Ana Garcia-Bernabeu

Portfolio Selection with Multiple Time Horizons: A Mean Variance - Stochastic Goal Programming Approach

Abstract Standard approaches to portfolio selection from classical Markowitz mean-variance model require using a time horizon of historical returns over a period that the investor defines in a conventional way. To avoid arbitrary choice of the time horizon, this paper proposes a satisfying compromise solution relying on mean variance—stochastic goal programming (EV-SGP), where the goals are defined from the different time horizons under consideration. As the information on returns provided by each horizon is of different quality and reliability, critical parameters in this method are Arrows absolute risk aversion (ARA) coefficients and the investors preferences for each horizon. After formulating the proposed method, a suitable technique to determine the ARA coefficients in our context is given in a strict way according to Arrows risk theory. An actual numerical example is developed throughout the paper leading to consistent results. The sensitivity analysis shows robust solutions. A generalization of results requires further examples.

Photovoltaic power plants: a multicriteria approach to investment decisions and a case study in western Spain

This paper proposes a compromise programming (CP) model to help investors decide whether to construct photovoltaic power plants with government financial support. For this purpose, we simulate an agreement between the government, who pursues political prices (guaranteed prices) as low as possible, and the project sponsor who wants returns (stochastic cash flows) as high as possible. The sponsor’s decision depends on the positive or negative result of this simulation, the resulting simulated price being compared to the effective guaranteed price established by the country legislation for photovoltaic energy. To undertake the simulation, the CP model articulates variables such as ranges of guaranteed prices, technical characteristics of the plant, expected energy to be generated over the investment life, investment cost, cash flow probabilities, and others. To determine the CP metric, risk aversion is assumed. As an actual application, a case study on photovoltaic power investment in Extremadura, western Spain, is developed in detail.

Compromise Programming and Utility Functions

Proposed in the last decades of the twentieth century, the Compromise Programming (CP) model assumes that the decision maker looks for a compromise between objectives of different character, financial, ethical or others. As described by CP, the decision maker has in mind an ideal point, which is a basket containing the best feasible level of each objective. This ideal is a utopian infeasible basket of reference because all the best objectives cannot be simultaneously reached. Given an efficient frontier of baskets, the CP satisfying solution is to choose the basket closer to the ideal. More precisely, the CP solution is obtained by minimizing the distance between a frontier basket and the ideal. Distances are not necessarily measured by the Euclidean quadratic metric but by a conventional metric between one and infinity. Moreover, the distance in CP is not a purely geometric notion but a composite measure in which the geometric components are multiplied by the decision maker’s preference weights for each objective. Years later the CP proposal, a linkage between CP and utility theory was investigated. Finally, Linear–quadratic composite metric looks for a compromise between aggressive (large risky acnievements) and conservative (balanced solutions) objectives.

Evaluating Fund Performance from Financial and SRI Criteria

Classical approaches to financial performance of funds have the following characteristics. First, the performance composite measure is only capable of combining two criteria, which are usually profitability and risk. In purely financial analyses, this limitation is justified because profitability and risk are the more interesting criteria for most investors in funds. However, in ethical financial analysis this limitation prevents the possibility of combining multiple SRI and financial criteria. Second, the classical approaches are designed regardless of the investor’s preferences for each criterion. An advantage is that the performance ranking of funds can be used whatever the investor. A disadvantage is that many investors want to manage performance rankings constructed from their preferences for ethical and financial criteria. To overcome these difficulties, the performance ranking can be constructed by a CP-based model extended to multiple SRI and financial criteria with the possibility of introducing preference weights. In this chapter, a CP model with linear-quadratic achievement function is presented and applied to an actual financial case as well as to a combined SRI-financial case.

Portfolio Selection by Compromise Programming

CP is a deterministic model like WGP in this aspect. Therefore, CP seems inappropriate to select stock portfolios from the Eu(R) maximization theory. In contrast to MV-SGP model, CP does not generalize Markowitz M-V model to multiple objectives. This lack of strictness is mitigated by the linkage between CP and utility theory established in Chap. 8. This linkage allows us to extend utility properties to CP approaches. We show the CP setting for portfolio selection by establishing and graphing its main elements: profitability-safety efficient frontier, ideal point and the bounds of Yu compromise set, which is the landing area on which the profitability-safety utility function reaches its maximum. From these variables, expected return and safety, the portfolio selection problem is defined in terms of CP.

