Noise-proofing Universal Portfolio Shrinkage

ArXiv ID: 2511.10478 “View on arXiv”

Authors: Paul Ruelloux, Christian Bongiorno, Damien Challet

Abstract

We enhance the Universal Portfolio Shrinkage Approximator (UPSA) of Kelly et al. (2023) by making it more robust with respect to estimation noise and covariate shift. UPSA optimizes the realized Sharpe ratio using a relatively small calibration window, leveraging ridge penalties and cross-validation to yield better portfolios. Yet, it still suffers from the staggering amount of noise in financial data. We propose two methods to make UPSA more robust and improve its efficiency: time-averaging of the optimal penalty weights and using the Average Oracle correlation eigenvalues to make covariance matrices less noisy and more robust to covariate shift. Combining these two long-term averages outperforms UPSA by a large margin in most specifications.

Keywords: Universal Portfolio Shrinkage Approximator (UPSA), Ridge penalties, Cross-validation, Covariate shift, Average Oracle correlation eigenvalues, Equities / Portfolio Allocation

Complexity vs Empirical Score

  • Math Complexity: 8.0/10
  • Empirical Rigor: 7.0/10
  • Quadrant: Holy Grail
  • Why: The paper introduces advanced statistical estimation techniques, including spectral decomposition and a novel ‘Average Oracle’ method, representing high mathematical density. It also presents concrete empirical results, performance metrics (Herfindahl index), and references backtesting on financial data, demonstrating substantial empirical rigor.
  flowchart TD
    A["Research Goal: Enhance UPSA<br>robustness to noise & covariate shift"] --> B["Proposed Enhancements<br>1. Time-averaged penalty weights<br>2. Average Oracle correlation eigenvalues"]
    B --> C["Methodology: Apply enhancements<br>to UPSA framework"]
    C --> D["Input: Equities Data<br>(Relative prices / log returns)"]
    D --> E["Compute: Ridge Penalties<br>+ Cross-Validation"]
    E --> F["Compute: Covariance Matrices<br>via Average Oracle eigenvalues"]
    F --> G["Process: Time-averaging<br>optimal penalty weights"]
    G --> H["Key Outcome: Enhanced Portfolio<br>Sharpe Ratio & Robustness"]
    
    style A fill:#e1f5fe
    style H fill:#e8f5e8