My daughter Jessica, a cognitive science major at university, caught me with a fun brain-teaser. It came up in a psychology class she was taking with Professor Phil Tetlock, author of Expert Political Judgment: How Good Is It? and leader of The Good Judgment Project.

The problem goes like this: A fund of funds manager is telling a prospective client why he should engage him, by the following logic: 1) there are over 10,000 hedge funds out there, but only a small fraction, say 5%, are worth investing in, and 2) therefore you need an expert to sort the wheat from the chaff. Through years of experience and hard work, this manager is just such an expert and can discern the good from the bad with 90% accuracy.

Taking his assertions at face value, how convinced should the potential client be by his logic? Of course, your antennae are up and you suspect the obvious answer, that the manager will create a portfolio wherein 90% of the funds are good ones, probably isn’t right. But it’s easy to see how if we think about this casually, we’d probably be taken in by this cognitive bias, known as Base Rate Neglect.

What I liked about this problem is that I could imagine a real fund of funds manager actually making this argument, without realizing that in doing so, he’d be hoisting himself with his own petard.¹ As you can see with a moment’s reflection, the high incidence of false positives means we should expect just under 1/3rd of the funds in the portfolio to be good funds. In case you don’t have a moment for reflection, the calculation is in the footnote below.² True, this is better than how we’d do without expert selection, but it’s probably well under the threshold that we’d require to commit our savings to this manager. And, this is a case where we assume the expert actually is an expert!

Normally we see this cognitive bias in cases of medical tests or military intelligence reports, but there are certainly many fitting examples in the realm of investing, where we’re always hoping to identify that rare, neglected gem. This little brainteaser teaches us it’s a lot more challenging than we’re apt to think.

1. As you know, I don’t normally draw attention to the difficulties faced by traditional active managers, preferring to focus on the positive attributes of what we’re doing at Elm Partners, but I thought this little puzzle was interesting enough that our readers would want us to violate our policy at least this one time.
   
2. Imagine the manager inspects 1,000 hedge funds. We’d expect 50 of them to be good ones and 950 to be not so good. Our expert would correctly select 90% of the 50 good ones, or 45, but he’d also incorrectly select 10% of the 950 not good ones, for 95. So, he’d select 140 in total, of which only 45, or 32%, are good ones.