Multi-Attribute Portfolio Selection: New Perspectives

Annals of Operations Research, 2000

The portfolio selection problem is usually considered as a bicriteria optimization problem where a reasonable trade-off between expected rate of return and risk is sought. In the classical Markowitz model the risk is measured with variance, thus generating a quadratic programming model. The Markowitz model is frequently criticized as not consistent with axiomatic models of preferences for choice under risk. Models consistent with the preference axioms are based on the relation of stochastic dominance or on expected utility theory. The former is quite easy to implement for pairwise comparisons of given portfolios whereas it does not offer any computational tool to analyze the portfolio selection problem. The latter, when used for the portfolio selection problem, is restrictive in modeling preferences of investors. In this paper, a multiple criteria linear programming model of the portfolio selection problem is developed. The model is based on the preference axioms for choice under risk. Nevertheless, it allows one to employ the standard multiple criteria procedures to analyze the portfolio selection problem. It is shown that the classical mean-risk approaches resulting in linear programming models correspond to specific solution techniques applied to our multiple criteria model.

European Journal of Operational Research, 2011

A fundamental principle of modern portfolio theory is that comparisons between portfolios are generally made using two criteria, corresponding to the first two moments of return distributions, namely the expected return and portfolio variance. According to this model and according to most of the portfolio models derived from the stochastic dominance approach, the group of portfolios open to comparisons is divided into two parts: on the one hand there are the efficient portfolios (those that are not dominated by any other portfolio in the group), and on the other, those that are dominated. In other words, these models do not solve for one optimal portfolio, but rather solve for an efficient set of portfolios, among which the investor must choose, given his preference system. One criticism over these models, which has often been addressed both by practitioners and academics, is that they fail to embody the objectives of the decision maker (DM), through the various stages of the decision process. Our purpose in this article is to present an integrated and innovative methodological approach for the construction and selection of equity portfolios, which will take into account the inherent multidimensional nature of the problem, while allowing the DM to incorporate his preferences in the decision process. The proposed approach, which grounds its basis on the field of multiple criteria decision making (MCDM) and more specifically on multiobjective mathematical programming (MMP), is implemented in the IPSSIS (Integrated Portfolio Synthesis and Selection Information System) decision support system (DSS). The validity of the proposed approach is tested through an illustrative application in the Athens Stock Exchange (ASE).

Journal of Multi-Criteria Decision Analysis, 2005

Portfolio-type problems arise in many decision-making situations. In this paper, we consider these problems in the context of multiple criteria model that takes into account two types of criteria, which are used in decision maker's preferences: criteria of the first type are used to characterize both the entire portfolio and its individual elements, whereas criteria of the second type are solely used to evaluate the portfolio as a whole but not its elements. When formulating our multiple criteria model, we assume that criteria of the first type are quantitative and that they represent a higher priority for the decision maker compared to criteria of the second type. While we acknowledge the existence of other approaches, in this paper we focus on those portfolio selection problems that match the above structure of the criteria set. After formulating the portfolio selection problem, we offer a two-phase portfolio selection procedure that allows to choose an optimal portfolio by operating in two separate criteria spaces.

2015

We begin this paper by first comparing the theory of present-day portfolio selection, which is a theory for standard investors (whose utility functions take on only the single argument of portfolio return), with a developing theory for non-standard investors (whose utility functions are allowed to take on additional arguments). Examples of additional arguments are dividends, liquidity, social responsibility, amount of short selling, and so forth. Then, with portfolio se-lection for non-standard investors taking on the form of a multi-objective stochastic programming problem, equivalent deterministic formulations involving more than mean and variance are explored. With the nondominated sets of non-standard investors no longer frontiers, but now surfaces, the tools and techniques that must be imported from multiple criteria optimization to compute and analyze them are next discussed. The paper concludes with a list of research top-ics that are candidates for extending the multiple cri...

International Journal of Multicriteria Decision Making, 2016

The paper shows how to overcome practical difficulties of using the results of modern portfolio theory linked with high dimensions and the insufficient amount of information available about the input parameters, the factors that make the optimal solution unrobust. The modified mean-variance optimisation model shows that Markowitz's portfolio can be improved. The generalised optimal portfolio problem is formulated as a multicriteria problem. The performance index that presents linear convolution of the chosen criteria is considered. The closed-form solution is given under assumption that net short sales are allowed. In contrast to several known pure mathematical regularisation approaches applied to the portfolio selection problem, the considered portfolio model includes the average trading volume of shares of the portfolio's security for a specified period of time measured as a percentage of its total float number of shares, which is used to quantify the portfolio's components based on their potential price increase. The offered additional criterion, which has a clear economic interpretation allows investors to build portfolios that are more robust compared to mean-variance portfolios.

