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Random matrix theory for portfolio optimization: a stability approach

Sharifi, Saba and Crane, Martin and Shamaie, Atid and Ruskin, Heather J. (2004) Random matrix theory for portfolio optimization: a stability approach. Physica A: Statistical Mechanics and its Applications, 335 (3-4). pp. 629-643. ISSN 0378-4371

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Abstract

We apply Random Matrix Theory (RMT) on an empirically-measured financial correlation matrix, C, and show that this matrix contains a large amount of noise. In order to determine the sensitivity of the spectral properties of a random matrix to noise, we simulate a set of data and add different volumes of random noise. Having ascertained that the eigenspectrum is independent of the standard deviation of added noise, we use RMT to determine the noise percentage in a correlation matrix based on real data from S&P500. Eigenvalue and eigenvector analyses are applied and the experimental results for each of them are presented to identify qualitatively and quantitatively different spectral properties of the empirical correlation matrix to a random counterpart. Finally we attempt to separate the noisy part from the non-noisy part of C. We apply an existing technique to cleaning C and then discuss its associated problems. We propose a technique of filtering C which has many advantages, from a stability point of view over the existing method of cleaning.

Item Type:Article (Published)
Refereed:Yes
Uncontrolled Keywords:random matrix theory; portfolio optimization; correlation matrix; eigenvalues and eigenvectors;
Subjects:Mathematics > Statistics
Mathematics > Probabilities
DCU Faculties and Centres:DCU Faculties and Schools > Faculty of Engineering and Computing > School of Computing
Publisher:Elsevier
Official URL:http://dx.doi.org/10.1016/j.physa.2003.12.016
Copyright Information:Copyright © 2003 Elsevier
Use License:This item is licensed under a Creative Commons Attribution-NonCommercial-Share Alike 3.0 License. View License
ID Code:14831
Deposited On:08 Sep 2009 16:39 by Martin Crane. Last Modified 08 Sep 2009 16:39

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