What are the Chances of Finding an Active Manager with Skill?

For the purposes of this post, I will ask you to suspend your disbelief for a few minutes.

Assume I am talented fund selector and can differentiate between skilful* and unskilful active fund managers with a 65% success rate**.  I have an investable universe containing 500 active funds.  Of these 500 funds, 30% of the managers possess skill (if only).  If I select a manager from this universe, what is the probability that I can correctly identify whether they have skill?

There are four possible scenarios:

a) The manager has skill, which I correctly identify: 19.5% chance

b) The manager has skill, which I mistake for no skill: 10.5% chance

c) The manager has no skill which I correctly identify: 45.5% chance

d) The manager has no skill, which I mistake for skill: 24.5% chance

Despite having an edge in the identification of skill in active management, and the universe having a reasonably high proportion of skilful operators (compared to certain areas), the probability of me achieving my primary goal is only 19.5%.  More concerning is the differential between correctly identifying a skilful manager (a) and incorrectly identifying a manager with no skill as being skilful (d).  There is more chance of a false positive.

The crucial point here is that even if we believe that we have skill in a particular activity, we need to be acutely aware of the environment in which we are operating.   We tend to focus too much on how good we think we are at something when assessing our chances of success, and neglect the importance of the broader backdrop – what we might consider to be an outside view or base rate.  If we are operating in a barren opportunity set then the odds may be stacked against us even if we have expertise – the abundance of gold in a given area matters greatly for the success rate of even a highly skilled prospector.

In this simplified, one shot, example I have neglected a few important elements that are also crucial to success in active manager selection.  I have conflated skill and excess returns – the possession of fund management skill doesn’t necessarily result in the delivery of excess returns; it should certainly increase the probability, but there are no guarantees and the shorter the time horizon the more randomness will be the dominant influence in outcomes.  The possibility of bad luck is not insignificant.

There are also a host of acute behavioural issues that are likely to weigh on our ability to generate excess returns even if we identify a manager with skill***.  We are prone to invest in active managers following an abnormally strong period of returns, and mean reversion may then overwhelm any ‘alpha’ that can be derived from the manager’s skill.  We are also likely to sell at the wrong time – skilful managers will not generate consistent returns and during their more fallow periods the urge to capitulate will often be overwhelming.  Will you continue to believe a manager has skill even if performance is ‘telling you’ otherwise?

Even if you do not agree with the numbers I have used to create the above scenario; when deciding upon whether to participate in an activity that may involve skill it remains imperative that three issues are addressed:

Opportunity set: How much does skill influence outcomes? What are the chances of success if I have no skill?

Competition: If it is a zero sum game, it is crucial to know who the other competitors are – in the gold prospector example above, how many other people are doing the same thing and how good they are both crucial pieces of information. Michael Mauboussin has written extensively on this[i].

Level of skill: What would be an achievable and positive success rate?

Our tendency is to take an insular approach, focusing on our own perceived level of skill (which is often inflated), whilst ignoring the crucial external factors that will inevitably have a material influence on our outcomes.  This leads to us placing bets when the odds are not in our favour.

* For the purpose of this post, we can define skill in a very broad sense – fund managers with an approach that directly increases the probability that they can deliver excess returns ahead of their benchmark, other things being equal.

**  It is often said that a ‘hit rate’ for a stock picker above 50% is good enough to deliver excess returns – is this similar for fund selectors?

*** Let’s assume that skill is stable and persistent (even though it isn’t).

[i] Mauboussin, M. J. (2012). The success equation: Untangling skill and luck in business, sports, and investing. Harvard Business Press.