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In this paper, a new model is proposed to empirically test the Capital Asset Pricing Theory. This model is based on the EGARCH-type volatilities in Nelson (1991) and the non-Normal errors of SSAEPD in Zhu and Zinde-Walsh (2009). Is the CAPM theory in Sharpe (1964), Lintner (1965) and Mossin (1966) still alive? Returns of Fama-French 25 stock portfolios (1926-2011) are analyzed. The Maximum Likelihood Estimation Method is used. Likelihood Ratio test (LR) and Kolmogorov-Smirnov test (KS) are used to do model diagnostics. Akaike Information Criterion (AIC) is used for model comparison. Simulation results show the MatLab program is valid. Empirical results show with non-Normal errors and the EGARCH-type volatilities, the CAPM theory is not alive. This new model can capture the skewness, fat-tailness, asymmetric effects and volatility persistence in the data. This new model has better in-sample fit than others. Portfolios with smaller size have larger Beta value.

Testing the CAPM Theory Based on a New Model for Fama-French 25 Portfolio Returns