Volume 59, Number 4, August 2002
|Page(s)||500 - 506|
|Published online||01 August 2002|
Portfolio optimization and the random magnet problem
Center for Polymer Studies and Department
of Physics Boston University - Boston, MA 02215, USA
2 Institut für Theoretische Physik, Universität zu Köln - D-50937 Köln, Germany
3 Department of Physics, Boston College - Chestnut Hill, MA 02167, USA
Accepted: 17 May 2002
Diversification of an investment into independently fluctuating assets reduces its risk. In reality, movements of assets 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 C of stock returns. We find that random matrix theory allows us to make an estimate for C which outperforms the standard estimate in terms of constructing an investment which carries a minimum level of risk.
PACS: 05.45.Tp – Time series analysis / 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion / 75.10.Nr – Spin-glass and other random models
© EDP Sciences, 2002
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