We develop a model of the gambler's fallacy—the mistaken belief that random sequences should exhibit systematic reversals. We show that an individual who holds this belief and observes a sequence of signals can exaggerate the magnitude of changes in an underlying state but underestimate their duration. When the state is constant, and so signals are i.i.d., the individual can predict that long streaks of similar signals will continue—a hot-hand fallacy. When signals are serially correlated, the individual typically under-reacts to short streaks, over-reacts to longer ones, and under-reacts to very long ones. Our model has implications for a number of puzzles in finance, e.g. the active-fund and fund-flow puzzles, and the presence of momentum and reversal in asset returns.
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