Taras Bodnar: Shrinkage approaches in high-dimensional portfolio analysis: Estimation and test theory

Abstract

Optimal asset allocation is considered in the high-dimensional asymptotic setting, namely when the number of assets and the sample size tend to infinity at the same rate. Due to the curse of dimensionality, asset allocation for such portfolios becomes a challenging task. Using the techniques from random matrix theory, new shrinkage-type estimators for optimal portfolio weights are developed and inferential procedures for testing the mean-variance efficiency of a high-dimensional portfolio are established. In an extensive simulation study, the suggested approaches are compared with the existent alternatives. The practical advantage of the new procedures is also documented in an empirical study based on stocks included in the S&P 500 index.