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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.

Suggested Citation

  • Wenzelburger, Jan, 2008. "A Note on the Two-fund Separation Theorem," MPRA Paper 11014, University Library of Munich, Germany, revised 31 Sep 2008.
  • Handle: RePEc:pra:mprapa:11014
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    File URL: https://mpra.ub.uni-muenchen.de/11014/1/MPRA_paper_11014.pdf
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    References listed on IDEAS

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    1. 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.
    2. Bohm, Volker & Wenzelburger, Jan, 2005. "On the performance of efficient portfolios," Journal of Economic Dynamics and Control, Elsevier, vol. 29(4), pages 721-740, April.
    3. Lars Tyge Nielsen & Fatma Lajeri, 2000. "Parametric characterizations of risk aversion and prudence," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 15(2), pages 469-476.
    4. 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.
    5. J. Tobin, 1958. "Liquidity Preference as Behavior Towards Risk," Review of Economic Studies, Oxford University Press, vol. 25(2), pages 65-86.
    6. Nielsen, Lars Tyge, 1990. "Existence of equilibrium in CAPM," Journal of Economic Theory, Elsevier, vol. 52(1), pages 223-231, October.
    7. Dana, Rose Anne, 1993. "Existence and Uniqueness of Equilibria When Preferences Are Additively Separable," Econometrica, Econometric Society, vol. 61(4), pages 953-957, July.
    8. Ulrich Horst & Jan Wenzelburger, 2008. "On non-ergodic asset prices," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 34(2), pages 207-234, February.
    9. 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.
    10. 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.
    11. Lars Tyge Nielsen, 1990. "Equilibrium in CAPM Without a Riskless Asset," Review of Economic Studies, Oxford University Press, vol. 57(2), pages 315-324.
    12. 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.
    13. Nielsen, Lars Tyge, 1987. " Portfolio Selection in the Mean-Variance Model: A Note," Journal of Finance, American Finance Association, vol. 42(5), pages 1371-1376, December.
    14. 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.
    15. repec:dau:papers:123456789/6112 is not listed on IDEAS
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    More about this item

    Keywords

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

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium

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