Mar Arenas-Parra

Fuzzy compromise programming for portfolio selection

The aim of this paper is to solve a portfolio selection problem using Sharpes single index model in a soft framework. Estimations of subjective or imprecise future beta for every asset can be represented through fuzzy numbers constructed on the basis of statistical data and the relevant knowledge of the financial analyst; the model, therefore, works with data that contain more information than any classical model and dealing with it does not involve a great extra computational effort. In order to solve the portfolio selection problem we have formulated a Fuzzy Compromise Programming problem. For this task we have introduced the fuzzy ideal solution concept based on soft preference and indifference relationships and on canonical representation of fuzzy numbers by means of their @a-cuts. The accuracy between the ideal solution and the objective values is evaluated handling the fuzzy parameters through their expected intervals and using discrepancy between fuzzy numbers in our analysis. A major feature of this model is its sensitivity to the analysts opinion as well as to the decision-makers preferences. This allows interaction with both when it comes to design the best portfolio.

Socially responsible investment: A multicriteria approach to portfolio selection combining ethical and financial objectives

In a context of Socially Responsible Investment (SRI), this paper deals with portfolio selection for investors interested in ethical policies. In the opportunity set there are ethical assets and other assets which are not characterized as ethical. Two goals are considered, the traditional financial goal in the classical utility theory under uncertainty and an ethical goal in the same utility framework. A new financial-ethical bi-criteria model is proposed with absolute risk aversion coefficients and targets depending on the investor’s ethical profile. This approach is relevant as an increasing number of mutual funds are becoming interested in SRI strategies. From the proposed model, an actual case on green investment is developed. Concerning this case (without generalizing to other contexts), an analysis of the numerical results shows that efficient portfolios obtained by the traditional E-V model outperform the strong green portfolios in terms of expected return and risk, but this does not significantly occur with weak green investment.

Selecting Portfolios Given Multiple Eurostoxx-Based Uncertainty Scenarios: A Stochastic Goal Programming Approach from Fuzzy Betas

Abstract We deal with the buy-and-hold choice of fund portfolios by considering multiple states of nature (future market scenarios). These states are associated with goals in the sense that the investor pursues to optimize a classical financial objective function as much as possible whatever the states of nature. As this classical function is very cumbersome for handling, a satisficing proxy is used. This proxy is Stochastic Goal Programming (SGP), a recent uncertainty multiobjective model characterized as follows: (a) it relies on Von Neumann and Morgensterns-Arrows Eu(R) principles in a framework of bounded rationality; (b) its moderate computational burden allows easy application to large scale problems. In SGP, the variability matrices of goals are aggregated by Arrows risk aversion coefficients. Concerning the case study, the states of nature are Eurostoxx market index scenarios defined from time series. As an opportunity set of assets, we use a large set of funds managed by an international consultancy. Potential returns on each fund are related to each scenario by using betas. As eliciting betas can be made from different samples leading to different results, we use fuzzy logic to decide among these different results in a framework of imprecision/uncertainty. Our approach is new as it combines SGP and fuzzy tools.

Multi-criteria decision making for choosing socially responsible investment within a behavioral portfolio theory framework: a new way of investing into a crisis environment

The current economic crisis fuels the financial social responsibility after an epoch of many excesses with damaging effects. This work tackles two emerging streams in the financial literature: the behavioral portfolio theory with mental accounting and the socially responsible investment (SRI). Promoting SRI is regarded by a lot of financial experts, policymakers and researchers from the field of economic and social sciences, as one of the potential solutions in order to avoid future crises. Therefore, new models for this investment approach are necessary. We try to support the class of investors that select their investments under a mental accounting framework and also they want to achieve a certain level of SR quality in their portfolios. In order to reconcile the two choice frames, avoiding unnecessary sacrifices in financial performance, we have designed a model based on goal programming that integrates the two cornerstones of the investor. Furthermore, we propose a fuzzy inference system to determine the amount of money allocated to each mental account as well as the confidence level assigned to each mental account. This tool is based on expert knowledge modeled by fuzzy if–then rules.

A sequential goal programming model with fuzzy hierarchies to sustainable and responsible portfolio selection problem

Sustainable and responsible (SR) investors have to address two criteria types: both financial ones and those pertaining to sustainability and social responsibility. We present a comfortable tool for SR investors that allow them to express their preferences at two levels: first, by comparing criteria of the same nature, and second, via the comparison between the two superior level criteria (the financial and the SR objectives). Owing to the difficulty involved in determining a precise preference between the conflicting objectives, we address this by goal programming with fuzzy hierarchies (GPFH) modelling. This methodology is a modification of the lexicographic GP approach whereby the relative importance relations among the criteria are modelled by fuzzy relations. The proposed sequential handling for the SR portfolios selection provides information to the investors on the best result they can achieve in regard to their goals. An application to a set of UK-SR mutual funds is presented.

