# 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

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In this case, the p value of gamma 1 is 0.18, which indicates that it cannot reject the null hypothesis of zero gamma 1. Therefore, the model is interpreted as being false. The CAPM is rejected by the fact that the slope in period two is not statistically significant.

We plot the values of Rj-Rf’s against betaj’s in both time periods. The Fig. 1 demonstrates the excess return of 25 portfolios in period one and their beta accordingly. These two curves are both wave-like pattern but not exactly follow the same movement. As discussed in previous section, higher estimated beta is not always necessarily correlated to higher excess return. These graphs are more vivid to illustrate this point. Majority portfolios follows the rule that higher beta is linked to bigger excess return. But special cases may be seen as portfolio one, six etc. Similarly, in Fig.2 which is for period two, most of the 25 portfolios obey the rule that higher risk more return. But portfolio one seems to be an extreme case as well as it has the highest beta among the 25 portfolios with the lowest excess return (discussed in previous beta section). Also in portfolio six, it generates second highest beta (1.4) but the excess return (-0.20, portfolio 6) falls behind portfolio five (0.61), which has much smaller beta (1.08).

3 The time-series test of the Fama-French three-factor model [pic] (7)

Table 5 presents basic statistics of the FF factors.