Portfolio Selection from Multiple Benchmarks: A Goal Programming Approach to an Actual Case

Abstract

This paper deals with benchmark-based portfolio choice for buy-and-hold strategies of investing. Multiple benchmarks for returns are considered, which is more realistic than taking a unique benchmark -a unique aspiration difficult to select in practice among the various aspirations for returns that the investor has in mind. Portfolio selection with multiple benchmarks leads to a multi-objective problem, which is addressed by mean value -stochastic goal programming. In particular, two benchmarks are considered, which involves two goals. Weights for goals depend on investor's preferences and Arrow's absolute risk aversion coefficients. An efficient frontier of portfolios is obtained. Advantages of this stochastic method in our context are as follows: (i) Mean value-stochastic goal programming relies on classical utility theory under uncertainty and Arrow's absolute risk aversion, which ensures soundness and strictness, and (ii) the numerical model is easily solved by using available software such as mean-variance software. Numerical results are tabulated and discussed.

Balancing the Portfolio of Urban and Public Projects with Distance-Dependent Coverage Facilities

“…Constraints (7) to (9) are written for each coverage indicator in each time period in each region. Constraints (10) and (11) guarantee that projects implementation periods and completion periods are synchronized. Constraints (12) guarantee that each project is finished within planning horizon.…”

“…In previous section, constraint (11) Evolutionary algorithms (EA) are stochastic population-based metaheuristics that have been successfully applied to many real and complex problems. They are the most studied populationbased algorithms [25].…”

“…The first model of goal programming in the project portfolio selection was presented by Sharma et al [10]. Bravo et al [11] developed a goal programming model for selecting project portfolio with multiple criteria. [12] presented a robust optimization model for selecting the project portfolio using goal programming technique.…”

Goal programming with extended factors for portfolio selection

“…Bravo et al. () develop a stochastic GP model for multiple benchmark of returns for a more realistic approach to portfolio analysis.…”

Evaluating Fund Performance by Compromise Programming with Linear‐Quadratic Composite Metric: An Actual Case on The CaixaBank in Spain

“…An assumption underlying E‐V is that historic results have predictive ability. There is a wide MCDM literature on portfolio choice and related issues, of which the following issues from year 2000 should be cited: (a) portfolio choice with fuzzy information (Arenas et al , ; Pérez‐Gladish et al , ); (b) CP applied to portfolio problems (Bilbao‐Terol et al , , ; Amiri et al , ); (c) approximating the optimum portfolio on the mean–variance efficient frontier by linkages between utility theory and compromise programming (Ballestero and Pla‐Santamaria, , , ); (d) extending the classical (risk–return) approach to other different criteria (Steuer et al , ); (e) novel approaches from multi‐objective programming (Steuer et al , ); (f) constructing equity mutual funds portfolios by goal programming (Pendaraki et al , ); (g) mean–semivariance efficient frontier (Ballestero, ); (h) hybrid models, neural networks and algorithms (Ong et al , ; Huang et al , ; Lin et al , ); (i) satisfaction functions are proposed to integrate the decision maker's preferences into GP models under uncertainty (Aouni et al , ); (j) fuzzy techniques are useful when probability distributions are unknown (Ben Abdelaziz and Masri, ); (k) fuzzy techniques are applied to portfolio choice with Sharpe's beta in Bilbao et al () and Ballestero et al (), the latter by using mean value‐stochastic goal programming (Ballestero, ); (l) other approaches to portfolio choice by stochastic programming are Ben Abdelaziz et al () and Abdelaziz et al (); (m) portfolio choice from multiple benchmarks is developed by Bravo et al (); and (n) a model of portfolio selection from the ethical principles of Socially Responsible Investment is proposed in Ballestero et al ().…”