Aggregation of Heterogenous Beliefs and Asset Pricing in Complete Financial Markets

We propose a method to aggregate heterogenous individual beliefs, given a competitive equilibrium in complete asset markets, into a single \market probability" such that it generates, if commonly shared by all investors, the same marginal valuation of assets by the market (the same equilibrium prices) as well as by each individual investor. As a result of the aggregation process, the market portfolio may have to be scalarly adjusted, upward or downward, a re ection of an \aggregation bias" due to the diversity of beliefs. From a \dual" viewpoint, the standard construction of an \expected utility maximizing aggregate investor" designed to \represent" the economy in equilibrium, is shown to be also valid in the case of heterogenous beliefs, modulo the above scalar adjustment of the market portfolio, thereby generating an \Adjusted" version of the \Consumption based Capital Asset Pricing Model" (ACCAPM). Heterogeneity of individual consumptions, or of the allocation of aggregate risks to individuals, is then analyzed in relation to deviations of individual beliefs from the aggregate \market probability". It is shown further that an upward ajustment of the market portfolio due to the heterogeneity of beliefs, may contribute to explaining such challenges as the so-called \equity premium puzzle" whenever aggregate relative risk aversion is decreasing with aggregate income. JEL Classi cation numbers : D50, D80, G11, G12

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