Arbitrage and Diversification in a General Equilibrium Asset Economy

Abstract

This paper presents a theory of equilibrium asset pricing that generalizes the recent work of Connor. The model extends Connor's results to more general sets of asset returns and consumer preferences, introduces production, and provides a framework for analyzing exact and approximate equilibrium asset pricing. The other major contribution of the paper is the introduction of geometric arguments that exploit the properties of induced prefer- ences over assets. This method of analyzing asset pricing provides an intuitively appealing way of analyzing equilibrium asset pricing theories. unifies several well-known asset-pricing models. This paper extends Connor's finite-asset model in a number of directions. These extensions are nontrivial, because they allow the theory to encompass asset-pricing models that were excluded by Connor's assumptions. The second major contribution of the paper is to introduce a method of argument that exploits the geometric properties of induced preferences over assets, and characterizes asset prices using these proper- ties. This technique provides an intuitively appealing way of analyzing asset pricing theories. (For a simple geometric exposition of the main ideas in this paper, see Milne (1987).) 0.2. To place this paper in the context of the literature, it is important to appreciate the development of asset-pricing models over the last two decades. The first-and perhaps the most famous-asset-pricing model is the Capital Asset Pricing Model (CAPM) developed by Sharpe (1964) and Lintner (1965). The model demonstrated a striking result: assuming (i) consumers characterize portfolios in terms of the means and variance of rates of return, (ii) there exists a risk-free asset, and (iii) asset equilibrium; then any asset's expected rate of return could be written as a linear function of the riskless interest rate, and the expected rate of return on the endowment of risky assets (the so-called market portfolio). The original CAPM result was derived from a one period model, but Merton (1973) showed that in a continuous time model where returns could be char- acterized by a diffusion process, the same mean-variance argument could be applied to obtain the CAPM formula. It was well-known that if consumers had von Neumann-Morgenstern prefer- ences, then either quadratic utility and/or multivariate normality of returns were