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Approximate CAPM When Preferences are CRRA

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  • P. Herings

    ()

  • Felix Kubler

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. Copyright Springer Science+Business Media, LLC 2007

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File URL: http://hdl.handle.net/10.1007/s10614-006-9061-3
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Bibliographic Info

Article provided by Society for Computational Economics in its journal Computational Economics.

Volume (Year): 29 (2007)
Issue (Month): 1 (February)
Pages: 13-31

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Handle: RePEc:kap:compec:v:29:y:2007:i:1:p:13-31

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Web page: http://www.springerlink.com/link.asp?id=100248
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Keywords: asset pricing; general equilibrium; incomplete markets; D52; D58; G11; G12;

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  1. Magill, Michael & Shafer, Wayne, 1991. "Incomplete markets," Handbook of Mathematical Economics, in: W. Hildenbrand & H. Sonnenschein (ed.), Handbook of Mathematical Economics, edition 1, volume 4, chapter 30, pages 1523-1614 Elsevier.
  2. John Heaton & Deborah Lucas, 1993. "Evaluating the Effects of Incomplete Markets on Risk Sharing and Asset Pricing," NBER Working Papers 4249, National Bureau of Economic Research, Inc.
  3. Berk, Jonathan B., 1997. "Necessary Conditions for the CAPM," Journal of Economic Theory, Elsevier, vol. 73(1), pages 245-257, March.
  4. Andrew Ang & Joseph Chen & Yuhang Xing, 2006. "Downside Risk," Review of Financial Studies, Society for Financial Studies, vol. 19(4), pages 1191-1239.
    • Andrew Ang & Joseph Chen & Yuhang Xing, 2005. "Downside risk," Proceedings, Board of Governors of the Federal Reserve System (U.S.).
  5. P.J.J. Herings & F. Kubler, 2001. "Computing Equilibria in Finance Economies," GE, Growth, Math methods 0205003, EconWPA.
  6. Fama, Eugene F & French, Kenneth R, 1992. " The Cross-Section of Expected Stock Returns," Journal of Finance, American Finance Association, vol. 47(2), pages 427-65, June.
  7. Tversky, Amos & Kahneman, Daniel, 1992. " Advances in Prospect Theory: Cumulative Representation of Uncertainty," Journal of Risk and Uncertainty, Springer, vol. 5(4), pages 297-323, October.
  8. Robert F. Dittmar, 2002. "Nonlinear Pricing Kernels, Kurtosis Preference, and Evidence from the Cross Section of Equity Returns," Journal of Finance, American Finance Association, vol. 57(1), pages 369-403, 02.
  9. John Geanakoplos & Martin Shubik, 1989. "The Capital Asset Pricing Model as a General Equilibrium with Incomplete Markets," Cowles Foundation Discussion Papers 913, Cowles Foundation for Research in Economics, Yale University.
  10. Mehra, Rajnish & Prescott, Edward C., 1985. "The equity premium: A puzzle," Journal of Monetary Economics, Elsevier, vol. 15(2), pages 145-161, March.
  11. Levy, H & Markowtiz, H M, 1979. "Approximating Expected Utility by a Function of Mean and Variance," American Economic Review, American Economic Association, vol. 69(3), pages 308-17, June.
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