Collective rationality and functional wisdom of the crowd in far-from-rational institutional investors

The average portfolio structure of institutional investors is shown to reproduce the structure which optimally accounts for transaction costs when investment constraints are weak. Strikingly, this result emerges even though these investors are not aware of the existence of such law and despite the fact that their aims and tools are very heterogeneous. This extends the so-called wisdom of the crowd to much more complex situations in two important ways. First, wisdom of the crowd also holds for whole functions instead of a point-wise estimates. Second, this shows that in socio-economic systems, the optimal individual choice may only be found when the diversity of individual decisions is averaged out. Thus, rationality at a collective level does not need nearly rational individuals with well-aligned incentives. Finally we discuss the importance of accounting for constraints when assessing the presence of wisdom of the crowd.