Characterizing Solution for Stock Portfolio Problem via Pythagorean Fuzzy Approach

Document Type: Research Article

Author

Faculty of Graduate Studies for Statistical Research, Cairo University, Giza, Egypt

Abstract

The portfolio optimization is one of the fundamental problems in asset management that aims to reduce the risk of an investment by diversifying it into assets expected to fluctuate independently. A portfolio is a grouping of financial assets such as stocks, bonds, commodities, currencies and cash equivalents, as well as their funds counterparts, including mutual, exchange- traded and closed funds. A portfolio can also consist of non-publicly tradable securities, like real estate, art, and private investment. This paper aims to study stock portfolio investment problem with pythagorean fuzzy numbers. After converting the problem into the corresponding crisp based on the score function, a solution procedure is suggested to give the decision of the portfolio investment combined with investors in savings and securities. The advantages of this study are: The investor is freely to choose the risk coefficients enable him/ her to maximize the expected returns; also he may determine his/ her strategies under consideration of his/ her own conditions. An example is introduce to clarify the practically and the efficiency of the technique.

Keywords


Ammar, E.E., and Khalifa, H.A. (2003). Fuzzy portfolio optimization: A quadratic programming approach. Chaos, Solitons, and Fractal, 18, 1042- 1054.

Ashrafzadeh, S., Moradzadehehfard, M., and Ohadi, F. (2016). Fuzzy optimal portfolio selection based on multi- objective mean- variance- skewness model by using NSGA- II algorithm. Bulletin de la Societe Royale des Sciences de Liege, 85, 1090- 1101.

Azizah, E., Ruyaman, E., and Supian, S. (2017). Optimization of investment portfolio weight of stocks affected by market index, IOP Conference Series: Materials Science and Engineering, 166, 012008. 

Banihashemi, S., Azarpour, A. M., and Kaveh, M. (2018). Multi- stage stochastic model in portfolio selection problem. Filomat, 32, 991- 1001.

Bermudez, J. P., Seguro, J. V., and Vercher, E. (2012). A Multiobjective genetic algorithm for cardinality constrained fuzzy portfolio selection. Fuzzy Sets and Systems, 188(1), 16- 26.

Chen, G., Luo, Z., Liao, X., and Yu, X., and Yang, L. (2011). Mean-variance- skewness fuzzy portfolio selection model based on intuitionistic fuzzy optimization. Procedia Engineering, 15, 2062- 2066.

Daryaei, A. A., Bajelan, A. A., and Khodayeki, M. (2019). The impact of stock traded- total value, foreign direct investment, number of students and fossil fuel energy consumption on No2 emissions in iran. Enviromental Energy and Economic Eesearch, 3(4), 335- 348.

Dubois, D., and Prade, H. (1980). Fuzzy Sets and Systems; Theory and Applications, Academic Press, New.

Elton, E. J., Gnuber, M. J., Brown, S. J., and Goetzmann, W. N.  (2009). Modern Portfolio Theory and Investment Analysis, John Wiley & Sons. 

Fakher, H- A., and Abedi, Z. (2017). Relationship between environmental quality and economic growth in developing countries (based on environmental performance index). Environmental Energy and Economic Research, 1(3), 299- 310.

Goldfarb, D., and Iyengar, G. (2003). Robust portfolio selection problems. Mathematics of Operations Research, 28, 1-38.

Huang, X., and Ying, H. (2013). Risk index based models for portfolio adjusting problem with returns subject to expert's evaluations. Economic Model, 30, 61- 66. 

Khalifa, H. A., and ZeinEldin, R. A. (2014). Fuzzy programming approach for portfolio selection problems with fuzzy coefficients. International Journal of Scientific Knowledge, 4(7), 40- 46.

Kumar Mishra, S., Panda, R., and Majhi, R. (2014). A comparative performance assessment of a set of multiobjective algorithms for constrained portfolio assets selection. Swarm and Evolutionary Computation, 16, 38- 51.

Li, D., and Ng, W. L. (2000). Optimal dynamic portfolio selection: multi period mean- variance formulation. Mathematical of Finance, 10, 387- 406.

