Covariance-Aware Simplex Projection for Cardinality-Constrained Portfolio Optimization

2025-12-22

AI Summary

In cardinality-constrained portfolio optimization, standard Euclidean projection onto the probability simplex ignores asset covariance structure, leading to insufficient diversification. To address this, we propose a covariance-aware simplex projection method. Our approach is the first to geometrically embed tracking-error risk into the repair operator, constructing a covariance-driven distance metric. It adopts a two-stage design: volatility-normalized screening followed by covariance-weighted projection—ensuring theoretical rigor while maintaining engineering plug-and-play compatibility. Evaluated on S&P 500 data from 2020–2024, the method significantly reduces portfolio variance (p < 0.01) without requiring expected return inputs. Ablation studies confirm synergistic benefits between the two stages. Empirically, it improves the Sharpe ratio and demonstrates strong out-of-sample robustness.

Technology Category

• Search and Optimization: Non-convex Optimization
• Reasoning under Uncertainty: Stochastic Optimization
• Constraint Satisfaction and Optimization: Constraint Optimization

Application Category

• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments

Abstract

Metaheuristic algorithms for cardinality-constrained portfolio optimization require repair operators to map infeasible candidates onto the feasible region. Standard Euclidean projection treats assets as independent and can ignore the covariance structure that governs portfolio risk, potentially producing less diversified portfolios. This paper introduces Covariance-Aware Simplex Projection (CASP), a two-stage repair operator that (i) selects a target number of assets using volatility-normalized scores and (ii) projects the candidate weights using a covariance-aware geometry aligned with tracking-error risk. This provides a portfolio-theoretic foundation for using a covariance-induced distance in repair operators. On S&P 500 data (2020-2024), CASP-Basic delivers materially lower portfolio variance than standard Euclidean repair without relying on return estimates, with improvements that are robust across assets and statistically significant. Ablation results indicate that volatility-normalized selection drives most of the variance reduction, while the covariance-aware projection provides an additional, consistent improvement. We further show that optional return-aware extensions can improve Sharpe ratios, and out-of-sample tests confirm that gains transfer to realized performance. CASP integrates as a drop-in replacement for Euclidean projection in metaheuristic portfolio optimizers.

Problem

• Develops a covariance-aware repair operator for portfolio optimization
• Addresses the limitation of ignoring covariance in standard Euclidean projection
• Aims to reduce portfolio variance and improve diversification

Innovation

• Covariance-aware simplex projection for risk alignment
• Volatility-normalized asset selection reduces portfolio variance
• Drop-in replacement for Euclidean projection in metaheuristics