Uncertain Portfolio Selection with Background Risk and Liquidity Constraint

This paper discusses an uncertain portfolio selection problem with consideration of background risk and asset liquidity. In addition, the transaction costs are also considered. The security returns, background asset return, and asset liquidity are estimated by experienced experts instead of historical data. Regarding them as uncertain variables, a mean-risk model with background risk, liquidity, and transaction costs is proposed for portfolio selection and the crisp forms of the model are provided when security returns obey different uncertainty distributions. Moreover, for better understanding of the impact of background risk and liquidity on portfolio selection, some important theorems are proved. Finally, numerical experiments are presented to illustrate the modeling idea

Fuzzy portfolio model with different investor risk attitudes

[[abstract]]We propose a fuzzy portfolio model designed for efficient portfolio selection with respect to uncertain or vague returns. Although many researchers have studied the fuzzy portfolio model, no researcher has yet attempted a behavioral analysis of the investor in the fuzzy portfolio model. To address this problem, we examined investor risk attitudes—risk-averse, risk-neutral, or risk-seeking behaviors—to discover an efficient method for fuzzy portfolio selection. In this study, we relied on the advantages of possibilistic mean–standard deviation models that we believed would fit the risk attitudes of investors. Thus, we developed a fuzzy portfolio model that focuses on different investor risk attitudes so that fuzzy portfolio selection for investors who possess different risk attitudes can be achieved more easily. Finally, we presented a numerical example of a portfolio selection problem to illustrate ways to address problems presented by a variety of investor risk attitudes.[[notice]]補正完畢[[incitationindex]]SCI[[booktype]]紙

An Artificial Bee Colony Algorithm for Uncertain Portfolio Selection

Portfolio selection is an important issue for researchers and practitioners. In this paper, under the assumption that security returns are given by experts’ evaluations rather than historical data, we discuss the portfolio adjusting problem which takes transaction costs and diversification degree of portfolio into consideration. Uncertain variables are employed to describe the security returns. In the proposed mean-variance-entropy model, the uncertain mean value of the return is used to measure investment return, the uncertain variance of the return is used to measure investment risk, and the entropy is used to measure diversification degree of portfolio. In order to solve the proposed model, a modified artificial bee colony (ABC) algorithm is designed. Finally, a numerical example is given to illustrate the modelling idea and the effectiveness of the proposed algorithm

