Research On Mean-variance Portfolio Model With Singular Covariance Matrix

After Harry Max Markowitz who is American economist proposed the Mean-Variance portfolio model in the Portfolio Selection,there was a study on the effective frontier of the Mean-Variance portfolio model.Others have studied this topic mainly from two aspects.On the one hand,it is the study of the Mean-Variance portfolio model with singular covariance matrix,and the other is the study of it with non-singular covariance matrix.Compared with the latter case,the effective frontier solu-tion method is less and imperfect in the former case.Based on this point,we expand the study of the Mean-Variance portfolio model with singular covariance matrix.In this paper,we firstly introduce the effective frontier solution process of asset-portfolio theory and the Mean-Variance portfolio model.Secondly,we transform the original model as a block matrix skillfully by the matrix theory and the algebraic operation.We solve the optimal solution and effective frontier by the Lagrange method.In order to validate the method we have in the article in this paper.On the one hand,we pro-gram by MATLAB,and use stochastic simulation experiments to obtain the effective frontier of the Mean-Variance portfolio model with singular covariance matrix.In the case of non-singular covariance matrix,we also apply this method.Comparing with the traditional Markowitz method,we find that under the same coordinate system,the effective frontier obtained by the two methods is exactly same.On the other hand,we obtain 1900 sets of data of a few stocks from the Yahoo Finance website.We have real case analysis by MATLAB.The results of the example analysis are consistent with the results of the stochastic simulation experiment.In a word,the method of this paper is valid for the Mean-Variance portfolio model when the covariance matrix is singular,and also can be used to solve the efficient frontier of the Mean-Variance portfolio model with nonsingular covariance matrix.