A credibilistic mean-semivariance-PER portfolio selection model for Latin America
Abstract
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.
Keyword : fuzzy portfolio selection, credibility theory, L-R power fuzzy numbers, mean-semi- variance-PER, evolutionary multiobjective optimization
How to Cite
García, 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. https://doi.org/10.3846/jbem.2019.8317
This work is licensed under a Creative Commons Attribution 4.0 International License.
References
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Huang, X. (2009). A review of credibilistic portfolio selection. Fuzzy Optimization and Decision Making, 8(3), 263-281. https://doi.org/10.1007/s10700-009-9064-3
Huang, X. (2010). Portfolio analysis, from probabilistic to credibilistic and uncertain approaches (Vol. 250). Berlin, Heidelberg: Springer-Verlag. https://doi.org/10.1007/978-3-642-11214-0
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Liagkouras, K., & Metaxiotis, K. (2015). Efficient portfolio construction with the use of multiobjective evolutionary algorithms: best practices and performance metrics. International Journal of Information Technology & Decision Making, 14(3), 535-564. https://doi.org/10.1142/S0219622015300013
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Liu, B., & Liu, Y. K. (2002). Expected value of fuzzy variable and fuzzy expected value models. IEEE Transactions on Fuzzy Systems, 10(4), 445-450. https://doi.org/10.1109/TFUZZ.2002.800692
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Barak, S., Abessi, M., & Modarres, M. (2013). Fuzzy turnover rate chance constraints portfolio model. European Journal of Operational Research, 228(1), 141-147. https://doi.org/10.1016/j.ejor.2013.01.036
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Chang, T. J., Meade, N., Beasley, J. E., & Sharaiha, Y. M. (2000). Heuristics for cardinality constrained portfolio optimisation. Computers & Operations Research, 27(13), 1271-1302. https://doi.org/10.1016/S0305-0548(99)00074-X
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De Oliveira, F. A., Nobre, C. N., & Zárate, L. E. (2013). Applying Artificial Neural Networks to prediction of stock price and improvement of the directional prediction index – Case study of PETR4, Petrobras, Brazil. Expert Systems with Applications, 40(18), 7596-7606. https://doi.org/10.1016/j.eswa.2013.06.071
Deb, K., Agrawal, K., Pratap, A., & Meyarivan, T. (2002). A Fast Elitist Non-dominated Sorting Genetic Algorithm for Multi-objective Optimization: NSGA-II. IEEE Transactions on Evolutionary Computation, 6(2), 182-197. https://doi.org/10.1109/4235.996017
Dubois, D. J., & Prade, H. (1980). Fuzzy sets and systems: theory and applications (Vol. 144). New York: Academic Press.
Dubois, D. J., & Prade, H. (1987). Fuzzy numbers: an overview. In J. Bezdek (Ed.), Analysis of fuzzy information (pp. 3-39). Boca Raton: CRC Press.
Fang, Y., Chen, L., & Fukushima, M. (2008). A mixed R&D projects and securities portfolio selection model. European Journal of Operational Research, 185(2), 700-715. https://doi.org/10.1016/j.ejor.2007.01.002
Fishburn, P. C. (1977). Mean-risk analysis with risk associated with below-target returns. The American Economic Review, 67(2), 116-126.
