Portfolio Optimization Based On Complex Network And Its Application

In essence,the stock market is a complex system.The stock market influences and interacts with each other,forming the ecological and price evolution process of the stock market.In recent years,the combination of complex network theory and stock market research has become a new trend.Scholars have done a lot of research in the hope of understanding the structure of the stock market,analyzing the risk of the stock market and even judging the future trend of the stock market.Most of the existing literatures build networks based on Pearson correlation coefficient and analyze network topology structure,but seldom use other nonlinear relationship measurement methods for modeling,and analyze portfolio through network centrality theory.Furthermore,the community detection theory in complex network theory has a natural relation with portfolio selection,but this kind of literature is still lacking.To this end,based on the predecessors,this paper conducts research from the following aspects:(1)The partial correlation coefficient is used to construct the stock network,and the optimal stock composition is analyzed with the network centrality theory.Pearson correlation coefficient is commonly used in existing literatures as a method to measure stock correlation.This method includes the influence of common market factors on stock correlation.Relevant studies have shown that the correlation coefficient after removing some common factors such as market returns can better reflect the true correlation between stocks.Firstly,the partial correlation coefficient is used to model the correlation of stock return series after removing market return factors,and the corresponding network and investment portfolio are constructed.Then combined with the network centrality theory,four network node centrality measures are used to analyze the stock composition of the optimal portfolio.Finally,the effectiveness of partial correlation portfolio and its comparative advantage in investment performance are verified.(2)Combined with stock volume and price information and based on standardized mutual information,the stock network is constructed.The existing literature only considers the measurement of the linear relationship between stocks and only uses the yield data,while the stock market,as a nonlinear complex system,is more suitable to use the standardized mutual information that measures the nonlinear relationship.Firstly,based on the important variables in the analysis of stock return rate and turnover rate,it is combined into the construction of stock correlation network.Then,the robustness of mutual information portfolio selection is studied by analyzing the network centrality theory.Finally,the effectiveness of mutual information portfolio is verified by cross section analysis,effective frontier analysis and out of sample rolling investment period performance analysis.(3)Combining with the community detection algorithm in the complex network theory,the structure of stock covariance matrix is changed to build a new portfolio selection model.Existing literatures that involve the combination of complex network association division and stock market often only use division algorithm to divide the network and carry out descriptive analysis for each association,and rarely further combine the portfolio theory to obtain the optimal weight for actual investment.However,because the network community detection is to divide the highly correlated nodes into the same community,it is naturally related to the risk diversification characteristics of the portfolio theory.Firstly,the block matrix portfolio model is built with the network community detection algorithm.Then the node composition of each community is described and analyzed based on two detection algorithms.Finally,the advantages of network block portfolio in risk control are verified by cross section analysis and effective frontier analysis.On the whole,by combining complex network theory and portfolio theory,the research ideas in related fields are expanded,and the empirical results have certain practical significance.