# Leptokurtic

## What is 'Leptokurtic'

Leptokurtic is a statistical distribution where the points along the X-axis are clustered, resulting in a higher peak, or higher kurtosis, than the curvature found in a normal distribution. This high peak and corresponding fat tails mean the distribution is more clustered around the mean than in a mesokurtic or platykurtic distribution and has a relatively smaller standard deviation. A distribution is leptokurtic when the kurtosis value is a large positive.

## BREAKING DOWN 'Leptokurtic'

The prefix "lepto-" means thin or skinny when referring to the shape of its peak, while "kurtosis" means arched or bulging based on its Greek origins. This leads to a full translation of "thin arch" or "skinny bulge." Serving as a probability distribution, leptokurtic distributions display a particularly sharp peak when compared to mesokurtic or platykurtic distributions. When analyzing historical returns, kurtosis helps gauge an asset's level of risk. A leptokurtic distribution means that small changes happen less frequently because historical values have clustered by the mean. However, this also means that large fluctuations are more likely within the fat tails.

## Leptokurtosis and Estimated Value at Risk

Leptokurtosis can impact how analysts estimate value at risk (VaR). An investor using a normal distribution to estimate VaR may overestimate at low levels of significance but might overestimate at high levels of significance if the return distribution is leptokurtic. This is the result of the leptokurtic distribution having a fatter tail. The fat tail means risk is coming from outlier events and extreme observations are much more likely to occur. Therefore, conservative investors should avoid this type of return distribution.

## Leptokurtosis and Normal Distribution

In order to determine the classification of kurtosis present, a normal distribution is used as a comparison point. In cases where a normal distribution is not known, a quantitative measurement is required based on the formula _4/_4, where _4 refers to the heaviness of the distribution in the tails, also known as Pearsonâ€™s fourth moment about the mean, and sigma refers to the standard deviation.

## Leptokurtosis, Mesokurtosis and Platykurtosis

While leptokurtosis demonstrates a tighter distribution in regards to the mean, mesokurtosis and playkurtosis describe the other potential distribution models. Mesokurtic distributions show a peak that is neither higher nor lower than that of a normal distribution, have an excess kurtosis of zero, and are considered a baseline upon which the other two distributions are classified. Platykurtic distributions exhibit less kurtosis than a normal distribution, resulting in a lower peak when compared to that displayed in the normal distribution graph, and have a negative excess kurtosis.