Enhancement of the Applicability of Markowitz's Portfolio Optimization by Utilizing Random Matrix Theory

29 Pages Posted: 21 Oct 2009

See all articles by Zhidong Bai

Zhidong Bai

Northeast Normal University

Huixia Liu

Northeast Normal University

Wing-Keung Wong

Asia University, Department of Finance

Date Written: 2008-04

Abstract

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 always  times larger than its theoretic counterpart, where  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.

Suggested Citation

Bai, Zhidong and Liu, Huixia and Wong, Wing-Keung, Enhancement of the Applicability of Markowitz's Portfolio Optimization by Utilizing Random Matrix Theory (2008-04). Mathematical Finance, Vol. 19, Issue 4, pp. 639-667, October 2009. Available at SSRN: https://ssrn.com/abstract=1491825 or http://dx.doi.org/10.1111/j.1467-9965.2009.00383.x

Zhidong Bai (Contact Author)

Northeast Normal University ( email )

Changchun
China

Huixia Liu

Northeast Normal University ( email )

Changchun
China

Wing-Keung Wong

Asia University, Department of Finance ( email )

Taiwan
Taiwan

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