The modelling of stock returns conditionally to the classes of volatility on the French market

This paper examines the empirical validity of the conditional capital asset pricing model (CAPM) with three betas. Specifically, having modelled the market volatility return like a GARCH (1,1) process and having defined three regimes of volatility (low, neutral and high), we find that most of the betas in volatility classes are meaningful and positive. We also note that the CAPM with three betas perform more in the case of the big size firms that in those of small sizes and that it is interesting to integrate the bullish and bearish character of the stock markets in this model.