García, 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. https://doi.org/10.3846/16111699.2012.668859
García, F., Guijarro, F., & Oliver, J. (2018). Index tracking optimization with cardinality constraint: a performance comparison of genetic algorithms and tabu search heuristics. Neural Computing and Applications, 30(8), 2625-2641. https://doi.org/10.1007/s00521-017-2882-2
Gerritsen, D. F. (2016). Are chartists artists? The determinants and profitability of recommendations based on technical analysis. International Review of Financial Analysis, 47, 179-196. https://doi.org/10.1016/j.irfa.2016.06.008
Gupta, P., Mehlawat, M. K., Inuiguchi, M., & Chandra, S. (2014a). Portfolio optimization using credibility. In Fuzzy Portfolio optimization. Studies in fuzziness and soft computing (Vol. 316, pp. 127-160). Berlin Heidelberg: Springer-Verlag. https://doi.org/10.1007/978-3-642-54652-5_5
Gupta, P., Mehlawat, M. K., Inuiguchi, M., & Chandra, S. (2014b). Portfolio optimization with interval coefficients. In Fuzzy portfolio optimization. Studies in fuzziness and soft computing (Vol. 316, pp. 33-59). Berlin, Heidelberg: Springer-Verlag. https://doi.org/10.1007/978-3-642-54652-5_2
Gupta, P., Mittal, G., & Mehlawat, M. K. (2013). Expected value multiobjective portfolio rebalancing model with fuzzy parameters. Insurance: Mathematics and Economics, 52(2), 190-203. https://doi.org/10.1016/j.insmatheco.2012.12.002
Gupta, P., Mittal, G., & Mehlawat, M. K. (2014). A multicriteria optimization model of portfolio rebalancing with transaction costs in fuzzy environment. Memetic Computing, 6(1), 61-74. https://doi.org/10.1007/s12293-012-0102-2
Huang, X. (2006). Fuzzy chance-constrained portfolio selection. Applied Mathematics and Computation, 177(2), 500-507. https://doi.org/10.1016/j.amc.2005.11.027
Huang, X. (2008). Mean-semivariance models for fuzzy portfolio selection. Journal of Computational and Applied Mathematics, 217(1), 1-8. https://doi.org/10.1016/j.cam.2007.06.009
Huang, X. (2009). A review of credibilistic portfolio selection. Fuzzy Optimization and Decision Making, 8(3), 263-281. https://doi.org/10.1007/s10700-009-9064-3
Huang, X. (2010). Portfolio analysis, from probabilistic to credibilistic and uncertain approaches (Vol. 250). Berlin, Heidelberg: Springer-Verlag. https://doi.org/10.1007/978-3-642-11214-0
Inuiguchi, M., Ichihashi, H., & Tanaka, H. (1990). Fuzzy programming: a survey of recent developments. In R. Slowinski & J. Teghem (Eds.), Stochastic versus fuzzy approaches to multiobjective mathematical programming under uncertainty (Vol. 6, pp. 45-68). Dordrecht: Springer-Verlag. https://doi.org/10.1007/978-94-009-2111-5_4
Jalota, H., Thakur, M., & Mittal, G. (2017a). A credibilistic decision support system for portfolio optimization. Applied Soft Computing, 59, 512-528. https://doi.org/10.1016/j.asoc.2017.05.054
Jalota, H., Thakur, M., & Mittal, G. (2017b). Modelling and constructing membership function for uncertain portfolio parameters: A credibilistic framework. Expert Systems with Applications, 71, 40-56. https://doi.org/10.1016/j.eswa.2016.11.014
León, T., & Vercher, E. (2004). Solving a class of fuzzy linear programs by using semi-infinite programming techniques. Fuzzy Sets and Systems, 146(2), 235-252. https://doi.org/10.1016/j.fss.2003.09.010
Li, B., Zhu, Y., Sun, Y., Aw, G., & Teo, K. L. (2018). Multi-period portfolio selection problem under uncertain environment with bankruptcy constraint. Applied Mathematical Modelling, 56, 539-550. https://doi.org/10.1016/j.apm.2017.12.016
Liagkouras, K., & Metaxiotis, K. (2015). Efficient portfolio construction with the use of multiobjective evolutionary algorithms: best practices and performance metrics. International Journal of Information Technology & Decision Making, 14(3), 535-564. https://doi.org/10.1142/S0219622015300013
Liu, B. (2004). Uncertainty theory: an introduction to its axiomatic foundations (Vol. 154). Berlin, Heidelberg: Springer-Verlag. https://doi.org/10.1007/978-3-540-39987-2
Liu, B. (2007). Uncertainty theory an introduction to its axiomatic foundations (2nd ed.). Berlin, Heidelberg: Springer-Verlag.
Liu, B., & Liu, Y. K. (2002). Expected value of fuzzy variable and fuzzy expected value models. IEEE Transactions on Fuzzy Systems, 10(4), 445-450. https://doi.org/10.1109/TFUZZ.2002.800692
Lwin, K., Qu, R., & Kendall, G. (2014). A learning-guided multi-objective evolutionary algorithm for constrained portfolio optimization. Applied Soft Computing, 24, 757-772. https://doi.org/10.1016/j.asoc.2014.08.026
Markowitz, H. (1952). Portfolio Selection. The Journal of Finance, 7(1), 77-91. https://doi.org/10.1111/j.1540-6261.1952.tb01525.x
Markowitz, H. (1959). Portfolio selection: efficient diversification of investments. New York: John Wiley & Sons, Inc.
