Weighing your Risk Appetite through Leptokurtic Distributions..
How can we increase the returns from investments by taking some risk?
First, let me give a big salute Carl Friedrich Gauss who developed two parameter exponential function in 1809 which is used throughout the world of statistics and called as Normal Distribution.
Before diving into the topic, let us understand few important details of any set of data points ( In this context data is “returns from an investment”).
Any quantity(/returns) whose variations depend on random causes is distributed according to gaussian normal law. Theoretically, anything what we see in the universe, approximate to gaussian distribution.
Shape of any distribution can be described with the moments of the distribution function. First moment is the center of the data or expected value or mean. Second moment is the variance from the mean. 3rd moment is the degree of asymmetry or the departure from symmetry or skewness. Fourth moment is the degree of peakedness of your data or kurtosis.
A careful analysis of any distribution tells you what you can expect and how distant the uncertainty is from the expected value. These theories are directly applicable in your financial planning while you want to invest your wealth.
Let’s understand what kurtosis is and how we can make use of this in our investment decisions. Kurtosis measures peakedness of the distribution. It defines how the tails of distribution are spread from mean. Based on kurtosis we can classify any data distributions to 3 types, 1. Mesokurtic (normal), 2. Platykurtic ( with thin tails) 3. Leptokurtic( with thick tails).
A Standard Normal gaussian distribution, peaks at mean value of the data, spreads its tails symmetrically and almost reaches 99.7 % of it’s data representation at a distance of 3 standard deviations. So, in a normal distribution, around 0.3% of data can go as outliers. Mesokurtic/Platokurtic distributions limits the distance of outliers from the mean. The outliers won’t be too far from the expected value. Your profit or loss won’t be too high.
In a Leptokurtic distribution, the standard deviation is less than Standard Normal distribution, that means majority of data points clustered around the expected value or mean. However as usual there would be outliers. The specialty of these outliers are, they would be too far from the expected value. So, if the data distribution is showing a leptokurtic trend, it means that you can expect few outlier events which can go to large distant from expected value, ( highly deviated from the mean). There is a chance of getting huge profit and equal chance of huge loss.
Understanding the skewness of the data in a leptokurtic distribution can reduce the chance of huge loss and increase the chance of getting high profit. If the distribution is positively skewed, the negative outliers are not too far from expected value, but the positive outliers are too far. That means you can expect high profit and limit the extend of loss.
If your risk appetite is high, then choose an investment which follows leptokurtic distribution with positive skewness. ( Note: you may expect frequent small losses, and you can also expect some very high profits.)
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