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 estimator becomes ill-conditioned , which negates the positive effect of diversification in an out-of-sample setting . To address this issue, we review recent covariance matrix estimators and extend the literature by suggesting a multi-fold cross-validation technique . In detail, conducting an extensive empirical analysis with four datasets based on the S\&P 500, we evaluate how the data-driven choice of specific tuning parameters within the proposed cross-validation approach affects the out-of-sample performance of the global minimum-variance portfolio . In particular, for cases in which the efficiency of a covariance estimator is strongly influenced by the choice of a tuning parameter, we detect a clear relationship between the optimality criterion for its selection within the cross-validation and the evaluated performance measure. Finally, we show that using cross-validation can improve the performance of highly efficient estimators even when the data-driven covariance parameter deviates from its theoretically optimal value .
Investors often prefer the global minimum-variance portfolio over the Markowitz portfolio as this allows the estimation risk to be confined to the covariance matrix of returns. For high-dimensional data, however, it is well-known that the sample covariance matrix is ill-conditioned and leads to suboptimal portfolios . To address this issue, we review recently proposed covariance matrix estimators and suggest a multi-fold cross-validation technique for selecting the necessary tuning parameters within each method. Conducting an extensive empirical analysis , we show how 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 .
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