Optimization Of Covariance Matrix Based On Gerber Statistics

In recent years,many studies have proved the importance of covariance matrix in mean-variance optimization(MVO).It is very meaningful to improve the estimation method of covariance matrix to enhance the optimization effect.By studying the calculation principle of different covariance matrices,this paper aims to allocate the portfolio composed of assets in a more efficient way by changing the input of covariance matrix in mean-variance optimization.In order to achieve this goal,In the second chapter,the mean-variance(MV)model and the theory and principle of optimal portfolio are introduced;The third chapter analyzes the principles and characteristics of the five main covariance matrix estimators.In chapter 4,the performance of sample covariance matrix(HC)in MVO is analyzed by Monte Carlo method.Fifth chapter keep all other factors constant conditions,at the same time in the real investment under the constraint of focus on the sample covariance matrix(HC)and define the Gerber statistics covariance estimation method(GS)to find the optimal quadratic programming portfolio is analyzed by sample analysis result and the put forward a new covariance matrix estimation method.Chapter six is the conclusion of the article and the shortcomings of the summary.In this paper,through analyzing the HC and GS respective characteristics of the two statistics,comparing history data,and the characteristics of the test data,have a history of share price change and the law of the covariance matrix expression,further put forward a new covariance matrix estimator of the estimator based on the idea of single factor contraction model(SM),by defining the assessment method of stocks falling to the two clever unifies in together.In this way,the influence of sample covariance matrix(HC)on abnormal data and extreme data is balanced,and the insensitivity of covariance estimation method(GS)defined under Gerber statistics to data is balanced,and the empirical results show that this method achieves good results.