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

Kwong Yu Chong

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arXiv · 2308.09264

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

Kwong Yu Chong

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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.

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Kwong Yu Chong. 2023-08-18. Black-Litterman, Bayesian Shrinkage, and Factor Models in Portfolio Selection: You Can Have It All. https://arxiv.org/abs/2308.09264

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