Premium
ENHANCEMENT OF THE APPLICABILITY OF MARKOWITZ'S PORTFOLIO OPTIMIZATION BY UTILIZING RANDOM MATRIX THEORY
Author(s) -
Bai Zhidong,
Liu Huixia,
Wong WingKeung
Publication year - 2009
Publication title -
mathematical finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.98
H-Index - 81
eISSN - 1467-9965
pISSN - 0960-1627
DOI - 10.1111/j.1467-9965.2009.00383.x
Subject(s) - portfolio optimization , portfolio , modern portfolio theory , dimension (graph theory) , mathematical optimization , variance (accounting) , asset allocation , efficient frontier , mathematics , sample size determination , asset (computer security) , sample (material) , econometrics , computer science , economics , statistics , financial economics , combinatorics , chemistry , accounting , computer security , chromatography
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.