A Unified Framework for Fast Large-Scale Portfolio Optimization

We develop a unified framework for fast large-scale portfolio optimization with shrinkage and regularization for different objectives such as minimum variance, mean-variance, and maximum Sharpe ratio with various constraints on the portfolio weights. For all of the optimization problems, we derive the corresponding quadratic programming problems and implement them in an open-source Python library. We use the proposed framework to evaluate the out-of-sample portfolio performance of popular covariance matrix estimators such as sample covariance matrix, linear and nonlinear shrinkage estimators, and the covariance matrix from the instrumented principal component analysis (IPCA). We use 65 years of monthly returns from (on average) 585 largest companies in the US market, and 94 monthly firm-specific characteristics for the IPCA model. We show that the regularization of the portfolio norms greatly benefits the performance of the IPCA model in portfolio optimization, resulting in outperformance linear and nonlinear shrinkage estimators even under realistic constraints on the portfolio weights.