I've been reading the original Fama-Macbeth (1973) paper as well as questions here and elsewhere. I feel like I'm beginning to run in circles and would like to clarify/confirm how FM regression is done, step by step. My interest is purely that of a practitioner's: I would like to run Fama-Macbeth regressions on a specific country's stock market to test difference risk factors' relevance in explaining returns.
Assume you are running FM for N securities over 1990 - 2010 period.
1) Step 1: For 1990-2000, run time-series regressions for each security i where R(i) = B(i)*RiskFactor + e(i). Store B(i)'s for each security. You will run N regressions here.
2) Step 2: Go to 2000-2010 period, run cross-section regressions for each month where R(i) = Lambda(i) * B(i) + e(i). Bi's are already calculated in step 1. You get Lambda(i)'s and e(i)'s in this step. You will run T regressions here.
3) Step 3: Calculate Lambda(i) average and e(i) average (simple average of each month's). Do tests of significance on them. If your factor has explanatory power over returns, then Lambda(i) should be statistically significant whereas e(i) should not be statistically significant.
Would highly appreciate if you could point to any errors in the above summary
*Also, I am confused about the use of portfolios. In their original paper Fama-Macbeth create 20 portfolios by Beta sort. From what I understand, they use these portfolios in step 2 above (cross-section regressions). They also state that they allow securities to go in and out of portfolios, however, I do not understand how this is possible given they are doing cross sectional regressions and allowing for portfolio changes would cause a lot of problems.
If there are any practical step by step guides I would highly appreciate it too.