Find what you are looking for: A data-driven covariance matrix estimation
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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.
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