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 that involves dividing the time period into three parts.
Step 1: Determine the betas of the assets/portfolios in the initial period. Some researchers use these betas to categorize assets into portfolios.
Step 2: Find the betas of these portfolios in the subsequent period.
Step 3: Calculate the portfolio returns in the final period and determine whether the betas from the second period can explain these returns. This step includes:
- Conducting cross-sectional regressions of the portfolio returns on the portfolio betas for each period.
- Averaging the coefficients obtained from the cross-sectional regressions over time. The standard errors are adjusted to account 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
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.