Research On The Estimation Of β Coefficient Based On The CAPM-GARCH-M Model

β Coefficient is an important indicator in evaluating the risk of individual stocks or stock portfolios when doing portfolio management, making risk control, and making return predictions. Derived from the capital asset pricing model (CAPM), it measures the systemic risk of the security. Reflecting the impact of changes in asset prices on the market by the average of movements in asset prices, it has an important position in both investment theory and practice. Under the current background of the growing enthusiasm. of domestic individual investors and the growing amount of surplus funds, this paper makes a comparative analysis of the static and dynamic estimation of β coefficients for the purpose of providing a rational investment advice. First we estimate the β coefficients of 19 randomly selected sections with static estimation based on the single index CAPM. Applying the CHOW stability test, we find the instability of the static β coefficients. Therefore we established GARCH, GARCH-M, EGARCH dynamic time series models for the yields of A-shares. By making the comparative analysis we find that the GARCH-M model has the best fitness of A-shares yields. At last we establish the CAPM-GARCH-M model, and estimate β coefficients of the 19 sections using CAPM-GARCH-M model and compare the outcome of static analysis. We come to conclusions that choosing sections does not make sense,β coefficients are unstable, and the volatility of sections are positively correlated with the volatility of A-shares market.