Testing the Capital Asset Pricing Model
And the Fama-French Three-Factor Model
By Jiaxin Ling (Cindy) March 19, 2013
Key words: Asset Pricing, Statistical Methods, CAPM, Fama-French Three-Factor Model
Abstract:
This paper examines the Capital Asset Pricing Model(CAPM) and the Fama-French three-factor model(FF) and the Fama-MacBeth model(FM) for the 201211 CRSP database using monthly returns from 25 portfolios for 2 periods ---July 1931 to June 2012 and July 1631 to June 2012. The theory’s prediction is that the intercept should equal to zero the slope should be the excess return on the market portfolio. The findings of this study are not substantiating the theory’s claim for the fact that in some portfolios the alpha is*…show more content…*

3) One may observe that the data in period two is a sub period of period one and the beta is not stable over time for more portfolios have less than unit value beta in period two and some portfolios tend to be more volatile in the whole period (July 1931 to June 2012) but in sub period (July 1963 to June 2012) is less volatile than market level, take portfolio 24 as an example: its beta is 1.14 in period one and in period two its beta is 0.83. 2. The OLS cross-sectional test of the CAPM The CAPM states that the securities plot on the Security Market Line (SML) in equilibrium. We do cross-sectional test is to identify whether the above statement is true with our two data set and whether or not it rejects the hypothesis that the slope is zero. In the equation 3, the gamma 0 is the excess return on a zero beta portfolio and gamma 1 (the slope of the regression) is the market portfolio's average risk premium. [pic] (3) We perform the OLS cross-sectional test of equation (3) for both two periods. The results have shown in Table 3that gamma1 in time period 1 is positive (0.55) and it is statistically significant for its p value is 0.05, which implies that it rejects the null hypothesis of zero slope of the model. The gamma0 is also positive (0.26) which suggests that the cross-sectional return of 25 sample portfolios during July 1931

3) One may observe that the data in period two is a sub period of period one and the beta is not stable over time for more portfolios have less than unit value beta in period two and some portfolios tend to be more volatile in the whole period (July 1931 to June 2012) but in sub period (July 1963 to June 2012) is less volatile than market level, take portfolio 24 as an example: its beta is 1.14 in period one and in period two its beta is 0.83. 2. The OLS cross-sectional test of the CAPM The CAPM states that the securities plot on the Security Market Line (SML) in equilibrium. We do cross-sectional test is to identify whether the above statement is true with our two data set and whether or not it rejects the hypothesis that the slope is zero. In the equation 3, the gamma 0 is the excess return on a zero beta portfolio and gamma 1 (the slope of the regression) is the market portfolio's average risk premium. [pic] (3) We perform the OLS cross-sectional test of equation (3) for both two periods. The results have shown in Table 3that gamma1 in time period 1 is positive (0.55) and it is statistically significant for its p value is 0.05, which implies that it rejects the null hypothesis of zero slope of the model. The gamma0 is also positive (0.26) which suggests that the cross-sectional return of 25 sample portfolios during July 1931

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