Stock portfolio optimization using reliability approach
Subject Areas :
Journal of Investment Knowledge
Mir Seyed Mohammad Mohsen Emamat
1
,
Payam Hanafizadeh
2
1 - Department of Industrial Management, Management and Accounting Faculty, Allame Tabataba’i University, Tehran, Iran
2 - Department of Industrial management, Faculty of management and accounting, Allameh Tabataba’i University, Tehran, Iran.
Received: 2020-02-13
Accepted : 2020-12-30
Published : 2020-12-21
Keywords:
investment,
Stochastic Optimization,
Stock Portfolio,
Nonlinear Programming,
Abstract :
The aim of this study is to optimize stock portfolios by considering uncertain returns and the investment’s utility function in the Tehran Stock Exchange. For this purpose, a two-stage recursive algorithm and a utility function have been used. Securities are selected according to the list of 50 most active companies that was published by the Securities and Exchange Organization per season between the years 1390 to 1394. Considering the returns in this five-year period, the returns vector and covariance matrix are determined and after modeling the optimal portfolio is presented. The results show that the optimal portfolio includes: Iran Transfo (0.15), Eghtesad Novin Bank (0.1), Saipa (0.15), Ghadir Investment Company (0.15), Foolad Mobarakeh Esfahan (0.15), Mokhaberat Iran (0.15) and Meli Sanaye Mess Iran (0.15). The quality of the results is compared with real returns in the following year (1395). The results show the high accuracy of the algorithm.
References:
Ayub, U., Shah, S. Z. A., & Abbas, Q. (2015). Robust analysis for downside risk in portfolio management for a volatile stock market. Economic Modelling, 44, 86-96.
Ben-Tal, A., & Nemirovski, A. (1998). Robust convex optimization. Mathematics of operations research, 23(4), 769-805.
Ben-Tal, A., & Nemirovski, A. (1999). Robust solutions of uncertain linear programs. Operations research letters, 25(1), 1-13.
Bertsimas, D., & Sim, M. (2006). Tractable approximations to robust conic optimization problems. Mathematical Programming, 107(1-2), 5-36.
Branger, N., & Larsen, L. S. (2013). Robust portfolio choice with uncertainty about jump and diffusion risk. Journal of Banking & Finance, 37(12), 5036-5047.
Chen, C., & Kwon, R. H. (2012). Robust portfolio selection for index tracking. Computers & Operations Research, 39(4), 829-837.
Chen, W., & Tan, S. (2009). Robust portfolio selection based on asymmetric measures of variability of stock returns. Journal of computational and applied mathematics, 232(2), 295-304.
Chen, W., Sim, M., Sun, J., & Teo, C. P. (2010). From CVaR to uncertainty set: Implications in joint chance-constrained optimization. Operations research, 58(2), 470-485.
Chen, X., Sim, M., & Sun, P. (2007). A robust optimization perspective on stochastic programming. Operations Research, 55(6), 1058-1071.
Chochola, O., Hušková, M., Prášková, Z., & Steinebach, J. G. (2014). Robust monitoring of CAPM portfolio betas II. Journal of Multivariate Analysis, 132, 58-81.
El Ghaoui, L., Oustry, F., & Lebret, H. (1998). Robust solutions to uncertain semidefinite programs. SIAM Journal on Optimization, 9(1), 33-52.
Fernandes, B., Street, A., Valladão, D., & Fernandes, C. (2016). An adaptive robust portfolio optimization model with loss constraints based on data-driven polyhedral uncertainty sets. European Journal of Operational Research, 255(3), 961-970.
Gabrel, V., Murat, C., & Thiele, A. (2014). Recent advances in robust optimization: An overview. European journal of operational research, 235(3), 471-483.
Ghaoui, L. E., Oks, M., & Oustry, F. (2003). Worst-case value-at-risk and robust portfolio optimization: A conic programming approach. Operations research, 51(4), 543-556.
Goldfarb, D., & Iyengar, G. (2003). Robust portfolio selection problems. Mathematics of operations research, 28(1), 1-38.
Halldórsson, B. V., & Tütüncü, R. H. (2003). An interior-point method for a class of saddle-point problems. Journal of Optimization Theory and Applications, 116(3), 559-590.
Han, Y., Li, P., & Xia, Y. (2016). Dynamic robust portfolio selection with copulas. Finance Research Letters.
Hanafizadeh, P., & Ponnambalam, K. (2009). Asset allocation using reliability method. Mathematical and Computer Modelling, 50(1), 21-31.
Hanafizadeh, P., & Seifi, A. (2004). A unified model for robust optimization of linear programs with uncertain parameters. Transactions on Operational Research, 16, 25-45.
Kakouris, I., & Rustem, B. (2014). Robust portfolio optimization with copulas. European Journal of Operational Research, 235(1), 28-37.
Kolm, P. N., Tütüncü, R., & Fabozzi, F. J. (2014). 60 Years of portfolio optimization: Practical challenges and current trends. European Journal of Operational Research, 234(2), 356-371.
Li, P., Han, Y., & Xia, Y. (2016). Portfolio optimization using asymmetry robust mean absolute deviation model. Finance Research Letters, 18, 353-362.
Markowitz, H. (1952). Portfolio selection. The journal of finance, 7(1), 77-91.
Moon, Y., & Yao, T. (2011). A robust mean absolute deviation model for portfolio optimization. Computers & Operations Research, 38(9), 1251-1258.
Rockafellar, R. T., & Uryasev, S. (2000). Optimization of conditional value-at-risk. Journal of risk, 2, 21-42.
Sadjadi, S. J., Gharakhani, M., & Safari, E. (2012). Robust optimization framework for cardinality constrained portfolio problem. Applied Soft Computing, 12(1), 91-99.
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. (2017a). Robust minimum variance portfolio optimization modelling under scenario uncertainty. Economic Modelling, 64, 60-68.
Xidonas, P., Mavrotas, G., Hassapis, C., & Zopounidis, C. (2017b). Robust multiobjective portfolio optimization: A minimax regret approach. European Journal of Operational Research.
Ziemba, W. T., & Mulvey, J. M. (1998). Worldwide asset and liability modeling (Vol. 10). Cambridge University Press
_||_