Beyond GMV: the relevance of covariance matrix estimation for risk-based portfolio construction

We empirically analyze the relevance of variance-covariance (VCV) estimators in equity portfolio construction. While traditional analyses of unconstrained global minimum-variance (GMV) portfolios support using shrinkage and modeling covariance dynamics, the resulting portfolios are often impractical due to high leverage, concentration, and costs. By examining constrained GMV and risk parity portfolios, we find a significantly reduced opportunity for alternative VCV estimators to outperform the sample estimator. Specifically, we show that a long-only portfolio with asset-level constraints and a transaction cost penalty produces similar results to shrinkage-based methods, even when using the sample VCV estimator. However, accounting for time-series dynamics in asset returns remains statistically relevant for volatility reduction. Our findings emphasize how the interaction between VCV estimators and portfolio construction choices shapes both the statistical and practical outcomes in portfolio management.