Research On Markowitz Theory Model Of Mean And Variance Changing

Markowitz portfolio model, as an important theoretical model for investors, provides a scientific method of asset allocation and has been widely studied and applied. It guides the investment activities for a future time using the asset returns of the history. However, due to the effectiveness of the security market, the yield of history can’t stand for the future assets earnings and will produce some estimation deviations. Since of the mean and variance of the yields often change, it will affect the actual application effect of the Markowitz portfolio theory.In this paper, we study the Markowitz portfolio model when the mean and variance changes and analyze the influences of the mean and variance changing on the portfolio frontier curve and the optimal portfolio. Firstly, we introduce the Markowitz portfolio model and explain the causes of the mean and variance changing, mainly estimation deviation, time-varying, and the changes of the macroeconomic situation. At the same time, through the derivation, we get the efficient frontier curve model and the partial derivative model of bending degree and the vertex whether the portfolio contains the risk-free assets when the mean changing, the variance changing and both changing of risk assets. Further, we get the partial derivative model of the returns and risk of optimal portfolio on the mean and variance changing. Finally, through empirical analysis, we obtain the conclusions of the changes of the efficient frontier curve and the optimal portfolio on the three changing modes and the influences on the actual investment activities.