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Skewness 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 the normal distribution for certain of its independent variables when the latter may be skewed much more than what the normal distribution can tolerate. You can determine whether a variable is normally distributed by using the Jarque-Bera test.

Ignoring skewness risk will cause any model to understate the risk of variables with high skewness. You do that (ignoring skewness) by assuming that variables are normally distributed when they are not.

Skewness risk plays an important role in hypothesis testing. The Student's t test, the most common test used in hypothesis testing, relies on the normal distribution. If the variables you are testing are not normally distributed because they are too skewed you can’t use the t test. Instead, you will have to use nonparametric tests such 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 you ignore either, your 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.

• 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