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  .
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 .
R
Investors often prefer the
The
R
over the Markowitz portfolio as this allows the estimation risk to be confined to the
is a typical choice for investors because of its simplicity and broad applicability. Although it requires only one input, namely the
R
returns. For high-dimensional data, however, it is well-known that
asset returns, estimating the optimal solution remains a challenge. In the presence of high-dimensionality in the data,
R
matrix is
estimator becomes
A
out-of-sample
R
covariance matrix estimators and suggest
efficient estimation methods for the covariance matrix and extend the literature by suggesting
A
with four datasets based on the S
A
P 500
R
how
that
A
. 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