Diverse Beliefs and Time Variability of Risk Premia

Abstract

Why do risk premia vary over time? We examine this problem theoretically and empirically by studying the effect of market belief on risk premia. Individual belief is taken as a fundamental state variables. Market belief is observable, it is central to the empirical evaluation and we show how to extract it from the data. The asset pricing model we use is familiar from the noisy REE literature but we adapt it to an economy with diverse beliefs. We derive the equilibrium asset pricing and the implied risk premium. Our approach permits a closed form solution of prices hence we trace the exact effect of market belief on the time variability of asset prices and risk premia. We test empirically the theoretical conclusions.

Our main result is that, above and beyond the effect of business cycles on risk premia, fluctuations in market belief have significant independent effect on the time variability of risk premia. We study the premia on long positions in Federal Funds Futures, 3-month and 6-month Treasury Bills. The annualized mean risk premium on holding such assets for 1-12 months is about 40-60 basis points and, on average, we find that the component of market belief in the risk premium at a random date exceeds 50% of the mean. Since time variability of market belief is large, this component frequently exceeds 50% of the mean premium. This component is larger the shorter is the holding period of an asset and it dominates the premium for very short holding returns of less than 2 months. As to the structure of the premium we show that when the market holds abnormally favorable belief about the future payoff of an asset the market views the long position as less risky hence the risk premium on that asset declines. More generally, periods of market optimism (i.e. "bull" markets) are shown to be periods when the market risk premium declines while in periods of pessimism (i.e. "bear" markets) the market's risk premium rises. Hence, fluctuations in risk premia are inversely related to the degree of market optimism about future prospects of asset payoffs. This effect is strong and economically very significant.

Keywords: Risk premium, heterogenous beliefs, market state of belief, asset pricing, Bayesian learning, updating beliefs, Rational Beliefs

JEL Classification: C53, D8, D84, E27, E4, G12, G14