Covariance Matrix Estimation Based On Cross-Validation And Its Application In Portfolio Selection

Covariance matrix characterizes the degree of discreteness and linear correlation among variables,which is widely used in portfolio,communication engineering and other fields.It is well known that when the dimension of the total covariance matrix is low,the sample covariance matrix is an unbiased estimation of the total covariance matrix.However,when the dimension increases gradually,the sample covariance matrix is no longer an unbiased and consistence estimation,and its inverse greatly enlarges the estimation error.Especially,when the dimension is larger than the number of samples,the sample covariance matrix is singular.Therefore,in the case of high-dimensional data,it is no longer appropriate to estimate the total covariance matrix with the traditional sample covariance matrix.The main content of this study is to compare the performance of different estimation matrices of total covariance matrix in China's securities market under the framework of global minimum variance portfolio and short-selling restriction,including two parts.The first part studies the estimation of covariance matrix.Firstly,the sample covariance matrix is combined with the diagonal matrix of unit matrix and sample covariance matrix.Secondly,the solution of shrinkage intensity is obtained by cross-validation method,and a new estimation matrix is proposed—Double Shrinkage Estimation Matrix(DSE),Finally,the performance of DSE estimation matrix is compared with that of several other covariance estimation matrices by simulation analysis.The second part is empirical analysis.Fifty-six stocks in the 180 Index of Shanghai Stock Exchange are selected for empirical research.Under the framework of global minimum variance portfolio and short-selling restriction,the value of performance rating indicators such as investment risk,Sharp ratio,turnover rate and utility function are calculated by rolling window method.The welfare benefits of investment portfolios corresponding to different estimation matrices are compared.Empirical results show that when the estimated interval length is 400,the performance evaluation of DSE estimation matrix Price index is better than other estimating matrices and can make investors obtain higher economic benefits.