ENHANCEMENT OF THE APPLICABILITY OF MARKOWITZ'S PORTFOLIO OPTIMIZATION BY UTILIZING RANDOM MATRIX THEORY

The traditional estimated return for the Markowitz mean-variance optimization has been demonstrated to seriously depart from its theoretic optimal return. We prove that this phenomenon is natural and the estimated optimal return is alwaysv root gamma times larger than its theoretic counterpart, where gamma = 1/1-y with y as the ratio of the dimension to sample size. Thereafter, we develop new bootstrap-corrected estimations for the optimal return and its asset allocation and prove that these bootstrap-corrected estimates are proportionally consistent with their theoretic counterparts. Our theoretical results are further confirmed by our simulations, which show that the essence of the portfolio analysis problem could be adequately captured by our proposed approach. This greatly enhances the practical uses of the Markowitz mean-variance optimization procedure.