Robust Portfolio Optimization based on Evidence Theory

Articles in Press

Document Type : Article

Authors

School of Industrial Engineering, Iran University of Science and Technology, Tehran, P. O. Box:16846-13114, Iran

Abstract

During the past few years, there have been some turbulent events in the world's economy, which have significantly influenced the performance of companies. Therefore, there is an urgent need to use a robust method to handle the existing uncertainties on the performance of the companies. This paper uses Evidence Theory (ET) to present an innovative and practical approach to consider the experts’ opinions which are based on the available evidence regarding the factors that influence the stock market. Subsequently, the study proposes a way to determine the changes in these factors from possible scenarios on historical data to find the return range of different investment alters to be used in robust optimization. Moreover, in a case study, the study examined the sensitivity of the Iranian capital market to exchange rate fluctuations under different scenarios which were due to the lack of a unified view of that rate’s value among experts as one of the mentioned factors. The preliminary results of a real-life case study reveal that the submitted approach is productive and practically useful.

Keywords

References

  1. Best, M.J., and Grauer, R.R. “On the sensitivity of mean-variance-efficient portfolios to changes in asset means: some analytical and computational results”, The review of financial studies, 4(2), pp. 315-342 (1991).
  2. Jobson, J.D., and Korkie, B., “Statistical inference in two-parameter portfolio theory with multiple regression software”, Journal of Financial and Quantitative Analysis, 18(2), pp.189-197 (1983).
  3. Yin, C., Perchet, R., and Soupé, F., “A practical guide to robust portfolio optimization”, Quantitative Finance, 21(6), pp.911-928 (2021).
  4. Chopra, V.K., and Ziemba, W.T., “The Effect of Errors in Means, Variances, and Covariances on Optimal”, Worldwide asset and liability modeling, pp. 53-61 (1998).
  5. Peykani, P., Mohammadi, E., Saen, R.F., Sadjadi, S.J., and Rostamy‐Malkhalifeh, M., “Data envelopment analysis and robust optimization: A review”,Expert Systems, 37(4), pp. 12534 (2020).
  6. Sharpe, W.F., “A simplified model for portfolio analysis”, Management science, 9(2), pp.277-293(1963).
  7. Grossman, S.J., and Stiglitz, J.E., “On the impossibility of informationally efficient markets”, The American economic review, 70(3), pp. 393-408 (1980).
  8. Yunusoglu, M.G., and Selim, H., “A fuzzy rule based expert system for stock evaluation and portfolio construction: An application to Istanbul Stock Exchange”, Expert Systems with Applications, 40(3), pp. 908-920 (2013).
  9. Xidonas, P., Mavrotas, G., and Psarras, J., “A multicriteria methodology for equity selection using financial analysis”, Computers & operations research, 36(12), pp. 3187-3203 (2009).
  10. Konno, H., and Yamazaki, H., “Mean-absolute deviation portfolio optimization model and its applications to Tokyo stock market”. Management science, 37(5), pp.519-531 (1991).
  11. Pavlou, A., Doumpos, M., and Zopounidis, C., “The robustness of portfolio efficient frontiers: A comparative analysis of bi-objective and multi-objective approaches”, Management Decision, pp. 300-313 (2018).
  12. Xidonas, P., Mavrotas, G., Zopounidis, C., and Psarras, J., “IPSSIS: An integrated multicriteria decision support system for equity portfolio construction and selection”, European Journal of Operational Research, 210(2), pp.398-409 (2011).
  13. Feiring, B.R., and Lee, S.W., “A chance-constrained approach to stock selection in hong kong”, International journal of systems science, 27(1), pp.33-41 (1996).
  14. Markowitz, H.M., “Portfolio selection”, In Portfolio selection, Yale University Press (1968).
  15. Ben-Tal, A., Margalit, T., and Nemirovski, A., “Robust modeling of multi-stage portfolio problems”, High Performance Optimization, Springer, Boston, MA, pp. 303-328 (2000).
  16. Moon, Y., and Yao, T., “A robust mean absolute deviation model for portfolio optimization”. Computers & Operations Research, 38(9), pp.1251-1258 (2011).
  17. Kim, J.H., Kim, W.C., and Fabozzi, F.J., “Recent advancements in robust optimization for investment management”, Annals of Operations Research, 266(1), pp.183-198 (2018).
