Applying the Relative Robust Approach for Selection of Optimal Portfolio in the Tehran Stock Exchange by Second-order Conic Programming

Document Type : Research Paper

Authors

1 Prof., Department of Finance, Faculty of Management, University of Tehran, Tehran, Iran.

2 Assistant Prof., Department of Finance, Faculty of Management, University of Tehran, Tehran, Iran.

3 MSc., Department of Finance, Faculty of Management, University of Tehran, Tehran, Iran.

Abstract

Objective: The purpose of this study was to apply the relative robust approach that minimizes the maximum regret to deal with the present uncertainty in the input data of the Markowitz mean-variance portfolio optimization model by reconstructing that model as a second-order conic program. Regret is defined as the difference between the obtained solution and the optimal solution under a specified input data set. This approach uses scenarios to consider the present uncertainty in the input data. Moreover, the robust portfolio optimization model introduced by Bertsimas and Sim, which considers uncertainty as an interval, was used to be compared with the relative robust approach and the Markowitz model.
Methods: In this research, the return of 50 more active stocks of the Tehran Stock Exchange (TSE) was used to obtain the optimal portfolio using the minimax regret method based on the Markowitz Model. Then, using the out-of-sample Sharpe criterion, the results of the minimax regret method were compared with the classic methods.
Results: Based on the research findings, the relative robust approach in the out-of-sample test on most corresponding points of the efficient frontier showed better performance in comparison with the Markowitz model. Also, the Bertsimas and sim approach delivered better performance than the Markowitz model in the out-of-sample test. The results did not prove any significant difference for out-of-sample outputs between the relative robust and Bertsimas and sim approaches.
Conclusion: According to the obtained results, the relative robust approach can surpass the mean-variance approach for investors with almost all levels of risk-return preferences. The approach presented in this research can provide investors with a new risk criterion that can be considered in choosing the optimal portfolio. Furthermore, the results confirmed that investors act indifferently in choosing between the relative robust solution and the solution of Bertsimas and Sim's approach. This method can be applied as a portfolio optimization approach and also different markets can be considered under this technique to have a better understanding of its capability.

Keywords

References

Bagheri Naghneh, A., Davoodi, S. M., & Mirsalehi Borojeni, V. (2020, September). Optimize the relative strength of the portfolio portfolio by taking into account the regret criteria. Paper presented at the second International Conference on innovations in Bussiness administration and Economics, Tehran, Iran. (in Persian)
Bertsimas, D., & Sim, M. (2004). The price of robustness. Operations research, 52(1), 35-53.
Bertsimas, D., & Thiele, A. (2006). Robust and Data-Driven Optimization: Modern Decision Making Under Uncertainty. Models, Methods, and Applications for Innovative Decision Making, (March), 95-122.
Caçador, S. C., Godinho, P. M. C., & Dias, J. M. P. C. M. (2020). A minimax regret portfolio model based on the investor’s utility loss. Operational Research, 22, 449-484.
Caçador, S., Dias, J. M., & Godinho, P. (2021). Portfolio selection under uncertainty: a new methodology for computing relative‐robust solutions. International Transactions in Operational Research, 28(3), 1296-1329.
Cornuejols, G., Pena, J., & Tütüncü, R. (2018). Optimization methods in finance (2th Ed.). Cambridge University Press.
Didar, H., & Beiki, K. (2017). Reviewing the Effect of Corporate Governance Quality on Relationship between Capital Structure and Additional Return on Companies Listed in Tehran Stock Exchang. Journal of the Iranian Accounting and Auditing Review, 24(2), 197-220. (in Persian)
Eslami-Bidgoli, G., & Sarenj, A. (2009). Portfolio Selection Using Return Mean, Return Standard Deviation and Liquidity in Tehran Stock Exchange. Journal of the Iranian Accounting and Auditing Review, 15(4), 3-16. (in Persian)
Fallahpour, S., & Tondnevis, F. (2014). Robust model for optimal portfolio selection. Investment science, 3(10), 67-84. (in Persian)
Hauser, R., Krishnamurthy, V., & Tütüncü, R. (2013). Relative robust portfolio optimization. arXiv preprint arXiv:1305.0144.
Kouvelis, P., & Yu, G. (1997). Robust Discrete Optimization and Its Applications. Springer Science & Business Media.
Li, J., & Wang, L. (2020). A minimax regret approach for robust multi-objective portfolio selection problems with ellipsoidal uncertainty sets. Computers & Industrial Engineering, 147, 106646.
Markowitz, H. (1952). Portfolio Selection. The Journal of Finance, 7(1), 77–91.
Mohammadi, S. E., & Mohammadi, E. (2018). Robust portfolio optimization based on minimax regret approach in Tehran stock exchange market. Journal of Industrial and Systems Engineering, 11(Special issue: 14th International Industrial Engineering Conference), 51-62.
MOSEK ApS. (2021, March 18). MOSEK Modeling Cookbook. Mosek. https://docs.mosek.com/modeling-cookbook/index.html
Mulvey, J. M., Vanderbei, R. J., & Zenios, S. A. (2008). Robust Optimization of Large-Scale Systems. Operations Research, 43(2), 264-281.
Raei, R. (2006). Risky Portfolio Selection through Neural Networks. Journal of the Iranian Accounting and Auditing Review, 13(4), 70-83. (in Persian)
Raei, R., & Hashemi, S. M. A. (2016). Robust Asset Allocation Based on Forecasts of Econometric Methods (ARMA & GARCH) and Uncertainty for Return & Covariance. Financial Research Journal, 18(3), 415-436. (in Persian)
Simões, G., McDonald, M., Williams, S., Fenn, D., & Hauser, R. (2018). Relative Robust Portfolio Optimization with benchmark regret. Quantitative Finance, 18(12), 1991–2003.
Soyster, A. L. (1973). Convex Programming with Set-Inclusive Constraints and Applications to Inexact Linear Programming. Operations Research, 21(5), 1154–1157.
Tütüncü, R. H., & Koenig, M. (2004). Robust asset allocation. Annals of Operations Research, 132(1), 157-187.
Xidonas, P., Hassapis, C., Soulis, J., & Samitas, A. (2017). Robust minimum variance portfolio optimization modelling under scenario uncertainty. Economic Modelling, 64, 60-71.
Xidonas, P., Mavrotas, G., Hassapis, C., & Zopounidis, C. (2017). Robust multiobjective portfolio optimization: A minimax regret approach. European Journal of Operational Research, 262(1), 299-305.
Financial Research Journal
Volume 24, Issue 2
2022
Pages 184-213

Files

Share

How to cite

Statistics