Portfolio Analysis Based On Two-Steps Method

In recent years,research on the construction of high-dimensional portfolios has received considerable attention in the financial field.The difficulty of highdimensional portfolio construction is that when the number of asset is large,the estimation of the covariance matrix will become particularly difficult.At present,there are many methods to deal with this problem:using the technique of shrinkage functions,which push up the small eigenvalues and pull down the large eigenvalues of the sample covariance,aiming to make them closed to the true eigenvalues;or impose structural assumptions on covariance matrix,in order to realize the dimensionality reduction of the estimation of the covariance matrix;or use high-frequency data to broaden the time length in the estimation of the covariance matrix;and so on.These methods are expected to obtain a better estimator of the high-dimensional covariance matrix,so as to achieve the purpose of improving the performance of the portfolio.This thesis constructs a two-step portfolio based on the minimum variance portfolio model with norm constraints.In the first step,a minimum variance portfolio model with norm constraints is employed to obtain a sparse portfolio,and then an appropriate number of assets are selected according to actual investment needs;in the second step,the minimum variance portfolio model is used to construct a two-step portfolio among the selected asset in the first step.The two-step portfolio make it possible for investors to select assets first and then invest,which reduces the number of investment assets.Theoretically speaking,after the first step of the twostep method,the number of assets is greatly reduced.When the covariance matrix is estimated in the second step,the estimation difficulty caused by excessively high dimensions will be greatly reduced;Practically speaking,too many assets will attract too much attention of the investors,through the first selecting step,investors can focused more on a small number of assets,which is easy to manage.In the empirical study,this thesis constructs different portfolios such as minimumvariance portfolios and two-steps portfolio under low-frequency data and high frequency date respectively,and we also use real data from the financial market to evaluate the performance of these portfolios.Through several sets of empirical study,this thesis finds that whether using low-frequency data or high-frequency data,the two-steps portfolio earns a certain degree of improvement in the return-to-risk ratio compared to the minimum variance portfolio;the performance of two-steps portfolio is stable among different data sets and different time intervals.The empirical results of this thesis can also shed light for investors in the large portfolio management.