Factor Investing with Black–Litterman–Bayes: Incorporating Factor Views and Priors in Portfolio Construction

Abstract

The authors propose a general framework referred to as Black–Litterman–Bayes (BLB) for constructing optimal portfolios for factor-based investing. In the spirit of the classical Black–Litterman model, the framework allows for the incorporation of investor views and priors on factor risk premiums, including data-driven and benchmark priors. Computationally efficient closed-form formulas are provided for the (posterior) expected returns and return covariance matrix that result from integrating factor views into an arbitrage pricing theory multi-factor model. In a step-by-step procedure, the authors show how to build the prior and incorporate the factor views, demonstrating in a realistic empirical example and using a number of well-known cross-sectional US equity factors, that the BLB approach can add value to mean–variance-optimal multi-factor risk premium portfolios.

TOPICS: Factor-based models, factors, risk premia, portfolio construction, portfolio theory

Key Findings

• ▪ The authors propose a general framework referred to as Black–Litterman–Bayes (BLB) for constructing optimal portfolios for factor-based investing.

• ▪ The framework allows for the incorporation of investor views and priors on factor risk premiums, including data-driven and benchmark priors.

• ▪ The authors provide computationally efficient closed-form formulas for the (posterior) expected returns and return covariance matrix.

• ▪ In a realistic empirical example, using a number of well-known cross-sectional US equity factors, they demonstrate that the BLB approach can add value to mean–variance-optimal multi-factor risk premium portfolios.