ALL OUR PREVIOUS CASES had one common aspect: investors agreed on the probabilities of future states. While people chose to hold different portfolios, in an important sense all their actions were based on the same predictions. There was no distinction between what our investors did and what they should have done. They correctly chose different portfolios because they had different preferences and/or positions.
Anyone who has observed or participated in the investment world knows that the assumption of agreement is a fanciful representation of reality. Much of the behavior of real investors can be explained only by acknowledging that they make bets with one another, whether they know it or not.
Betting is most obvious in circumstances in which people take risks that need not be borne. When you and I bet on a football game, it is because we have different views of the likely outcomes. No productive purpose is served by our wager unless one or both of us are hedging to have some good news (“I won”) if the outcome inflicts emotional or other financial pain (“my team lost”).
Betting in financial markets may be less obvious. When I hold less than my proportionate share of Hewlett Packard stock, someone must hold more than his or her proportionate share. Do our portfolios differ because we have different positions or preferences? Perhaps, but we may hold different portfolios because we have different predictions, or because we have faith in different people (investment managers) who themselves have different predictions.
Consider an investor who puts all of her equity money in a single mutual fund that holds stocks of only 200 companies. How could one possibly argue that her positions or preferences make it optimal to overweight these companies and underweight all the companies not represented in the portfolio? Absent very unusual circumstances, she was likely motivated in part by a belief that the manager of the mutual fund could find mispriced securities, and thereby “beat the market.” Most mutual funds suggest that they can do so, but of course not all can. Given sufficient time, one would imagine that diversity in predictions would decrease. If you want to trade with me at a price that seems a bargain to me, I may question my own predictions. Bids, offers, and prices of actual transactions can carry information about others' predictions, although such information is difficult to infer owing to the influence of diverse positions and preferences