Algebraic Theory of Portfolio Allocation, An
AbstractDiversification, a central issue in the study of capital allocation, has much to do with symmetries and asymmetries in the distribution of asset returns. A diversified portfolio imposes symmetry on the allocation vector in order to balance out much of the asymmetries in the returns vector. Using group and majorization theory, we explore what can be established about the allocation vector when the 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 group elements. It is shown that transitive permutation groups, rather than the more structured permutation symmetric group, suffice to ensure complete portfolio diversification. Point-wise stabilizer subgroups admit separability in the allocation of funds across sectors. When, together with imperfect symmetry in the sources of randomness, asset returns differ by heterogeneity in location or scale parameters then we bound the admissible allocation vector by a set of linear constraints. For a distribution that is symmetric under reflection groups, the linear constraints may be further strengthened whenever there exists an hyperplane that separates convex sets.
Download InfoTo our knowledge, this item is not available for download. To find whether it is available, there are three options:
1. Check below under "Related research" whether another version of this item is available online.
2. Check on the provider's web page whether it is in fact available.
3. Perform a search for a similarly titled item that would be available.
Bibliographic InfoPaper provided by Iowa State University, Department of Economics in its series Staff General Research Papers with number 10109.
Date of creation: 01 Aug 2003
Date of revision:
Publication status: Published in Economic Theory, August 2003, vol. 22 no. 1, pp. 193-210
Contact details of provider:
Postal: Iowa State University, Dept. of Economics, 260 Heady Hall, Ames, IA 50011-1070
Phone: +1 515.294.6741
Fax: +1 515.294.0221
Web page: http://www.econ.iastate.edu
More information through EDIRC
This paper has been announced in the following NEP Reports:
- NEP-ALL-2003-10-12 (All new papers)
- NEP-CFN-2003-10-12 (Corporate Finance)
- NEP-FIN-2003-10-12 (Finance)
You can help add them by filling out this form.
CitEc Project, subscribe to its RSS feed for this item.
- 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.
- Hennessy, David A. & Lapan, Harvey E., 2006. "Harmonic Symmetries of Imperfect Competition on Circular City," Staff General Research Papers 12551, Iowa State University, Department of Economics.
- Ibragimov, Rustam & Ibragimov, Marat, 2007. "Market Demand Elasticity and Income Inequality," Scholarly Articles 2623728, Harvard University Department of Economics.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Stephanie Bridges) The email address of this maintainer does not seem to be valid anymore. Please ask Stephanie Bridges to update the entry or send us the correct address.
If references are entirely missing, you can add them using this form.