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I need to conduct the Fama-MacBeth (FM) procedure for my thesis to test the ability of the Fama-French (2015) and Carhart (1997) six-factor model to predict future expected returns. In univariate regressions of expected excess returns on the market excess return, both average intercept and slope coefficients are statistically significant at the 1% level. When augmenting the regression model with the FF (2015) and Carhart (1997) factors, all variables are insignificant, but the intercept coefficient remains highly significant at the 1% level.

Basically, what I need to know is whether the CAPM holds. I know that, in a cross-sectional OLS setup, the intercept has to be statistically insignificant and close to zero (α = 0), while the coefficient on the market excess return should be statistically significant and close to one (β = 1). However, I'm a bit confused as to how FM regression results are supposed to be interpreted.

Two questions:

  • What does the significant intercept in the CAPM regression exactly mean in the FM approach? Does it imply that the CAPM fails?
  • What is the reason for beta to be significant in the simple regression, but insignificant in the multivariate specification?

Any help is much appreaciated! Thank you in advance.

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First I will mention that this type of test of the CAPM and related models have been shown to be invalid by Roll's critique of tests of the CAPM.

However, to answer your question according to the way people historically thought about testing the CAPM by looking at regression alpha, alpha should be statistically insignificantly different from zero if the CAPM is working. If your alpha is statistically nonzero, then your asset pricing model is not adequate for the returns you are looking at--the assets are earning a premium that is not accounted for in the model. I guess you could say that CAPM, as you implemented it, has failed.

When you say beta is "significant," I assume you mean it is significantly different from zero. Remember that in a CAPM context, the default beta should generally be one, since by construction that is the average beta of assets in the market. If you are testing beta, usually you are testing whether it is significantly different from one.

In general, when you add a variable to a regression and some other variable becomes less significant, it means the two variables are correlated. We say things like "the market factor is no longer significant after controlling for SMB" or whatever. It means that in the CAPM regression, the effect that you attributed to the market factor was actually just SMB, but because you did not include SMB in your regression, there was an omitted variable bias that cased your market factor to seem statistically significant.

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  • Thank you so much for this clarification farnsy! Been waiting and searching so long for such an answer! – Ben May 17 at 1:37

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