A new approach of Romero’s extended lexicographic goal programming: fuzzy extended lexicographic goal programming

Goal programming (GP) is perhaps one of the most widely used approaches in the field of multicriteria decision making. The major advantage of the GP model is its great flexibility which enables the decision maker to easily incorporate numerous variations on constraints and goals. Romero provides a general structure, extended lexicographic goal programming (ELGP) for GP and some multiobjective programming approaches. In this work, we propose the extension of this unifying framework to fuzzy multiobjective programming. Our extension is carried out by several methodologies developed by the authors in the fuzzy GP approach. An interval GP model has been constructed where the feasible set has been defined by means of a relationship between fuzzy numbers. We will apply this model to our fuzzy extended lexicographic goal programming (FELGP). The FELGP is a general primary structure with the same advantages as Romero’s ELGP and moreover it has the capacity of working with imprecise information. An example is given in order to illustrate the proposed method.

A group decision making model based on goal programming with fuzzy hierarchy: an application to regional forest planning

In this paper a multi-criteria group decision making model is presented in which there is a heterogeneity among the decision makers due to their different expertise and/or their different level of political control. The relative importance of the decision makers in the group is handled in a soft manner using fuzzy relations. We suppose that each decision maker has his/her preferred solution, obtained by applying any of the techniques of distance-based multi-objective programming [compromise, goal programming (GP), goal programming with fuzzy hierarchy, etc.]. These solutions are used as aspiration levels in a group GP model in which the differences between the unwanted deviations are interpreted in terms of the degree of achievement of the relative importance amongst the group members. In this way, a group GP model with fuzzy hierarchy (Group-GPFH) is constructed. The solution for this model is proposed as a collective decision. To show the applicability of our proposal, a regional forest planning problem is addressed. The objective is to determine tree species composition in order to improve the values achieved by Pan-European indicators for sustainable forest management. This problem involves stakeholders with competing interests and different preference schemes for the aforementioned indicators. The application of our proposal to this problem allows us to be able to comfortably address all these issues. The results obtained are consistent with the preferences of each stakeholder and their hierarchy within the group.

Standard goal programming with fuzzy hierarchies: a sequential approach

This paper proposes a pragmatic model for multi-objective decision-making processes involving clusters of objectives which have a decisional meaning for the decision maker (DM). We provide the DMs with a comfortable tool that allows them to express their preferences both by comparing criteria of the same cluster and via the comparison between the different clusters. In standard goal programming the importance of the goals is modeled by the introduction of preferential weights or/and the incorporation of pre-emptive priorities. However, in many cases the DM is not able to establish a precise preference structure. Even in the case of precise weights the solution does not match necessarily the relative weights or, in the case of precise pre-emptive priority, the result could be very restrictive. In order to overcome these drawbacks, in this paper the normalized unwanted deviations are interpreted in terms of achievement degrees of the goals and fuzzy relations are used to model the relative importance of the goals. Thus, we show how several methodologies from the fuzzy goal programming literature can be tailored for solving standard GP problems. We apply this new modeling to problems where there is a “natural” clustering between goals of the same class. We address this situation by solving two phases; in the first one each class is handled separately taking into account the hierarchy of their goals and, in the second phase, we integrate the results of the first phase and the imprecise hierarchy of the different classes. We formulate a new goal programming model called as sequential goal programming with fuzzy hierarchy model. Because many real situations involve decision making in this environment, our proposal can be a useful tool of broad application. A numerical example illustrates the methodology.

Multi-criteria analysis of the GRI sustainability reports: an application to Socially Responsible Investment

The aim of this paper is to construct a support decision-making system to evaluate the different items of corporate social responsibility. For this purpose, we propose a multi-criteria model that runs on two levels of decision-making in accordance with the hierarchical structure designed by the Global Reporting Initiative (GRI). Tools for modelling preferences and aggregating information are used in this framework. Arrays of normalized scores reflecting the company performance in the Aspects and Categories of GRI are then made available for the stakeholders. The design of investment portfolios uses the obtained measures of sustainability in an Extended Goal Programming model that combines financial and sustainability objectives. The proposal enables more informed decision-making for investors with social concerns that prefer direct investment and wish to make their own financial decisions. The developed methodology has been applied to 8 Spanish companies, which have been selected for their relevance in the Spanish stock market.

A model for solving incompatible fuzzy goal programming: an application to portfolio selection

For many fuzzy goal programming (GP) approaches, in order to build the membership functions of fuzzy aspiration levels, a tolerance threshold for each one of them should be determined. In this paper, we address the case in which the decision maker proposes incompatible thresholds, which could lead to an infeasible problem. We propose an alternative algebraic formulation of the membership functions, which allows us to formulate models capable of providing solutions, although some tolerance thresholds are surpassed. The objective values that do not violate their corresponding threshold are evaluated positively according to the degree of achievement to their fuzzy target, and in turn those who violate the threshold are penalized according to their unwanted deviation with respect to the threshold. Thus, our model jointly uses the fuzzy GP approach and the standard GP approach, which also allows incorporating fuzzy and crisp targets into the same problem. The proposed procedure is applied to socially responsible portfolio selection problems.