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A Note on the Two-fund Separation Theorem

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  • Wenzelburger, Jan

Abstract

This note contains two remarks on the traditional capital asset pricing model (CAPM) with one risk-free asset. Firstly, an elementary proof of the two-fund separation theorem is provided showing that asset-demand may become undefined if the limiting slope of the investor's indifference curves is finite. Secondly, it is shown that an additional limiting condition on the risk aversion is generally necessary to guarantee existence of an equilibrium in the CAPM with one risk-free asset. The role of these two limiting conditions seems to have been overlooked in the established literature. A generalized existence result is formulated which allows for the case in which in equilibrium not all investors participate in the market for risky assets.

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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 11014.

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Date of creation: 08 Feb 2008
Date of revision: 31 Sep 2008
Handle: RePEc:pra:mprapa:11014

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Keywords: Portfolio choice; CAPM; risk aversion; equilibrium; market participation;

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  1. Volker Böhm & Carl Chiarella, 2005. "Mean Variance Preferences, Expectations Formation, And The Dynamics Of Random Asset Prices," Mathematical Finance, Wiley Blackwell, vol. 15(1), pages 61-97.
  2. Dana, Rose-Anne, 1999. "Existence, uniqueness and determinacy of equilibrium in C.A.P.M. with a riskless asset," Journal of Mathematical Economics, Elsevier, vol. 32(2), pages 167-175, October.
  3. Hens, Thorsten & Laitenberger, Jorg & Loffler, Andreas, 2002. "Two remarks on the uniqueness of equilibria in the CAPM," Journal of Mathematical Economics, Elsevier, vol. 37(2), pages 123-132, April.
  4. Lajeri, Fatma & Nielsen, Lars Tyge, 1997. "Parametric Characterizations of Risk Aversion and Prudence," CEPR Discussion Papers 1650, C.E.P.R. Discussion Papers.
  5. Nielsen, Lars Tyge, 1988. "Uniqueness of Equilibrium in the Classical Capital Asset Pricing Model," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 23(03), pages 329-336, September.
  6. Dana, Rose Anne, 1993. "Existence and Uniqueness of Equilibria When Preferences Are Additively Separable," Econometrica, Econometric Society, vol. 61(4), pages 953-57, July.
  7. Volker Böhm & Nicole Deutscher & Jan Wenzelburger, 2000. "Endogenous Random Asset Prices in Overlapping Generations Economies," Mathematical Finance, Wiley Blackwell, vol. 10(1), pages 23-38.
  8. Dana, Rose-Anne, 1999. "Existence, uniqueness and determinacy of equilibrium in C.A.P.M. with a riskless asset," Economics Papers from University Paris Dauphine 123456789/6112, Paris Dauphine University.
  9. Nielsen, Lars Tyge, 1987. " Portfolio Selection in the Mean-Variance Model: A Note," Journal of Finance, American Finance Association, vol. 42(5), pages 1371-76, December.
  10. Nielsen, Lars Tyge, 1990. "Existence of equilibrium in CAPM," Journal of Economic Theory, Elsevier, vol. 52(1), pages 223-231, October.
  11. Jan Wenzelburger & Volker Boehm, 2004. "On the performance of efficient portfolios," Computing in Economics and Finance 2004 197, Society for Computational Economics.
  12. Nielsen, Lars Tyge, 1990. "Equilibrium in CAPM without a Riskless Asset," Review of Economic Studies, Wiley Blackwell, vol. 57(2), pages 315-24, April.
  13. Merton, Robert C., 1972. "An Analytic Derivation of the Efficient Portfolio Frontier," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 7(04), pages 1851-1872, September.
  14. Ulrich Horst & Jan Wenzelburger, 2008. "On non-ergodic asset prices," Economic Theory, Springer, vol. 34(2), pages 207-234, February.
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