Application Research Of Random Matrix Theory In Portfolio Optimization

Global stock market has developed for more than 400 years,which has experienced from laissez-faire to legal norms and then developing quickly,and Chinese stock market have already had a history of 25 years since 1990.Along with the development of scientific theory and information technology,the global capital market has made substantial progress and development.The stock market is always regarded as the barometer of a country’s economy,and stock,the main financial instruments,has become one of the main means of asset allocation.The development of capital market and the related optimization of investment portfolio are two important topics in financial field,and it will affect managers’administrative methods and investors’ decision-making process.In July 2007,the American sub-prime mortgage crisis broke out,caused the global financial crisis.The crisis brought new thinking,how can the regulators control the market’s risk and how can the individual investors effectively reduce their risk.With the above two problems,we choose 503 Chinese stocks from CSI 300、CSI 500 and CSI 800(total 1477 stocks)and 1215 U.S.stocks from S&P500、S&P mid-cap 400 and S&P small-cap 600(total 1461 stocks),the number of stocks have accounted for about 20%of their respective markets,the stock market capitalization accounted for more than 60%of their respective markets.In this paper,we use detrended fluctuation analysis(DFA)and detrended cross-correlation analysis(DCCA)to explore the difference information characteristics,include stock’s long-rang memory、fluctuation and cross-correlation.,further,we use random matrix theory(RMT)to study the differences of the effectiveness between Chinese and American stock market,and give the analysis and summarization about the performance of RMT to optimize the investment portfolio under different market environment.Compared with the previous research,this paper has following characteristic.Firstly,we compare the DCCA coefficient and Pearson correlation coefficient,and explore the rationality of the combination of RMT and DCCA.Secondly,we compare the difference of information characteristic between China’s market and US’s market under the same framework so as to strengthen the comparability of result.Thirdly,the optimization effect of RMT is related to the market environment,such a perspective is not exist in the past,we can examine the reasonability of using RMT and give investor more specific advices.Through the empirical research,we draw the following main conclusions.Firstly,DCCA method is able to measure the correlation between variables,but the spectral distribution of the correlation matrix does not satisfy the M-P law,so DCCA can’t be used in combination with RMT.Secondly,the difference of information characteristics between China’s market and US’s market is obvious,no matter from the long-range memory or fluctuation or cross-correlation.Thirdly,we compare the eigenvalue distributions of China’s market and US’s market,we find 66.6%of eigenvalue of Chinese data agreed with RMT predictions while which of American data is 82%,the result shows that the effectiveness of Chinese stock market is weaker than US stock market.Fourthly,RMT method has the ability to optimize the investment portfolio,the optimal portfolio tends to be more decentralized and balanced.Fifthly,RMT method in US’s market behave better and more stable than China’s market,this indicate that the market environment can affect the performance of RMT.Besides,the performance of RMT is not closely related to investment period,but when investment period is 20 to 30 days,the optimization effect is more stable.