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Portfolio Optimization and the Random Magnet Problem

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  • B. Rosenow
  • V. Plerou
  • P. Gopikrishnan
  • H. E. Stanley

Abstract

Diversification of an investment into independently fluctuating assets reduces its risk. In reality, movement of assets are are mutually correlated and therefore knowledge of cross--correlations among asset price movements are of great importance. Our results support the possibility that the problem of finding an investment in stocks which exposes invested funds to a minimum level of risk is analogous to the problem of finding the magnetization of a random magnet. The interactions for this ``random magnet problem'' are given by the cross-correlation matrix {\bf \sf C} of stock returns. We find that random matrix theory allows us to make an estimate for {\bf \sf C} which outperforms the standard estimate in terms of constructing an investment which carries a minimum level of risk.

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  • B. Rosenow & V. Plerou & P. Gopikrishnan & H. E. Stanley, 2001. "Portfolio Optimization and the Random Magnet Problem," Papers cond-mat/0111537, arXiv.org.
    • Handle: RePEc:arx:papers:cond-mat/0111537
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    Cited by:

    1. McCauley, Joseph L. & Gunaratne, Gemunu H., 2003. "On CAPM and Black-Scholes, differing risk-return strategies," MPRA Paper 2162, University Library of Munich, Germany.
    2. McCauley, Joseph L. & Gunaratne, Gemunu H., 2003. "On CAPM and Black–Scholes differing risk-return strategies," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 329(1), pages 170-177.
    3. A. Schianchi & L. Bongini & M. D. Esposti & C. Giardinà, 2003. "Multiple Optimal Solutions in the Portfolio Selection Model with Short-Selling," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 6(07), pages 703-720.

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