When Bayes-Stein Meets Machine Learning: A Generalized Approach for Portfolio Optimization

The Bayes-Stein model provides a framework for remedying parameter uncertainty in the Markowitz mean-variance portfolio optimization. The classical version, however, suffers from estimation errors of model components and fails to consistently outperform the naive 1/N asset allocation rule. We comprehensively investigate the drawbacks of the traditional Bayes-Stein model and develop a generalized counterpart by refining model components with various well-tailored machine learning techniques, expanding the scope and applicability of the original Bayes-Stein model. Specifically, we propose a time-dependent weighted Elastic Net (TW-ENet) approach predicting expected asset returns, a hybrid double selective clustering combination (HDS-CC) strategy calibrating shrinkage factors, and a graphical adaptive Elastic Net (GA-ENet) algorithm estimating the inverse covariance matrix. Empirical studies demonstrate that our generalized Bayes-Stein framework can always offer better out-of-sample performance than the 1/N strategy. Importantly, our study tailors existing machine learning methods considering the specifics of financial issues, illustrating appealing directions for solving challenging financial problems with machine learning.