# Approximate CAPM when preferences are CRRA

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DOI 10.1007/s10614-006-9061-3 © Springer 2006 Computational Economics (2007) 29:13–31 Approximate CAPM When Preferences are CRRA∗ P. JEAN-JACQUES HERINGS1 and FELIX KUBLER2 1Department of Economics, Maastricht University, P.O. Box 616, MD 6200 Maastricht, The Netherlands. E-mail: [email protected]; 2Lehrstuhl fu¨r Wirtschaftstheorie, Universita¨t Mannheim, 68131Mannheim, Germany Accepted 31 August 2006 / Published online: 21 October 2006 Abstract. In general equilibrium models of financial markets, the capital asset pricing formula does not hold when agents have von Neumann–Morgenstern utility with constant relative risk aversion. In this paper we examine under which conditions on endowments and dividends the pricing formula provides a good benchmark for equilibrium returns. While it is easy to construct examples where equilibrium returns are arbitrarily far from those predicted by CAPM, we show that there is a large class of economies where CAPM provides a very good approximation. Although the pricing formula does not hold exactly for the chosen specification, it turns out that pricing-errors are extremely small. Key words: asset pricing, general equilibrium, incomplete markets. JEL classification: D52; D58; G11; G12 1. Introduction The Capital Asset Pricing Model (CAPM) of Sharpe (1964) and Lintner (1965) predicts that equilibrium returns of assets are a linear function of their market β, the slope in the regression of a security’s return on the market’s return. This intu- itively appealing result has long shaped the way practitioners think about average returns and risk. While the empirical validity of the model is very controversial (see for example Fama and French (1992)), it remains one of the central building blocks in financial economics. However, in consumption based asset pricing models where agents choose port- folios in order to maximize von Neumann–Morgenstern utility over non-negative ∗ This paper is a substantial revision of our 2000 METEOR working p

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