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. Skewness risk applies to any quantitative model that relies on a symmetric distribution (such as the normal distribution).
Ignoring skewness risk, by assuming that variables are symmetrically distributed when they are not, will cause any model to understate the risk of variables with high skewness.
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 is 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, such as the Mann–Whitney test for unpaired situation or the sign test for paired situation.
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 model and CAPM). He explained his views and alternative finance theory in a book: The (Mis)Behavior of Markets: A Fractal View of Risk, Ruin and Reward.
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 and time to maturity.)
See also 
- Mandelbrot, Benoit B., and Hudson, Richard L., The (mis)behaviour of markets : a fractal view of risk, ruin and reward, London : Profile, 2004, ISBN 1-86197-765-4
- Johansson, A. (2005) "Pricing Skewness and Kurtosis Risk on the Swedish Stock Market", Masters Thesis, Department of Economics, Lund University, Sweden