Quants want to find a way to measure active alpha compare to a determined benchmark and that is very positive for the academic knowledge.

Using stats intuition to compare the intersection of the portfolio and benchmark to measure the aggregate overlaps and differences.

Minimised the sum of CovaR between benchmark and the equity.

A beautiful mind for a complex problem.

This could be true if there were no common sources of alpha in portfolios — an obviously false belief, if you look at how dramatically value or growth strategies differ, or how much similarity there is in performance within industries such as banking, drug stocks, etc. One down.

It could also be true if managers recognized the many sources of common patterns and completely neutralized all their “tilts” in their portfolios. In fact, many managers try to be more or less roughly sector neutral, but many more methodically over-weight sectors such as tech, where they feel they’ll get more bang for the buck, or shun sleepy sectors such as utilities. And virtually every manager these days has an “approach” to picking names, whether calling it “valuation” or “growth potential,” that tends to favor stocks with the same type of financing structure, recent market success, etc.

Finally, the stock-specific potential movement — often measured by the individual stock’s tracking error versus its benchmark — would have to be the same for each stock, a notion that’s utter hogwash.

There are hundreds of firms using sophisticated performance and risk measurement systems from MSCI/Barra, Wilshire, brokers and many independent consultants. I’ll guess that the huge majority of these firms completely ignore the simplistic formulas you describe, mostly because the summary number tells them NOTHING about their portfolio that they don’t have a better measure for.

Meanwhile, you could count the number of large asset managers who use Active Share and its ilk, to the exclusion of multi-factor systems, on the thumbs of your left foot. I doubt you’d find a single quant or 130/30 PM who even prefers A.S. — none of us see any reason to waste our time on it.

Several decades after economists fiddled around with the Herfindahl Index and other ad hoc concentration measures, the Finance guys are re-purposing methods that were discarded for lack of insight. I really don’t get it.