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Bachelor of Applied Mathematics from the Department of Mathematics, University of Isfahan, Isfahan, Iran, 1999.

 Research Description:

An important aspect of risk management in balancing portfolios consisting of financial stocks, is the estimation of the correlations between the price movements of different assets. The so called historical correlation matrix, C, has had a significant role in the finance after developing the modern portfolio theory over the last 50 years. However, this matrix has recently come into question, as a large part of it does not contain useful information but rather noise. In other words, recent works have indicated that the theory of optimal portfolios, which depends on C, is not adequate. In this study we use Random Matrix Theory in order to measure the noise component of C, and then we examine the methods of differentiating noise from information. We go on to develop a novel technique of stability analysis for the eigenvectors of C after noise removal.
Correlation matrix and 'Epochs'
Here, changes in the portfolio associated with the riskiest position, (as given by the largest eigenvalue and associated eigenvector), are investigated. From the results, we observe periods of co-movements of stocks, which change regularly because of some key events in the market. These periods are characterised by linear relationship between price and eigenvalue change. However, residuals in this model are strongly dependent on granularity (i.e. sampling rate) with fit breaking down at rates smaller than five days. Possible reasons for this breakdown are studied.

 Publications:

1- Random Matrix Theory for Portfolio Optimization: A stability Approach, S. Sharifi, M. Crane, A. Shamaie, and H. Ruskin, To appear in Physica A, Elsevier, 2004.

2- Noise in the correlation matrix: A simulation approach, S. Sharifi, A. Shamaie, and M. Crane, 23th Conference on Applied Statistics in Ireland, Ireland, May 2003.

3- Epochs in market sector index data- Empirical or Optimistic? G. Keogh, S. Sharifi, H. Ruskin, and M. Crane, to appear in Lecture Notes in Computer Science, Springer-Verlag, 2003.

4- Leverage & Cross-Asset Volatility Correlation - Empirical or Optimistic?, M. Crane, G. Keogh, H. Ruskin, and S. Sharifi, 2nd Nikkei Conference on Econophysics, Tokyo, Japan, November 2002.

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Professor Edwin J. Elton
Professor John Hull
Professor Martin J. Gruber
Professor Jean-Philippe Bouchaud
Professor Rosario N. Mantegna
Professor Didier Sornette
Professor Eugene Stanley
Dr. Rama Cont
Dr. Bernd Rosenow
Prof. Kian Esteghamat
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