Different Benchmarks: Factor-model based & Returns-based

In reviewing the advantages and disadvantages of different benchmarks, are these 2 even “investable”? If so, can someone provide an example? Or am I taking the word “investable” too literally and it means nothing more than being able to replicate…?

I think of the returns-based benchmark as kind of a reverse process. Instead of selecting an appropriate benchmark and then creating a portfolio based on matching its characteristics, a returns-based BM looks back over what your portfolio has done compared to a regression against several independent and mutually exclusive indices and THEN gives you an appropriate custom benchmark. So it’s not actionable in the sense that “this is what I’ll use as a base to build/mimic my portfolio” b/c it’s backward-looking (returns based). But it is useful for attribution analysis. At least that’s how I imagine it.