%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