Robust Portfolio Optimization under Interval-valued Conditional Value-at-Risk (CVaR) Criterion in the Tehran Stock Exchange

Document Type : Research Paper

Authors

1 Associate Prof., Department of Industrial Engineering, Payame Noor University, Tehran, Iran.

2 Associate Prof., Department of Management and Accounting, Karaj Branch, Islamic Azad University, Karaj, Iran.

3 MSc., Department of Industrial Engineering, Payame Noor University, Tehran, Iran.

10.22059/frj.2023.351106.1007412

Abstract

Objective
Ever since Harry Markowitz's groundbreaking paper on the mean-variance model was published in 1952, numerous efforts have been dedicated to exploring the applications and advancements of classical models. Following the development of financial markets, active portfolio optimization has become one of the most important topics in finance. This study aimed to examine active portfolio management, a critical and delicate choice for investors, particularly concerning overall portfolio risk. The determination of an optimal stock portfolio that offers both a substantial return rate and controlled risk is consistently a subject of keen interest for analysts, investors, and even portfolio managers.
 
Methods
Many methods have been developed to measure investment risk, and the price of risky assets changes rapidly and randomly due to the complexity of the financial market. A random interval is a suitable tool for describing uncertainty with randomness and imprecision. Given the uncertainty in financial markets, this study used stochastic intervals to describe the returns of risky assets and the tail sequence risk, called the interval-valued conditional value at risk (ICVaR). The interval value in this model is an extension of the classic portfolio model, which can comprehensively reflect the complexity of the financial market and the risk-taking behavior of investors.
 
Results
Following the findings from the real data of 10 out of 30 large corporates listed on the Tehran Stock Exchange, the ICVaR model is interpretable and compatible with the practical scenario and can be used to choose the optimal portfolio at different levels of risk and depending on the risk-taking degree of the investor. The present study used the portfolio optimization approach under a new criterion of ICVaR through the closing price, the highest price, and the lowest price on each trading day. In this model, the return range of the risky asset is taken as a random variable with an interval value. Besides, CVaR with an interval value is used to describe the risk instead of the variance at a certain level of return.
 
Conclusion
Uncertainties induced by asset transactions affect the predictions of investment plans. To address such challenging uncertainties in this study, a stable stochastic optimization approach was presented based on the range of optimal solutions produced by the proposed model to determine different operational options. Finally, the model developed in this study showed that investors’ subjective risk preference or aversion can be described by observing the principle of portfolio diversification, which reflects an innovation different from the classic portfolio model. Furthermore, the worst possible case was optimized in all scenarios in the model by robust optimization. The findings indicated that a narrower range corresponds to a higher level of risk aversion among investors.

