A Unified Framework for Fast Large-Scale Portfolio Optimization

Abstract: We introduce a unified framework for rapid, large-scale portfolio optimization that incorporates both shrinkage and regularization techniques. This framework addresses multiple objectives, including minimum variance, mean-variance, and the maximum Sharpe ratio, and also adapts to various portfolio weight constraints. For each optimization scenario, we detail the translation into the corresponding quadratic programming (QP) problem and then integrate these solutions into a new open-source Python library. Using 50 years of return data from US mid to large-sized companies, and 33 distinct firm-specific characteristics, we utilize our framework to assess the out-of-sample monthly rebalanced portfolio performance of widely-adopted covariance matrix estimators and factor models, examining both daily and monthly returns. These estimators include the sample covariance matrix, linear and nonlinear shrinkage estimators, and factor portfolios based on Asset Pricing (AP) Trees, Principal Component Analysis (PCA), Risk Premium PCA (RP-PCA), and Instrumented PCA (IPCA). Our findings emphasize that AP-Trees and PCA-based factor models consistently outperform all other approaches in out-of-sample portfolio performance. Finally, we develop new l1 and l2 regularizations of factor portfolio norms which not only elevate the portfolio performance of AP-Trees and PCA-based factor models but they have a potential to reduce an excessive turnover and transaction costs often associated with these models.