Promotion Of The Mean-variance Theory Of Markowitz (h. Markowitz,)

In the stock market, Index is the surface phenomenon. The change of daily trading volume can really reflect nature change of stock market. The risk of the stock market essentially comes from the change of daily trading volume, "quantitative change causes qualitative change" . Therefore, this paper generalizes the Markowitz mean-variance model. It regards the variance of trading volume vary rate as a new risk. It adds the variance of trading volume vary rate to the variance of return rate. Then the new risk becomes the linear combination of the two. In this way, the new optimization model is minimizing the risk in the condition of the given the rate of return and trading volume vary rate. Thereby, it generalizes portfolio frontier curve from hyperbola (parabola) to hyperboloid of two sheets (paraboloid). When there exists risk securities, it generalizes frontier from straight line to cone. Meanwhile it gives some corresponding conclusions. For example, When there exists risk-free securities, it gives some properties of the portfolio, the minimum variance portfolio, efficient portfolio and zero- covariance portfolio . It also gives the geometric significance of the zero-covariance portfolio and the pricing formula of the arbitrary portfolio. When there exists risk securities, it gives the assets pricing formula and the method to select the best portfolio . In the last part it combines the actual data to empirical analyze by using the software Matlab7.0,it studies the ability of the portfolio elude risk and the selection of the best portfolio about the new model.