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Random matrix theory for portfolio optimization: a stability approach
Sharifi, Saba; Crane, Martin; Shamaie, Atid; Ruskin, Heather J.
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.
Keyword(s): Statistics; Probabilities; random matrix theory; portfolio optimization; correlation matrix; eigenvalues and eigenvectors
Publication Date:
2004
Type: Other
Peer-Reviewed: Unknown
Language(s): English
Institution: Dublin City University
Citation(s): Sharifi, Saba, Crane, Martin ORCID: 0000-0001-7598-3126 <https://orcid.org/0000-0001-7598-3126>, Shamaie, Atid and Ruskin, Heather J. ORCID: 0000-0001-7101-2242 <https://orcid.org/0000-0001-7101-2242> (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
Publisher(s): Elsevier
File Format(s): application/pdf
Related Link(s): http://doras.dcu.ie/14831/1/SabaRMTphysica.pdf,
http://dx.doi.org/10.1016/j.physa.2003.12.016
First Indexed: 2009-11-05 02:01:41 Last Updated: 2019-02-09 06:58:00