Consensus consumer and intertemporal asset pricing with heterogeneous beliefs

The aim of the paper is to analyze the impact of heterogeneous beliefs in an otherwise standard competitive complete market economy. The construction of a consensus belief, as well as a consensus consumer, are shown to be valid modulo a finite variation aggregation bias, which takes the form of a discount factor. We then use our construction to rewrite in a simple way the equilibrium characteristics (state price density, market price of risk, risk premium, risk-free rate) in a heterogeneous beliefs framework and to analyze the impact of belief heterogeneity. We prove that in many cases, the impact of belief heterogeneity on the market price of risk can be easily estimated, with a relatively good precision, by considering the wealth-weighted average belief. The introduction of a discount factor in the aggregation procedure appears to be related to the interpretation of the heterogeneity of beliefs as a source of risk (see Cragg and Malkiel, 1982). However, our results permits us to explain why assets with higher belief dispersion have lower risk premia (Diether et al., 2002). Finally, we show that it is possible to construct specific parametrizations of the heterogeneous beliefs model that lead to globally higher risk premia, lower risk-free rates, and risk premia that are lower for assets with higher belief dispersion.