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A Dual Concept and Associated Algorithm in Mean-Variance Portfolio Analysis

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  • Roger J. Bowden

    (University of Western Australia)

Abstract

We consider in this paper the problem of allocation by an investor of his funds between a set of risky assets and a single safe asset, under conditions in which the separation theorem holds. Focussing in particular on the computationally more difficult case where no short sales are permitted, we exhibit a dual problem which arises naturally out of the saddle-point property implied in the Kuhn-Tucker optimising conditions. By showing how to solve this dual we derive a computationally straightforward method of solution for the optimum portfolio proportions and obtain a condition for every security to be held. We show briefly how the treatment can be extended to general homogeneous restrictions on portfolio proportions.

Suggested Citation

  • Roger J. Bowden, 1976. "A Dual Concept and Associated Algorithm in Mean-Variance Portfolio Analysis," Management Science, INFORMS, vol. 23(4), pages 423-432, December.
    • Handle: RePEc:inm:ormnsc:v:23:y:1976:i:4:p:423-432
    DOI: 10.1287/mnsc.23.4.423
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    Cited by:

    1. Sadreev, A.F. & Sukhinin, Yu.V., 1987. "Electrodynamics and thermodynamics of a paramagnetic system in a metallic resonator," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 140(3), pages 637-646.
    2. Gilmore, R., 1977. "Two nonlinear Dicke models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 86(1), pages 137-146.
    3. Bogolubov, N.N. & Shumovsky, A.S. & Kudryavtsev, I.K. & Lyagushin, S.F., 1988. "Superfluorescence in a system with external sources," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 151(2), pages 293-302.
    4. Martynov, S.N. & Sadreev, A.F., 1978. "Temperature dependent properties of the dynamics of a two-level system interacting with a radiation field," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 92(1), pages 268-281.
    5. Sadreev, A.F. & Slivinsky, A.P., 1978. "Phase transition to the spontaneous coherent state," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 92(1), pages 255-267.

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