Interior Point Algorithm in Multi-objective Portfolio Optimization: GlueVaR Approach

Document Type : Research Paper

Authors

1 MSe., Department of Accounting and Financial Management, Faculty of Economics and Management and, Urmia University, Urmia, Iran.

2 Associate Prof., Department of Accounting and Financial Management, Faculty of Economics and Management and, Urmia University, Urmia, Iran.

3 Assistant Prof., Department of Mathematics, Faculty of Mathematics, Urmia University of Technology, Urmia, Iran.

10.22059/frj.2023.352338.1007424

Abstract

Objective
Investors, in their pursuit to maximize expected returns, minimize risks in their stock portfolios, and achieve the desired benefits, require suitable methods and criteria to select stocks for their portfolios and allocate capital. One of the most important things in stock portfolio optimization is the use of a suitable optimization algorithm. The function of the multi-objective portfolio optimization model is quadratic. Quadratic functions are a special class of nonlinear programming problems in which the objective function is quadratic and the constraints are linear. Common algorithms for quadratic programming require certain parameters with fixed values. Such algorithms are extensively employed for solving real-world problems, particularly in financial contexts. The major objective of this research is to apply the inner point mathematical algorithm to optimize the stock portfolio and to use this algorithm to address the multi-objective portfolio optimization problem. With the GlueVaR risk measurement criterion, the problem of portfolio optimization takes into account the two objectives of maximizing returns during the research period and reducing investment risk, reassuring investors to make better and more accurate decisions about the final object of this research.
 
 
 
Methods
The necessary information for this study was provided by 50 active companies listed on the Tehran Stock Exchange. However, due to the availability of their daily prices during the study period, the final number of companies considered was reduced to 33. The inner point mathematical approach was utilized to optimize the model with the dual objectives of increasing efficiency and reducing risk. To demonstrate the effectiveness and capability of the algorithm in solving the problem of two-objective optimization, its output was compared with other risk measurement criteria such as variance, and value at risk (VaR). The investment risk in the stock portfolio was also calculated using the GlueVaR criterion. Comparing conditional (CVaR) was also done. The GlueVaR criterion has the advantage over the other criteria since it takes the investor's attitude toward risk into account. This advantage formed the basis of the calculation method in this research according to the mentioned algorithm.
 
Results
According to the research, value at risk (VaR) and conditional value at risk (CVaR) perform better than other variance risk measures in the portfolio optimization model with the GlueVaR risk measure and the internal point optimization method for determining the most effective border. Additionally, when applied to optimization problems, the internal point method discovers the optimal point with fewer iterations, providing strong evidence of the algorithm's effectiveness.
 
Conclusion
Based on the current findings, it is evident that the internal point algorithm is effective in resolving stock portfolio optimization issues. Additionally, the GlueVaR risk measurement criterion outperforms VaR, variance, and CVaR for most investors with diverse risk and return preferences

