Fama and MacBeth (1973) procedure can be used in testing asset pricing models and in other areas. In this post, my primary focus is on its use in testing asset pricing models.
FMB in asset pricing models
It is actually a three-step process. We would divide the time period into three parts.
1. The first step is to find the assets/portfolios betas in the first period. Some researchers would use these betas to classify assets into portfolios.
2. The second step is to find betas of these portfolios in the second period.
3. The third step is to find the portfolio returns in the third period and test whether the betas from the second period can explain these returns? This step involves:
(i) cross-sectional regressions of the portfolio returns on the portfolio betas in each period.
(ii) averaging coefficients from the cross-sectional regressions across time. The standard errors are adjusted for cross-sectional dependence.
What does asreg do in the above process
asreg with fmb option performs step 3(i) and 3(ii).
asreg can also help in step (1) where individual betas need to be calculated for each stock. The command might look like
bys company: asreg returns market_returns if period == 1
This means that for typical asset pricing tests, the researcher has to do step (1) and (2) and arrange the data in a panel format, listing portfolio returns and betas as variables in columns. And then use asreg with fmb option, e.g.
keep if period == 3 xtset company month asreg returns betas, fmb
Where else FMB regression can be used?
Fama and MacBeth (1973) procedure (i.e step 3(i) and (ii)) is also used in areas other than testing the asset pricing models. You can see one example in my paper, Table 3, column 8, page 264
Shah, Attaullah & Shah, Hamid Ali & Smith, Jason M. & Labianca, Giuseppe (Joe), 2017. “Judicial efficiency and capital structure: An international study,” Journal of Corporate Finance, Elsevier, vol. 44(C), pages 255-274.
Hi, thanks for the great guidance. For the third step, you say we should find the portfolio return of our stocks. Do you mean the excess return of the portfolio or monthly return of them? Also, I’d really appreciate it if you show me how can I do this in excel or R?
I have a table with 15 stocks including their average monthly returns and their betas. But, I don’t understand what does the first and the second period betas mean? I think for each stock for a given time period (let’s say with 200 periods) we can have only one beta.
Dear Professor Shah,
First, thank you for the blog posts and various responses on Statalist. These have been extremely informative and helpful. And thank you, of course, for writing and providing the asreg command for all–so fast!
I am writing this comment as I have a clarifying question that I couldn’t find a firm response to, and will be extremely grateful if you could answer.
Here is the issue: I am re-creating an analysis of Chen Roll and Ross 1986 “Economic Forces and the Stock Market” using the asreg command.
I did the step 1+2 before running the asreg with the fmb option (i.e., creating the betas using rolling regressions for each company).
I was just unclear whether the cross-sectional regressions of the Fama-MacBeth procedure take the lead return (time t+1) on the time-t betas, or do the cross-sectional regressions take the time-t return and regress it on the time-t betas.
I have a question, what is the justification for using Fama-Macbeth over fixed or random effects when conducting a panel study?
I have been looking for an answer to this, are there papers where a justification might be given as to why Fama Mabeth was chosen?
Thank you in advance :)