Correlation Analysis Of The Capital Market And The Optimization Method Of Multi-Objective Portfolio

Portfolio selection is a decision-making problem faced by investors on how to choose a portfolio under the uncertainty of risks and returns of investment.With the continuous development and standardization of China's capital market,it is widely recognized that an in-depth study of the applications of the theory of securities portfolio to the market in China is both of theoretical significance and of practical significance.The main research works covered in the thesis are as follows:(1)Based on random matrix theory,a systematic study on the related characteristics of China's stock market is carried out.The eigenvalues spectrum and the corresponding eigenvectors of the correlation matrix of stock returns are discussed in terms of distribution characteristics and stability.The results show that: the largest eigenvalue of the correlation matrix can be regarded as the market index.(2)Based on random matrix theory,the denoising-reconstruction method for the correlation matrix of stock returns in a portfolio is investigated.The thesis presents a new denoising method-“two points determined denoising method”.Empirical studies show that the new denoising method has better performance.(3)The minimum variance portfolios are discussed on risk,and the efficient frontiers of the portfolio with “noises” removed are compared with those of the portfolios with “noises” not removed.The results show that portfolios with the “noises”in the correlation matrix being removed present a great advantage in the aspects of risk prediction and efficient portfolio selection.(4)On the basis of the Markowitz mean-variance model,a portfolio optimization model concerning the mean-variance and the number of assets is established taking into account risk-free interest rates and the number of stocks.The model takes into account not only the benefits and risks,but also takes into account the number of assets in the portfolio,and therefore it is easy to manage and can reduce transaction costs.The model is solved by applying NSGA-? algorithm,and the method of orthogonal experiments is applied to optimize its parameters.(5)Using power spectrum analysis,R/S method and asymmetric detrended fluctuation analysis(A-DFA),the fractal structure and self-organized criticality are discussed.The results suggest that the evolution of Chinese stock market conforms to the basic characteristics of self-organized criticality of complex systems.Therefore,it can be concluded that behavior of self-organized criticality may be one of the internal mechanisms to control the evolution trend of the stock market.(6)The correlation matrix which is composed of the detrended cross-correlation coefficients is put into the portfolio model in order to get the investment risk and optimal portfolio with nonlinear properties and different time scales.This may expand the portfolio optimization theory and methods.(7)On the basis of the above works,from the practical point of view of investors,by taking the RMT and DCCA method,the portfolio optimization model on mean-variance-the numbers of assets,and NSGA-? algorithm as the core components,this research establishes both technical processes and a methodology system for the data analysis,processing and model solution of portfolio optimization.Further comprehensive empirical analysis is utilized to verify the effectiveness and the feasibility of the approach.The approach in total provides a theoretical basis and a technical support for portfolio management.