Noise Dressing of ECM and Investment Portfolio Selection Based on RMT in China Financial Market

Empirical Correlation Matrix (ECM) is considered to be the foundation of Markowitz Theory because it measures the statistical overlaps of the fluctuations between price changes of assets. But by applying Random Matrix Theory (RMT) to calculate and analyse empirically the ECM between pairs of price-changing profits of company stocks based on time-series data from both Shanghai and Shenzhen Stock Exchange A Shares, it was found that both ECM are all noise-dominated. Consequently, this paper put forward a new and Genuine Correlation Matrix (GCM) by noise dressing of the ECM based on RMT. Finally, this paper made decisions of optimal investment portfolios ground on three different measurement methods of the portfolio correlations with same return series and original time-series or processed, then forecasted and compared their risks. Evidences in this paper indicated that the optimal financial investment portfolio ground on GCM is better than ones ground on both traditional ECM and new Kendall ¿ . That is to say, the method of investment portfolio selection proposed in this paper is good and effect.