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

ArXiv ID: 2308.09264 “View on arXiv”

Authors: Unknown

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.

Keywords: Mean-Variance Analysis, Bayesian Inference, Factor Models, Shrinkage Estimators, Portfolio Management

Complexity vs Empirical Score

• Math Complexity: 8.0/10
• Empirical Rigor: 7.0/10
• Quadrant: Holy Grail
• Why: The paper proposes a Bayesian framework unifying shrinkage estimation and factor models, involving advanced probabilistic modeling and likely heavy mathematical derivations. Its empirical section details a decade-long US equity market backtest, explicitly comparing performance against benchmark portfolios, indicating substantial implementation and data rigor.

  flowchart TD
    A["Research Goal"] --> B["Methodology"]
    B --> C["Data Collection"]
    C --> D["Model Computation"]
    D --> E["Evaluation & Comparison"]
    E --> F["Findings"]

    subgraph A ["Research Goal"]
        A1["Unified Bayesian Framework for<br>Mean-Variance Portfolio Optimization"]
    end

    subgraph B ["Methodology: The "All-in-One" Model"]
        B1["Black-Litterman: Integrate Views"]
        B2["Bayesian Shrinkage: Estimate Parameters"]
        B3["Fama-French: Factor Models"]
        B1 & B2 & B3 --> B4["Fused Bayesian Blueprint"]
    end

    subgraph C ["Data Inputs"]
        C1["US Equity Market<br>10-Year Span"]
        C2["Fama-French Factors"]
    end

    subgraph D ["Computational Process"]
        D1["Posterior Estimation<br>Bayesian Update"]
        D2["Portfolio Optimization<br>Maximize Utility"]
    end

    subgraph E ["Evaluation"]
        E1["Backtesting Strategies"]
    end

    subgraph F ["Key Outcomes"]
        F1["Outperforms 1/N Portfolio"]
        F2["Outperforms Sample Estimators"]
    end