Covariance-Aware Simplex Projection for Cardinality-Constrained Portfolio Optimization

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.