Abstract
Short selling is one of the important financial vehicles for real investment activities. Most of the traditional fuzzy portfolio models are established without short selling, which cannot effectively guide investors to make profits when stock prices tend to fall. This paper aims to address the multi-period portfolio problem with short selling under fuzzy environment. To comprehensively consider the effect of short selling on the investment process, we propose three types of short selling constraints, i.e., total short selling proportion constraint, short selling cardinality constraint, and lower and upper bound constraint. Then, we establish a multi-period possibilistic mean-semi-variance portfolio selection model with multiple short selling constraints. Next, we design a multiple particle swarm optimization with simulated annealing to solve it. Finally, we illustrate the feasibility and effectiveness of the proposed model and algorithm via a numerical example using actual stock data. The results show that short selling has a significant impact on investment decisions, and our proposed model can help investors construct portfolio strategies with short selling to improve their investment return.
Similar content being viewed by others
References
Markowitz, H.: Portfolio selection. J. Financ. 7(1), 77–91 (1952)
Sharpe, W.F.: Capital asset price: a theory of market equilibrium under conditions of risk. J. Finance 19(3), 425–442 (1964)
Merton, R.C.: An analytic derivation of the efficient portfolio frontier. J. Financ. Quant. Anal. 7(4), 1851–1872 (1972)
Zhang, P., Dang, S.: The weighted lower and upper admissible mean downside semi-variance portfolio selection. Int. J. Fuzzy Syst. (2021). https://doi.org/10.1007/s40815-021-01055-4
Zadeh, L.A.: Fuzzy sets. Inform. Contr. 8(3), 338–353 (1965)
Huang, X.X.: A review of credibilistic portfolio selection. Fuzzy Optim. Decis. Ma. 8(3), 263–281 (2009)
Deng, X., Zhao, J., Li, Z.: Sensitivity analysis of the fuzzy mean-entropy portfolio model with transaction costs based on credibility theory. Int. J. Fuzzy Syst. 20(1), 209–218 (2017)
Mehlawat, M.K., Gupta, P., Kumar, A., Yadav, S., Aggarwal, A.: Multiobjective fuzzy portfolio performance evaluation using data envelopment analysis under credibilistic framework. IEEE Trans. Fuzzy Syst. 28(11), 2726–2737 (2020)
Kim, J.H., Kim, W.C., Fabozzi, F.J.: Portfolio selection with conservative short-selling. Financ. Res. Lett. 18, 363–369 (2016)
Zhang, M., Chen, P.: Mean–variance portfolio selection with regime switching under shorting prohibition. Oper. Res. Lett. 44(5), 658–662 (2016)
Dong, Y., Zheng, H.: Optimal investment of DC pension plan under short-selling constraints and portfolio insurance. Insur. Math. Econ. 85, 47–59 (2019)
Gómez, J.P., Sharma, T.: Portfolio delegation under short-selling constraints. Econ. Theory 28(1), 173–196 (2006)
Yu, J.R., Lee, W.Y.: Portfolio rebalancing model using multiple criteria. Eur. J. Oper. Res. 209(2), 166–175 (2011)
Gupta, P., Mehlawat, M.K., Kumar, A., Yadav, S., Aggarwal, A.: A credibilistic fuzzy DEA approach for portfolio efficiency evaluation and rebalancing toward benchmark portfolios using positive and negative returns. Int. J. Fuzzy Syst. 22(3), 824–843 (2020)
Khodamoradi, T., Salahi, M., Najafi, A.R.: Robust CCMV model with short selling and risk-neutral interest rate. Physica A 547, 124429 (2020)
Guo, S.N., Yu, L., Li, X., Kar, S.: Fuzzy multi-period portfolio selection with different investment horizons. Eur. J. Oper. Res. 254(3), 1026–1035 (2016)
Gupta, P., Mehlawat, M.K., Yadav, S., Kumar, A.: Intuitionistic fuzzy optimistic and pessimistic multi-period portfolio optimization models. Soft Comput. 24(7), 11931–11956 (2020)
Liu, Y.J., Zhang, W.G.: A multi-period fuzzy portfolio optimization model with minimum transaction lots. Eur. J. Oper. Res. 242(3), 933–941 (2015)
Liu, Y.J., Zhang, W.G.: Fuzzy portfolio selection model with real features and different decision behaviors. Fuzzy Optim. Decis. Ma. 17(3), 317–336 (2018)
Mehlawat, M.K.: Credibilistic mean-entropy models for multi-period portfolio selection with multi-choice aspiration levels. Inf. Sci. 345, 9–26 (2016)
Yang, X.Y., Liu, W.L., Chen, S.D., Zhang, Y.: A multi-period fuzzy mean-minimax risk portfolio model with investor’s risk attitude. Soft Comput. 25(4), 2949–2963 (2021)
Zhang, W.G., Liu, Y.J., Xu, W.J.: A possibilistic mean-semivariance-entropy model for multi-period portfolio selection with transaction costs. Eur. J. Oper. Res. 222(2), 341–349 (2012)
