Testing the Capital Asset Pricing Model and the Fama-French Three-Factor Model
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 statistically significant with non zero value and in some regression models, the slope is not statistically significant.
1. The BJS time-series test of the CAPM
Black, Jensen and Scholes introduced a time series test of CAPM which is based on time series regression of the portfolio’s excess return on excess market return. [pic] (2)
The intercept is known as Jensen’s alpha, which is a coefficient that is proportional to the excess return of a portfolio over its expected return, for its expected risk as measured by beta. Hence, alpha is determined by the fundamental values of the company in contrast to beta, which measures the return due to its volatility. If CAPM holds, by definition the intercept of all portfolios (Jensen’s alpha) are zero. Also note that, if the alpha is negative, then the portfolio underperforms the market. Table One presents the estimated alpha coefficients and the p values. Sample size for the regression is 972 for time period one and 588 for time period two respectively and period two is a sub period of period one. The following conclusions can be drawn from the table one and two available in appendix:
1) In period one, all estimated alphas are non zero ranging from
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 statistically significant with non zero value and in some regression models, the slope is not statistically significant.
1. The BJS time-series test of the CAPM
Black, Jensen and Scholes introduced a time series test of CAPM which is based on time series regression of the portfolio’s excess return on excess market return. [pic] (2)
The intercept is known as Jensen’s alpha, which is a coefficient that is proportional to the excess return of a portfolio over its expected return, for its expected risk as measured by beta. Hence, alpha is determined by the fundamental values of the company in contrast to beta, which measures the return due to its volatility. If CAPM holds, by definition the intercept of all portfolios (Jensen’s alpha) are zero. Also note that, if the alpha is negative, then the portfolio underperforms the market. Table One presents the estimated alpha coefficients and the p values. Sample size for the regression is 972 for time period one and 588 for time period two respectively and period two is a sub period of period one. The following conclusions can be drawn from the table one and two available in appendix:
1) In period one, all estimated alphas are non zero ranging from