Keywords

Main Subjects

References

 
Abdul Alizadeh Shahir, S. & Eshghi, K. (2012). Application of Genetic Algorithm in the selection of a set of assets from Stock Exchange stocks. Iran Economic Research Quarterly, 5(17), 175-192. (in Persian)
Agha Mohammadi, A., Sojodi, M., Sojodi, M. & Tavousi, M.J. (2016). Introducing the new GlueVaR risk measure and its estimation using the combined quantile regression model, Journal of Financial Engineering and Securities Management, 8(31), 1-17. (in Persian)
Ahmadi Aghdam, M., Taghizadeh Yazdi, M. & Fallahpour, S. (2015). Choosing the optimal portfolio using meta-optimal planning and extended sequential optimal planning. Journal of Financial Research, 18 (4), 591-612. (in Persian)
Alipour Jourshari, A., Yakideh, K. & Mahfovi, G. R. (2016). Investigating the performance of Markowitz and GMD models in choosing the optimal portfolio. The second international industrial management conference, April 30 and 31, Mazandaran University. (in Persian)
Aqbal-Nia, M. (2004). Designing a model for investment risk management in Tehran Stock Exchange using the concept of value at risk. Master's thesis, Department of financial management, Shahid Beheshti University, Tehran. (in Persian)
Artzner, P.H., Delbaen Freddy, E. & Jean-Marc, H.D. (1999). Coherent Measures of Risk. Journal of Mathematical Finance, 9(3), 203-228.
Asefi, S., Fallah Tafti, S., Bagheri Kazemabadi, M. & Fallahpour, S. (2017). Optimizing portfolios using the meta-heuristic algorithm of the whale with the criterion of expected drop risk. Quarterly Journal of Financial Engineering and Securities Management, 9(37), 110-132. (in Persian)
Belles – Sampera, J., Guillen, M. & Santolino, M. (2014). Beyond Value-at-Risk: GlueVaR distortion risk measure. Risk Analysis, 34 (1), 121-134.
Belles-Sampera, J., Guillen, M. & Santolino, M. (2016). The use of flexible quantile-based measures in risk assessment. Communications in Statistics – Theory and Methods, 45(6), 1670-1681.
Belles-Sampera, J., Guillen, M. & Santolino, M. (2014). GlueVaR risk measures in capital allocation applications. Mathematics and Economics, 58:132-37.
Campbel, R., Huisman, R. & Koedijk, K. (2001). Optimal portfolio selection in a value-at-risk framework. Journal of Banking and Finance, 25, 1789-1804.
Cornuejols, G. Pena, J. & Tütüncü, R. (2018). Optimization methods in finance (2nd Ed.). Cambridge University Press.
Daryaei, F., Atai, A. & Scroochi, M.R. (2019). A new algorithm based on the interior point method for solving semi-infinite optimization problems. The 13th International Conference of the Iranian Association for Operations Research, 16-19 September 2019, Shahrood University of Technology. (in Persian)
Demone, C., Di Matteo, O. & Collignon, B. (2020). Classical Decomposition of Markowitz Portfolio Selection. Https://dio.org/10.34989/swp-2020-21.
Erica, E., Handari, B. D. & Hertono, G. F. (2018). Agglomerative Clustering and Genetic Algorithm in Portfolio Optimization. AIP Conference Proceedings 2023, 02017, Https://dio.org/10.1063/1.506421.
Ghandehari, M., Azar, A., Yazdanian, A. R., & Golarzi, GH. (2018). Presenting a combination of approximate stochastic dynamic programming and genetic algorithm in multi-stage optimization of portfolios with GlueVaR risk criterion. Industrial Management, 11 (3), 517-542. (in Persian)
Golarzi, G. & Ansari, H. (2022). Performance comparison of Non-dominated sorting genetic algorithm with strength Parto evolutionary algorithm in selecting optimal portfolios in Tehran Stock Exchange. Financial Research Journal, 24(3), 410-430. (in Persian)
Gondzio, J. & Grothey, A. (2007). Solving Nonlinear Portfolio Optimization Problems with the Primal-Dual Interior Point Method. European Journal of Operational Research,181(3), 1019-1029.
Hasheminejad, S. A., & Bagherpour, M. (2020). Venture Capital Portfolio Optimization through Hybrid Approach of Agent-Based Modeling and Modified Harmony Search. Financial Research Journal, 21(4), 493-516. doi: 10.22059/frj.2019.277295.1006833 (in Persian)
Huang, Y. & Yin, C. (2019). Optimal reciprocal reinsurance under GlueVaR distortion risk measures. Journal of Mathematical Finance, 9(1), 11-24.
Jetpipattanapong, D. & Srijuntongsiri, G. (2021). An efficient method to compute search directions of an infeasible primal-dual path-following interior-point method for large-scale block diagonal quadratic programming. Journal of Science & Technology, 43(5), 1449-1455.
