Information and dynamic trading with the Gambler’s fallacy

A multi-period stock trading model is developed in which there are two types of traders—a “rational” type and a “gambler’s fallacy” type—both observing a public signal about the fundamental value in each period. The rational type holds correct beliefs on the signals, whereas the gambler’s fallacy type mistakenly believes that the sequence of the signals exhibits systematic reversals. We explore the dynamic equilibrium in which the two types trade with each other to speculate future price changes based on their inferences about the fundamental value. It is shown that the presence of the gambler’s fallacy type can generate both short-term momentum and long-term reversal. Furthermore, the pattern is robust even in a market with a large proportion of rational traders as the price is closer to the gambler’s fallacy type’s valuation. We also show that the gambler’s fallacy type becomes more influential in determining the price as the market switches from momentum to reversal. Interestingly, to an outside observer, it would appear as though the rational traders act as if they have “hot-hand” fallacy in prices, and that a trend following strategy is optimal in this model.