, these Excel functions make your financial statement analysis more dynamic. Discover more about mesokurtic distributions here. Platykurtosis is a statistical term that refers to the relative flatness of a probability distribution. The measure is best used in variables that demonstrate a linear relationship between each other. Such a phenomenon is known as kurtosis risk. 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. Types of Kurtosis . The leptokurtic distribution shows heavy tails on either side, indicating large outliers. Also, the small outliers and flat tail indicate the less risk involved in such investments. Below is the pictorial representation of the kurtosis (all three types, each one is explained in detail in the subsequent paragraph) #1 – Mesokurtic. The greater the excess for any investment data set, the greater will be its deviation from the mean. In finance, such a pattern depicts risk at a moderate level. The first category of kurtosis is a mesokurtic distribution. Kurtosis is a statistical measure that defines how heavily the tails of a distribution differ from the tails of a normal distribution. The "skinniness" of a leptokurtic distribution is a consequence of the outliers, which stretch the horizontal axis of the histogram graph, making the bulk of the data appear in a narrow ("skinny") vertical range. The prefix of "lepto-" means "skinny," making the shape of a leptokurtic distribution easier to remember. Learn risk analysis. Examples of leptokurtic distributions are the T-distributions with small degrees of freedom. Dr. Wheeler defines kurtosis as: The kurtosis parameter is a measure of the combined weight of the tails relative to the rest of the distribution. It means the generated returns can either be very high or very low as per the outliers in the distribution. Three different types of curves, courtesy of Investopedia, are shown as follows − It is difficult to discern different types of kurtosis from the density plots (left panel) because the tails are close to zero for all distributions. 1. This phenomenon is known as kurtosis risk. The offers that appear in this table are from partnerships from which Investopedia receives compensation. For investment advisors, kurtosis is a crucial factor in defining the investment risk associated with the portfolio of the fund. However, the two concepts must not be confused with each other. Risk management encompasses the identification, analysis, and response to risk factors that form part of the life of a business. This can swing both the ways that are either positive returns of extreme negative returns. The green curve on the above picture represents the leptokurtic distribution. Characteristics of this distribution is one with long tails (outliers.) In other words, kurtosis identifies whether the tails of a given distribution contain extreme values. To keep learning and advancing your career, the following CFI resources will be helpful: Become a certified Financial Modeling and Valuation Analyst (FMVA)®FMVA® CertificationJoin 350,600+ students who work for companies like Amazon, J.P. Morgan, and Ferrari by completing CFI’s online financial modeling classes and training program! This means such an investment has the potential to generate higher returns or to deplete the investment value to a greater extent. Uniform distributions are platykurtic and have broad peaks, but the beta (.5,1) distribution is also platykurtic and has an infinitely pointy peak. Quantitative analysis is the process of collecting and evaluating measurable and verifiable data such as revenues, market share, and wages in order to understand the behavior and performance of a business. CFI offers the Financial Modeling & Valuation Analyst (FMVA)™FMVA® CertificationJoin 350,600+ students who work for companies like Amazon, J.P. Morgan, and Ferrari certification program for those looking to take their careers to the next level. Tail risk is portfolio risk that arises when the possibility that an investment will move more than three standard deviations from the mean is greater than what is shown by a normal distribution. The fit of the data can be visually represented in a scatterplot. Below is the pictorial representation of the kurtosis (all three types, each one is explained in detail in the subsequent paragraph). The more the kurtosis more is the financial risk associated with the concerned data set. Next, we subtract 3 from the sample kurtosis and get the excess kurtosis. If the kurtosis of data falls close to zero or equal to zero, it is referred to as Mesokurtic. Data that follows a mesokurtic distribution shows an excess kurtosis of zero or close to zero. Join 350,600+ students who work for companies like Amazon, J.P. Morgan, and Ferrari. CFA® And Chartered Financial Analyst® Are Registered Trademarks Owned By CFA Institute.Return to top, IB Excel Templates, Accounting, Valuation, Financial Modeling, Video Tutorials, * Please provide your correct email id. If the kurtosis of data falls close to zero or equal to zero, it is referred to as Mesokurtic. This does not have to do with skewness. More specifically, kurtosis refers to the tails or the 2 ends of the curve. In finance, a leptokurtic distribution shows that the investment returns may be prone to extreme values on either side. 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. To calculate kurtosis in excel, there is a built-in function Kurt in excel. INDEX, MATCH, and INDEX MATCH MATCH Functions, Combining CELL, COUNTA, MID and OFFSET in a Formula. Skewness essentially measures the symmetry of the distribution, while kurtosis determines the heaviness of the distribution tails. This is calculated on the data set of the investment; the value obtained can be used to depict the nature of the investment. What Are the Odds? Skewness is a measure of symmetry in distribution, whereas the kurtosis is the measure of heaviness or the density of distribution tails. For investors, high kurtosis of the return distribution implies the investor will experience occasional extreme returns (either positive or negative), more extreme than the usual + or - three standard deviations from the mean that is predicted by the normal distribution of returns.

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