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

Yue Qi (), Ralph E. Steuer () and Maximilian Wimmer ()
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Yue Qi: Nankai University
Ralph E. Steuer: University of Georgia
Maximilian Wimmer: University of Regensburg

Annals of Operations Research, 2017, vol. 251, issue 1, No 10, 177 pages

Abstract: 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 (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (18)

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DOI: 10.1007/s10479-015-1900-y

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