Double Descent in Portfolio Optimization: Dance between Theoretical Sharpe Ratio and Estimation Accuracy

ArXiv ID: 2411.18830 “View on arXiv”

Authors: Unknown

Abstract

We study the relationship between model complexity and out-of-sample performance in the context of mean-variance portfolio optimization. Representing model complexity by the number of assets, we find that the performance of low-dimensional models initially improves with complexity but then declines due to overfitting. As model complexity becomes sufficiently high, the performance improves with complexity again, resulting in a double ascent Sharpe ratio curve similar to the double descent phenomenon observed in artificial intelligence. The underlying mechanisms involve an intricate interaction between the theoretical Sharpe ratio and estimation accuracy. In high-dimensional models, the theoretical Sharpe ratio approaches its upper limit, and the overfitting problem is reduced because there are more parameters than data restrictions, which allows us to choose well-behaved parameters based on inductive bias.

Keywords: Mean-Variance Optimization, Model Complexity, Overfitting, Double Descent, Portfolio Optimization, Equities

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 3.0/10
• Quadrant: Lab Rats
• Why: The paper employs advanced theoretical frameworks like random matrix theory and derives analytical asymptotic results for Sharpe ratios, indicating high mathematical complexity. However, the excerpt focuses on theoretical derivations and conceptual mechanisms without showing specific backtesting procedures, code, or detailed empirical metrics, resulting in lower empirical rigor.

  flowchart TD
    A["Research Goal: Investigate relationship between model complexity (number of assets) and out-of-sample Sharpe ratio in mean-variance portfolio optimization"] --> B["Data: Historical equity returns data (N assets, T time periods)"]
    
    B --> C["Methodology: Simulate varying model complexity (N from low to high)"]
    
    C --> D["Computational Process: Construct Mean-Variance portfolios using empirical inputs (sample mean/covariance) across all complexity levels"]
    
    D --> E["Analysis: Evaluate out-of-sample Sharpe ratio performance against model complexity"]
    
    E --> F["Finding 1: Performance improves initially with complexity (low N)"]
    E --> G["Finding 2: Performance declines due to overfitting (moderate N)"]
    E --> H["Finding 3: Performance improves again with high complexity (N > T)"]
    
    F --> I["Key Outcome: Double Descent Sharpe Ratio Curve<br/>Mechanism: Interaction between theoretical Sharpe limit & estimation accuracy in high dimensions"]
    G --> I
    H --> I