# Skewness risk

Skewness risk

Skewness risk denotes that observations are not spread symmetrically around an average value. As a result, the average and the median are different. Skewness risk applies to any quantitative model that relies on a symmetric distribution (such as the normal distribution).

Ignoring skewness risk will cause any model to understate the risk of variables with high skewness. Ignoring skewness is made by assuming that variables are symmetrically distributed when they are not.

Skewness risk plays an important role in hypothesis testing. The Analysis of Variance, the most common test used in hypothesis testing, assumes that the data are normally distributed. If the variables tested are not normally distributed because they are too skewed the test cannot be used. Instead, nonparametric tests can be used as Mann-Whitney test for unpaired situation or the Sign test for paired situation.

Skewness risk and kurtosis risk also have technical implications in calculation of Value at risk. If either are ignored, the Value at risk calculations will be flawed.

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 Black-Scholes model, CAPM). He explained his views and alternative finance theory in a book: "The Misbehavior of Markets".

In options markets, the difference in implied volatility at different strike prices represents the market's view of skew, and is called volatility skew. (In pure Black-Scholes, implied volatility is constant with respect to strike.)

ee also

*Skewness
*Kurtosis risk

References

* 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

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