Random Matrix Approach for Portfolio Optimization Problem

• Published in: Journal of Japan Industrial Management Association Vol. 65; no. 1; pp. 17 - 28
• Main Authors: Wakai, Ryosuke, Shinzato, Takashi, Shimazaki, Yoshiaki
• Format: Journal Article
• Language: Japanese
• Published: Japan Industrial Management Association 2014
• Subjects: asymptotic distribution; mean-variance model; portfolio diversification investment; Portfolio optimization; random matrix theory
• ISSN: 1342-2618; 2187-9079
• DOI: 10.11221/jima.65.17

This paper analyzes typical performance of the optimal portfolio of the meanvariance model using a random matrix approach, one of the most potent methods in the econophysics literature. In the analysis, indicators representing the risk and the concentrated investment level (or the inverse dispersion) of the optimal solution are defined and analyzed under the assumption of equivalent investment strategy studied in previous works. The expected risk and dispersion for a given portfolio can be readily assessed, but not for the defined indicators of the optimal portfolio. We demonstrate the usefulness of a random matrix in the evaluation of those indicators under some simple problem settings, relying on the Marcenko-Pastur law known as asymptotic eigenvalue distribution. Moreover, the effectiveness of the proposed scheme is verified using numerical simulations.