Skip to main content

KURTOSIS

 

KURTOSIS

Kurtosis- definition, explanation and relevance to finance

Kurtosis in stats is used to describe the distribution of the data set. Kurtosis depicts to what extent the data set points of a particular distribution differs from the data of a normal distribution. Kurtosis is used to determine whether a distribution contains extreme values. In the area of finance the kurtosis is used to measure the volume of financial risk associated with any instrument or a transaction. More the kurtosis more is the financial risk associated with the concerned data set.

Skewness is a measure of symmetry in a distribution whereas the kurtosis is the measure of heaviness or the density of distribution tails. These two factor differ from each other in their definition, Kurtosis is an important descriptive statistic of data distribution. An excess kurtosis is a metric which compares distribution kurtosis against normal distribution kurtosis.

Excess Kurtosis= Kurtosis-3

 

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

 

Graphical representation of kurtosis in simple terms



Types of Kurtosis: There are three types of kurtosis

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 distribution. The series2 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 kurtosis. Leptokurtic kurtosis has heavy steap curves on both the 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 huge scale on either sides. 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 series 3 curve on the above picture represents the leptokurtic distribution.

3.     Platykurtic: whenever the kurtosis is less than zero or negative, it refers to platykurtic Kurtosis. The distribution set follows subtle or pale curve and those curve indicates the small number of outliers in a distribution. An investment falling under platykurtic are usually demanded by investors because of small probability to generate extreme return. Also the small outliers and flat tail indicates the less risk involved in such investments. The series 1 in the above graphical representation depicts a platykurtic distribution or a safe investment.

Significance of kurtosis in finance and its application for the investment world:

From the perspective of investors, high kurtosis of the return distribution implies that an investment will yield occasional extreme return. This can swing both the ways that is 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 measure 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 the value of kurtosis and the type of kurtosis 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 chose to go about the investment. To calculate kurtosis in excel, there is a built in function Kurt in excel.

 

            Difference between kurtosis and Skewness in statistics and finance:

·       Skewness is a measure of the degree of lopsided nature (with one side of the curve lower than the other) in the frequency distribution of a dataset. Whereas kurtosis is a measure of deviation in the normal distribution

·       Skewness is indicator of lack of symmetry in the distribution whereas kurtosis is a measure of pointedness (sharpness of the curve) of the peak in the frequency distribution.

·       Skewness is an indicator of lack of equivalence in the frequency distribution, on the other hand kurtosis is the measure of data which is peaked or flat in relation with the normal distribution.

·       Skewness represents the amount and direction of the skew whereas the kurtosis represents the length and sharpness of the peak compared with the normal distribution.

·       Kurtosis show how tall the deviation is from the central peak.

 

Advantages/uses of kurtosis

When the kurtosis 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 high return from the investment is low and will generate high returns in only few scenarios, on a regular basis the return is not so high on the investment. High excess kurtosis means that the return on the investment can swing both the ways. It means the generated returns can either be very high or very low as per the outliers in the distribution. When the kurtosis is negative, it indicates that the deviation of data set from the mean is flat.

 

Conclusion.

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

 

              

 

 

 

 

Comments

Post a Comment

Popular posts from this blog

SHAREHOLDER

  SHAREHOLDER A person who legally owns one or more shares of stock in a public or a private corporation. A shareholder can be an individual or an institution. In layman terms a shareholder is the owner of the company. The number of shares he/she holds defines his/her percentage of ownership of the company. The law defines the shareholder only after his/her name or the entity’s name (in case of institution) is mentioned in the company’s register of shareholder or members. Shareholders of a company or the corporation are legally separate from the corporation itself and thus are not liable for the corporation’s liability. Until and unless the shareholder has offered guarantee, he/she has limited liability to the unpaid share price underlying. Shareholder can acquire share either from primary market (during the IPO of the company) and thus provide the capital for the corporation or from the secondary market. Shareholders are considered to be the subset of stakeholders of the com...
Post a Comment
Read more

CLOSED ECONOMY

  CLOSED ECONOMY Closed economy is a type of economy where the import and export of goods and services doesn’t happen. Such economy has no trade activity from outside economics. Closed economy is self-sufficient economy, the sole purpose of the economy is to meet all the domestic consumers’ needs within country’s border. No trade activity is conducted outside the national borders in a closed economy. In practical there are no countries with closed economies at present. Brazil has the closest to the closed economy. It has the least import of goods compared to the countries from rest of the world. It is impossible to meet the all the goods and service demands with in the domestic boundary. With the globalization and technology dependency building and maintaining such economies can be a herculean task. It can be considered that India was a closed economy till 1991 and so are the other countries across the globe. At present it is not quite possible to run a closed economy. The ne...
Post a Comment
Read more

Statement of operations

Statement of operations Company’s overall performance is usually assessed by three financial statement. Balance sheet, cash flow statement are the first two and the last one is known as statement of operations. This is also known as income statement, profit-loss statement or statement of income. The statement of operations is to report the income of the corporation for that particular period. It records the income and expenses due to operations in a standard format accepted broadly. The format is common for all companies from all industries. The standard format and flow of statement of operations is as below. For the organization ABC and for the period, the income statement looks as below. The reporting period income statement can be quarterly, monthly or yearly as in case of other financial statements. How to create statement of operations? Consider a company with net sales of 5 million. The expenses (COGS and Operating expense) for the company are removed from net sales to arrive at ...
Post a Comment
Read more