Risk-return Structure In Financial Markets Based On The Random Matrix Decomposition

Financial market is a complex system with multi-body interactions. In recent years, physicists apply the concepts and methods of statistical physics to study the financial markets, and observe the local interactions between the business sectors by analyzing a large number of historical data, which has great meanings to understand the microscopic mechanism of financial markets.Risk is not uniformly spread across financial markets. This feature of markets can be applied to select stocks with low risk and high returns for investment. Recently, using network methods to choose these kind of stocks has become the focus of research. We employ centrality measures to build an effective portfolio, which may well reduce the risk of investment. The real interactions between business sectors have been covered in the financial networks, structured by full matrix. Therefore, we define the sector mode matrix, with the random matrix theory, to subtract the global motion mode. Based on the empirical research on the SSE market, we have found that to invest the securities located in the peripheries of PMFG, with lower correlations, can be more effective in improving the ratio of average return and standard deviation, i.e., a higher returns per unit of risk. On the contrary, selecting the centrality stocks, suffers higher risk and lower return. The result of NYSE stock market is consistent with the result of SSE stock market.