Jia, J. & Dyer, J.S. (2000). A standard measure of risk and risk-value models. Management Science, 42 (12), 1691-1705.
Kardos, J. (2020). High-performance interior point methods. Doctoral Dissertation, Faculty of Informatics, University della Svizzera, Italiana.
Karimi, M. (2007). Portfolio optimization using the value-at-risk model in Tehran Stock Exchange. Master's thesis, Faculty of Social and Economic Sciences, Al-Zahra University, Tehran. (in Persian)
Khoshbin, R., Rezei, F. & Rastakhiz Sorkhe, M. (2021). Liquidity risk management in open banking market operations with GlueVaR criteria. Financial Engineering and Securities Management Quarterly, 45:199-223.
Krezolek, D. & Trzpiot, G. (2017). The Effectiveness of the GlueVaR Risk Measure on the Metals – the Application of Omega Performance Measure. Journal of Folia Oeconomica, 5(331), 153-167.
Krezolek, D. (2017). The use of Value-at-Risk methodology in the assessment of investor's risk attitudes on the precious metals market. Journal of Ekonometria Econometrics, 3(57), 101-112.
Lau, M. S. K., Yue, S. P., Ling, K. V. & Maciejowski, J. M. (2009). A Comparison of Interior Point and Active Set Methods for FPGA Implementation of Model Predictive Control. European Control Conference (ECC), Budapest, Hungary, August 23-26, 156-161.
Li, D. (2016). Optimal Dynamic Portfolio Selection: Multiperiod Mean Variance Formulation. Mathematical Finance, 10(5), 387-406.
Markowitz, H. (1952). Portfolio Selection. The Journal of Finance, 7 (1), 77 – 91.
Neshatizadeh, L. & Heydari, H. (2018). Investigating volatility and risk criteria in constrained optimization models using colonial competition algorithm. Econometric modeling, 3(4), 11-35. (in Persian)
Nilchi, M., Farid, D. & Zare, M. H. (2018). Comparative evaluation of Markowitz approach with a hybrid method to form optimal portfolio using DNN deep learning and gravity search algorithm. Journal of Financial Management Perspectives, 9(4), 165-188.
(in Persian)
Nocedal, J. & Wright, S. (2006). Numerical optimization. Springer Science & Business Media, Printed in the United States of America.
Raei, R. (2006). Risk capital portfolio selection using neural networks. Accounting and auditing reviews, 13(4), 70-83. (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(3), 184-213. (in Persian)
Rahnemaye Rudposhti, F., Chavoshi, K. & Saber, A. (2013). Optimization of the portfolio consisting of shares of joint investment funds of the Tehran Stock Exchange with the approach of genetic algorithm. Scientific Research Quarterly of Investment Knowledge, 3(12), 217-231. (in Persian)
Rezaei, A., Falahati, A. & Sohaili, K. (2017). Optimizing stocks using a three-objective particle aggregation algorithm. Quarterly Journal of Applied Economic Theories, 5(4), 31-52.
(in Persian)
Shirkund, S. & Fedai, H. (2022). Optimizing portfolios using multivariate models and omega-value under conditional risk based on minimum maximum regret criteria. Journal of Financial Research, 24(1), 1-17. (in Persian)
Sinayi, H.A. & Zamani, S. (2013). Decision-making for stock portfolio selection and comparison of genetic and bee algorithms. Executive Management Scientific Research Journal, 6 (11), 102-83. (in Persian)
Takehara, H. (1993). An interior point algorithm for large-scale portfolio optimization. Annals of Operations Research, 45: 373-386.
Taleb-nia, G. & Fathi, M. (2010). Comparative evaluation of optimal stock portfolio selection in Tehran Stock Exchange through Markoitz and value at risk models. Journal of Financial Knowledge of Securities Analysis (Financial Studies), 3(6), 71-93. (in Persian)
Woodside – Oriakhi, M. Lucas, C. Beasly, J. E. (2011). Heuristic Algorithms for the cardinality constrained efficient, frontier. European Journal of Operational Research, 213 (3), 538 – 550.
Yamai, Y. & Yoshiba, T. (2002). On the Validity of Value-at-Risk: Comparative Analyses with Expected Shortfall. Monetary and Economic Studies, 20 (1), 57-85.
Yin, C. & Zhu, D. (2016). A new class of distortion risk measures and their tail asymptotics with emphasis on VaR. dio.org/10.48550/arXiv.1503.08586.
Yi-Shuai, N. Wang, Y. J. (2022). Higher-order Moment Portfolio Optimization via an Accelerated Difference-of-Convex Programming Approach and Sums-of-Squares. Mathematics of Operations Research.
Financial Research Journal
Volume 25, Issue 3
2023
Pages 453-484

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