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Diverse beliefs and time variability of risk premia

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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 primitive state variable. Market belief is observable; it is central to the empirical evaluation and we show how to measure it. Our asset pricing model is familiar from the noisy REE literature but we adapt it to an economy with diverse beliefs. We derive equilibrium asset prices and 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 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- and 6-month Treasury Bills (T-Bills). The annual mean risk premium on holding such assets for 1–12 months is about 40–60 basis points and we find that, on average, the component of market belief in the risk premium 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 is low while in periods of pessimism (i.e. “bear” markets) the market’s risk premium is high. Fluctuations in risk premia are thus inversely related to the degree of market optimism about future prospects of asset payoffs. This effect is strong and economically very significant.

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Authors and Affiliations

  1. Department of Economics, Stanford University, Serra Street at Galvez, Stanford, CA, 94305-6072, USA

    Mordecai Kurz

  2. Istituto di Politica Economica, Università Cattolica del Sacro Cuore, L.go A. Gemelli, 1, 20123, Milan, Italy

    Maurizio Motolese

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  1. Mordecai Kurz
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  2. Maurizio Motolese
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Correspondence to Maurizio Motolese.

Additional information

This research was supported by a grant of the Smith Richardson Foundation to the Stanford Institute for Economic Policy Research (SIEPR). We thank Robert Bliss for providing us with data, routines and documentation to compute zero coupon rates. We also thank Marco Aiolfi, Wen Chung Guo, Peter Hammond, Ken Judd, Stephen Morris, Hiroyuki Nakata, Carsten Nielsen, John O’Leary and Ho-Mou Wu for helpful discussions of the ideas of this paper and to Min Fan for extensive technical assistance and helpful comments on an earlier draft. Songtao Wang was helpful in detecting an error in Appendix B.

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Kurz, M., Motolese, M. Diverse beliefs and time variability of risk premia. Econ Theory 47, 293–335 (2011). https://doi.org/10.1007/s00199-010-0550-1

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