Kurtosis risk
Encyclopedia
Kurtosis risk in statistics
Statistics
Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....

 and decision theory
Decision theory
Decision theory in economics, psychology, philosophy, mathematics, and statistics is concerned with identifying the values, uncertainties and other issues relevant in a given decision, its rationality, and the resulting optimal decision...

 denotes the fact that observations are spread in a wider fashion than the normal distribution entails. In other words, fewer observations cluster near the average, and more observations populate the extremes either far above or far below the average compared to the bell curve
Bell curve
Bell curve can refer to:* A Gaussian function, a specific kind of function whose graph is a bell-shaped curve* Normal distribution, whose density function is a Gaussian function...

 shape of the normal distribution.

Kurtosis risk applies to any kurtosis related quantitative model that relies on the normal distribution for certain of its independent variables when the latter may have kurtosis much greater than the normal distribution. Kurtosis risk is commonly referred to as "fat tail
Fat tail
A fat-tailed distribution is a probability distribution that has the property, along with the heavy-tailed distributions, that they exhibit extremely large skewness or kurtosis. This comparison is often made relative to the ubiquitous normal distribution, which itself is an example of an...

" risk. The "fat tail" metaphor explicitly describes the situation of having more observations at either extreme than the tails of the normal distribution would suggest; therefore, the tails are "fatter".

Ignoring kurtosis risk will cause any model to understate the risk of variables with high kurtosis. For instance, Long-Term Capital Management
Long-Term Capital Management
Long-Term Capital Management L.P. was a speculative hedge fund based in Greenwich, Connecticut that utilized absolute-return trading strategies combined with high leverage...

, a hedge fund
Hedge fund
A hedge fund is a private pool of capital actively managed by an investment adviser. Hedge funds are only open for investment to a limited number of accredited or qualified investors who meet criteria set by regulators. These investors can be institutions, such as pension funds, university...

 cofounded by Myron Scholes
Myron Scholes
Myron Samuel Scholes is a Canadian-born American financial economist who is best known as one of the authors of the Black–Scholes equation. In 1997 he was awarded the Nobel Memorial Prize in Economic Sciences for a method to determine the value of derivatives...

, ignored kurtosis risk to its detriment. After four successful years, this hedge fund had to be bailed out by major investment banks in the late 90s because it understated the kurtosis of many financial securities
Security (finance)
A security is generally a fungible, negotiable financial instrument representing financial value. Securities are broadly categorized into:* debt securities ,* equity securities, e.g., common stocks; and,...

 underlying the fund's own trading positions.

Benoît Mandelbrot
Benoît Mandelbrot
Benoît B. Mandelbrot was a French American mathematician. Born in Poland, he moved to France with his family when he was a child...

, a French mathematician, extensively researched this issue. He felt that the extensive reliance on the normal distribution for much of the body of modern finance and investment theory is a serious flaw of any related models including the Black–Scholes option model developed by Myron Scholes and Fischer Black
Fischer Black
Fischer Sheffey Black was an American economist, best known as one of the authors of the famous Black–Scholes equation.-Background:...

, and the capital asset pricing model
Capital asset pricing model
In finance, the capital asset pricing model is used to determine a theoretically appropriate required rate of return of an asset, if that asset is to be added to an already well-diversified portfolio, given that asset's non-diversifiable risk...

 developed by William Sharpe
William Forsyth Sharpe
William Forsyth Sharpe is the STANCO 25 Professor of Finance, Emeritus at Stanford University's Graduate School of Business and the winner of the 1990 Nobel Memorial Prize in Economic Sciences....

. Mandelbrot explained his views and alternative finance theory in a book: The (Mis)Behavior of Markets: A Fractal View of Risk, Ruin, and Reward.

See also

  • Skewness risk
    Skewness risk
    Skewness risk in financial modeling denotes that observations are not spread symmetrically around an average value. As a result, the average and the median can be different...

  • Kurtosis
    Kurtosis
    In probability theory and statistics, kurtosis is any measure of the "peakedness" of the probability distribution of a real-valued random variable...

  • Taleb distribution
    Taleb Distribution
    In economics and finance, a Taleb distribution is a term coined by U.K. economists/journalists Martin Wolf and John Kay to describe a returns profile that appears at times deceptively low-risk with steady returns, but experiences periodically catastrophic drawdowns. It does not describe a...

  • Stochastic Volatility
    Stochastic volatility
    Stochastic volatility models are used in the field of mathematical finance to evaluate derivative securities, such as options. The name derives from the models' treatment of the underlying security's volatility as a random process, governed by state variables such as the price level of the...

  • The Black Swan
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