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Symmetry and order in the portfolio allocation problem

Author

Listed:
  • Harvey E. Lapan

    () (Department of Economics, Iowa State University, Ames, IA 50011-1070, USA)

  • David A. Hennessy

    () (Department of Economics, Iowa State University, Ames, IA 50011-1070, USA)

Abstract

This research studies the role of multivariate distribution structures on random asset returns in determining the optimal allocation vector for an expected utility maximizer. All our conclusions pertain for the set of risk averters. By carefully disturbing symmetry in the distribution of the, possibly covarying, returns, we ascertain the ordinal structure of the optimized allocation vector. Rank order of allocations is also established when a permutation symmetric random vector is mapped into the returns vector through location and scale shifts. It is shown that increased dispersion in the vectors of location and scale parameters benefit, ex-ante, investors as does a decrease in the rank correlation coefficient between the location and scale parameter vectors. Revealed preference comparative static results are identified for the location and scale vectors of asset returns. For most issues addressed, we arrive at much stronger inferences when a safe asset is available.

Suggested Citation

  • Harvey E. Lapan & David A. Hennessy, 2002. "Symmetry and order in the portfolio allocation problem," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 19(4), pages 747-772.
  • Handle: RePEc:spr:joecth:v:19:y:2002:i:4:p:747-772
    Note: Received: August 8, 2000; revised version: January 8, 2001
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    Cited by:

    1. Hennessy, David A. & Lapan, Harvey, 2007. "When different market concentration indices agree," Economics Letters, Elsevier, vol. 95(2), pages 234-240, May.
    2. Lapan, Harvey E. & Hennessy, David A., 2006. "A note on cost arrangement and market performance in a multi-product Cournot oligopoly," International Journal of Industrial Organization, Elsevier, vol. 24(3), pages 583-591, May.
    3. Cheung, Ka Chun, 2006. "Optimal portfolio problem with unknown dependency structure," Insurance: Mathematics and Economics, Elsevier, vol. 38(1), pages 167-175, February.
    4. Lapan, Harvey E. & Hennessy, David A., 2004. "Cost Arrangement and Welfare in a Multi-Product Cournot Oligopoly," Staff General Research Papers Archive 12207, Iowa State University, Department of Economics.
    5. Hennessy, David A. & Saak, Alexander E. & Babcock, Bruce A., 2003. "Fair Value Of Whole-Farm And Crop-Specific Revenue Insurance," 2003 Annual meeting, July 27-30, Montreal, Canada 21988, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    6. 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.
    7. repec:ebl:ecbull:v:7:y:2004:i:1:p:1-7 is not listed on IDEAS
    8. 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.

    More about this item

    Keywords

    Arrangement increasing; Location and scale; Majorization; Ordinal structure; Permutation symmetry; Revealed preference; Schur-concave.;

    JEL classification:

    • D8 - Microeconomics - - Information, Knowledge, and Uncertainty
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • G1 - Financial Economics - - General Financial Markets

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