What Is Leptokurtic?

Leptokurtic distributions are statistical distributions with occurrences plotted beyond three standard deviations. This results in more occurrences farther from the mean and a higher kurtosis.

Leptokurtic distributions are known for having more than three standard deviations, which is beyond that of a normal distribution. They are also known for having fatter tails because a higher number of occurrences are plotted beyond three standard deviations.

Understanding Leptokurtic

Leptokurtic is one of three major categories found in kurtosis analysis. Its other two counterparts are mesokurtic and platykurtic. Leptokurtic distributions are distributions with positive excess kurtosis beyond that of a normal distribution. A normal distribution has kurtosis of three standard deviations. Therefore, a distribution with three standard deviations or greater 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 plus 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 standard deviations. In general, the fewer the standard deviations 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 standard deviations. This typically decreases the confidence levels within the excess standard deviations creating less reliability. Leptokurtic distributions with more than three standard deviations 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.