> Their opposites, passive investors, will by definition do about average. In aggregate their positions will more or less approximate those of an index fund. Therefore the balance of the universe—the active investors—must do about average as well. However, these investors will incur far greater costs. So, on balance, their aggregate results after these costs will be worse than those of the passive investors.
This argument is wrong? edit: it's like saying this about strategies of chess players, one group is using strategy A and another is using strategy B:
Chess players using strategy A are known to perform about average (by the nature of their strategy). So this new strategy, B, has to perform about average too.
This neglects that there are other strategies than A and B. The whole world is not either passive investors or hedge funds.
And he's saying something even stronger: there is no subset of B players that is better than average.
So while he may well be correct in his prediction, he makes it sound like he has a mathematically tight argument for why he is correct. But the conclusion of his argument (that active investors will perform about average) is not the prediction of his bet (that hedge funds will perform about average, and because they have higher operating cost they will lose).