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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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