Precision versus Shrinkage: A Comparative Analysis of Covariance Estimation Methods for Portfolio Allocation

In this paper, we perform a comprehensive study of different covariance and precision matrix estimation methods in the context of minimum variance portfolio allocation. The set of models studied by us can be broadly categorized as: Gaussian Graphical Model (GGM) based methods, Shrinkage Methods, Thresholding and Random Matrix Theory (RMT) based methods. Among these, GGM methods estimate the precision matrix directly while the other approaches estimate the covariance matrix. We perform a synthetic experiment to study the network learning and sample complexity performance of GGM methods. Thereafter, we compare all the covariance and precision matrix estimation methods in terms of their predictive ability for daily, weekly and monthly horizons. We consider portfolio risk as an indicator of estimation error and employ it as a loss function for comparison of the methods under consideration. We find that GGM methods outperform shrinkage and other approaches. Our observations for the performance of GGM methods are consistent with the synthetic experiment. We also propose a new criterion for the hyperparameter tuning of GGM methods. Our tuning approach outperforms the existing methodology in the synthetic setup. We further perform an empirical experiment where we study the properties of the estimated precision matrix. The properties of the estimated precision matrices calculated using our tuning approach are in agreement with the algorithm performances observed in the synthetic experiment and the empirical experiment for predictive ability performance comparison. Apart from this, we perform another synthetic experiment which demonstrates the direct relation between estimation error of the precision matrix and portfolio risk.