document: Portfolio optimization and the random magnet problem 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
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