Leptokurtic Distributions

What Is Leptokurtic?

Leptokurtic distributions are statistical distributions with kurtosis greater than three. It very well may be portrayed as having a more extensive or compliment shape with fatter tails bringing about a greater chance of extreme positive or negative occasions.

It is one of three major categories found in kurtosis analysis. Its other two partners are mesokurtic, which has no kurtosis and is associated with the normal distribution, and platykurtic, which has more slender tails and less kurtosis.

Grasping Leptokurtic

Leptokurtic distributions are distributions with positive kurtosis bigger than that of a normal distribution. A normal distribution has a kurtosis of precisely three. Thusly, a distribution with kurtosis greater than three would be named a leptokurtic distribution.

By and large, leptokurtic distributions have heavier tails or a higher likelihood of extreme exception values when compared to mesokurtic or platykurtic distributions.

While dissecting historical returns, kurtosis can assist an investor with checking a resource's level of risk. A leptokurtic distribution means that the investor can experience more extensive vacillations (e.g., at least three standard deviations from the mean) bringing about greater potential for extremely low or high returns.

Leptokurtosis and Estimated Value at Risk

Leptokurtic distributions can be implied while investigating value at risk (VaR) probabilities. A normal distribution of VaR can give more grounded outcome expectations since it incorporates up to three kurtoses. As a general rule, the less the kurtosis and the greater the confidence inside each, the more dependable and more secure a value at risk distribution is.

Leptokurtic distributions are known for going past three kurtoses. This regularly diminishes the confidence levels inside the excess kurtosis, making less unwavering quality. Leptokurtic distributions can likewise show a higher value at risk in the passed on tail due to the bigger amount of value under the curve in the most pessimistic scenario situations. Overall, a greater likelihood for negative returns farther from the mean on the left half of the distribution prompts a higher value at risk.

Leptokurtosis, Mesokurtosis, and Platykurtosis

While leptokurtosis alludes to greater anomaly potential, mesokurtosis and platykurtosis portray lesser exception potential. Mesokurtic distributions have kurtosis close to 3.0, meaning that their anomaly character is like that of the normal distribution. Platykurtic distributions have kurtosis under 3.0, in this manner showing less kurtosis than a normal distribution.

Investors will consider which statistical distributions are associated with various types of investments while choosing where to invest. More risk-averse investors could favor assets and markets with platykurtic distributions since those assets are less inclined to create extreme outcomes, while risk-searchers might look for leptokurtosis.

Illustration of Leptokurtosis

We should utilize a speculative illustration of excess positive kurtosis. On the off chance that you track the closing value of stock ABC consistently for a year, you will have a record of how frequently the stock closed at a given value. Assuming you build a graph with the closing values along the X-hub and the number of examples of that closing value that happened along the Y-hub of a graph, you will make a bell-formed curve showing the distribution of the stock's closing values. In the event that there are a high number of events for just a couple closing prices, the graph will have an extremely slim and soak bell-molded curve. In the event that the closing values vary widely, the bell will have a more extensive shape with less steep sides. The tails of this bell will show you how frequently intensely strayed closing prices happened, as graphs with bunches of anomalies will have thicker tails falling off each side of the bell.

Highlights

• Risk-seeking investors can zero in on investments whose returns follow a leptokurtic distribution, to expand the chances of rare occasions — both positive and negative.
• Leptokurtotic distributions are those with excess positive kurtosis.
• These have a greater probability of extreme occasions as compared to a normal distribution.