Eawp Documentos De Trabajo En Analisis Economico Economical Analysis Working Papers, 2009

In this paper we select an optimal portfolio on the Croatian capital market by using the multicriterial programming. In accordance with the modern portfolio theory maximisation of returns at minimal risk should be the investment goal of any successful investor. However, contrary to the expectations of the modern portfolio theory, the tests carried out on a number of financial markets reveal the existence of other indicators important in portfolio selection. Considering the importance of variables other than return and risk, selection of the optimal portfolio becomes a multicriterial problem which should be solved by using the appropriate techniques.

International Journal of Latest Engineering and Management Research (IJLEMR), 2018

: In this paper, a method for reducing the number of criteria for the multi objective optimization problem is proposed.The result is two really conflicting criteria in which the improvement of any of them inevitably leads to the deterioration of others.The Markowitz model, modified by the addition of two criteria, reduction of their one-criterion optimization problem by means of a linear convolution of the criteria is considered.The article analyzes the stock market papers of the American stock market in real period.

Journal of Business & Economics Research (JBER), 2011

Investment decision-making problems are generally multi-objective in nature such as minimization of the risk and maximization of the return. These problems can be solved efficiently and effectively using multi-objective decision making (MODM) tools such as a lexicographic goal programming (LGP). This paper applies the LGP model for selecting an optimum mutual fund portfolio for an investor, while taking into account specific parameters including risk, return, expense ratio and others. Using sensitivity analysis on the weights in a priority structure of the goals identifies all possible solutions in the decision-making process. The Euclidean distance method is then used, to measure distances of all possible solutions from the identified ideal solution. The optimum possible solution is determined by the minimum distance between the ideal solution and other possible solutions of the problem. The associated weights will be the most appropriate weights in a given priority structure. The effectiveness and applicability of the LGP model is demonstrated via a case example from broad categories of mutual funds.

Neural computing & applications, 2024

Optimal portfolio selection-composing a set of stocks/assets that provide high yields/returns with a reasonable risk-has attracted investors and researchers for a long time. As a consequence, a variety of methods and techniques have been developed, spanning from purely mathematics ones to computational intelligence ones. In this paper, we introduce a method for optimal portfolio selection based on multi-objective evolutionary algorithms, specifically Nondominated Sorting Genetic Algorithm-II (NSGA-II), which tries to maximize the yield and minimize the risk, simultaneously. The system, named EvoFolio, has been experimented on stock datasets in a three-years time-frame and varying the configurations/specifics of NSGA-II operators. EvoFolio is an interactive genetic algorithm, i.e., users can provide their own insights and suggestions to the algorithm such that it takes into account users' preferences for some stocks. We have performed tests with optimizations occurring quarterly and monthly. The results show how EvoFolio can significantly reduce the risk of portfolios consisting only of stocks and obtain very high performance (in terms of return). Furthermore, considering the investor's preferences has proved to be very effective in the portfolio's composition and made it more attractive for end-users. We argue that EvoFolio can be effectively used by investors as a support tool for portfolio formation.

Swarm and Evolutionary Computation, 2014

This paper addresses a realistic portfolio assets selection problem as a multiobjective optimization one, considering the budget, floor, ceiling and cardinality as constraints. A novel multiobjective optimization algorithm, namely the non-dominated sorting multiobjective particle swarm optimization (NS-MOPSO), has been proposed and employed efficiently to solve this important problem. The performance of the proposed algorithm is compared with four multiobjective evolution algorithms (MOEAs), based on nondominated sorting, and one MOEA algorithm based on decomposition (MOEA/D). The performance results obtained from the study are also compared with those of single objective evolutionary algorithms, such as the genetic algorithm (GA), tabu search (TS), simulated annealing (SA) and particle swarm optimization (PSO). The comparisons of the performance include three error measures, four performance metrics, the Pareto front and computational time. A nonparametric statistical analysis, using the Sign test and Wilcoxon signed rank test, is also performed, to demonstrate the superiority of the NS-MOPSO algorithm. On examining the performance metrics, it is observed that the proposed NS-MOPSO approach is capable of identifying good Pareto solutions, maintaining adequate diversity. The proposed algorithm is also applied to different cardinality constraint conditions, for six different market indices, such as the Hang-Seng in Hong Kong, DAX 100 in Germany, FTSE 100 in UK, S&P 100 in USA, Nikkei 225 in Japan, and BSE-500 in India.