What Is Leptokurtic?
Leptokurtic distributions are statistical distributions with kurtosis over three. It is one of three major categories found in kurtosis analysis. Its other two counterparts are mesokurtic and platykurtic.
Leptokurtic distributions are distributions with kurtosis larger than that of a normal distribution. A normal distribution has kurtosis of three. Therefore, a distribution with kurtosis greater than three would be labeled a leptokurtic distribution.
In general, leptokurtic distributions have heavier tails or a higher probability of extreme outlier values when compared to mesokurtic or platykurtic distributions.
When analyzing historical returns, kurtosis can help an investor gauge an asset's level of risk. A leptokurtic distribution means that the investor can experience broader fluctuations (e.g. three or more standard deviations from the mean) resulting in greater potential for extremely low or high returns.
Leptokurtosis and Estimated Value at Risk
Leptokurtic distributions can be involved when analyzing value at risk (VaR) probabilities. A normal distribution of VaR can provide stronger result expectations because it includes up to three kurtosis. In general, the fewer the kurtosis and the greater the confidence within each, the more reliable and safer a value at risk distribution is.
Leptokurtic distributions are known for going beyond three kurtosis. This typically decreases the confidence levels within the excess kurtosis, creating less reliability. Leptokurtic distributions can also show a higher value at risk in the left tail due to the larger amount of value under the curve in the worst-case scenarios. Overall, a greater probability for negative returns farther from the mean on the left side of the distribution leads to a higher value at risk.
Leptokurtosis, Mesokurtosis, and Platykurtosis
While leptokurtosis refers to greater outlier potential, mesokurtosis and platykurtosis describe lesser outlier potential. Mesokurtic distributions have kurtosis near 3.0, meaning that their outlier character is similar to that of the normal distribution. Platykurtic distributions have kurtosis less than 3.0, thus exhibiting less kurtosis than a normal distribution.