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I get the first part of the regression, basically it is a time series regression of returns on the proposed factors.

So, I need to run the regression of monthly return on the monthly time series of the factors from 2000 to 2005. So from this, we get the alpha and beta for this stock from the period 2000 to 2005. Now, let’s say we have 10 stocks, so we have 10 alphas and 10 betas.

Now, the part I don’t get is the second part, the cross section regression.

I don’t understand the dependent variables for this regression.

So, do I regress the monthly return of each stock on its beta over and over again? Because for each stock we have one beta and one alpha, so each month from 2000 to 2005, do I run a regression of each stock on its beta? This beta from that time period won’t be changing though?

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Yes, the second step of the Fama MacBeth procedure requires you to run a cross-sectional regression of the monthly returns of each stock against their betas for each month. This regression gives you a return for each factor for each period. The average factor return is the risk premium for the factor - see Rationale of Fama Macbeth procedure for a good description of the overall procedure, and Interpreting the coefficients of Fama-MacBeth regression for a discussion about what these second-stage coefficients mean.

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  • $\begingroup$ So, for the period of 2000 to 2005, I got a “market” beta each for stocks A, B, C. Now, for the same period, I run a cross section regression every month for these stocks on their respective beta. So, we are assuming here that the beta is the same for each stock for that period, beta stays constant, meaning the independent variable is the same every month? And only the month return changes? $\endgroup$
    – user3672855
    Jun 23, 2020 at 22:23
  • $\begingroup$ Fama-MacBeth ran the cross-sectional regression with a different period from that which was used to obtain the individual stock betas. So, for example, they would use 2000 - 2003 to estimate $\beta$, and then 2004 - 2005 to run the cross-sectional regressions with the $\beta$ from the earlier period. This avoids the influence of the estimation error for $\beta$ on the final results. There are all sorts of minor variants of this approach. $\endgroup$
    – Tim Wilding
    Jun 24, 2020 at 14:23
  • $\begingroup$ That answered all my question, thanks. $\endgroup$
    – user3672855
    Jun 24, 2020 at 14:35

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