I have a question regarding the use of the FF5 Factors in an industry-fixed effects model. In order to clearify my question I'll post an example of my dataset
Note that this is just an example, the values for the FF5 factors and the Return(Y) are just random numbers.And there are a total of 70 industries, spanning across 15 years.
What I am trying to do: Let's for example take industry A; I am trying to see whether the industry-portfolio A has a significant alpha, or if it's returns can be attributed to any of the FF5 factors. This can, of course, be done by a simple FF5 regression, but the problem is that I have over 70 industries to check. So my thesis supervisor recommended that I use an industry-fixed effect model
So, my question are:
(1) Since the portfolio returns (Return(Y)) are collected on an indistry-level, do the FF5 factors have to be specific for that industry as well? The FF5 factors will, of course, vary over time, but as of now they are the same across all industries (A,B,C,...)
(2) And, as I understand, doing a industry-fixed effect model will force the Betas to have the same slope across all industries, but the intercept (Alpha) will vary. Since the alpha is what I'm looking for, this seems to be a nice approach, but I am worried that the Beta coefficients will be insignificant
(3) And thirdly, is it possible to run industry-fixed effect models like this with multiple predictor variables (FF5 factors)? My statistics teacher (and the textbook) only show these fixed-effects models with one predictor.
I hope my question is understandable. I highly appreciate any form of help. Thank you all in advance