  18. Goldfarb, D., and Iyengar, G., “Robust portfolio selection problems”, Mathematics of operations research, 28(1), pp.1-38 (2003).
  19. Ling, A.F., and Xu, C.X., “Robust portfolio selection involving options under a “marginal+ joint” ellipsoidal uncertainty set”, Journal of Computational and Applied Mathematics, 236(14), pp.3373-3393 (2012).
  20. Heckel, T., de Carvahlo, R., Lu, X., and Perchet, R., “Insights into robust optimization: decomposing into mean–variance and risk-based portfolios”, The Journal of Investment Strategies, 6(1), pp.1-24 (2016).
  21. Quaranta, A.G., and Zaffaroni, A., “Robust optimization of conditional value at risk and portfolio selection”, Journal of Banking & Finance, 32(10), pp.2046-2056 (2008).
  22. Bertsimas, D., and Pachamanova, D., “Robust multiperiod portfolio management in the presence of transaction costs”, Computers & Operations Research, 35(1), pp.3-17 (2008).
  23. Chen, W., and Tan, S., “Robust portfolio selection based on asymmetric measures of variability of stock returns”, Journal of computational and applied mathematics, 232(2), pp.295-304 (2009).
  24. Ghahtarani, A., and Najafi, A.A., “Robust goal programming for multi-objective portfolio selection problem”, Economic Modelling, 33, pp.588-592 (2013).
  25. Pınar, M.Ç., and Paç, A.B., “Mean semi-deviation from a target and robust portfolio choice under distribution and mean return ambiguity”, Journal of Computational and Applied Mathematics, 259, pp.394-405 (2014).
  26. Ling, A., Sun, J., and Wang, M., “Robust multi-period portfolio selection based on downside risk with asymmetrically distributed uncertainty set”, European Journal of Operational Research, 285(1), pp.81-95 (2020).
  27. Tütüncü, R.H., and Koenig, M., “Robust asset allocation”, Annals of Operations Research, 132(1), pp.157-187 (2004).
  28. Bertsimas, D. and Sim, M., “The price of robustness”, Operations research, 52(1), pp.35-53 (2004).
  29. Bertsimas, D., and Thiele, A., “Robust and data-driven optimization: modern decision making under uncertainty”, In Models, methods, and applications for innovative decision making 95-122 (2006).
  30. Dimmock, S.G., Kouwenberg, R., Mitchell, O.S., and Peijnenburg, K., “Ambiguity aversion and household portfolio choice puzzles: Empirical evidence”, Journal of Financial Economics, 119(3), pp.559-577 (2016).
  31. Ji, R., and Lejeune, M.A., “Data-driven optimization of reward-risk ratio measures” INFORMS Journal on Computing, 33(3), pp.1120-1137 (2021).
  32. Sharma, A., and Mehra, A., “Extended omega ratio optimization for risk‐averse investors”,International Transactions in Operational Research, 24(3), pp.485-506 (2017).
  33. PEYKANI, P., BARZINJPOUR, F., and JANDAGHIAN, A., “Portfolio selection under trading constraints and data uncertainty using robust optimization approach and NSGA-II algorithm”, pp. 195-206 (2020).
  34. Georgantas, A., Doumpos, M., and Zopounidis, C., “Robust optimization approaches for portfolio selection: a comparative analysis”, Annals of Operations Research, pp.1-17 (2021).
  35. Ghahtarani, A., Saif, A., and Ghasemi, A., “Robust portfolio selection problems: a comprehensive review”, Operational Research, pp.1-62 (2022).
  36. Mohammadi, S.E., and Mohammadi, E., “Robust portfolio optimization based on minimax regret approach in Tehran stock exchange market”, Journal of Industrial and Systems Engineering,  pp.51-62 (2018).
  37. Peykani, P., Mohammadi, E., Jabbarzadeh, A., Rostamy-Malkhalifeh, M., and Pishvaee, M.S., “A novel two-phase robust portfolio selection and optimization approach under uncertainty: A case study of Tehran stock exchange”, Plos one, 15(10), p.e0239810 (2020).
  38. Xidonas, P., Steuer, R., and Hassapis, C., “Robust portfolio optimization: A categorized bibliographic review”, Annals of Operations Research, 292(1), pp.533-552 (2020).
  39. Thakur, G.S.M., Bhattacharyya, R., and Sarkar, S., “Stock portfolio selection using Dempster–Shafer evidence theory”, Journal of King Saud University-Computer and Information Sciences, 30(2), pp.223-235 (2018).
  40. Skoruchi, A., and Mohammadi, E., “Uncertain portfolio optimization based on Dempster-Shafer theory”, Management Science Letters, 12(3), pp.207-214 (2022).
  41. Thomsett, M.C., Mastering fundamental analysis. Dearborn Trade Publishing (1998).
