# Lies, Damn Lies and Active Share

These days it is fashionable to evaluate investment managers on a statistic called active share. Active share measures the similarity between a fund and a benchmark. Specifically, it compares the weighted portfolio holdings of a given portfolio to those of a benchmark index.

If I own everything in the S&P 500 portfolio in the same proportions my active share is 0%. In theory an index fund would have 0% active share but transactional frictions will create small differences.

Anyway, if I want high active share I can get it in several ways:

• Own things that aren’t in the benchmark
• Refuse to own things that are in the benchmark
• Underweight things versus the benchmark
• Overweight things versus the benchmark

All active share can tell you is that a thing is different from a given index. Full stop.

Shrewd marketing people have done their best to distort this to mean “funds with high active share are better.” This is nonsense. If I pick 10 stocks outside the S&P 500 at random I will show an active share of 100%. You would have to be an idiot to buy my fund on the basis of its active share.

Shrewd marketing people get traction with the notion that “funds with high active share are better” because it IS true that dramatic outperformance results from being 1) very different, and 2) very right. Very different on its own doesn’t get the job done. Being very different and very wrong for example is ticket to the poorhouse.

Active share is a popular statistic because it is easy to calculate and easy to understand. People are always on the lookout for that “one weird trick” they can use to hack the system for more money, better looks and lots of sex.

Unfortunately that’s not how quantitative analysis works.

Quantitative analysis isn’t “pure” mathematical reasoning. It’s inductive reasoning. When we prove things in mathematics, we know they are true. We don’t actually prove anything using statistics. Rather, we “fail to reject the null hypothesis at such-and-such a confidence interval.” This is the problem of induction.

Doing a statistical analysis of an investment strategy is like trying to assemble a puzzle where the pieces are constantly changing shape (albeit pretty slowly and by pretty small amounts). Active share is just one of those pieces. Even then you have to recognize that the results of the analysis are backward looking. There’s no guarantee those statistical relationships will persist in the future.

So, you know, caveat emptor.