  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 multi-fold cross-validation technique for selecting
the necessary tuning parameters within each method. Conducting an extensive
empirical analysis with four datasets based on the S&P 500, we show that the
data-driven choice of 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.
