Can investors with irrational beliefs be neglected as long as they are rational on average? Do their trades cancel out with no consequences on prices, as implicitly assumed by traditional models? We consider a model with irrational investors, who are rational on average. We obtain waves of pessimism and optimism that lead to countercyclical market prices of risk and procyclical risk-free rates. The variance of the state price density is greatly increased. The long run risk-return relation is modified; in particular, the long run market price of risk might be higher than both the instantaneous and the rational ones.

Why do investors keep different opinions even though they learn from their own failures and successes? Why do investors keep different opinions even though they observe each other and learn from their relative failures and successes? We analyze beliefs dynamics when beliefs result from a very general learning process that favors beliefs leading to higher absolute or relative utility levels. We show that such a process converges to the Nash equilibrium in a game of strategic belief choices. The asymptotic beliefs are subjective and heterogeneous across the agents. Optimism (respectively overconfidence) as well as pessimism (respectively doubt) emerge from the learning process. Furthermore, we obtain a positive correlation between pessimism (respectively doubt) and risk tolerance. Under reasonable assumptions, beliefs exhibit a pessimistic bias and, as a consequence, the risk premium is higher than in a standard setting.

This paper presents an equilibrium model in a pure exchange economy when investors have three possible sources of heterogeneity. Investors may differ in their beliefs, in their level of risk aversion, and in their time preference rate. The authors study the impact of investors’ heterogeneity on equilibrium properties and, in particular, on the consumption shares, the market price of risk, the risk-free rate, the bond prices at different maturities, the stock price and volatility as well as on the stock's cumulative returns, and optimal portfolio strategies. The authors relate the heterogeneous economy with the family of associated homogeneous economies with only one class of investors. Cross-sectional as well as long-run properties are analyzed.