Kurtosis risk
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Kurtosis risk denotes 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 shape of the normal distribution.
Kurtosis risk applies to any 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” risk. The “fat tail” metaphor explicitly describes that you have more observations at the extremes than the tails of the normal distribution suggests. Thus, 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, a hedge fund cofounded by Myron Scholes, 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 underlying the fund's own trading positions.[1]
Benoît Mandelbrot, a French mathematician, extensively researched this issue. He feels 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, and the Capital Asset Pricing Model developed by William Sharpe). He explained his views and alternative finance theory in a book: The Misbehavior of Markets.
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- Mandelbrot, Benoit B., and Hudson, Richard L., The (mis)behaviour of markets : a fractal view of risk, ruin and reward, London : Profile, 2004, ISBN 1861977654
