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Diversification, 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 preferencesdoi:10.1007/s00199-002-0284-9 fatcat:a7l4u4k5grhkrkavlql6il7gde