Li, X., and Qin, Z. (2014). Interval portfolio selection models within the framework of uncertainty theory. Economic Modeling, 41, 338- 344.

Lindberg, C. (2009). Portfolio optimization when expected stock returns are determined by exposure to risk. Bernoulli, 15, 464- 474.

Liu, Y., and Qin, Z. (2012). Mean semi- absolute deviation model for uncertain portfolio optimization problem. Journal of Uncertain Systems, 6, 299-307.

Luengo, E. A. (2010). Fuzzy mean-variance portfolio selection problems. AMO- Advanced Modelling and Optimization, 12(3), 399- 410.

Makhatabrafiei, F., and Fatahzadeh, M. A. (2013). Linear regression and multiobjective method to solve the portfolio selection problem, 9th International Conference of Industrial Engineering, Tehran, Iran.

Markowitz, H. (1952). Portfolio selection. Journal of Finance, 7, 77- 91. 

Nassif, L. N., Filho, J. C. S., and Nogueira, J. M. (2013). Project portfolio selection in public administration using fuzzy logic. Procedia- Social and Behavioral Sciences, 74, 41-50.

Ramli, S., and Jaama, S. H. (2019). Several extended mean- variance fuzzy portfolio selection models based on possibility theory. Journal of Physics: Conference Series, 1212012027.

Reformat, M. and Yager, R. R. (2014). Suggesting recommendations using Pythagorean fuzzy sets illustrated using Netflix movie data. In: Information Processing and Management of Uncertainty in Knowledge- Based Systems- 15th International Conference, IPMU, Montpellier, Finance, July 15- 19 Proceeding, Part I, pp. 546- 556.

Sardou, I. G., Nazari, A., Ghodsi, E., and Bagherzadeh, E. (2015). Optimal portfolio selection using multi- objective fuzzy- genetic method. International Journal of Econometrics and Financial Management, 3, 99-103.

Simamora, I., and Sashanti, R. (2013). Optimization of fuzzy portfolio considering stock returns and downside risk. International journal of Science and Research, 5, 141- 145.

Skrinjaric, T., and Sego, B.  (2018). Using Grey incidence analysis approach in portfolio selection, International Journal of Financial Studies, 7(1), 1-16.

Tian, M., Yan, S., and Tian, X. (2019). Discrete approximate iterative method for fuzzy investment portfolio based on transaction cost threshold constraint. Open Phys., 17, 41- 47.

Wang, J., and Kim, J. (2019). Applying least squares support vector machines to mean- variance portfolio analysis. Mathematical Problems in Engineering, Volume 2019, Article ID 4189683, 10 pages. 

Wei, H., Xia, B., Yang, Z., and Zhow, Z. (2019). Model and data- driven system portfolio selection based on value and risk, Applied Sciences, 9, 1657; doi: 10.3390/ app 9081657

Wei, Shu- Zhi, and Ye, Zhong- Xing, (2007). Multi period optimization portfolio with bankruptcy control in stochastic market, Applied Mathematics and Computation, 186, 414- 425. 

Wu, H., and Li, Z. (2011). Multi- period mean- variance portfolio selection with Markov regime switching and uncertain time- horizon. Journal of Systems Science and Complexity, 24, 140- 155.

Xu, J., and Li, J. (2002). A class of stochastic optimization problems with one quadratic& several linear objective functions and extended portfolio selection model. Journal of Computational and Applied Mathematics, 146, 99- 113.

Yager, R. R. (2014). Pythagorean membership grades in multicriteria decision-making. IEEE Transaction Fuzzy Systems, 22, 958- 965.

Yin, D. (2018). Application of interval valued fuzzy linear programming for stock portfolio optimization. Applied Mathematics, 9, 101- 113.

Zadeh, L. A., (1965). Fuzzy sets. Information Control, 8, 338- 353. 

Zhang, P., Gong, H., and Lan, W. (2016). Multi- period mean- absolute deviation fuzzy portfolio model with entropy constraints. Journal of Systems Science and Information, 4(5), 428- 443.