The Ethical Financial Question and the MCDM Framework

This chapter explains the financial meaning and importance of Socially Responsible Investment (SRI), also called ethical investment. Currently, SRI is a private initiative to invest increasing flows of financial resources in environmentally and socially sustainable activities and to invest nothing in anti-ethical projects. Main SRI agents are banks and institutional investors who are engaged in policies such as sustainable consumption of energy and natural resources, ecosystem protection, advanced medical projects, technological research, education of young entrepreneurs, anti-tobacco campaigns, safety and healthcare in the workplace, and others. These agents think that traditional financial criteria such as profitability and risk should be combined with SRI criteria to select stock portfolios. In SRI, Multiple Criteria Decision Making (MCDM) approaches seem to be helpful as several criteria, not only financial but also environmental, social or governance concerns are taken into account. Regarding MCDM, a brief overview is included in this chapter to introduce this methodology into SRI decision problems.

Selecting SRI Financial Portfolios Applying MV-SGP Model

In this chapter, the second stage to stock portfolio selection combining ethical and financial objectives is described. For this purpose, MV-SGP model is used. As a prior question, the financial and ethical goals under uncertainty are formulated. Once the goals are specified, the statement of MV-SGP requires defining financial and SRI targets. A significant question is how to estimate Arrow’s absolute risk aversion (ARA) coefficients. This question is examined in detail. The ARA coefficients are critical parameters to state the achievement function in MV-SGP model, while preference weights for the goals are not considered. This is because SRI preferences widely differ from an investor to another. Only in the case that portfolio selection is addressed to one given investor, his/her preferences are introduced into the achievement function

Ethically Constrained Portfolio Selection of Funds by CP Modelling: A Real World Environmental Case

In CP models to select ethical financial portfolios of securities, the ethical component can be articulated either by introducing SRI objectives or by introducing SRI constraints. None of these procedures is free of drawbacks. To place SRI objectives seems appealing because trade-offs can be stated between SRI goals and financial goals. However, to build these trade-offs requires articulating investor’s preference weights for SRI and financial objectives. To elicit these weights is quite impossible in mutual funds because preferences differ from one investor to another in the fund. We propose a multicriteria portfolio selection model for mutual funds based on CP which takes into account both, a financial and a non-financial dimension taking into account the subjective and individual preferences of an individual investor under two different scenarios: a low social responsibility degree and a high social responsibility degree scenario. An real case study is performed on 110 large cap equity mutual funds.

Portfolio Selection by Goal Programming Techniques

Goal programming stems from the Simonian paradigm describing decision makers as seekers of satisfying solutions rather than optimal solutions. Weighted Goal Programming (WGP) is usually viewed as a deterministic model, which provides satisfying solutions to multi-objective technological and economic problems in multiple criteria decision making analysis. Deterministic WGP is less appropriated to select securities portfolios because returns on securities are random variables. To accommodate WGP to portfolio selection, some stochastic versions of different strictness had been proposed. In this chapter, we deal with Mean-Variance Stochastic Goal Programming (MV-SGP) model, which relies on classic expected utility maximization theory, also known as Eu(R), Arrow’s risk aversion and Pratt’s approximation to expected utility.

An Actual Case of SRI Financial Portfolio Choice by MV-SGP

An illustrative example of ethical financial portfolio selection by MV-SGP model is developed through tables and numerical statements. Empirical data are real wide observations coming from international sources. This includes an opportunity set of 80 funds with historical series of weekly returns on the funds and SRI achievement indexes over 5 years time horizon. On this actual database, mean values vectors and covariance matrices are computed as a previous step required to formulate the objective function and constraints of the model. Since the computational structure of MV-SGP is the same as the computational structure of Markowitz-MV, the model is solved by using a Markowitz software application. The results are tabulated and discussed.