Document Type : Original Article

Authors

School of Industrial Engineering, Iran University of Science and Technology, Tehran, Iran

Abstract

In this study, a multi-stage stochastic portfolio selection procedure is proposed. Specifically, to deal with market uncertainty, a three-pronged goal and a Wealth-Mean absolute semi deviation-Liquidity (WML) portfolio selection model based on a scenario tree are developed. Due to duration, continuity of the horizon, and uncertainty, the scenario tree is an ideal tool for modeling multi-period portfolio problems. Wealth, risk, asset investment threshold, transaction cost, and liquidity are important variables for the problem under investigation. This study uses rebalancing and mean absolute semi-deviation as measures of portfolio risk. A Node-Based Modelling (NBM) method is used to develop effective investment strategies for the long-term investment horizon. In addition, using a goal programming approach, the investigated multi-objective model converts to a single-objective model. To demonstrate the effectiveness of the proposed model, a real-world empirical application with data set from a Tehran stock market (TSE) is carried out. The experimental findings indicate the applicability of the developed model. 

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Carino, D. R., Kent, T., Myers, D. H., Stacy, C., Sylvanus, M., Turner, A. L. and Watanabe, K. (n.d.). és Ziemba, W. T. (1994). Russell-Yasuda Kasai model: An asset/liability model for a japanese insurance company using multistage stochastic programming. Interfaces, 24(1), 24-49.
Charnes, A. and Cooper, W. W. (1977). Goal programming and multiple objective optimizations: Part 1. European Journal of Operational Research, 1(1), 39-54.
Chen, Z., Liu, J., Li, G. and Yan, Z. (2016). Composite time-consistent multi-period risk measure and its application in optimal portfolio selection. Top, 24(3), 515-540.
Chung, K. H. and Zhang, H. (2014). A simple approximation of intraday spreads using daily data. Journal of Financial Markets, 17(1), 94-120. 
Dupačová, J. (1999). Portfolio optimization via stochastic programming: Methods of output analysis. Mathematical Methods of Operations Research, 50, 245-270.
Edirisinghe, N. C. P. and Patterson, E. I. (2007). Multi-period stochastic portfolio optimization: Block-separable decomposition. Annals of Operations Research, 152(1), 367-394.
Fong, K. Y. L., Holden, C. W. and Trzcinka, C. A. (2017). What are the best liquidity proxies for global research? Review of Finance, 21(4), 1355-1401.
Gülpinar, N. and Rustem, B. (2007). Worst-case robust decisions for multi-period mean-variance portfolio optimization. European Journal of Operational Research, 183, 981-1000.
Gupta, P., Mehlawat, M. K., Yadav, S. and Kumar, A. (2019). A polynomial goal programming approach for intuitionistic fuzzy portfolio optimization using entropy and higher moments. Applied Soft Computing, 85, 105781.
Hibiki, N. (2006). Multi-period stochastic optimization models for dynamic asset allocation. Journal of Banking & Finance, 30(2), 365-390.
Ji, R. and Lejeune, M. A. (2018). Risk-budgeting multi-portfolio optimization with portfolio and marginal risk constraints. Annals of Operations Research, 262(2), 547-578.
Kall, P., Wallace, S. W. and Kall, P. (1994). Stochastic Programming. Springer.
Liu, J. and Chen, Z. (2018). Time consistent multi-period robust risk measures and portfolio selection models with regime-switching. European Journal of Operational Research, 268(1), 373-385.
Ma, R., Anderson, H. D. and Marshall, B. R. (2018). Stock market liquidity and trading activity: Is China different? International Review of Financial Analysis, 56, 32-51
Markowitz, H. (1952). Portfolio selection. The Journal of Finance, 7(1), 77-91.
Markowitz, H. M. and Todd, G. P. (2000). Mean-variance Analysis in Portfolio Choice and Capital Markets. Vol. 66, John Wiley & Sons.
Mehlawat, M. K., Gupta, P. and Khan, A. Z. (2021). Portfolio optimization using higher moments in an uncertain random environment. Information Sciences, 567, 348-374.
Mohebbi, N. and Najafi, A. A. (2018). Credibilistic multi-period portfolio optimization based on scenario tree. Physica A: Statistical Mechanics and Its Applications, 492, 1302-1316.
Mulvey, J. M., Rosenbaum, D. P. and Shetty, B. (1997). Strategic financial risk management and operations research. European Journal of Operational Research, 97(1), 1-16.
Mulvey, J. M. and Shetty, B. (2004). Financial planning via multi-stage stochastic optimization. Computers and Operations Research, 31(1), 1-20.  
Mulvey, J. M. and Vladimirou, H. (1989). Stochastic network optimization models for investment planning. Annals of Operations Research, 20(1), 187-217.
Mulvey, J. M. and Ziemba, W. T. (1995). Asset and liability allocation in a global environment. Handbooks in Operations Research and Management Science, 9, 4350-463.
Najafi, A. A. and Mushakhian, S. (2015). Multi-stage stochastic mean-semivariance-CVaR portfolio optimization under transaction costs. Applied Mathematics and Computation, 256, 445-458.
Nesaz, H. H., Jasemi, M. and Monplaisir, L. (2020). A new methodology for multi-period portfolio selection based on the risk measure of lower partial moments. Expert Systems with Applications, 144, 113032.
Nouri, M. and Mohammadi, E. (2018). Portfolio optimization using chance constrained compromise programming. Financial Engineering and Portfolio Management, 9(35), 221-241.
Nouri, M., Mohammadi, E. and Rahmanipour, M. (2019). A novel efficiency ranking approach based on goal programming and data envelopment analysis for the evaluation of iranian banks. International Journal of Data Envelopment Analysis, 7(1), 57-80.
Patel, N. R. and Subrahmanyam, M. G. (1982). A simple algorithm for optimal portfolio selection with fixed transaction costs. Management Science, 28(3), 303-314.
Peykani, P., Namakshenas, M., Nouri, M., Kavand, N. and Rostamy-Malkhalifeh, M. (2022). A possibilistic programming approach to portfolio optimization problem under fuzzy data. In: Advances in Econometrics, Operational Research, Data Science and Actuarial Studies: Techniques and Theories, 377-387.
Peykani, P., Nouri, M., Eshghi, F., Khamechian, M. and Farrokhi-Asl, H. (2021). A novel mathematical approach for fuzzy multi-period multi-objective portfolio optimization problem under uncertain environment and practical constraints. Journal of Fuzzy Extension and Applications, 2(3), 191-203.
Peykani, P., Nouri, M. and Farrokhi-Asl, H. (2021). Uncertain multi-period portfolio management under fuzzy environment: an alpha-cut method. 3th international conference on recent innovation in industrial engineering & mechanichal engineering.
Pinar, M. Ç. (2007). Robust scenario optimization based on downside-risk measure for multi-period portfolio selection. OR Spectrum, 29(2), 295-309.
Tuncer Şakar, C. and Köksalan, M. (2013). A stochastic programming approach to multicriteria portfolio optimization. Journal of Global Optimization, 57, 299-314.
Ziemba, W. T., Ziemba, W. T., Mulvey, J. M., Moffatt, H. K. and Mulvey, J. M. (1998). Worldwide Asset and Liability Modeling. Vol. 10, Cambridge University Press.
Yu, G. F., Li, D. F., Liang, D. C. and Li, G. X. (2021). An intuitionistic fuzzy multi-objective goal programming approach to portfolio selection. International Journal of Information Technology & Decision Making, 20(05), 1477-1497.