  42. Dempster, A.P., “Upper and lower probabilities induced by a multivalued mapping”, In Classic works of the Dempster-Shafer theory of belief functions. Springer, Berlin, Heidelberg pp. 57-72 (2008).
  43. Shafer, G., “A mathematical theory of evidence”, A Mathematical Theory of Evidence. Princeton University Press (2021).
  44. Mohammadi, S.E., and Makui, A., “Multi-attribute group decision making approach based on interval-valued intuitionistic fuzzy sets and evidential reasoning methodology”, Soft Computing, 21(17), pp.5061-5080 (2017).
  45. Petretto, A., “Optimal social health insurance with supplementary private insurance”, Journal of Health Economics, 18(6), pp.727-745 (1999).
  46. Xu, D.L., “An introduction and survey of the evidential reasoning approach for multiple criteria decision analysis”, Annals of Operations Research, 195(1), pp.163-187 (2012).
  47. Soraggi, S., Wiuf, C. and Albrechtsen, A., “Powerful inference with the D-statistic on low-coverage whole-genome data”, G3: Genes, Genomes, Genetics, 8(2), pp.551-566 (2018).
  48. Huynh, V.N., Nakamori, Y., Ho, T.B., and Murai, T., “Multiple-attribute decision making under uncertainty: the evidential reasoning approach revisited” IEEE Transactions on Systems, Man, and Cybernetics-Part A: Systems and Humans, 36(4), pp.804-822 (2006).
  49. Seyedhosseini, S.M., Esfahani, M.J., and Ghaffari, M., “A novel hybrid algorithm based on a harmony search and artificial bee colony for solving a portfolio optimization problem using a mean-semi variance approach”, Journal of Central South University, 23(1), pp.181-188 (2016).
  50. Kong, X., Chang, J., Niu, M., Huang, X., Wang, J., and Chang, S.I., “Research on real time feature extraction method for complex manufacturing big data”, The International Journal of Advanced Manufacturing Technology, 99(5), pp.1101-1108 (2018).
  51. Cornuejols, G., and Tütüncü, R., Optimization methods in finance(Vol. 5). Cambridge University Press (2006).
  52. Pishvaee, M.S., Razmi, J., and Torabi, S.A., “Robust possibilistic programming for socially responsible supply chain network design: A new approach”, Fuzzy sets and systems, 206, pp.1-20 (2012).
  53. Soyster, A.L., “Convex programming with set-inclusive constraints and applications to inexact linear programming”, Operations research, 21(5), pp.1154-1157 (1973).
  54. Mulvey, J.M., Vanderbei, R.J., and Zenios, S.A., “Robust optimization of large-scale systems”, Operations research, 43(2), pp.264-281 (1995).
  55. Yu, C.S., and Li, H.L., “A robust optimization model for stochastic logistic problems”, International journal of production economics, 64(1-3), pp.385-397 (2000).
  56. El Ghaoui, L., Oustry, F., and Lebret, H., “Robust solutions to uncertain semidefinite programs”, SIAM Journal on Optimization, 9(1), pp.33-52 (1998).
  57. Ben-Tal, A., and Nemirovski, A., “Robust convex optimization”, Mathematics of operations research, 23(4), pp.769-805 (1998).
  58. Ben-Tal, A., and Nemirovski, A., “Robust solutions of uncertain linear programs”, Operations research letters, 25(1), pp.1-13 (1999).
  59. Ben-Tal, A., and Nemirovski, A., “Robust solutions of linear programming problems contaminated with uncertain data”, Mathematical programming, 88(3), pp.411-424 (2000).
  60. Bertsimas, D., and Sim, M., “Robust discrete optimization and network flows”, Mathematical programming, 98(1), pp.49-71 (2003).
  61. Shang, C., Huang, X., and You, F., “Data-driven robust optimization based on kernel learning”, Computers & Chemical Engineering, 106, pp.464-479 (2017).
  62. Bertsimas, D., Gupta, V., and Kallus, N., “Data-driven robust optimization”, Mathematical Programming, 167(2), pp.235-292 (2018).
  63. Kang, Z., Li, X., Li, Z., and Zhu, S., “Data-driven robust mean-CVaR portfolio selection under distribution ambiguity”, Quantitative Finance, 19(1), pp.105-121 (2019).
  64. Namakshenas, M., and Pishvaee, M.S., “Data-driven Robust Optimization Robust and Constrained Optimization: Methods and Applications”, pp. 1–40 (2019).
Scientia Iranica

Articles in Press, Accepted Manuscript
Available Online from 07 June 2022

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History

  • Receive Date: 03 January 2022
  • Revise Date: 26 April 2022
  • Accept Date: 07 June 2022

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