Liagkouras, K., Metaxiotis, K.: Multi-period mean-variance fuzzy portfolio optimization model with transaction costs. Eng. Appl. Artif. Intell. 67, 260–269 (2018)
Jia, T., Pan, Y., Liang, H., Lam, H.K.: Event-based adaptive fixed-time fuzzy control for active vehicle suspension systems with time-varying displacement constraint. IEEE Trans. Fuzzy Syst. (2021). https://doi.org/10.1109/TFUZZ.2021.3075490
Liu, P., Hendalianpour, A., Fakhrabadi, M., Feylizadeh, M.: Integrating IVFRN-BWM and goal programming to allocate the order quantity considering discount for green supplier. Int. J. Fuzzy Syst. (2021). https://doi.org/10.1007/s40815-021-01181-z
Pan, Y., Li, Q., Liang, H., Lam, H.K.: A novel mixed control approach for fuzzy systems via membership functions online learning policy. IEEE Trans. Fuzzy Syst. (2021). https://doi.org/10.1109/TFUZZ.2021.3130201
Carlsson, C., Robert, F., Péter, M.: A possibilistic approach to selecting portfolios with highest utility score. Fuzzy Sets Syst. 131(1), 13–21 (2002)
Chen, F.I., Tsaur, R.C.: Fuzzy portfolio selection using a weighted function of possibilistic mean and variance in business cycles. Int. J. Fuzzy Syst. 18(2), 151–159 (2016)
Chen, W., Xu, W.: A hybrid multiobjective bat algorithm for fuzzy portfolio optimization with real-world constraints. Int. J. Fuzzy Syst. 21(1), 291–307 (2019)
Tsaur, R.C., Chiu, C.L., Huang, Y.Y.: Guaranteed rate of return for excess investment in a fuzzy portfolio analysis. Int. J. Fuzzy Syst. 23(1), 94–106 (2020)
Gong, X., Yu, C., Min, L., Ge, Z.: Regret theory-based fuzzy multi-objective portfolio selection model involving DEA cross-efficiency and higher moments. Appl. Soft Comput. 100, 106958 (2021)
Mossin, J.: Optimal multiperiod portfolio policies. Core Discuss. Papers Rp 41(2), 215–229 (1968)
Li, C., Wu, Y., Lu, Z., Wang, J.: A multiperiod multiobjective portfolio selection model with fuzzy random returns for large scale securities data. IEEE Trans. Fuzzy Syst. 29(1), 59–74 (2021)
Guo, S.N., Ching, W.K., Li, W.K., Siu, T.K., Zhang, W.G.: Fuzzy hidden Markov-switching portfolio selection with capital gain tax. Expert Syst. Appl. 149(1), 113304 (2020)
Sadjadi, S.J., Seyedhosseini, S.M., Hassanlou, K.: Fuzzy multiperiod portfolio selection with different rates for borrowing and lending. Appl. Soft Comput. 11(4), 3821–3826 (2011)
Thi, H.A.L., Moeini, M.: Long-short portfolio optimization under cardinality constraints by difference of convex functions algorithm. J. Optim. Theory Appl. 161(1), 199–214 (2014)
Guerra, M.L., Stefanini, L.: Approximate fuzzy arithmetic operations using monotonic interpolations. Fuzzy Sets Syst. 150(1), 5–33 (2005)
Carlsson, C., Fullér, R.: On possibilistic mean value and variance of fuzzy numbers. Fuzzy Sets Syst. 122(2), 315–326 (2001)
Lin, C.C.: A weighted max-min model for fuzzy goal programming. Fuzzy Sets Syst. 142(3), 407–420 (2004)
Hendalianpour, A., Fakhrabadi, M., Sangari, M.S., Razmi, J.: A combined benders decomposition and Lagrangian relaxation algorithm for optimizing a multi-product, multi-level omni-channel distribution system. Int. J. Sci. Technol. (2020). https://doi.org/10.24200/SCi.2020.53644.3349.
Liu, P., Hendalianpour, A.: A branch & cut/metaheuristic optimization of financial supply chain based on input-output network flows: investigating the Iranian orthopedic footwear. Int. J. Fuzzy Syst. (2021). https://doi.org/10.3233/JIFS-201068
Vercher, E., José, D.: Fuzzy portfolio optimization under downside risk measures. Fuzzy Sets Syst. 158(7), 769–782 (2007)
Zhang, W.G., Wang, Y.L., Chen, Z.P., Nie, Z.K.: Possibilistic mean–variance models and efficient frontiers for portfolio selection problem. Inf. Sci. 177(13), 2787–2801 (2007)
Chang, E.C., Yan, L., Ren, J.: Short-selling, margin-trading, and price efficiency: evidence from the Chinese market. J. Bank Financ. 48, 411–424 (2012)
Acknowledgements
The work was supported by the National Natural Science Foundation of China (No. 71501049) and the Humanities and Social Science Foundation of the Ministry of Education of China (No. 21YJA630117).
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflicts of interest
The authors declare that they have no conflict of interest regarding the publication of this paper.
Rights and permissions
About this article
Cite this article
Yang, XY., Chen, SD., Liu, WL. et al. A Multi-period Fuzzy Portfolio Optimization Model with Short Selling Constraints. Int. J. Fuzzy Syst. 24, 2798–2812 (2022). https://doi.org/10.1007/s40815-022-01294-z
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s40815-022-01294-z