%0 Journal Article
%T Portfolio Optimization and the Random Magnet Problem
%A B. Rosenow
%A V. Plerou
%A P. Gopikrishnan
%A H. E. Stanley
%J Quantitative Finance
%D 2001
%I arXiv
%R 10.1209/epl/i2002-00135-4
%X 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.
%U http://arxiv.org/abs/cond-mat/0111537v1