Black–Litterman and Beyond: The Bayesian Paradigm in Investment Management

Abstract

The Black–Litterman model is one of the most popular models in quantitative finance, with numerous theoretical and practical achievements. From the standpoint of investment theory, the Black–Litterman model allows seamless incorporation of Bayesian statistics into the portfolio optimization process. From a practical standpoint, it provides portfolio managers with a structured approach to express subjective views, thereby freeing their investment processes from a total reliance on backward-looking historical data. In this article, the authors provide an overview of the original Black–Litterman model and its various extensions and enhancements addressing issues in real-world trading and investment management.

TOPICS: Statistical methods, portfolio construction, performance measurement

Key Findings

• ▪ The authors provide an overview of the original Black–Litterman model and its various extensions and enhancements, addressing issues in real-world trading and investment management.

• ▪ Many important practical considerations in implementing the Black-Litterman model are discussed including choice of priors, view generation, and transaction costs.

• ▪ Particular emphasis is given to the extensions of the Black-Litterman model of significant practical relevance to today’s investors such as factor models, model misspecification, non-normality, and multiperiod portfolio optimization.