On the Computation of the Efficient Frontier of the Portfolio Selection Problem

Abstract

An easy-to-use procedure is presented for improving theε-constraint method for computing the efficient frontier of the portfolio selection problem endowed with additional cardinality and semicontinuous variable constraints. The proposed method provides not only a numerical plotting of the frontier but also an analytical description of it, including the explicit equations of the arcs of parabola it comprises and the change points between them. This information is useful for performing a sensitivity analysis as well as for providing additional criteria to the investor in order to select an efficient portfolio. Computational results are provided to test the efficiency of the algorithm and to illustrate its applications. The procedure has been implemented in Mathematica.

Finding socially responsible portfolios close to conventional ones

“…1 (right). It has been calculated by means of the techniques developed by the authors in Calvo et al (2012).…”

“…In fact, it is not the only one, but the others are too small to be seen in the figure. The following data are obtained with the computational techniques described in Calvo et al (2012). The "big gap" on the efficient frontier happens at the critical return ρ = 0.3088564154…, where the risk jumps from R − = 1.7863 to R + = 1.87842.…”

“…Computation of the efficient frontier (in an exact or approximate way) has been widely dealt with in the academic literature (some examples can be found in Merton (1972), Kolm, Tütüncü, and Fabozzi (2014) and more recently for the tri-criteria portfolio selection problem in Hirschberger, Steuer, Utz, Wimmer, and Qi (2013), Utz, Wimmer, Hirschberger, and Steuer (2014), and Calvo, Ivorra, and Liern (2012)). Obtaining the efficient frontier is a purely mathematical problem which does not require any subjective choice.…”

Portfolio Selection with SRI Synthetic Indicators: A Reference Point Method Approach

“…The auxiliary binary variables have been introduced in the model in order to model the constraints that ensure that the investment bounds constraints are only active for those funds already selected to be included in the portfolio (see, e.g. Calvo et al 2012Calvo et al , 2014.…”

GASRP-FP: A hybrid metaheuristic to solve fuzzy portfolio selection with non-financial goals

“…In [6], a model for solving a fuzzy portfolio selection problem with cardinality constraints, semicontinuous variables and non-financial goals is proposed. In a first step, the efficient financial solutions, in terms of risk and return, are obtained as proposed in [5]. Then, in a second step a nonfinancial secondary goal is considered and new solutions are offered to the investor (interesting solutions from a financial point of view are not discarded as a result of the introduction of the non-financial constraints).…”