Machine Learning Meets Markowitz

Abstract

The standard approach to portfolio selection involves two stages: forecast the asset returns and then plug them into an optimizer. We argue that this separation is deeply problematic. The first stage treats cross-sectional prediction errors as equally important across all securities.  However, given that final portfolios might differ given distinct risk preferences and investment restrictions, the standard approach fails to recognize that the investor is not just concerned with the average forecast error - but the precision of the forecasts for the specific assets that are most important for their portfolio.  Hence, it is crucial to integrate the two stages.  We propose a novel implementation utilizing machine learning tools that unifies the expected return generation process and the final optimized portfolio. Our empirical example provides convincing evidence that our end-to-end method outperforms the traditional two-stage approach.  In our framework, each investor has their own, endogenously determined, efficient frontier that depends on risk preferences, investor-specific constraints, as well as exposure to market frictions.

Keywords: Asset Pricing, Portfolio Optimization, Machine Learning, End-to-end Learning

JEL Classification: G11, G12, C61