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

TL;DR

This paper introduces a cross-validation approach for selecting tuning parameters in covariance estimators, significantly improving the out-of-sample performance of high-dimensional minimum-variance portfolios.

Contribution

It extends existing covariance estimation methods by incorporating a multi-fold cross-validation technique for better parameter tuning in high-dimensional settings.

Findings

Cross-validation improves portfolio out-of-sample performance.

Certain estimators are highly sensitive to tuning parameters.

A relationship exists between cross-validation criteria and performance measures.

Abstract

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.