Diverse Beliefs and Time Variability of Risk Premia

This work presents a theoretical and empirical evaluation of the role of market belief in the structure of risk premia. To that end we employ a model for which we develop in detail the belief structure. 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 rational expectations 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 and hence we can trace the exact effect of market belief on the time variability of risk premia. The theoretical conclusions are tested empirically for investments in the futures and in the Treasury Bills markets. Our main result is that fluctuations in market belief are large contributors to the time variability of risk premia. We study the premia on long positions in Federal Funds Futures, 3-month and 6-month Treasury Bills. On average, the risk premium on holding such assets for 6-12 months is about 40-60 basis points. We show that over 50% of the time market beliefs contribute more than 25-30 basis points to the premium. Moreover, the time variability of market belief is so large that this contribution is frequently larger than 50 basis points. As to the structure of the premium we show that when the market holds abnormally favorable belief about an asset's future payoffs the market views the long position as less risky and hence the risk premium on that asset declines. Generalizing to the market as a whole we show that periods of market optimism (i.e. bull markets) are periods when the market risk assessment falls while in periods of pessimism the market's risk assessment rises. That is, fluctuations in risk premia are inversely related to the degree of market optimism about future prospects of asset payoffs.