Black-Litterman, Bayesian Shrinkage, and Factor Models in Portfolio Selection: You Can Have It All

TL;DR

This paper introduces a Bayesian framework that combines shrinkage estimators, investor views, and factor models to improve portfolio selection, demonstrating superior performance over traditional methods in empirical US market data.

Contribution

It develops a unified Bayesian model integrating shrinkage, views, and factor models, filling a gap in portfolio optimization methodologies.

Findings

The Bayesian model outperforms simple $1/N$ portfolios.

It surpasses portfolios based on sample estimators.

The approach is validated with a decade of US market data.

Abstract

Mean-variance analysis is widely used in portfolio management to identify the best portfolio that makes an optimal trade-off between expected return and volatility. Yet, this method has its limitations, notably its vulnerability to estimation errors and its reliance on historical data. While shrinkage estimators and factor models have been introduced to improve estimation accuracy through bias-variance trade-offs, and the Black-Litterman model has been developed to integrate investor opinions, a unified framework combining three approaches has been lacking. Our study debuts a Bayesian blueprint that fuses shrinkage estimation with view inclusion, conceptualizing both as Bayesian updates. This model is then applied within the context of the Fama-French approach factor models, thereby integrating the advantages of each methodology. Finally, through a comprehensive empirical study in the US equity market spanning a decade, we show that the model outperforms both the simple $1/N$ portfolio and the optimal portfolios based on sample estimators.