Annals of Operations Research

, Volume 251, Issue 1–2, pp 161–177 | Cite as

An analytical derivation of the efficient surface in portfolio selection with three criteria

Article

Abstract

In standard mean-variance bi-criterion portfolio selection, the efficient set is a frontier. While it is not yet standard for there to be additional criteria in portfolio selection, there has been a growing amount of discussion in the literature on the topic. However, should there be even one additional criterion, the efficient frontier becomes an efficient surface. Striving to parallel Merton’s seminal analytical derivation of the efficient frontier, in this paper we provide an analytical derivation of the efficient surface when an additional linear criterion (on top of expected return and variance) is included in the model addressed by Merton. Among the results of the paper there is, as a higher dimensional counterpart to the 2-mutual-fund theorem of traditional portfolio selection, a 3-mutual-fund theorem in tri-criterion portfolio selection. 3D graphs are employed to stress the paraboloidic/hyperboloidic structures present in tri-criterion portfolio selection.

Keywords

Multiple criteria optimization Tri-criterion portfolio selection Minimum-variance frontier e-Constraint method Efficient surface Paraboloids 

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Department of Financial Management, Business SchoolNankai UniversityTianjinChina
  2. 2.Department of FinanceUniversity of GeorgiaAthensUSA
  3. 3.Department of FinanceUniversity of RegensburgRegensburgGermany

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