Passive investors achieve the average return. Active investors receive some distribution of return but obviously it must range from some above to some below average. 1/x investors get a worse than average return, despite their efforts. For simplicity, let's say that 1/2 of the investors 'win' and half 'lose'.
That losing half would do better if they moved to passive investments, allowing the top half to make the real gains. Now, we're back in the same situation. Does this not continue on until it's selfishly best for everyone to be a passive investor, even though overall that might be worse?
Ways I think I might be wrong:
- The maths doesn't really work quite that way once the balance shifts away from 50% each side. It may be possible that some proportion of active investors will always make more profit than the passive investors. I don't think this is right but if it is then it'd entirely break the reasoning.
- Changes that happen from one step to the next. The winners now own more capital and therefore we don't see the same converging series. I don't think that matters other than prolonging the outcome, but I'd not be surprised if I'm wrong on this count, I've not thought it through fully.
(I'm trying to be more cautious about making overly bold claims and so am trying to point to things I know might invalidate what I'm saying, if it seems annoying then let me know)
Put transaction costs there, and you get an adversarial system. Now the top investors will try to convince the others of their own incompetence. Didn't do the math, but the outcome is probably bad.
Now, fill the market with real humans and irrationality will make sure enough incompetent investors will be active to let a big enough amount of competent ones make a win. Stable again.
I'm really unconcerned about index funds.
[1] A spherical cow in vacuum.
All counted, isn't it great when incentives align almost perfectly with the global optimum?