Asset Prices with Rational Beliefs

November 28, 1995 (First draft: June 1992) This paper introduces the concept of Rational Belief Equilibrium (RBE) as a basis for a new theory of asset pricing. Rational Beliefs are probability beliefs about future economic variables which cannot be contradicted by the data generated by the economy. RBE is an equilibrium in which the diverse beliefs of all the agents induce an equilibrium stochastic process of prices and quantities and these beliefs are, in general, wrong in the sense that they are different from the true probability of the equilibrium process. These beliefs are, however, Rational. Consequently, in an RBE agents use the wrong forecasting functions and their forecasting mistakes play a crucial role in the analysis. First, we show that these mistakes are the reason why stock returns are explainable in retrospect and forecastable whenever the environment remains unchanged over a long enough time interval for agents to learn the forecasting function. Second, the aggregation of these mistakes generates Endogenous Uncertainty: it is that component of the variability of stock prices and returns which is endogenously induced by the beliefs and actions of the agents rather than by the standard exogenous state variables. The paper develops some basic propositions and empirical implications of the theory of RBE. Based on the historical background of the post world war II era, we formulate an econometric model of stock returns which allows non-stationarity in the form of changing environments ("regimes"). A sequence of econometric hypotheses are then formulated as implications of the theory of RBE and tested utilizing data on common stock returns in the post war period. Apart from confirming the validity of our theory, the empirical analysis shows that (i) common stock returns are forecastable within each environment but it takes time for agents to learn and approximate the forecasting functions. For some agents the time is too short so that it is too late to profit from such learning; (ii) the equilibrium forecasting functions change from one environment to the other in an unforecastable manner so that learning the parameters of one environment does not improve the ability to forecast in the subsequent environments. (iii) more than 2/3 of the variability of stock returns is due to endogenous uncertainty rather than exogenous causes. The paper analyzes one example of a gross market overvaluation which was induced in the 1960's by an aggregation of agent's Mistakes. JEL Classification: D5, E17, G12