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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Forecasting the Environmental, Social, and Governance Rating of Firms by Using Corporate Financial Performance Variables: A Rough Set Approach. Sustainability, 12(8), 3324. doi:10.3390/su12083324García, González-Bueno, Oliver, & Riley. (2019). Selecting Socially Responsible Portfolios: A Fuzzy Multicriteria Approach. Sustainability, 11(9), 2496. doi:10.3390/su11092496García, F., González-Bueno, J., Oliver, J., & Tamošiūnienė, R. (2019). A CREDIBILISTIC MEAN-SEMIVARIANCE-PER PORTFOLIO SELECTION MODEL FOR LATIN AMERICA. Journal of Business Economics and Management, 20(2), 225-243. doi:10.3846/jbem.2019.8317García, F., Guijarro, F., & Moya, I. (2013). A MULTIOBJECTIVE MODEL FOR PASSIVE PORTFOLIO MANAGEMENT: AN APPLICATION ON THE S&P 100 INDEX. Journal of Business Economics and Management, 14(4), 758-775. doi:10.3846/16111699.2012.668859García, F., Guijarro, F., & Oliver, J. (2017). 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Efficient Portfolio Construction with the Use of Multiobjective Evolutionary Algorithms: Best Practices and Performance Metrics. International Journal of Information Technology & Decision Making, 14(03), 535-564. doi:10.1142/s0219622015300013Liu, B. (2004). Uncertainty Theory. Studies in Fuzziness and Soft Computing. doi:10.1007/978-3-540-39987-2Baoding Liu, & Yian-Kui Liu. (2002). Expected value of fuzzy variable and fuzzy expected value models. IEEE Transactions on Fuzzy Systems, 10(4), 445-450. doi:10.1109/tfuzz.2002.800692Liu, N., Chen, Y., & Liu, Y. (2018). Optimizing portfolio selection problems under credibilistic CVaR criterion. Journal of Intelligent & Fuzzy Systems, 34(1), 335-347. doi:10.3233/jifs-171298Liu, Y.-J., & Zhang, W.-G. (2018). Multiperiod Fuzzy Portfolio Selection Optimization Model Based on Possibility Theory. International Journal of Information Technology & Decision Making, 17(03), 941-968. doi:10.1142/s0219622018500190Mansour, N., Cherif, M. S., & Abdelfattah, W. (2019). Multi-objective imprecise programming for financial portfolio selection with fuzzy returns. Expert Systems with Applications, 138, 112810. doi:10.1016/j.eswa.2019.07.027Markowitz, H. (1952). PORTFOLIO SELECTION*. The Journal of Finance, 7(1), 77-91. doi:10.1111/j.1540-6261.1952.tb01525.xMarkowitz, H., Todd, P., Xu, G., & Yamane, Y. (1993). Computation of mean-semivariance efficient sets by the Critical Line Algorithm. Annals of Operations Research, 45(1), 307-317. doi:10.1007/bf02282055Martin, R. D., Rachev, S. (Zari), & Siboulet, F. (2003). Phi-alpha optimal portfolios and extreme risk management. Wilmott, 2003(6), 70-83. doi:10.1002/wilm.42820030619Mehlawat, M. K. (2016). Credibilistic mean-entropy models for multi-period portfolio selection with multi-choice aspiration levels. Information Sciences, 345, 9-26. doi:10.1016/j.ins.2016.01.042Mehlawat, M. K., Gupta, P., Kumar, A., Yadav, S., & Aggarwal, A. (2020). 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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. Helsinki: Academic Bookstore.Ballestero, E. (2005). Mean-semivariance efficient frontier: a downside risk model for portfolio selection. Applied Mathematical Finance, 12(1), 1–15.Ballestero, E., & Pla-Santamaria, D. (2004). Selecting portfolios for mutual funds. Omega, 32, 385–394.Ballestero, E., & Pla-Santamaria, D. (2005). Grading the performance of market indicators with utility benchmarks selected from Footsie: a 2000 case study. Applied Economics, 37, 2147–2160.Ballestero, E., Pérez-Gladish, B., Arenas-Parra, M., & Bilbao-Terol, A. (2009). Selecting portfolios given multiple Eurostoxx-based uncertainty scenarios: a stochastic goal programming approach from fuzzy betas. INFOR. Information Systems and Operational Research, 47(1), 59–70.Ben Abdelaziz, F., & Masri, H. (2005). Stochastic programming with fuzzy linear partial information on time series. European Journal of Operational Research, 162(3), 619–629.Ben Abdelaziz, F., Aouni, B., & El Fayedh, R. (2007). Multi-objective stochastic programming for portfolio selection. European Journal of Operational Research, 177(3), 1811–1823.Bermúdez, J. D., Segura, J. V., & Vercher, E. (2012). A multi-objective genetic algorithm for cardinality constrained fuzzy portfolio selection. Fuzzy Sets and Systems, 188, 16–26.Bilbao, A., Arenas, M., Jiménez, M., Pérez- Gladish, B., & Rodríguez, M. V. (2006). An extension of Sharpe’s single-index model: portfolio selection with expert betas. Journal of the Operational Research Society, 57(12), 1442–1451.Chang, T. J., Yang, S. Ch., & Chang, K. J. (2009). Portfolio optimization problems in different risk measures using genetic algorithm. IEEE Intelligent Systems & Their Applications, 36, 10529–10537.Haugen, R. A. (1997). Modern investment theory. Upper Saddle River: Prentice-Hall.Huang, H. J., Tzeng, G. H., & Ong, C. S. (2006). A novel algorithm for uncertain portfolio selection. Applied Mathematics and Computation, 173(1), 350–359.Konno, H., Waki, H., & Yuuki, A. (2002). Portfolio optimization under lower partial risk measures. Asia-Pacific Financial Markets, 9, 127–140.Lin, C. M., Huang, J. J., Gen, M., & Tzeng, G. H. (2006). Recurrent neural network for dynamic portfolio selection. Applied Mathematics and Computation, 175(2), 1139–1146.Markowitz, H. M. (1952). Portfolio selection. The Journal of Finance, 7, 77–91.Ong, C. S., Huang, J. J., & Tzeng, G. H. (2005). A novel hybrid model for portfolio selection. Applied Mathematics and Computation, 169(2), 1195–1210.Pendaraki, K., Doumpos, M., & Zopounidis, C. (2004). Towards a goal programming methodology for constructing equity mutual fund portfolios. Journal of Asset Management, 4(6), 415–428.Pérez-Gladish, B., Jones, D. F., Tamiz, M., & Bilbao-Terol, A. (2007). An interactive three-stage model for mutual funds portfolio selection. Omega, 35(1), 75–88.Pratt, J. W. (1964). 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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

