Multiobjective Approach to Portfolio Optimization in the Light of the Credibility Theory

[EN] The present research proposes a novel methodology to solve the problems faced by investors who take into consideration different investment criteria in a fuzzy context. The approach extends the stochastic mean-variance model to a fuzzy multiobjective model where liquidity is considered to quantify portfolio's performance, apart from the usual metrics like return and risk. The uncertainty of the future returns and the future liquidity of the potential assets are modelled employing trapezoidal fuzzy numbers. The decision process of the proposed approach considers that portfolio selection is a multidimensional issue and also some realistic constraints applied by investors. Particularly, this approach optimizes the expected return, the risk and the expected liquidity of the portfolio, considering bound constraints and cardinality restrictions. As a result, an optimization problem for the constraint portfolio appears, which is solved by means of the NSGA-II algorithm. This study defines the credibilistic Sortino ratio and the credibilistic STARR ratio for selecting the optimal portfolio. An empirical study on the S&P100 index is included to show the performance of the model in practical applications. The results obtained demonstrate that the novel approach can beat the index in terms of return and risk in the analyzed period, from 2008 until 2018.García García, F.; González-Bueno, J.; Guijarro, F.; Oliver-Muncharaz, J.; Tamosiuniene, R. (2020). Multiobjective Approach to Portfolio Optimization in the Light of the Credibility Theory. Technological and Economic Development of Economy (Online). 26(6):1165-1186. https://doi.org/10.3846/tede.2020.13189S11651186266Acerbi, C., & Tasche, D. (2002). On the coherence of expected shortfall. Journal of Banking & Finance, 26(7), 1487-1503. doi:10.1016/s0378-4266(02)00283-2Ahmed, A., Ali, R., Ejaz, A., & Ahmad, I. (2018). 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Portfolio optimization based on downside risk: a mean-semivariance ef¿cient frontier from Dow Jones blue chips

To create efficient funds appealing to a sector of bank clients, the objective of minimizing downside risk is relevant to managers of funds offered by the banks. In this paper, a case focusing on this objective is developed. More precisely, the scope and purpose of the paper is to apply the mean-semivariance efficient frontier model, which is a recent approach to portfolio selection of stocks when the investor is especially interested in the constrained minimization of downside risk measured by the portfolio semivariance. Concerning the opportunity set and observation period, the mean-semivariance efficient frontier model is applied to an actual case of portfolio choice from Dow Jones stocks with daily prices observed over the period 2005¿2009. From these daily prices, time series of returns (capital gains weekly computed) are obtained as a piece of basic information. Diversification constraints are established so that each portfolio weight cannot exceed 5 per cent. The results show significant differences between the portfolios obtained by mean-semivariance efficient frontier model and those portfolios of equal expected returns obtained by classical Markowitz mean-variance efficient frontier model. Precise comparisons between them are made, leading to the conclusion that the results are consistent with the objective of reflecting downside riskPla Santamaría, D.; Bravo Selles, M. (2013). Portfolio optimization based on downside risk: a mean-semivariance ef¿cient frontier from Dow Jones blue chips. Annals of Operations Research. 205(1):189-201. doi:10.1007/s10479-012-1243-xS1892012051Aouni, B. (2009). Multi-attribute portfolio selection: new perspectives. INFOR. Information Systems and Operational Research, 47(1), 1–4.Arenas, M., Bilbao, A., & Rodríguez, M. V. (2001). A fuzzy goal programming approach to portfolio selection. European Journal of Operational Research, 133, 287–297.Arrow, K. J. (1965). Aspects of the theory of risk-bearing. 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What is the cost of maximizing ESG performance in the portfolio selection strategy? The case of The Dow Jones Index average stocks

[EN] Portfolio selection is one of the main financial topics. The original portfolio selection problem dealt with the trade-off between return and risk, measured as the mean returns and the variance, respectively. For investors more variables other than return and risk are considered to select the stocks to be included in the portfolio. Nowadays, many investors include corporate social responsibility as one eligibility criterion. Additionally, other return and risk measures are being employed. All of this, together with further constraints such as portfolio cardinality, which mirror real-world demands by investors, have made the multicriteria portfolio selection problem to be NP-hard. To solve this problem, heuristics such as the non-dominated sorting genetic algorithm II have been developed. The aim of this paper is to analyse the trade-off between return, risk and corporate social responsibility. To this end, we construct pareto efficient portfolios using a fuzzy multicriteria portfolio selection model with real-world constraints. The model is applied on a set of 28 stocks which are constituents of the Dow Jones Industrial Average stock index. The analysis shows that portfolios scoring higher in corporate social responsibility obtain lower returns. As of the risk, the riskier portfolios are those with extreme (high or low) corporate social responsibility scores. Finally, applying the proposed portfolio selection methodology, it is possible to build investment portfolios that dominate the benchmark. That is, socially responsible portfolios, measured by ESG scores, must not necessarily be penalized in terms of return or risk.García García, F.; Gankova-Ivanova, T.; González-Bueno, J.; Oliver-Muncharaz, J.; Tamosiuniene, R. (2022). What is the cost of maximizing ESG performance in the portfolio selection strategy? The case of The Dow Jones Index average stocks. Enterpreneurship and Sustainability Issues. 9(4):178-192. https://doi.org/10.9770/jesi.2022.9.3(9)1781929

