Taras Bodnar: Testing the mean-variance efficiency of a high-dimensional portfolio

Abstract

Optimal asset allocation is considered in a high-dimensional asymptotic regime when the number of assets and the sample size tend to infinity at the same rate. Using the techniques from random matrix theory, new inferential procedures based on the optimal shrinkage intensity for testing the mean-variance efficiency of a high-dimensional portfolio are developed and the asymptotic distributions of the proposed test statistics are derived. The practical advantage of the proposed procedures is demonstrated in an empirical study based on stocks included into the S&P 500 index. We found that there are periods of time where one can clearly reject the null hypothesis of mean-variance optimality of the equally weighted portfolio.