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Journal of Probability and Statistics
Volume 2015 (2015), Article ID 235452, 11 pages
Research Article

Portfolio Theory for -Symmetric and Pseudoisotropic Distributions: -Fund Separation and the CAPM

Department of Economics, University of Oslo, P.O. Box 1095, Blindern, 0317 Oslo, Norway

Received 30 June 2015; Revised 6 October 2015; Accepted 12 October 2015

Academic Editor: Chunsheng Ma

Copyright © 2015 Nils Chr. Framstad. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The shifted pseudoisotropic multivariate distributions are shown to satisfy Ross’ stochastic dominance criterion for two-fund monetary separation in the case with risk-free investment opportunity and furthermore to admit the Capital Asset Pricing Model under an embedding in condition if , with the betas given in an explicit form. For the -symmetric subclass, the market without risk-free investment opportunity admits -fund separation if , , generalizing the classical elliptical case , and we also give the precise number of funds needed, from which it follows that we cannot, except degenerate cases, have a CAPM without risk-free opportunity. For the symmetric stable subclass, the index of stability is only of secondary interest, and several common restrictions in terms of that index can be weakened by replacing it by the (no smaller) indices of symmetry/of embedding. Finally, dynamic models with intermediate consumption inherit the separation properties of the static models.