The Effect of Regularization in Portfolio Selection Problems

Portfolio selection problems have been thoroughly studied under the risk-and-return paradigm introduced by Markowitz. However, the usefulness of this approach has been hindered by some practical considerations that have resulted in poorly diversified portfolios or solutions that are extremely sensitive to parameter estimation errors. In this work, we use sampling methods to cope with these issues, and compare pure sampling schemes to a performance-based regularization (PBR) method that appeared recently in the literature. We derive the relevant regularization formulas for three risk measures: integrated chance-constraints, quantile deviation, and absolute semi-deviation, and present promising numerical results based on historic data that include the subprime crisis