@dryflower, the studies along these lines do not model the reality correctly and so come up with incorrect conclusions when they generalize it.
Imagine, if you were to conduct a similar study of multiple choice test scores of all high school students over a number of tests with no selection criterion, you may conclude that the test scores across all students were determined more by luck than skill because random answering shows similar distribution. Or if there was skill that you could not reliably select students that had skill or that they showed no persistence or if it did it was because those students studied more broadly than others (took more risk). :-)
Studies that lie behind this indexing cult usually follow the same cyclic argument as follows, including the study linked in the other thread.
1. In the aggregate over all funds, the active funds do not perform over index funds.
But wait, you say, I do not select funds by throwing darts and there are a lot of bad funds. So what if I select the good funds?
2. Even if you were somehow able to select good funds they do not show persistence over time. So, it is futile.
But wait, you say, you require the fund to beat the index every year or in two consecutive periods and consider it a fail even if the fund underperforms in one period by a mere 0.
5% while it gained by 2% in the previous period. So, it isn't necessary to be persistent in YOUR definition for the fund to do well over time.
3. But active funds in general do not beat indices over time. See 1 above.
See the cyclic argument?
I am waiting for somebody to do a simple study. Find the cumulative performance over a reasonable period of time of active funds selected with multiple criterion available at the beginning of the period and see if any of the criterion select for over performing funds with statistical significance. This is what models reality better. If none of the selection criterion comes out with a reliable way to select a fund, then there is a good case to make against choosing active funds
Because reality is complex, choosing a mathematical or statistical model to draw conclusions from is not trivial and requires some simplifying assumptions. That can lead to incorrect conclusions in the general case.
As a very simple example of incorrect modeling leading to incorrect conclusions, consider
@mjg's charming anecdote in another thread of using probabilities to make shooting decisions in basketball (not to pick on
@mjg here).
On the surface, it looks perfectly reasonable. The math is correct. So, the conclusion of going for 3 pointers should be valid, right? It might be, if the opposing coach is a total idiot as might happen in a junior team of 12 year olds. However, it does not apply in general because the reality is different for that simple modeling to apply.
When you have two opposing teams making strategic decisions in a zero sum game, it needs to be modeled with game theory rather than simple probability to reflect what happens in reality better. Game theory applied to this suggests that the fixed point equilibrium reduces the efficacy of the 3 pointers to a level where it provides no advantage over a 2 point attempt.
The plain English translation is that, if the 3 point tries start to win with higher probability in successive games, the opposing team will start to guard against 3 pointers more, which leaves them vulnerable to 2 point attacks and so a higher probability doing that, etc., until an equilibrium is reached.
So real world coach decisions are much more complex relying on luck and skill to outplay the other teams based on the players, how they are playing at that moment, probability of refs in that game to be lenient towards fouls in that game, the strengths or weaknesses of the opposing coach, etc. Good coaches do this by intuition and aren't helped by a probability calculator to consult. It is not just luck either.
Good fund managers and good coaches have a lot of things in common. :-)
