The Improvements And Empirical Research Of The Portfolio Model Based On The Gray Theory

The portfolio theory appeared in 1950s. It has developed for a half century, and the Portfolio Theory become more and more perfectly. But for the Chinese finance market, The Portfolio Theory has the character of practicability and localization. For these reasons, the grey system theory was used to improve the measure of the portfolio risk, which is calculated by the mean-semi Absolute Deviation in this paper, and then explain some phenomenon of stocks in the industry of coal.At first, we introduce the background, motivation and aim of this paper. And then expound the history of the portfolio, included the mean-variance model, The Capital Asset Pricing Model (CAPM) and the Arbitrage Pricing theory (APT).Chapter 2 depicts the improvement of the mean-variance model. First of all, chapter 2 employed the concept of grey number grey relational degree and grey prediction, and then introduced their application in the field of modeling of portfolio, the forecasting of the return rate and the forecasting of risk.The forecasting return rate by improving of the mean-variance model was proposed in section 3. The proposed method which takes the influence of historical data, market index and currency affairs into consideration, is adapted to the Chinese securities market. GM (1,1) is employed to measure the influence of historical data. The relational degree between the return rate of securities and the market index is calculated by degree of grey incidence. A numerical example is also used to illustrate the proposed method. From the results, we conclude that the new model can provide an accurate result without strict condition in modeling.At the section 4, the improved mean-variance model which incorporates the grey number, measure the risk by the method of mean-semi Absolute Deviation. Then we solve the problem by translate the multiple objective linear programming into single objective linear programming. At the end, the return rates of 16 stocks in the industry of coal from securities market are illustrated to show the measure of the improved return rates model.