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

Research output: Working paper / PreprintWorking paper


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.
Original languageEnglish
Number of pages72
Publication statusIn preparation - 6 Feb 2023


  • Bayes-Stein
  • portfolio optimization
  • 1/N
  • machine Learning

ASJC Scopus subject areas

  • Finance
  • Economics, Econometrics and Finance (miscellaneous)
  • Management Science and Operations Research
  • Statistics, Probability and Uncertainty


Dive into the research topics of 'When Bayes-Stein Meets Machine Learning: A Generalized Approach for Portfolio Optimization'. Together they form a unique fingerprint.

Cite this