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Portfolio Theory for Independent Assets

Author

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  • Paul L. McEntire

    (Strategic Investment Services, Inc., Riverside, California, and Engineering-Economic Systems Department, Stanford University, Stanford, California 94305)

Abstract

This paper presents several new concepts for portfolio problems with independently distributed asset prices. A criterion is developed for including or excluding assets in an optimal portfolio for an investor maximizing the expected value of a von Neumann--Morgenstern utility function. The central concept of the generalized harmonic mean is introduced: it is shown to be the analogue of the riskless rate of return for problems without a riskless asset. A new ordering theorem is proven, showing that an optimal portfolio always consists of positive amounts of the assets with the largest mean values. Next, the concept of independence from irrelevant alternatives is introduced for portfolio problems; this is a property of utility functions and is proven to be true for most of the commonly used utility functions. Altogether, the results provide new insights and tools for portfolio problems with independent assets and extend earlier results by Samuelson, and Fishburn and Porter.

Suggested Citation

  • Paul L. McEntire, 1984. "Portfolio Theory for Independent Assets," Management Science, INFORMS, vol. 30(8), pages 952-963, August.
    • Handle: RePEc:inm:ormnsc:v:30:y:1984:i:8:p:952-963
    DOI: 10.1287/mnsc.30.8.952
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    Cited by:

    1. David A. Hennessy, 2006. "On Monoculture and the Structure of Crop Rotations," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 88(4), pages 900-914.
    2. Hennessy, David A. & Lapan, Harvey E., 2006. "On the nature of certainty equivalent functionals," Journal of Mathematical Economics, Elsevier, vol. 43(1), pages 1-10, December.
    3. Masamitsu Ohnishi & Yusuke Osaki, 2004. "The Comparative Statics of Equilibrium Derivative Prices," Discussion Papers in Economics and Business 04-19, Osaka University, Graduate School of Economics.
    4. Cheung, Ka Chun & Yang, Hailiang, 2004. "Ordering optimal proportions in the asset allocation problem with dependent default risks," Insurance: Mathematics and Economics, Elsevier, vol. 35(3), pages 595-609, December.
    5. Ephraim Clark & Octave Jokung, 1999. "A Note on Asset Proportions, Stochastic Dominance, and the 50% Rule," Management Science, INFORMS, vol. 45(12), pages 1724-1727, December.

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