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.

A distribution is more leptokurtic (peaked) when the kurtosis value is a large positive value.

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 Pearson’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.

  1. Platykurtic

    A type of statistical distribution where the points along the ...
  2. Kurtosis

    A statistical measure used to describe the distribution of observed ...
  3. Excess Kurtosis

    Excess kurtosis describes a probability distribution with fat ...
  4. Platykurtosis

    A statistical measure that indicates the level of peakedness ...
  5. Tail Risk

    A form of portfolio risk that arises when the possibility that ...
  6. T Distribution

    A T distribution is a type of probability function that is appropriate ...
Related Articles
  1. Investing

    Find The Right Fit With Probability Distributions

    Discover a few of the most popular probability distributions and how to calculate them.
  2. Investing

    Lognormal and Normal Distribution

    When and why do you use lognormal distribution or normal distribution for analyzing securities? Lognormal for stocks, normal for portfolio returns.
  3. Investing

    Using Normal Distribution Formula To Optimize Your Portfolio

    Normal or bell curve distribution can be used in portfolio theory to help portfolio managers maximize return and minimize risk.
  4. Financial Advisor

    How to Save Clients from RMD Aggregation Mistakes

    Advisors can help clients avoid required minimum distribution mistakes in their retirement plans.
  5. Investing

    Fat Tail Risk Makes Global Warming Scarier

    The cost of global warming does not take into account climate change-related catastrophes. Here's where fat-tail distributions come in.
  6. Investing

    A Simplified Approach To Calculating Volatility

    Though most investors use standard deviation to determine volatility, there's an easier and more accurate way of doing it: the historical method.
  7. Investing

    Expect Big Capital Gains Distributions from These Funds (AGTHX, ACRNX)

    The steady rise in the markets since 2009 has led to some outsized gains in a few funds that are finally being realized as long-term winning holdings.
  8. Financial Advisor

    Combining Your Plan Assets? Not So Fast!

    You might reduce the costs of maintaining more than one account, but you could also be forfeiting tax benefits.
  1. What does Value at Risk (VaR) say about the "tail" of the loss distribution?

    Learn about value at risk and conditional value at risk and how both models interpret the tail ends of an investment portfolio's ... Read Answer >>
  2. Is my non-qualified Roth IRA distribution subject to taxes or early distribution ...

    The ordering rules must be applied to determine whether the distribution is subject to income taxes and/or the early distribution ... Read Answer >>
Hot Definitions
  1. Entrepreneur

    An Entrepreneur is an individual who founds and runs a small business and assumes all the risk and reward of the venture. ...
  2. Money Market

    The money market is a segment of the financial market in which financial instruments with high liquidity and very short maturities ...
  3. Perfect Competition

    Pure or perfect competition is a theoretical market structure in which a number of criteria such as perfect information and ...
  4. Compound Interest

    Compound Interest is interest calculated on the initial principal and also on the accumulated interest of previous periods ...
  5. Income Statement

    A financial statement that measures a company's financial performance over a specific accounting period. Financial performance ...
  6. Leverage Ratio

    A leverage ratio is any one of several financial measurements that look at how much capital comes in the form of debt, or ...
Trading Center