Leptokurtic distributions are statistical distributions characterized by a kurtosis greater than three. This means they tend to have a wider, flatter shape with thicker tails, leading to a higher likelihood of extreme positive or negative events.
In kurtosis analysis, leptokurtic is one of the three major categories, alongside mesokurtic (no excess kurtosis, normal distribution) and platykurtic (less kurtosis, thinner tails).
Key Takeaways
- Leptokurtic distributions feature excess positive kurtosis.
- They have a greater likelihood of extreme events compared to normal distributions.
- Risk-seeking investors may focus on leptokurtic investments to maximize chances of rare events—both positive and negative.
Understanding Leptokurtic
Leptokurtic distributions have a positive kurtosis larger than that found in a normal distribution, which has a kurtosis of exactly three. Hence, a distribution with a kurtosis greater than three is deemed leptokurtic.
Generally, leptokurtic distributions are marked by heavier tails, indicating a higher probability of extreme outlier values compared to mesokurtic or platykurtic distributions.
When examining historical returns, kurtosis can aid investors in gauging an asset’s risk level. A leptokurtic distribution signals the potential for broader fluctuations (e.g., three or more standard deviations from the mean), leading to a higher probability of extremely low or high returns.
Leptokurtosis and Estimated Value at Risk
Leptokurtic distributions come into play when analyzing value at risk (VaR) probabilities. A normal distribution of VaR provides stronger result expectations as it includes up to three standard deviations. The fewer the kurtosis, the greater the confidence in distribution outcomes, making them more reliable and safer.
Leptokurtic distributions, often exceeding three kurtoses, typically reduce confidence within the excess kurtosis, making them less reliable. They show a higher value at risk in the left tail due to larger value under the curve, indicating potential for negative returns further from the mean, leading to a higher value at risk overall.
Leptokurtosis, Mesokurtosis, and Platykurtosis
- Leptokurtosis: Greater outlier potential with kurtosis > 3.0.
- Mesokurtosis: Similar outlier potential to the normal distribution with kurtosis near 3.0.
- Platykurtosis: Lesser outlier potential with kurtosis < 3.0.
Investors may align their strategies based on these distributions. Risk-averse investors might prefer platykurtic distributions for less extreme results, while risk-seekers might opt for leptokurtic distributions.
Example of Leptokurtosis
Consider the closing value of stock ABC tracked daily for a year. This record would show how often the stock closed at different values. A graph of these closing values (X-axis) against their frequencies (Y-axis) would typically form a distribution curve.
If there are many occurrences for a few closing prices, the curve will be steeper. Conversely, wide variations in closing values would create a flatter curve. The tails of this curve illustrate the frequency and extent of extreme closing prices. Wide tails, indicative of more outliers, would characterize leptokurtic distributions.
Related Terms: mesokurtic, platykurtic, historical returns, value at risk, normal distribution.
