Applications of Robust Statistical Methods in Quantitative Finance
Green, Christopher George
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Financial asset returns and fundamental factor exposure data often contain outliers, observations that are inconsistent with the majority of the data. Both academic finance researchers and quantitative finance professionals are well aware of the occurrence of outliers in financial data, and seek to limit the influence of such observations in data analyses. Commonly used outlier mitigation techniques assume that it is sufficient to deal with outliers in each variable separately. Such approaches can easily miss multivariate outliers, observations that are outlying in higher dimensions without being outlying in any individual variable. Robust statistical methods are a better approach to building reliable financial models in the presence of multivariate outliers, but they are unfortunately underused by academic researchers and practitioners. This dissertation motivates greater use of robust statistical methods in quantitative finance research via two applications to outlier detection and asset pricing research. We first demonstrate the use of robust Mahalanobis distances (RSDs) based on the minimum covariance determinant (MCD) robust mean and covariance estimates to detect multivariate outliers in asset returns time series data and fundamental factor exposure data. We improve upon a result of Hardin and Rocke for approximating the distribution of such distances, and use our result to improve the accuracy of the Iterated Reweighted MCD (IRMCD) technique of Cerioli for testing MCD-based RSDs with sample sizes as small as n = 60 and with high-efficiency versions of the MCD. We show that, with our improvements, outlier detection via RSDs combined with IRMCD is more accurate than both common univariate approaches and multivariate Mahalanobis distances based on the classical sample mean and covariance estimates. Second, we illustrate the benefits of robust MM-regression for empirically testing factor-based asset pricing models by revisiting the classic 1992 asset pricing study of Fama and French with data updated through December 2015. Our analysis using cross-sectional robust MM-regression reveals the surprising extent to which influential outliers, mainly small firms with isolated large returns, drove some of the main conclusions of the Fama and French study. Specifically, we demonstrate that the relationship between average returns and firm size is positive for nearly all stocks. The negative relationship found by Fama and French and most other asset pricing studies arises from a small percentage, usually less than 2%, of small stocks each month with unusually large returns. Similarly, we find a significant and complex relationship between average returns and firm betas, in contrast to Fama and French's assertion of the lack of such a relationship. We furthermore find that there is a non-trivial interaction between beta and size that must be included in an asset pricing model to fully explain the relationship between average returns and beta. Finally, while we confirm the positive relationship between average returns and firm book-to-market ratios found by Fama and French, we also confirm results due to Loughan demonstrating that this relationship is only significant in smaller stocks. Overall our robust regression analysis demonstrates the danger of relying solely upon classical statistical methods, such as least squares regression, in empirical asset pricing studies and encourages the use of modern robust methods in asset pricing research.
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