Non-Normality Facts and Fallacies

David N. Esch

Volume 8, Number 1, First Quarter 2010

Recently there has been an increasing trend in the quantitative finance community to call for statistical models which are explicitly model returns with non-normal probability distributions (e.g. Sheikh and Qiao, 2009, Bhansali, 2008, Harvey and Siddique, 2004). In this paper, we explain why summary rejection of normal distributions is almost always ill-advised. First, we examine some of the motivations for using normal models in financial applications. These models can account for non-normal return distributions despite their normal model components. We then demonstrate some consequences of switching to more complicated and less well-known non-normal models. These models almost always have more parameters to fit from the same data. All else being equal, rational investors should prefer parsimonious models, especially when the historical signal is weak, as is often the case in finance. We survey the shortcomings of several popular non-normal financial modeling techniques, especially when implemented naively. Although certain problems may warrant the use of other statistical return distributions, we argue that it is still important to exhaust the possibilities of normal models before switching to them. Models with normal distributions can be extended through methods such as conditioning on other variables, inequality constraints, mixtures, integration and resampling over unknown parameter distributions, or in some cases non-linear transformations. The mathematical properties of the normal distribution facilitate these model-building techniques and allow for thorough post-analysis and model-validation to ensure the best choice for the final model. Because of the preceding arguments, we reject the popular fallacy that normal models cannot be valid or useful because return distributions have marginal non-normal distributions.