Symmetry and order in the portfolio allocation problem |
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Authors: | Harvey E Lapan David A Hennessy |
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Institution: | (1) Department of Economics, Iowa State University, Ames, IA 50011-1070, USA (e-mail: hennessy@iastate.edu) , US |
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Abstract: | Summary. 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.
Received: August 8, 2000; revised version: January 8, 2001 |
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Keywords: | and Phrases: Arrangement increasing Location and scale Majorization Ordinal structure Permutation symmetry Revealed preference Schur-concave |
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