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

Petter N. Kolm and Gordon Ritter
The Journal of Portfolio Management Quantitative Special Issue 2021, 47 (2) 113-126; DOI: https://doi.org/10.3905/jpm.2020.1.196
Petter N. Kolm
is a clinical professor and director of the Mathematics in Finance Master’s Program in the Courant Institute of Mathematical Sciences at New York University in New York, NY
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Gordon Ritter
is an adjunct professor at the Courant Institute of Mathematical Sciences, NYU Tandon School of Engineering, Baruch College, Columbia University in New York, NY and General Partner/CIO at Ritter Alpha, LP in New York, NY
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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, 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.

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The Journal of Portfolio Management: 47 (2)
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Quantitative Special Issue 2021
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Factor Investing with Black–Litterman–Bayes: Incorporating Factor Views and Priors in Portfolio Construction
Petter N. Kolm, Gordon Ritter
The Journal of Portfolio Management Dec 2020, 47 (2) 113-126; DOI: 10.3905/jpm.2020.1.196

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Factor Investing with Black–Litterman–Bayes: Incorporating Factor Views and Priors in Portfolio Construction
Petter N. Kolm, Gordon Ritter
The Journal of Portfolio Management Dec 2020, 47 (2) 113-126; DOI: 10.3905/jpm.2020.1.196
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  • Article
    • Abstract
    • THE BLACK–LITTERMAN MODEL
    • BLACK–LITTERMAN FOR FACTOR INVESTING
    • AN EMPIRICAL CASE STUDY
    • CONCLUSIONS
    • REFERENCES
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