Large-scale minimum variance portfolio allocation using double regularization

Abstract

Estimation of time-varying covariances is a crucial input in minimum variance (MV) portfolio allocations. Rolling window-based sample estimates are widely used for this purpose, but they usually suffer from two major issues when applied to a moderately large number of assets: the “curse of dimensionality” and “temporal instability.” Here, we propose a double-regularized estimator for a high dimensional covariance matrix in which we impose both a temporal and cross-sectional sparsity regularization on the sample-based estimates to simultaneously mitigate these two issues. We investigate the performance of our proposed covariance estimator for MV portfolio construction using Monte Carlo experiments and empirical examples. We find that the resulting MV portfolio strikes a good balance between risk and turnover reduction, and produces more accurate equivalent returns after transaction costs are taken into account when compared to four other MV strategies.