Cross-validated covariance estimators for high-dimensional minimum-variance portfolios

The global minimum-variance portfolio is a typical choice for investors because of its simplicity and broad applicability. Although it requires only one input, namely the covariance matrix of asset returns, estimating the optimal solution remains a challenge. In the presence of high dimensionality in the data, the sample covariance estimator becomes ill-conditioned and leads to suboptimal portfolios out-of-sample. To address this issue, we review recently proposed efficient estimation methods for the covariance matrix and extend the literature by suggesting a multifold cross-validation technique for selecting the necessary tuning parameters within each method. Conducting an extensive empirical analysis with three datasets based on the Russell 3000, we show that choosing the specific tuning parameters with the proposed cross-validation improves the out-of-sample performance of the global minimum-variance portfolio. In addition, we identify estimators that are strongly influenced by the choice of the tuning parameter and detect a clear relationship between the selection criterion within the cross-validation and the evaluated performance measure.