What Is Leptokurtic?

What Is Leptokurtic?

Let me explain what leptokurtic distributions are: they're statistical distributions with kurtosis greater than three. You can think of them as having a wider or flatter shape with fatter tails, which means there's a greater chance of extreme positive or negative events happening.

This is one of three major categories in kurtosis analysis. The other two are mesokurtic, which has no excess kurtosis and lines up with the normal distribution, and platykurtic, which has thinner tails and less kurtosis overall.

Key Takeaways

Leptokurtic distributions come with excess positive kurtosis, so they have a greater likelihood of extreme events compared to a normal distribution. If you're a risk-seeking investor, you might focus on investments whose returns follow a leptokurtic distribution to maximize the chances of those rare events—both the positive and negative ones.

Understanding Leptokurtic

Leptokurtic distributions have positive kurtosis larger than that of a normal distribution, which sits exactly at three. So, if a distribution's kurtosis is greater than three, you label it leptokurtic.

In general, these distributions have heavier tails or a higher probability of extreme outlier values when you compare them to mesokurtic or platykurtic ones.

When you're analyzing historical returns, kurtosis helps you gauge an asset's level of risk. A leptokurtic distribution means you could experience broader fluctuations—like three or more standard deviations from the mean—leading to greater potential for extremely low or high returns.

Leptokurtosis and Estimated Value at Risk

Leptokurtic distributions play a role when you're analyzing value at risk (VaR) probabilities. A normal distribution for VaR can give you stronger result expectations because it includes up to three kurtoses. Generally, the fewer the kurtosis and the greater the confidence within each, the more reliable and safer your value at risk distribution is.

But leptokurtic distributions go beyond three kurtoses, which typically decreases the confidence levels in that excess kurtosis and creates less reliability. They can also show a higher value at risk in the left tail because there's a 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 points to greater outlier potential, mesokurtosis and platykurtosis describe lesser outlier potential. Mesokurtic distributions have kurtosis near 3.0, so their outlier character is similar to the normal distribution. Platykurtic distributions have kurtosis less than 3.0, exhibiting less kurtosis than a normal one.

As an investor, you'll consider which statistical distributions are associated with different types of investments when deciding where to put your money. If you're more risk-averse, you might prefer assets and markets with platykurtic distributions because they're less likely to produce extreme results, while if you're a risk-seeker, you may go for leptokurtosis.

Example of Leptokurtosis

Let's use a hypothetical example to illustrate excess positive kurtosis. Suppose you track the closing value of stock ABC every day for a year; you'll have a record of how often the stock closed at each value. If you build a graph with closing values on the X-axis and the number of instances on the Y-axis, you'll get a bell-shaped curve showing the distribution.

If there are a high number of occurrences for just a few closing prices, the graph will have a very slender and steep bell-shaped curve. If the closing values vary widely, the bell will have a wider shape with less steep sides. The tails of this bell will show you how often heavily deviated closing prices occurred, and graphs with lots of outliers will have thicker tails coming off each side of the bell.