A Cholesky decomposition-based asset selection heuristic for sparse tangent portfolio optimization

ArXiv ID: 2502.11701 “View on arXiv”

Authors: Unknown

Abstract

In practice, including large number of assets in mean-variance portfolios can lead to higher transaction costs and management fees. To address this, one common approach is to select a smaller subset of assets from the larger pool, constructing more efficient portfolios. As a solution, we propose a new asset selection heuristic which generates a pre-defined list of asset candidates using a surrogate formulation and re-optimizes the cardinality-constrained tangent portfolio with these selected assets. This method enables faster optimization and effectively constructs portfolios with fewer assets, as demonstrated by numerical analyses on historical stock returns. Finally, we discuss a quantitative metric that can provide a initial assessment of the performance of the proposed heuristic based on asset covariance.

Keywords: mean-variance portfolio, asset selection heuristic, cardinality-constrained optimization, tangent portfolio, Stocks

Complexity vs Empirical Score

• Math Complexity: 7.0/10
• Empirical Rigor: 6.5/10
• Quadrant: Holy Grail
• Why: The paper introduces a novel heuristic (OSCAR) with detailed mathematical derivations, including Cholesky decomposition and angle-based optimization, leading to a high math score. It validates the method with numerical experiments on historical stock returns, providing implementation and performance analysis, though it lacks full backtest-ready details like transaction costs.

  flowchart TD
    A["Research Goal: Sparse Tangent Portfolio<br/>Minimize transaction costs by selecting assets"] --> B{"Methodology"}
    B --> C["Data: Historical Stock Returns<br/>Covariance Matrix Σ"]
    C --> D["Cholesky Decomposition-based<br/>Heuristic: Surrogate Formulation"]
    D --> E["Select k Assets from Candidate List"]
    E --> F["Re-optimize Cardinality-constrained<br/>Tangent Portfolio"]
    F --> G{"Numerical Analysis"}
    G --> H["Findings: Faster Optimization<br/>& Effective Asset Reduction"]
    H --> I["Outcome: Quantitative Metric<br/>for Heuristic Assessment"]