Fuzzy portfolio model with fuzzy-input return rates and fuzzy-output proportions

[[abstract]]In the finance market, a short-term investment strategy is usually applied in portfolio selection in order to reduce investment risk; however, the economy is uncertain and the investment period is short. Further, an investor has incomplete information for selecting a portfolio with crisp proportions for each chosen security. In this paper we present a new method of constructing fuzzy portfolio model for the parameters of fuzzy-input return rates and fuzzy-output proportions, based on possibilistic mean–standard deviation models. Furthermore, we consider both excess or shortage of investment in different economic periods by using fuzzy constraint for the sum of the fuzzy proportions, and we also refer to risks of securities investment and vagueness of incomplete information during the period of depression economics for the portfolio selection. Finally, we present a numerical example of a portfolio selection problem to illustrate the proposed model and a sensitivity analysis is realised based on the results.[[notice]]補正完畢[[incitationindex]]SCI[[booktype]]紙

Characterizing compromise solutions for investors with uncertain risk preferences

[EN] The optimum portfolio selection for an investor with particular preferences was proven to lie on the normalized efficient frontier between two bounds defined by the Ballestero (1998) bounding theorem. A deeper understanding is possible if the decision-maker is provided with visual and quantitative techniques. Here, we derive useful insights as a way to support investor's decision-making through: (i) a new theorem to assess balance of solutions; (ii) a procedure and a new plot to deal with discrete efficient frontiers and uncertain risk preferences; and (iii) two quality metrics useful to predict long-run performance of investors.Work partially funded by projects Collectiveware TIN2015-66863-C2-1-R (MINECO/FEDER) and 2014 SGR 118Salas-Molina, F.; Rodriguez-Aguilar, JA.; Pla Santamaría, D. (2019). Characterizing compromise solutions for investors with uncertain risk preferences. Operational Research. 19(3):661-677. https://doi.org/10.1007/s12351-017-0309-6S661677193Amiri M, Ekhtiari M, Yazdani M (2011) Nadir compromise programming: a model for optimization of multi-objective portfolio problem. Expert Syst Appl 38(6):7222–7226Ballestero E (1998) Approximating the optimum portfolio for an investor with particular preferences. J Oper Res Soc 49:998–1000Ballestero E (2007) Compromise programming: a utility-based linear-quadratic composite metric from the trade-off between achievement and balanced (non-corner) solutions. Eur J Oper Res 182(3):1369–1382Ballestero E, Pla-Santamaria D (2004) Selecting portfolios for mutual funds. Omega 32(5):385–394Ballestero E, Pla-Santamaria D, Garcia-Bernabeu A, Hilario A (2015) Portfolio selection by compromise programming. In: Ballestero E, Pérez-Gladish B, Garcia-Bernabeu A (eds) Socially responsible investment. A multi-criteria decision making approach, vol 219. Springer, Switzerland, pp 177–196Ballestero E, Romero C (1996) Portfolio selection: a compromise programming solution. J Oper Res Soc 47(11):1377–1386Ballestero E, Romero C (1998) Multiple criteria decision making and its applications to economic problems. Kluwer Academic Publishers, BerlinBilbao-Terol A, Pérez-Gladish B, Arenas-Parra M, Rodríguez-Uría MV (2006) Fuzzy compromise programming for portfolio selection. Appl Math Comput 173(1):251–264Bravo M, Ballestero E, Pla-Santamaria D (2012) Evaluating fund performance by compromise programming with linear-quadratic composite metric: an actual case on the caixabank in spain. J Multi-Criteria Decis Anal 19(5–6):247–255Ehrgott M, Klamroth K, Schwehm C (2004) An MCDM approach to portfolio optimization. Eur J Oper Res 155(3):752–770Fawcett T (2006) An introduction to ROC analysis. Pattern Recognit Lett 27(8):861–874Hernández-Orallo J, Flach P, Ferri C (2013) ROC curves in cost space. Mach Learn 93(1):71–91Markowitz H (1952) Portfolio selection. J Finance 7(1):77–91Pla-Santamaria D, Bravo M (2013) Portfolio optimization based on downside risk: a mean-semivariance efficient frontier from dow jones blue chips. Ann Oper Res 205(1):189–201Ringuest JL (1992) Multiobjective optimization: behavioral and computational considerations. Springer Science & Business Media, BerlinSteuer RE, Qi Y, Hirschberger M (2007) Suitable-portfolio investors, nondominated frontier sensitivity, and the effect of multiple objectives on standard portfolio selection. Ann Oper Res 152(1):297–317Xidonas P, Mavrotas G, Krintas T, Psarras J, Zopounidis C (2012) Multicriteria portfolio management. Springer, BerlinYu P-L (1973) A class of solutions for group decision problems. Manag Sci 19(8):936–946Yu P-L (1985) Multiple criteria decision making: concepts, techniques and extensions. Plenum Press, BerlinZeleny M (1982) Multiple criteria decision making. McGraw-Hill, New Yor

