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

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 Lα condition if 1<α≤2,...

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Main Author: Nils Chr. Framstad
Format: Article
Language:English
Published: Wiley 2015-01-01
Series:Journal of Probability and Statistics
Online Access:http://dx.doi.org/10.1155/2015/235452
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author Nils Chr. Framstad
author_facet Nils Chr. Framstad
author_sort Nils Chr. Framstad
collection DOAJ
description 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 Lα condition if 1<α≤2, with the betas given in an explicit form. For the α-symmetric subclass, the market without risk-free investment opportunity admits 2d-fund separation if α=1+1/(2d-1), d∈N, generalizing the classical elliptical case d=1, 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.
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spelling doaj-art-f19ece2c837c4461b072b46cc7f4a5ca2025-08-20T02:21:52ZengWileyJournal of Probability and Statistics1687-952X1687-95382015-01-01201510.1155/2015/235452235452Portfolio Theory for α-Symmetric and Pseudoisotropic Distributions: k-Fund Separation and the CAPMNils Chr. Framstad0Department of Economics, University of Oslo, P.O. Box 1095, Blindern, 0317 Oslo, NorwayThe 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 Lα condition if 1<α≤2, with the betas given in an explicit form. For the α-symmetric subclass, the market without risk-free investment opportunity admits 2d-fund separation if α=1+1/(2d-1), d∈N, generalizing the classical elliptical case d=1, 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.http://dx.doi.org/10.1155/2015/235452
spellingShingle Nils Chr. Framstad
Portfolio Theory for α-Symmetric and Pseudoisotropic Distributions: k-Fund Separation and the CAPM
Journal of Probability and Statistics
title Portfolio Theory for α-Symmetric and Pseudoisotropic Distributions: k-Fund Separation and the CAPM
title_full Portfolio Theory for α-Symmetric and Pseudoisotropic Distributions: k-Fund Separation and the CAPM
title_fullStr Portfolio Theory for α-Symmetric and Pseudoisotropic Distributions: k-Fund Separation and the CAPM
title_full_unstemmed Portfolio Theory for α-Symmetric and Pseudoisotropic Distributions: k-Fund Separation and the CAPM
title_short Portfolio Theory for α-Symmetric and Pseudoisotropic Distributions: k-Fund Separation and the CAPM
title_sort portfolio theory for α symmetric and pseudoisotropic distributions k fund separation and the capm
url http://dx.doi.org/10.1155/2015/235452
work_keys_str_mv AT nilschrframstad portfoliotheoryforasymmetricandpseudoisotropicdistributionskfundseparationandthecapm