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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?

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    $\begingroup$ I'm not sure what your queation is... for the first few decades after Harry Markowitz's 1952 dissertation, the "standard" way to implement his ideas was to to identify a few hundred stocks expected to perform well accirfing to some screening critetia, calculate their covariance matrix based on 2-5 years of historical data, and use a quadratic optimizer to find a minimum-covariance portfolio, subject to some linear constraints and perhaps some tweaks in the objective function. There were several practical "engeering" problems that French+Fama, Barra Alexander, and many others were trying to $\endgroup$
    – Dimitri Vulis
    Jun 4 at 13:43
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    $\begingroup$ (Sorry "Barr" Alexander.) to work around. D8mensionality was definitely one of the practical problems. Few asset managers had access to computrts powerful enough to decompose a covariance matrix for a few thousand stocks and to look for principal components. $\endgroup$
    – Dimitri Vulis
    Jun 4 at 13:57
  • $\begingroup$ And of course it was equally impractical to run a quadratic optimizatuon on a covarisnce matrix for more than a few hundred stocks. But, for example, another practical problem was that the assumption that the future will be like the history made it difficult to include in the portfolio those stocks that only recently had an IPO - and such stocks sometimes perform well. Something like Batra's "ptedictive betas" lets you tell the optimizer how you expect some all-new stock to be correlated with the rest, or how you expect its behavior to change because of mergers or spinoffs. $\endgroup$
    – Dimitri Vulis
    Jun 4 at 15:16
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    $\begingroup$ (Many ppl worked on programming this stuff in the early days, I think two of them were Barr Rosenberg (whose inital company was called Barra) and Gordon J. Alexander a Minnesota professor. Two of many, Sharpe also worked on implementation AFAIK). $\endgroup$
    – nbbo2
    Jun 4 at 15:22
  • $\begingroup$ thanks yes I meant Barr Rosenberg from Berkeley. Indeed, lots of people worked on this. I should also mention that in the 1990s, some people looked down a little on "data mining" statistical analysis . The OP may want to see The Econometrics of Financial Markets by Campbell, Lo, MacKinlay (1997) section 6.4 "Selection of Factors" for example. $\endgroup$
    – Dimitri Vulis
    Jun 5 at 11:22

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