University of Washington - Department of Statistics
Advisor: R. Douglas Martin
The literature on use of robust estimates, skewed distribution MLEâ€™s and non-normal distribution hierarchical Bayes models for multi-factor models in finance is surprisingly thin, and limited for the most part to single factor models (SFMâ€™s). The ultimate goal of our research is the study of the relative merits of robust versus non-normal MLE estimation of multi-factor models and the use of hierarchical Bayes modeling of multi-factor models using skewed fat-tailed distributions. As first steps in that direction we have done the following: (1) Extensive study of robust versus skewed t-distribution estimation of SFM betas, including introducing a new test statistic for determining significant differences between OLS and robust estimates and an extensive empirical comparative study, (2) The SFM study also shows how to choose the loss function for robust regression so as to deliver reliable tests, (3) Extensive comparative study of robust versus skewed distribution MLEâ€™s for estimating alphas, with the result that a bias corrected robust estimate is preferred to skewed t-distribution MLEâ€™s, (4) Initial application of skewed fat-tailed distributions to decomposition of tail risk into market tail risk and specific tail risk, and (5) Initial use of non-normal distribution hierarchical Bayes models for the SFM. Additional work needed to complete the overall dissertation is discussed.