Leptokurtic Distributions

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What is leptokurtic?

Leptokurtic distributions are statistical distributions with kurtosis out of three. This is one of the three main categories found in the analysis of kurtosis. Its two other counterparts are mesokurtic and platykurtic.

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Understanding Leptokurtic

Leptokurtic distributions are distributions with greater kurtosis than that of a normal distribution. A normal distribution has a kurtosis of three. Therefore, a distribution with kurtosis greater than three would be called a leptokurtic distribution.

In general, leptokurtic distributions have heavier tails or a higher probability of outliers compared to mesokurtic or platykurtic distributions.

When analyzing historical returns, kurtosis can help an investor assess the risk level of an asset. A leptokurtic distribution means that the investor may experience greater fluctuations (for example, three or more standard deviations from the average), which increases the potential for extremely low or high returns.

Leptokurtosis and estimated risk value

Leptokurtic distributions can be involved when analyzing value-at-risk (VaR) probabilities. A normal distribution of VaR may provide higher expectations of results, as it includes up to three kurtosis. In general, the less kurtosis and the more confidence there is in each, the more reliable and secure the distribution of the value at risk.

Leptokurtic distributions are known to go beyond three kurtosis. This generally lowers confidence levels in excess kurtosis, creating less reliability. Leptokurtic distributions can also show a higher risk value in the left tail due to the greater value under the curve in the worst scenarios. Overall, a higher probability of negative returns further from the average on the left side of the distribution leads to a higher risk value.

Leptokurtosis, Mesokurtosis and Platykurtosis

While leptokurtosis refers to greater aberrant potential, mesokurtosis and platykurtosis describe less aberrant potential. The mesokurtic distributions have a kurtosis close to 3.0, which means that their aberration is similar to that of the normal distribution. Platykurt distributions have a kurtosis of less than 3.0, thus showing less kurtosis than a normal distribution.

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