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Portfolio Optimization and the Random Magnet Problem

B. Rosenow·V. Plerou·P. Gopikrishnan·H. E. Stanley
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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. 2001-11-28. Portfolio Optimization and the Random Magnet Problem. https://doi.org/10.1209/epl%2Fi2002-00135-4

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