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Restrictions on Asset-Price Movements Under Rational Expectations: Theory and Evidence

How restrictive is the assumption of rational expectations in asset markets? We provide two contributions to address this question. First, we derive restrictions on the admissible variation in asset prices in a general class of rational-expectations equilibria. The challenge in this task is that asset prices reflect both beliefs and preferences. We gain traction by considering market-implied, or risk-neutral, probabilities of future outcomes, and we provide a mapping between the variation in these probabilities and the minimum curvature of utility — or, more generally, the slope of the stochastic discount factor — required to rationalize the marginal investor’s beliefs. Second, we implement these bounds empirically using S&P 500 index options. We find that very high utility curvature is required to rationalize the behavior of risk-neutral beliefs, and in some cases, no stochastic discount factor in the class we consider is capable of rationalizing these beliefs. This provides evidence of overreaction to new information relative to the rational benchmark. We show further that this overreaction is strongest for beliefs over prices at distant horizons, and that our findings cannot be explained by factors specific to the option market.