I am looking to do some basic portfolio constructions as an experiment to learn more about it. I have been researching a bit and what I have found is that one of the purposes of factors models (Fama-French e.g.) is that it would allow us to model the variance/covariance of the factor portfolios themselves rather than the individual stocks. So, in my understanding, it's a dimensionality reduction technique (microeconomic factors rather than statistical ones, as one would do with a PCA).
However, doesn't this imply that we would still need to have a model (say, OLS) per individual stock? Doesn't this sort of defeat the purpose of the factorization?
Thinking about this, I also thought about fitting a factor model in a panel data time-series context. Is this a way to circumvent this issue?