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An algebraic theory of portfolio allocation

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  • David A. Hennessy
  • Harvey E. Lapan

Abstract

Using group and majorization theory, we explore what can be established about allocation of funds among assets when asymmetries in the returns vector are carefully controlled. The key insight is that preferences over allocations can be partially ordered via majorized convex hulls that have been generated by a permutation group. Group transitivity suffices to ensure complete portfolio diversification. Point-wise stabilizer subgroups admit sectoral separability in fund allocations. We also bound the admissible allocation vector by a set of linear constraints the coefficients of which are determined by group operations on location and scale asymmetries in the rate of returns vector. For a distribution that is symmetric under a reflection group, the linear constraints may be further strengthened whenever there exists an hyperplane that separates convex sets. Copyright Springer-Verlag Berlin Heidelberg 2003

Suggested Citation

  • David A. Hennessy & Harvey E. Lapan, 2003. "An algebraic theory of portfolio allocation," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 22(1), pages 193-210, August.
    • Handle: RePEc:spr:joecth:v:22:y:2003:i:1:p:193-210
    DOI: 10.1007/s00199-002-0284-9
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    Cited by:

    1. David A. Hennessy, 2004. "Orthogonal Subgroups for Portfolio Choice," Economics Bulletin, AccessEcon, vol. 7(1), pages 1-7.
    2. Marat Ibragimov & Rustam Ibragimov, 2007. "Market Demand Elasticity and Income Inequality," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 32(3), pages 579-587, September.
    3. Hennessy, David A. & Lapan, Harvey E., 2009. "Harmonic symmetries of imperfect competition on circular city," Journal of Mathematical Economics, Elsevier, vol. 45(1-2), pages 124-146, January.
    4. repec:ebl:ecbull:v:7:y:2004:i:1:p:1-7 is not listed on IDEAS

    More about this item

    Keywords

    Keywords and Phrases: Convex hull; Group majorization; Permutation group; Point-wise stabilizer subgroup; Separability; Transitive group.; JEL Classification Numbers: G11; D8; C6.;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • D8 - Microeconomics - - Information, Knowledge, and Uncertainty

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