Constrained Multicriteria Sorting Method Applied to Portfolio Selection

Abstract

International audienceThe paper focuses on portfolio selection problems which aim at selecting a subset of alternatives considering not only the performance of the alternatives evaluated on multiple criteria, but also the performance of portfolio as a whole, on which balance over alternatives on specific attributes is required by the Decision Makers (DMs). We propose a two-level method to handle such decision situation. First, at the individual level, the alternatives are evaluated by the sorting model Electre Tri which assigns alternatives to predefined ordered categories by comparing alternatives to profiles separating the categories. The DMs' preferences on alternatives are expressed by some assignment examples they can provide, which reduces the DMs' cognitive efforts. Second, at the portfolio level, the DMs' preferences express requirements on the composition of portfolio and are modeled as constraints on category size. The method proceeds through the resolution of a Mixed Integer Program (MIP) and selects a satisfactory portfolio as close as possible to the DMs' preference. The usefulness of the proposed method is illustrated by an example which integrates a sorting model with assignment examples and constraints on the portfolio definition. The method can be used widely in portfolio selection situation where the decision should be made taking into account the performances of individual alternatives and portfolio simultaneously

A Bicriteria Approach Identifying Nondominated Portfolios

“…Criteria used for selection and composition are grouped into three categories: criteria regarding expected outcome of investment in a mutual fund; criteria measuring risk to obtain an outcome; and criteria about efficiency of mutual funds. In [5] a two-level process is applied for selection and composition of portfolios from a set of projects. In the first level, the ELECTRE TRI decision aid method is used to sort projects according to given categories, for instance, good, average, and bad projects.…”

“…Since the portfolio selection problem intrinsically incorporates business criteria, budget restrictions, and returns volatility [4], in the literature the problem is formulated as the maximization of the expected return, under uncertainty of returns. When the multicriteria version is considered, several utility functions need to be maximized, subject to constrains defining the feasible portfolios [1,4,5]. In this context, nondominated portfolios may be computed using multiobjective algorithms [6], evolutionary methods for multiobjective models [7,8], or preference programming [9].…”

Vendor/Contractor Relationship Management

“…Zheng et al [ZCM11] ont proposé une méthode basée sur une formulation comme un problème de tri contraint. L'aide à la décision se déroule en deux phases.…”

Post factum analysis for robust multiple criteria ranking and sorting

“…In particular, one may elicit holistic judgments, such as pairwise comparisons of alternatives or criteria (see, e.g., [12,29]), assignment-based pairwise comparisons [19], assignment examples (see, e.g., [9,33]), rank-related requirements [22], or desired class-cardinalities (see, e.g., [23,42]). Furthermore, one may also specify some imprecise statements, like lower and upper bounds for comprehensive scores (see, e.g., [40]) or preference ratios (see, e.g., [28]).…”