What is Leptokurtic?
Statistical distributions with kurtosis greater than three are known as leptokurtic distributions. It can be characterized as having fatter tails and a more comprehensive, flatter shape, which increases the likelihood of severe positive or negative outcomes.
Kurtosis analysis has three main categories, and this one is one of them. The other two types are platykurtic, which has thinner tails and less kurtosis, and mesokurtic, which has no kurtosis and is related to the normal distribution.
Understanding Leptokurtic
Distributions with a positive kurtosis greater than a normal distribution are leptokurtic distributions. The kurtosis of a normal distribution is precisely three. Consequently, a distribution would be classified as leptokurtic if its kurtosis was more than three. Compared to mesokurtic or platykurtic distributions, leptokurtic distributions typically have heavier tails or a higher likelihood of severe outlier values.
Kurtosis can assist an investor in determining the degree of risk associated with an asset when examining past returns. A leptokurtic distribution increases the potential for very low or high returns by allowing the investor to experience wider variations (three or more standard deviations from the mean).
Leptokurtosis and Estimated Value at Risk
Value at risk (VaR) probability can be analyzed using leptokurtic distributions. Because a normal distribution of VaR includes up to three kurtoses, it can yield more considerable expectations for the results. Generally speaking, a value-at-risk distribution is more trustworthy and safe the lower its kurtosis and confidence within each.
It is known that leptokurtic distributions have more kurtoses than three. This usually results in reduced reliability because it lowers the confidence levels within the excess kurtosis. In addition, leptokurtic distributions may have a more significant value at risk in the left tail because of the more significant value beneath the curve in extreme circumstances. Generally, a higher value at risk is associated with a greater probability of negative returns farther from the mean on the left side of the distribution.
Leptokurtosis, Mesokurtosis, and Platykurtosis
Mesokurtosis and platykurtosis indicate lower outlier potential, but leptokurtosis indicates more considerable outlier potential. Kurtosis for mesokurtic distributions is close to 3.0, indicating that the distribution’s outlier characteristics are comparable to those of a normal distribution. With a kurtosis of less than 3.0, platykurtic distributions have a lower kurtosis than normal distributions.
Investors will consider which statistical distributions are linked to various investment kinds when choosing where to invest. While risk-takers may want leptokurtosis, more cautious investors may favor assets and markets with platykurtic distributions since they are less likely to provide extreme outcomes.
A Leptokurtosis Example
Let us consider an imaginary case of excess positive kurtosis. You can determine how frequently the stock closes at a particular value if you monitor the closing value of stock ABC daily for a year. A bell-shaped curve representing the distribution of the stock’s closing values can be created by plotting the closing values along the X-axis and the number of instances of that closing value that happened along the graph’s Y-axis. A thin, steep, bell-shaped curve will appear on the graph if there are many occurrences of a small number of closing prices. The bell will have a broader form and less steep edges if the closing numbers differ significantly. The bell’s tails will indicate the frequency of very out-of-the-ordinary closing prices; graphs with many outliers will have thicker tails on either side of the bell.
Conclusion
- Leptokurtotic distributions have too much positive kurtosis.
- Extreme events are more likely to happen in these than in a standard range.
- Investors who like taking risks can focus on investments whose profits follow a leptokurtic distribution. This will increase the chances of rare events, whether good or bad.
