Symmetry and order in the portfolio allocation problem

Harvey Lapan and David Hennessy

Economic Theory, 2002, vol. 19, issue 4, 747-772

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.

Keywords: Arrangement increasing; Location and scale; Majorization; Ordinal structure; Permutation symmetry; Revealed preference; Schur-concave. (search for similar items in EconPapers)
JEL-codes: C61 D8 G1 (search for similar items in EconPapers)
Date: 2002-02-06
Note: Received: August 8, 2000; revised version: January 8, 2001
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Citations: View citations in EconPapers (11)

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