Enhancing Portfolio Performance: The Efficacy of Direct Precision Matrix Estimation in Low-sample Settings

In low-sample settings, minimum variance portfolios often rely on covariance matrix inversion, introducing noise in such settings. This study explores the usage of Gaussian graphical models, which directly estimate the precision matrix for portfolio allocation and compare them with shrinkage, thresholding and other approaches, which estimate the covariance matrix. Using the Nifty 500 dataset, where true covariance and precision matrices are unknown, we compare portfolio allocation methods with the model confidence set approach, using portfolio variance as the performance metric. A comparative analysis of precision matrix estimators across different concentration ratios highlights that graphical Lasso and GreedyPrune outperform traditional covariance-based methods. Synthetic and empirical results consistently show that directly estimating the precision matrix yields superior portfolios in low-sample regimes. Among covariance estimators, nonlinear shrinkage delivers lower out-of-sample portfolio variance than linear shrinkage and thresholding methods. JEL Code: G11