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Mathematical Programming of Admissible Portfolios

Author

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  • Vijay S. Bawa

    (Bell Laboratories, Holmdel, New Jersey)

Abstract

It is well known that when the distribution of portfolio returns is normal, the admissible set of portfolios for risk-averse investors with increasing and concave utility functions is the Markowtiz-Tobin mean-minimum variance admissible boundary: The admissible set is obtained by minimizing a convex quadratic function subject to linear constraints and can be obtained efficiently using Markowitz-Sharpe critical line algorithm. We show that the admissible set of portfolios for all investors (with increasing utility functions, including risk-averters, risk-seekers, risk-neutral and Friedman-Savage-type individuals) is the Markowitz-Tobin boundary plus a portion of the mean-maximum variance boundary. We propose a simple algorithm to obtain the mean-maximum variance boundary. Thus, our algorithm plus Markowitz-Sharpe algorithm obtains the admissible set of portfiolios for all investors.

Suggested Citation

  • Vijay S. Bawa, 1977. "Mathematical Programming of Admissible Portfolios," Management Science, INFORMS, vol. 23(7), pages 779-785, March.
    • Handle: RePEc:inm:ormnsc:v:23:y:1977:i:7:p:779-785
    DOI: 10.1287/mnsc.23.7.779
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    Cited by:

    1. Colson, Gérard, 1993. "Prenons-nous assez de risque dans les théories du risque?," L'Actualité Economique, Société Canadienne de Science Economique, vol. 69(1), pages 111-141, mars.
    2. Douglas W. Blackburn & Andrey D. Ukhov, 2013. "Individual vs. Aggregate Preferences: The Case of a Small Fish in a Big Pond," Management Science, INFORMS, vol. 59(2), pages 470-484, August.

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