The uncertain representation ranking framework for concept-based video retrieval

Concept based video retrieval often relies on imperfect and uncertain concept detectors. We propose a general ranking framework to define effective and robust ranking functions, through explicitly addressing detector uncertainty. It can cope with multiple concept-based representations per video segment and it allows the re-use of effective text retrieval functions which are defined on similar representations. The final ranking status value is a weighted combination of two components: the expected score of the possible scores, which represents the risk-neutral choice, and the scores’ standard deviation, which represents the risk or opportunity that the score for the actual representation is higher. The framework consistently improves the search performance in the shot retrieval task and the segment retrieval task over several baselines in five TRECVid collections and two collections which use simulated detectors of varying performance

Tri-Criterion Model for Constructing Low-Carbon Mutual Fund Portfolios: A Preference-Based Multi-Objective Genetic Algorithm Approach

[EN] Sustainable finance, which integrates environmental, social and governance criteria on financial decisions rests on the fact that money should be used for good purposes. Thus, the financial sector is also expected to play a more important role to decarbonise the global economy. To align financial flows with a pathway towards a low-carbon economy, investors should be able to integrate into their financial decisions additional criteria beyond return and risk to manage climate risk. We propose a tri-criterion portfolio selection model to extend the classical Markowitz's mean-variance approach to include investor's preferences on the portfolio carbon risk exposure as an additional criterion. To approximate the 3D Pareto front we apply an efficient multi-objective genetic algorithm called ev-MOGA which is based on the concept of epsilon-dominance. Furthermore, we introduce a-posteriori approach to incorporate the investor's preferences into the solution process regarding their climate-change related preferences measured by the carbon risk exposure and their loss-adverse attitude. We test the performance of the proposed algorithm in a cross-section of European socially responsible investments open-end funds to assess the extent to which climate-related risk could be embedded in the portfolio according to the investor's preferences.Hilario Caballero, A.; Garcia-Bernabeu, A.; Salcedo-Romero-De-Ávila, J.; Vercher, M. (2020). Tri-Criterion Model for Constructing Low-Carbon Mutual Fund Portfolios: A Preference-Based Multi-Objective Genetic Algorithm Approach. International Journal of Environmental research and Public Health. 17(17):1-15. https://doi.org/10.3390/ijerph17176324S1151717Morningstar Low Carbon Designationhttps://bit.ly/2SfAFUAKrueger, P., Sautner, Z., & Starks, L. T. (2020). 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Markowitz-based portfolio selection with minimum transaction lots, cardinality constraints and regarding sector capitalization using genetic algorithm. Expert Systems with Applications, 36(3), 5058-5063. doi:10.1016/j.eswa.2008.06.007Anagnostopoulos, K. P., & Mamanis, G. (2011). The mean–variance cardinality constrained portfolio optimization problem: An experimental evaluation of five multiobjective evolutionary algorithms. Expert Systems with Applications. doi:10.1016/j.eswa.2011.04.233Woodside-Oriakhi, M., Lucas, C., & Beasley, J. E. (2011). Heuristic algorithms for the cardinality constrained efficient frontier. European Journal of Operational Research, 213(3), 538-550. doi:10.1016/j.ejor.2011.03.030Meghwani, S. S., & Thakur, M. (2017). Multi-criteria algorithms for portfolio optimization under practical constraints. Swarm and Evolutionary Computation, 37, 104-125. doi:10.1016/j.swevo.2017.06.005Liagkouras, K., & Metaxiotis, K. (2016). A new efficiently encoded multiobjective algorithm for the solution of the cardinality constrained portfolio optimization problem. Annals of Operations Research, 267(1-2), 281-319. doi:10.1007/s10479-016-2377-zMetaxiotis, K., & Liagkouras, K. (2012). Multiobjective Evolutionary Algorithms for Portfolio Management: A comprehensive literature review. Expert Systems with Applications, 39(14), 11685-11698. doi:10.1016/j.eswa.2012.04.053Silva, Y. L. T. V., Herthel, A. B., & Subramanian, A. (2019). A multi-objective evolutionary algorithm for a class of mean-variance portfolio selection problems. Expert Systems with Applications, 133, 225-241. doi:10.1016/j.eswa.2019.05.018Chang, T.-J., Yang, S.-C., & Chang, K.-J. (2009). Portfolio optimization problems in different risk measures using genetic algorithm. Expert Systems with Applications, 36(7), 10529-10537. doi:10.1016/j.eswa.2009.02.062Liagkouras, K. (2019). 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