Symmetry and Order in the Portfolio Allocation Problem

This research studies the role of multivariate distribution structure on random asset returns in determining the optimal allocation vector for an expected utility maximizing agent. By carefully disturbing symmetry in the distribution of the, possibly covarying, returns, we ascertain the ordinal structure of the allocation vector. Rank order of allocations is also established when a permutation symmetric vector is mapped into the returns vector through location and scale shifts. The results are extended to pertain for partitions of the state space.