Book excerpt: This paper presents the classic-static beta values and beta values estimated by an asymmetric beta model. In asymmetric model we have the possibility to estimate the upside and downside betas, while in the static model we are not able to work it out. We will estimate the static and asymmetric betas of two stocks in France Exchange stock market, Michelin and Tf1. So the data consists of daily returns of France Exchange stock market index CAC and the above two stocks. Actually this paper examines the estimation of betas under bull and bear market conditions. Then we apply GARCH models where necessary and we apply also the GRNN (Generalized regression of neural networks) and we compare the forecasting performance of the above models. The purpose of the paper is not to reach to a conclusion that there are asymmetries, but even with two stocks and GRNN estimation, we have better forecasting results than GARCH.