Keywords

Main Subjects

References

 
Ahmadi, S., Lotfi, H., Rajabi, V. (2020). Determine the optimal portfolio weights var-stock approach And compare it with the Markowitz model. Financial Engineering and Portfolio Management, 11(45), 571-586. (in Persian)
Ben-Tal, A., & Nemirovski, A. (2000). Robust solutions of linear programming problems contaminated with uncertain data. Mathematical Programming, (88), 411-424.
Bertsimas, D., & Sym, M. (2004). The Price of the Robustness. Operations Research, (52), 35-53.
Bodnar, T., Lindholm, M., Niklasson, V., & Thorsén, E. (2022). Bayesian portfolio selection using VaR and CVaR. Applied Mathematics and Computation, 427, 127120.‏
Dai, Z., & Wang, F. (2019). Sparse and robust mean–variance portfolio optimization problems. Physica A: Statistical Mechanics and its Applications, 523, 1371-1378.
Fakhar, M., Mahyarinia, M. R., & Zafarani, J. (2018). On nonsmooth robust multiobjective optimization under generalized convexity with applications to portfolio optimization. European Journal of Operational Research, 265(1), 39-48.‏
Rachev, S. & Fabozzi, F.G. (2018). Advanced stochastic models of risk assessment and portfolio optimization (Fakhrhosseini and Kaviani, Trans.). Tehran, Mehraban.
 (in Persian)
Gabrel, V., & Murat, C. (2018). Portfolio optimization with pw-robustness. EURO Journal on Computational Optimization, 6(3), 267-290.‏
Ghahtarani, A. (2021). A new portfolio selection problem in bubble condition under uncertainty: Application of Z-number theory and fuzzy neural network. Expert Systems with Applications, 177, 114944.‏
Giove, S., Funari, S. and Nardelli, C. (2006). An interval portfolio selection problem based on regret function. European Journal of Operational Research, 170(1): 253-264.
Gohania, E., Mansourfar, G., & Biglari, F. (2023). Interior point algorithm in multi-objective portfolio optimization: GlueVaR approach. Financial Research Journal. (in Persian)
Haddadi, M., Nademi, Y., Tafi, F. (2021). Stock Portfolio Optimization with MAD and CVaR Criteria by Comparing Classical and Metaheuristic Methods. Financial Engineering and Portfolio Management, 12(47), 514-533. (in Persian)
Hosseini-Nodeh, Z., Khanjani-Shiraz, R., & Pardalos, P. (2022). Distributionally robust portfolio optimization with second-order stochastic dominance based on wasserstein metric. Information Sciences, 613, 828-852.
Ida, M. (2003). Portfolio selection problem with interval coefficients. Applied Mathematics Letters, 16(5), 709-713.‏
Kara, E. K., & Kemaloglu, S. A. (2017). Risk Measures of the ERNB Distribution Generated by G-NB Family. Mathematical Sciences and Applications E-Notes, 5(1), 77-84.‏
Marty, W. (2022). Portfolio analysis (an introduction to risk and return measurement), (Kaviani, M and Fakhrhosseini, S. F., Trans.). Arvan Publications, Tehran. (in Persian)
Konno, H., & Yamazaki, H. (1991). Mean-absolute deviation portfolio optimization model and its applications to Tokyo stock market. Management science, 37(5), 519-531.‏
Li, Z., Zhang, J. & Wang, X. (2017). Interval-valued risk measure models and empirical analysis. Fuzzy Systems Association, International Conference on Soft Computing & Intelligent Systems. IEEE.
Lu, Z. (2011). Robust portfolio selection based on a joint ellipsoidal uncertainty set, Optimization Methods and Software, 26(1), 89–104.
Min, L., Dong, J., Liu, J. & Gong, X. (2021). Robust mean-risk portfolio optimization using machine learning-based trade-off parameter. Applied Soft Computing, 113, 107948.
Mulvey, J., Vanderberi, R., & Zenios, S. (1995). Robust Optimization of Large-Scale Systems. Operations research. Operations Research, 43, 264-281.
Plachel, L. (2019). A unified model for regularized and robust portfolio optimization. Journal of Economic Dynamics and Control, 109, 103779.
Raei, R., Basakha, H., & Mahdikhah, H. (2020). Equity Portfolio Optimization Using Mean-CVaR Method Considering Symmetric and Asymmetric Autoregressive Conditional Heteroscedasticity. Financial Research Journal, 22(2), 149-159. (in Persian)
Raei, R., Namaki, A., & Ahmadi, M. (2022). Applying the Relative Robust Approach for Selection of Optimal Portfolio in the Tehran Stock Exchange by Second-order Conic Programming. Financial Research Journal, 24(2), 184-213. (in Persian)
Sehgal, R. & Mehra, A. (2020). Robust portfolio optimization with second order stochastic dominance constraints. Computers & Industrial Engineering, 144, 106396.
Sharma, A., Utz, S. & Mehra, A. (2017). Omega-CVaR portfolio optimization and its worst case analysis. OR Spectrum, 39(2), 505–539.
Shiri Ghahi, A., Didehkhani, H., Khalili Damghani, K., & Saeedi, P. (2017). A Comparative Study of Multi-Objective Multi-Period Portfolio Optimization Models in a Fuzzy Credibility Environment Using Different Risk Measures. Financial Management Strategy, 5(3). (in Persian)
Sina, A., & Fallah, M. (2020). Comparison of Value Risk Models and Coppola-CVaR in Portfolio Optimization in Tehran Stock Exchange. Journal of Financial Management Perspective, 10(29). (in Persian)
Soyster, A. (1973). Convex programming with set-inclusive constraints and applications to inexact linear programming. Operation Research. (21), 1154-1157.
Taghizadegan, G. R., Zomorodian, G., Falah Shams, M. & Saadi, R. (2023). Comparing the performance of Markowitz models and value-at-risk model based on illiquidity risk-T-Cupola with dynamic conditional correlation (DCC t-Cupola LVaR) for portfolio optimization in Tehran Stock Exchange. Financial Research Journal, 25(1), 152-179.
(in Persian)
Taleblou, R., & Davoudi, M. (2018). Estimation of Optimal Investment Portfolio Using Value at Risk (VaR) and Expected Shortfall (ES) Models: GARCH-EVT-Copula Approach. Economics Research, 18(71), 91-125. (in Persian)
Chen, W. (2015). Artificial bee colony algorithm for constrained possibilistic portfolio optimization problem. Physica A Statistical Mechanics and its Applications, 429, 125-139.
Yu, C. S., & Li, H. L. (2000). A robust optimization model for stochastic logistic problems.
International Journal of Production Economics, 64(1-3), 385-397.
Yu, J. R., Chiou, W. J. P., Lee, W. Y., & Chuang, T. Y. (2019). Realized performance of robust portfolios: Worst-case Omega vs. CVaR-related models. Computers & Operations Research, 104, 239-255.‏
Zhang, J. & Zhang, K. (2022). Portfolio selection models based on interval-valued conditional value at risk (ICVaR) and empirical analysis. Fractal Fract. arXiv preprint arXiv:2201.02987.‏
Zhang, J., Li, S., Mitoma, I., & Okazaki, Y. (2009). On set-valued stochastic integrals in an M-type 2 Banach space. Journal of mathematical analysis and applications, 350(1), 216-233.‏
Zymler, S., Rustem, B. & Kuhn, D. (2011). Robust portfolio optimization with derivative insurance guarantees. European Journal of Operational Research, 210 (2), 410-424.
Financial Research Journal
Volume 25, Issue 3
2023
Pages 508-528

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