Markowitz, 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. https://doi.org/10.1007/BF02282055
Masa’deh, R., Tayeh, M., Al-Jarrah, I. M., & Tarhini, A. (2015). Accounting vs. market-based measures of firm performance related to information technology investments. International Review of Social Sciences and Humanities, 9(1), 129-145.
Metaxiotis, K., & Liagkouras, K. (2012). Multiobjective Evolutionary Algorithms for portfolio management: a comprehensive literature review. Expert Systems with Applications, 39(14), 11685-11698. https://doi.org/10.1016/j.eswa.2012.04.053
Morgan, J. P. (1996). Riskmetrics technical document (4th ed.). New York: Morgan Guaranty Trust Company of New York.
Narkunienė, J., & Ulbinaitė, A. (2018). Comparative analysis of company performance evaluation methods. Entrepreneurship and Sustainability Issues, 6(1), 125-138. https://doi.org/10.9770/jesi.2018.6.1(10)
Omidi, F., Abbasi, B., & Nazemi, A. (2017). An efficient dynamic model for solving a portfolio selection with uncertain chance constraint models. Journal of Computational and Applied Mathematics, 319, 43-55. https://doi.org/10.1016/j.cam.2016.12.020
Pouya, A. R., Solimanpur, M., & Rezaee, M. J. (2016). Solving multi-objective portfolio optimization problem using invasive weed optimization. Swarm and Evolutionary Computation, 28, 42-57. https://doi.org/10.1016/j.swevo.2016.01.001
Rockafellar, R. T., & Uryasev, S. (2000). Optimization of conditional value-at-risk. Journal of Risk, 2(3), 21-41. https://doi.org/10.21314/JOR.2000.038
Saborido, R., Ruiz, A. B., Bermúdez, J. D., Vercher, E., & Luque, M. (2016). Evolutionary multi-objective optimization algorithms for fuzzy portfolio selection. Applied Soft Computing, 39, 48-63. https://doi.org/10.1016/j.asoc.2015.11.005
Schmitt, N., & Westerhoff, F. (2017). On the bimodality of the distribution of the S&P 500’s distortion: Empirical evidence and theoretical explanations. Journal of Economic Dynamics and Control, 80, 34-53. https://doi.org/10.1016/j.jedc.2017.05.002
Shen, K.-Y., Yan, M.-R., & Tzeng, G.-H. (2014). Combining VIKOR-DANP model for glamor stock selection and stock performance improvement. Knowledge-Based Systems, 58, 86-97. https://doi.org/10.1016/j.knosys.2013.07.023
Sobreiro, V. A., Cruz Cacique da Costa, T. R., Farias Nazário, R. T., Lima e Silva, J., Moreira, E. A., Lima Filho, M. C., … Arismendi Zambrano, J. C. (2016). The profitability of moving average trading rules in BRICS and emerging stock markets. The North American Journal of Economics and Finance, 38, 86-101. https://doi.org/10.1016/j.najef.2016.08.003
Speranza, M. (1993). Linear programming models for portfolio optimization. Finance, 14, 107-123.
Torre, A., & Schmukler, S. (2007). Emerging Capital markets and globalization. The Latin American experience. Washington: Stanford University Press & World Bank.
Vercher, E., & Bermúdez, J. D. (2012). Fuzzy Portfolio selection models: a numerical study. In M. Doumpos, C. Zopounidis, & P. M. Pardalos (Eds.), Springer optimization and its applications (Vol. 70, pp. 253-280). Boston, MA: Springer. https://doi.org/10.1007/978-1-4614-3773-4_10
Vercher, E., & Bermúdez, J. D. (2013). A Possibilistic mean-downside risk-skewness model for efficient portfolio selection. IEEE Transactions on Fuzzy Systems, 21(3), 585-595. https://doi.org/10.1109/TFUZZ.2012.2227487
Vercher, E., & Bermúdez, J. D. (2015). Portfolio optimization using a credibility mean-absolute semi-deviation model. Expert Systems with Applications, 42(20), 7121-7131. https://doi.org/10.1016/j.eswa.2015.05.020
Vercher, E., Bermúdez, J. D., & Segura, J. V. (2007). Fuzzy portfolio optimization under downside risk measures. Fuzzy Sets and Systems, 158(7), 769-782. https://doi.org/10.1016/j.fss.2006.10.026
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