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Existence Theorems in the Capital Asset Pricing Model

Name: Existence Theorems in the Capital Asset Pricing Model
Creator: Allingham, Michael
Keywords: Economic growth models, capital asset pricing, satiation portfolio, 0502 economics and business, 05 social sciences, General equilibrium theory, Microeconomic theory (price theory and economic markets), risk aversion function, Finance etc., Utility theory

Existence theorems in the capital asset pricing model

descriptionPublicationkeyboard_double_arrow_right Article 01 Jul 1991Publisher:JSTORJournal:Econometrica, volume 59, page 1,169 (issn: 0012-9682,

Authors: Allingham, Michael;

doi: 10.2307/2938180

Existence Theorems in the Capital Asset Pricing Model

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Abstract

In the capital asset pricing model (CAPM) a finite number of traders exchange assets, starting with an initial portfolio. Preferences among portfolios of assets are given by a utility function in terms of mean and variance of the returns of the portfolio and characterized by the risk aversion function corresponding to the utility. An equilibrium requires a price with zero excess demand. An equilibrium may fail to exist for two distinct reasons: (i) existence of a satiation portfolio for some or all agents, (ii) by non-monotonicity of the utility, equilibrium would require a non-positive price vector. It is proved that both problems disappear of the supremum of the risk aversion function (which equals minus the ratio if the derivatives of the utility w.r.t. the variance and the mean) of each trader is sufficiently low.

Keywords

Economic growth models, capital asset pricing, satiation portfolio, General equilibrium theory, Microeconomic theory (price theory and economic markets), risk aversion function, Finance etc., Utility theory

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