Mean--Variance Portfolio Selection Model Based On Shrinkage Covariance Matrix And Random Matrix Theory

For the traditional Markowitz portfolio model,a key parameter-covariance matrix needs to be input.However,in the traditional model,the covariance matrix can only be obtained from historical data,which contains a lot of noise,which leads to instability of the model and excessive error.Therefore,how to effectively improve the covariance matrix and make the portfolio model more stable and practical is the main direction of modern portfolio theory research.It has important theoretical and practical significance for portfolio performance research.In this paper,we start from the direction of improving the model covariance matrix,and study two methods to improve the covariance matrix,and add sparse processing,and then use the rolling backtest method to empirically analyze.This article is divided into five chapters.The first chapter introduces the research background and significance,research status,main content and innovation of this paper.The second chapter introduces the basic financial related theories,including effective market theory,Markowitz mean variance models sparseization theory,Sharpe ratio,and rolling backtesting test methods.The third chapter focuses on improving the covariance matrix in the mean-variance model by shrinking the covariance matrix and adding sparse processing.We use the performance of seven indicators such as income,variance,Sharpe rate,turnover rate,maximum weight,minimum weight,and number of assets to compare the advantages and disadvantages of the improved model.Finally,we conclude that the Sharpe rate of the model after shrinkage treatment is significantly better than the traditional model;after adding the sparse treatment,the combined weight is more stable,the turnover rate and the number of assets are significantly reduced,and the Sharpe rate is also better than the traditional model.Excellent performance.The fourth chapter focuses on the operation of stochastic matrix theory in the portfolio,and the covariance matrix in the mean-variance model is improved by the stochastic theory.Portfolios introduce additional noise while introducing new stocks,and some properties of random matrices just eliminate noise,so introducing random matrix theory into the model will be a good performance.Finally,we conclude that the effective boundary of the mean-variance model processed by the random matrix theory is much better than that of the traditional model,and the Sharpe performance is more prominent,so the improved model is better than the traditional model.At the end of this chapter,we try to combine the contraction model of Chapter 3 with the stochastic model of this chapter to form a new model.Although the effect is better than the traditional model,it is not better than the optimization alone.The fifth chapter is the summary and deficiencies of this article and the prospects for the follow-up.In this chapter we will summarize the conclusions of the previous two chapters,and the shortcomings in the article,as well as the prospects for the follow-up.