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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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    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.
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    More about this item

    Keywords

    Portfolio choice; CAPM; risk aversion; equilibrium; market participation;
    All these keywords.

    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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