| In recent years,the international financial market economy has shown diversification and integration,and the world economic development has entered a new period.Along with the national development economic policy and comprehensive deepening reform,China’s social economy continues to develop rapidly,and along with it,people’s income level also continues to grow,people’s demand for investment gradually rises,and the importance of investment portfolio becomes more and more prominent.The biggest challenge in using portfolios for asset allocation is how to estimate the covariance matrix in the mean-variance model.Traditionally,the covariance matrix is estimated by directly using the sample covariance matrix instead,and when the dimensionality of financial data becomes larger,the sample covariance matrix will no longer be valid and will make the meancovariance model unsolvable.Therefore,how to estimate a valid covariance matrix when using the mean-variance model is a central issue in the portfolio.On the basis of summarizing the currently available methods for estimating the covariance matrix,this paper first briefly describes portfolio theory and asset pricing models,followed by introducing the traditional methods for estimating the covariance matrix: estimation methods using factor models,principal component analysis,threshold methods and shrinkage methods,and summarizing their shortcomings pointed out.On this basis,this paper considers the peer effect among stocks,combines the spatial network with the factor model,and constructs the network autoregressive factor model.The innovation of this paper is that not only the influence of public factors on stock returns is considered,but also the peer effect of stocks,which is mainly reflected in the fact that stocks in the same industry will influence each other and stocks in the same company location will influence each other.Therefore,this paper is constructing the network in two ways: the industry to which the stock belongs and the province where the company is located,i.e.,industry network and geographical network.At the same time,this paper conducted an empirical study using A-share data.First,the covariance matrix was estimated using the network autoregressive factor model proposed in this paper,and then the estimated covariance matrix was brought into the mean-variance model to construct the portfolio and obtain the corresponding portfolio evaluation indexes--annualized return,volatility,Sharpe ratio and maximum retracement.This paper also compares the effectiveness of the covariance matrix obtained from the network autoregressive factor model in the portfolio with the sample covariance traditionally obtained from historical data and the covariance matrix estimated based on the factor model,and draws the following conclusions.(1)Compared with the factor model and the traditional sample covariance,the covariance matrix estimated by the network autoregressive factor model proposed in this paper is closer to the true covariance matrix.And its application in the portfolio is better,and the corresponding annualized return is higher than the covariance matrix estimated by the factor model and the sample covariance matrix in the portfolio.The covariance matrix is more accurate and has better application effect.(2)In this paper,the peer effect of stocks is reflected by constructing network relationships,and the network relationships are constructed in two ways,one using industry to construct network relationships and the other using geography to construct network relationships.The empirical results show that the covariance matrix estimated by the network autoregressive factor model constructed using industry network relationships has higher returns in the portfolio than the network autoregressive factor model constructed using geographical networks.It indicates that the intercorrelation information among stock industries has more impact on stock returns than the intercorrelation information among geographic regions has on stock returns. |
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