Enhancement of the applicability of markowitz's portfolio optimization by utilizing random matrix theory

Zhidong Bai, Huixia Liu, Wing Keung WONG*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

83 Citations (Scopus)

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 √γ times larger than its theoretic counterpart, where γ = 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.

Original languageEnglish
Pages (from-to)639-667
Number of pages29
JournalMathematical Finance
Volume19
Issue number4
DOIs
Publication statusPublished - Oct 2009

Scopus Subject Areas

  • Accounting
  • Finance
  • Social Sciences (miscellaneous)
  • Economics and Econometrics
  • Applied Mathematics

User-Defined Keywords

  • Bootstrap method
  • Large random matrix
  • Mean-variance optimization
  • Optimal portfolio allocation

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