Shocks-adaptive Robust Minimum Variance Portfolio for a Large Universe of Assets

ArXiv ID: 2410.01826 “View on arXiv”

Authors: Unknown

Abstract

This paper proposes a robust, shocks-adaptive portfolio in a large-dimensional assets universe where the number of assets could be comparable to or even larger than the sample size. It is well documented that portfolios based on optimizations are sensitive to outliers in return data. We deal with outliers by proposing a robust factor model, contributing methodologically through the development of a robust principal component analysis (PCA) for factor model estimation and a shrinkage estimation for the random error covariance matrix. This approach extends the well-regarded Principal Orthogonal Complement Thresholding (POET) method (Fan et al., 2013), enabling it to effectively handle heavy tails and sudden shocks in data. The novelty of the proposed robust method is its adaptiveness to both global and idiosyncratic shocks, without the need to distinguish them, which is useful in forming portfolio weights when facing outliers. We develop the theoretical results of the robust factor model and the robust minimum variance portfolio. Numerical and empirical results show the superior performance of the new portfolio.

Keywords: robust factor model, principal component analysis, minimum variance portfolio, large-dimensional assets, shrinkage estimation, Multi-Asset

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 7.0/10
• Quadrant: Holy Grail
• Why: The paper presents high mathematical complexity with advanced statistical theory (robust PCA, asymptotic results, factor models with heavy tails) but also demonstrates empirical rigor through numerical simulations and backtests on real market data (S&P 500, Russell 2000).

  flowchart TD
    A["Research Goal<br>Develop Robust Portfolio for Large Universe<br>Adaptive to Shocks & Outliers"] --> B["Key Methodology"]
    B --> B1["Robust PCA<br>for Factor Model"]
    B --> B2["Shrinkage Estimation<br>for Covariance Matrix"]
    B --> B3["Adaptive Robust<br>Minimum Variance Portfolio"]
    
    B --> C["Data & Inputs"]
    C --> C1["High-Dimensional<br>Asset Returns"]
    C --> C2["Large Universe<br>n ≈ T or n > T"]
    C --> C3["Heavy Tails &<br>Sudden Shocks"]
    
    C --> D["Computational Process"]
    D --> D1["Estimate Factors<br>with Outlier Robustness"]
    D --> D2["Shrink Error Covariance<br>to Improve Stability"]
    D --> D3["Solve Portfolio<br>Optimization"]
    
    D --> E["Key Findings & Outcomes"]
    E --> E1["Superior Performance<br>vs. Benchmark Methods"]
    E --> E2["Effective Adaptiveness<br>to Global & Idiosyncratic Shocks"]
    E --> E3["Robust to Outliers<br>in Large n Settings"]