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Two-Fund separation and positive marginal utility

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  • Breuer, Wolfgang
  • Gürtler, Marc

Abstract

The requirement of positive marginal utility only makes it possible to derive a restricted twofund separation theorem for portfolio selection problems replacing the original separation theorem of Cass and Stiglitz (1970). We use our findings for a re-examination of the bias-in-beta problem in mutual funds performance evaluation and of the relevance of the standard CAPM without borrowing restrictions. We also present empirical evidence for the only limited validity of the separation theorem when explicitly recognizing positive marginal utility. Moreover, quadratic utility functions are not apt to approximate the admissible range of risk preferences in the case of higher-order utility functions.

Suggested Citation

  • Breuer, Wolfgang & Gürtler, Marc, 2004. "Two-Fund separation and positive marginal utility," Working Papers FW11V3, Technische Universität Braunschweig, Institute of Finance.
    • Handle: RePEc:zbw:tbsifw:fw11v3
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    References listed on IDEAS

    as
    1. Wolfgang Breuer & Marc Gurtler, 2006. "Performance Evaluation, Portfolio Selection, and HARA Utility," The European Journal of Finance, Taylor & Francis Journals, vol. 12(8), pages 649-669.
    2. Paul A. Samuelson, 1970. "The Fundamental Approximation Theorem of Portfolio Analysis in terms of Means, Variances and Higher Moments," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 37(4), pages 537-542.
    3. Eugene F. Fama & Kenneth R. French, 2002. "The Equity Premium," Journal of Finance, American Finance Association, vol. 57(2), pages 637-659, April.
    4. Jobson, J D & Korkie, Bob, 1984. "On the Jensen Measure and Marginal Improvements in Portfolio Performance: A Note," Journal of Finance, American Finance Association, vol. 39(1), pages 245-251, March.
    5. Treynor, Jack L & Black, Fischer, 1973. "How to Use Security Analysis to Improve Portfolio Selection," The Journal of Business, University of Chicago Press, vol. 46(1), pages 66-86, January.
    6. Kroll, Yoram & Levy, Haim & Markowitz, Harry M, 1984. "Mean-Variance versus Direct Utility Maximization," Journal of Finance, American Finance Association, vol. 39(1), pages 47-61, March.
    7. Cass, David & Stiglitz, Joseph E., 1970. "The structure of investor preferences and asset returns, and separability in portfolio allocation: A contribution to the pure theory of mutual funds," Journal of Economic Theory, Elsevier, vol. 2(2), pages 122-160, June.
    8. Black, Fischer, 1972. "Capital Market Equilibrium with Restricted Borrowing," The Journal of Business, University of Chicago Press, vol. 45(3), pages 444-455, July.
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    More about this item

    Keywords

    two-fund separation; HARA utility; positive marginal utility; borrowing restrictions; Capital Asset Pricing Model; bias in beta; performance evaluation;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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