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Returns-based style analysis (RBSA) question

Is there a chicken-and-egg problem with RBSA?
The textbook says, regress the stock’s returns vs various categories like (for example) large-cap value, large-cap growth, small-cap value, small-cap growth.
My question is, how do you construct these categories in the first place without resorting to a holding-based analysis? If you don’t know where a stock goes, how would you what stocks are in (say) the large-cap growth category?

Holdings based analysis is based on the Holdings you (investor/institution) has ON THEIR CURRENT PORTFOLIO.
Large Cap Value/Growth etc. is based on “classification” by which the stock is placed in particular indices provided by providers.

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Understood, but consider the providers. How did they arrive at value vs growth, small-cap vs large-cap classification? They could not have used RBSA. So when you’re looking at your stock returns, why should you?
Concrete example: I have 5 stocks, 2 large-cap growth and 3 small-cap value stocks, as defined by the providers, equal-weighted. You don’t want to go into details of my holdings or you are skeptical of my claims that that’s what I have, so you regress my aggregate  returns against all 4 classes and find (for some reason) that my style is small-cap growth. Of what use is this information? My portfolio is not going to track small-cap growth no matter what the current correlation is. Eventually my portfolio and small-cap growth index will part ways anyway.

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I agree that in the first place you couldn’t use RBSA to identify the style of the benchmarks.  But once those benchmarks are in place, and are well-known as value or growth, regressing your returns against the benchmarks can get close to identifying the style of your holdings without having to undertake a detailed holding-by-holding analysis.  I think the primary benefit of RBSA is “its less intense data needs”.  Further, the text says that it might be performed first, to see how close (coeff. of determination) you are to a given style, and then analyze the individual holdings as a second step.

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