The Role of Diverse Beliefs in Asset Pricing and Equity Premia

Why do risk premia vary over time? We examine this problem theoretically and empirically by studying the effect of market belief onrisk premia. Individual belief is taken as a fundamental, primitive, state variable. Market belief which is the distribution of individualbeliefs is observable, it is central to the empirical evaluation and we show how to measure it. Our asset pricing model is familiar fromthe noisy REE literature but we adapt it to an economy with diverse beliefs. We derive closed form solution of equilibrium assetprices and implied risk premium and hence we can trace the exact effect of market belief on the time variability of asset prices andrisk premia. We test empirically the theoretical conclusions and find the data to be consistent with the theory.We study premia on long positions of S&P500 for investment periods of 6 -12 months and find that, on average, a change inthe mean market belief by 1 standard deviation changes the equity premium by about 0.4 standard deviation of excess returns. Wealso find that the introduction of belief variables reduces the effect of the traditional Fama and French (1989) variables used toforecast excess returns. More specifically, we find that given information about market belief the term premium, the default premiumand Lettau and Ludvigson’s (2001) CAY variables have no significant effect. As to the structure of the premium we show that whenthe market holds abnormally favorable belief about the future payoff on the S&P500 the market views the long position as less riskyhence the equity risk premium declines. This inverse relationship between market belief and equity premium predicted by the theoryis found to be statistically significant in the data.