Research On The Application Of Bayesian Method In Securities Investment

Avoiding investment risk and increasing investment return are the key points of investment analysis.Markowitz's theory uses mean and variance to measure the expected return and risk respectively.He expounded the main principles and methods about securities return with risk,and established the basic framework of mean-variance portfolio model in his paper named"Portfolio Selection".However,the mean-variance model based on Markowitz theory is on base of classical statistics,all the unknown parameters in these models are used to calculate the future means and variances.It causes too large errors in predicted results,and causes the solutions unstable.Bayesian statistical methods are the statistical inference based on general information,sample information and prior information.The key difference between Bayesian and classical statistical methods is whether prior information is used or not.Bayesian statistical method pays attention to the observed values of samples that have already appeared,and does not consider the observed values of samples that have not yet occurred.Bayesian statistical method collects and processes prior information,quantifies prior information,forms prior distribution and applies prior distribution to statistical inference to improve the quality of statistical prediction.This paper draw on the experience of Markowitz mean variance optimal portfolio model.The Bayesian statistical theory is introduced into the portfolio and capital asset pricing model.The mean and covariance of prior distribution density function are used to replace the sample mean and variance in the original model,which can greatly reduce the model error,make the results that the model are closer to the actual situation.This article is divided into the following sections:The first chapter introduces the research background,significance,research contents and innovations,domestic and foreign research status,the structure of this paper and the knowledge prepared for this article.The second chapter firstly introduces the theory of mean variance model,gives the model parameters and applies the Lagrange multiplier method to get the optimal solution of the model,then this chapter gains the minimum variance parameter by combining the hyperbolic property.The third chapter is the focus of this article.Firstly,a portfolio selection model based on Bayesian method is established,and the Information-Free prior distribution of parameters is obtained by using the location scale parameter method.The posterior distribution of unknown parameters can be obtained by Bayesian formula.Secondly,the prediction function and its covariance matrix can be obtained according to the prior distribution and posterior distribution to increase the predictiop accuracy of the model.Finally,it is concluded that the portfolio model based on Bayesian method is better than that based on traditional method by empirical analysis.The fourth chapter is the summary and prospect of the paper.