A credibilistic mean-semivariance-PER portfolio selection model for Latin America

Many real-world problems in the financial sector have to consider different objectives which are conflicting, for example portfolio selection. Markowitz proposed an approach to determine the optimal composition of a portfolio analysing the trade-off between return and risk. Nevertheless, this approach has been criticized for unrealistic assumptions and several changes have been proposed to incorporate investors’ constraints and more realistic risk measures. In this line of research, our proposal extends the mean-semivariance portfolio selection model to a multiobjective credibilistic model that besides risk and return, also considers the price-to-earnings ratio to measure portfolio performance. Uncertain future returns and PER ratio of each asset are approximated using L-R power fuzzy numbers. Furthermore, we consider budget, bound and cardinality constraints. To solve the constrained portfolio optimization problem, we use the algorithm NSGA-II. We assess the proposed approach generating a portfolio with shares included in the Latin American Integrated Market. Results show that this new approach is a good alternative to solve the portfolio selection problem when multiple objectives are considered

Strict Solution Method for Linear Programming Problem with Ellipsoidal Distributions under Fuzziness

This paper considers a linear programming problem with ellipsoidal distributions including fuzziness. Since this problem is not well-defined due to randomness and fuzziness, it is hard to solve it directly. Therefore, introducing chance constraints, fuzzy goals and possibility measures, the proposed model is transformed into the deterministic equivalent problems. Furthermore, since it is difficult to solve the main problem analytically and efficiently due to nonlinear programming, the solution method is constructed introducing an appropriate parameter and performing the equivalent transformations

An intelligent system for risk classification of stock investment projects

The proposed paper demonstrates that a hybrid fuzzy neural network can serve as a risk classifier of stock investment projects. The training algorithm for the regular part of the network is based on bidirectional incremental evolution proving more efficient than direct evolution. The approach is compared with other crisp and soft investment appraisal and trading techniques, while building a multimodel domain representation for an intelligent decision support system. Thus the advantages of each model are utilised while looking at the investment problem from different perspectives. The empirical results are based on UK companies traded on the London Stock Exchange

Moments and Semi-Moments for fuzzy portfolios selection

The aim of this paper is to consider the moments and the semi-moments (i.e semi-kurtosis) for portfolio selection with fuzzy risk factors (i.e. trapezoidal risk factors). In order to measure the leptokurtocity of fuzzy portfolio return, notions of moments (i.e. Kurtosis) kurtosis and semi-moments(i.e. Semi-kurtosis) for fuzzy port- folios are originally introduced in this paper, and their mathematical properties are studied. As an extension of the mean-semivariance-skewness model for fuzzy portfolio, the mean-semivariance-skewness- semikurtosis is presented and its four corresponding variants are also considered. We briefly designed the genetic algorithm integrating fuzzy simulation for our optimization models.Fuzzy moments, Credibility theory, Portfolios, Asset allocation, multi-objective optimization

Asset Allocation with Aversion to Parameter Uncertainty: A Minimax Regression Approach

This paper takes a minimax regression approach to incorporate aversion to parameter uncertainty into the mean-variance model. The uncertainty-averse minimax mean-variance portfolio is obtained by minimizing with respect to the unknown weights the upper bound of the usual quadratic risk function over a fuzzy ellipsoidal set. Beyond the existing approaches, our methodology offers three main advantages: first, the resulting optimal portfolio can be interpreted as a Bayesian mean-variance portfolio with the least favorable prior density, and this result allows for a comprehensive comparison with traditional uncertainty-neutral Bayesian mean-variance portfolios. Second, the minimax mean-variance portfolio has a shrinkage expression, but its performance does not necessarily lie within those of the two reference portfolios. Third, we provide closed form expressions for the standard errors of the minimax mean-variance portfolio weights and statistical significance of the optimal portfolio weights can be easily conducted. Empirical applications show that incorporating aversion to parameter uncertainty leads to more stable optimal portfolios that outperform traditional uncertainty-neutral Bayesian mean-variance portfolios.Asset allocation, estimation error, aversion to uncertainty, min-imax regression, Bayesian mean-variance portfolios, least favorable prior