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An algebraic theory of portfolio allocation


  • David A. Hennessy
  • Harvey E. Lapan


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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    References listed on IDEAS

    1. Hansen, Gary D., 1985. "Indivisible labor and the business cycle," Journal of Monetary Economics, Elsevier, vol. 16(3), pages 309-327, November.
    2. Jean-Pierre DANTHINE & John B. DONALDSON, 1993. "Computing Equilibria of Non-Optimal Economies," Cahiers de Recherches Economiques du Département d'Econométrie et d'Economie politique (DEEP) 9306, Université de Lausanne, Faculté des HEC, DEEP.
    3. Hansen, Gary D & Imrohoroglu, Ayse, 1992. "The Role of Unemployment Insurance in an Economy with Liquidity Constraints and Moral Hazard," Journal of Political Economy, University of Chicago Press, vol. 100(1), pages 118-142, February.
    4. Steven J. Davis & John C. Haltiwanger & Scott Schuh, 1998. "Job Creation and Destruction," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262540932, July.
    5. Rogerson, Richard, 1988. "Indivisible labor, lotteries and equilibrium," Journal of Monetary Economics, Elsevier, vol. 21(1), pages 3-16, January.
    6. Long, John B, Jr & Plosser, Charles I, 1983. "Real Business Cycles," Journal of Political Economy, University of Chicago Press, vol. 91(1), pages 39-69, February.
    7. Loungani, Prakash & Rogerson, Richard, 1989. "Cyclical fluctuations and sectoral reallocation : Evidence from the PSID," Journal of Monetary Economics, Elsevier, vol. 23(2), pages 259-273, March.
    8. Jeremy Greenwood & Gregory W. Huffman, 1988. "On Modelling the Natural Rate of Unemployment with Indivisible Labour," Canadian Journal of Economics, Canadian Economics Association, vol. 21(3), pages 587-609, August.
    9. Lilien, David M, 1982. "Sectoral Shifts and Cyclical Unemployment," Journal of Political Economy, University of Chicago Press, vol. 90(4), pages 777-793, August.
    10. Rogerson, Richard & Wright, Randall, 1988. "Involuntary unemployment in economies with efficient risk sharing," Journal of Monetary Economics, Elsevier, vol. 22(3), pages 501-515.
    11. John M. Barron & Wesley Mellow, 1979. "Search Effort in the Labor Market," Journal of Human Resources, University of Wisconsin Press, vol. 14(3), pages 389-404.
    12. Andolfatto, David, 1996. "Business Cycles and Labor-Market Search," American Economic Review, American Economic Association, vol. 86(1), pages 112-132, March.
    13. Lucas, Robert Jr. & Prescott, Edward C., 1974. "Equilibrium search and unemployment," Journal of Economic Theory, Elsevier, vol. 7(2), pages 188-209, February.
    14. Gary D. Hansen & Randall Wright, 1992. "The labor market in real business cycle theory," Quarterly Review, Federal Reserve Bank of Minneapolis, issue Spr, pages 2-12.
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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 and Phrases: Convex hull; Group majorization; Permutation group; Point-wise stabilizer subgroup; Separability; Transitive group.; JEL Classification Numbers: G11; D8; C6.;

    JEL classification:

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


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