Aggregation of heterogenous beliefs, asset pricing, and risk sharing in complete financial markets

Abstract

Given a competitive equilibrium in complete asset markets, we propose a method that aggregates heterogeneous individual beliefs into a single “market probability,” which, if commonly shared by investors, generates the same marginal valuation of assets by the market 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 reflection 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 heterogeneous beliefs, modulo the above scalar adjustment of the market portfolio, thereby generating an Adjusted version of the Consumption based Capital Asset Pricing Model (ACCAPM). We analyze how the allocation of aggregate and individual risks relates to deviations of individual beliefs from the aggregate market probability. Finally, we identify the channels through which the distribution of beliefs and other microeconomic characteristics (incomes, attitudes toward risk) across investors impact the pricing of risky assets an may contribute to explaining the equity premium puzzle.