Mathematical modeling for a new portfolio selection problem in bubble condition, using a new risk measure

Document Type : Article

Authors

1 Faculty of Industrial and Systems Engineering, Tarbiat Modares University, Tehran, Iran

2 Faculty of Industrial Engineering, K.N. Toosi University of Technology, Tehran, Iran

Abstract

A portfolio selection model is developed in this study, using a new risk measure. The proposed risk measure is based on the fundamental value of stocks. For this purpose, a mathematical model is developed and transformed into an integer linear programming. In order to analyze the model's efficiency, the actual data of the Tehran Stock Exchange market are used in 12 scenarios to solve the proposed model. In order to evaluate the scenarios, data mining approaches are employed. Data mining methods which are used in this paper include ANFIS, decision tree, random forest, ADF, and GEP. The best method for scenario evaluation is GEP based on numerical results. Hence, the market values are evaluated by this algorithm. Software packages like MATLAB, GEP xpero tools, and LINGO are used to solve the model. Different trends of market value and fundamental value volatility in the optimum stock portfolio are determined. It is possible to examine the optimum portfolio profitability in different scenarios. By using real-world data, trends are extracted and analyzed. Results show that the developed model can be effectively applied in bubble situations.

Keywords

References

References
[1] Markowitz, H. “Portfolio selection”, The journal of finance, 7. 77-91. (1952)
[2] Konno, H. Yamazaki, H. “Mean-absolute deviation portfolio optimization model and its applications to Tokyo stock market”, Management science, 37. 519-531. (1991)
[3] Rockafellar, R.T.  Uryasev, S.  “Optimization of conditional value-at-risk”, Journal of risk, 2. 21-42. (2000)
[4] Bernardi, M.  Maruotti, A.  Petrella, L.” Multiple risk measures for multivariate dynamic heavy–tailed models”, Journal of Empirical Finance, 43.1-32. (2017)
[5] Kuzubaş, T.U.  Ömercikoğlu, I.  Saltoğlu, B. “Network centrality measures and systemic risk: An application to the Turkish financial crisis”, Physica A: Statistical Mechanics and its Applications, 405.203-215. (2014)
[6] Fu, T.  Zhuang, X.  Hui, Y.  Liu, J.  “Convex risk measures based on generalized lower deviation and their applications”, International Review of Financial Analysis, 52.27-37. (2017)
[7] Gong, X.  Zhuang, X.  “Measuring financial risk and portfolio reversion with time changed tempered stable Lévy processes”, The North American Journal of Economics and Finance, 40.148-159. (2017)
[8] Sorwar, G.  Dowd, K.  “Estimating financial risk measures for options”, Journal of Banking & Finance, 34.1982-1992. (2010)
[9] Gao, J.  Xiong, Y.  Li, D.  “Dynamic mean-risk portfolio selection with multiple risk measures in continuous-time”, European Journal of Operational Research, 249.647-656. (2016)
[10] Beauchamp, J.P.  Cesarini, D.  Johannesson, M.  “The psychometric and empirical properties of measures of risk preferences”, Journal of Risk and uncertainty, 54.203-237. (2017)
[11] Righi, M.B.  Borenstein, D. “A simulation comparison of risk measures for portfolio optimization”, Finance Research Letters, 24.105-112. (2018)
[12] Sawik, B. “Triple-objective models for portfolio optimisation with symmetric and percentile risk measures”, International Journal of Logistics Systems and Management, 25.96-107. (2016)
[13] Bernard, C.  Denuit, M.  Vanduffel, S.  “Measuring portfolio risk under partial dependence information”, Journal of Risk and Insurance, 85.843-863. (2018)
[14] Grechuk, B.  Zabarankin, M. “Inverse portfolio problem with coherent risk measures”, European Journal of Operational Research, 249.740-750. (2016)
[15] Ghahtarani, A.  Najafi, A.A.  “Robust optimization in portfolio selection by m-MAD model approach”, Economic Computation & Economic Cybernetics Studies & Research, 52 (2018).
[16] Domeij, D.  Ellingsen, T.  “Rational bubbles and public debt policy: A quantitative analysis”, Journal of Monetary Economics, 96.109-123. (2018)
[17] Barberis, N.  Greenwood, R.  Jin, L.  Shleifer, A.  “Extrapolation and Bubbles (No. w21944)”, in, National Bureau of Economic Research, 2016.
[18] Lee, J.H.  Phillips, P.C.  “Asset pricing with financial bubble risk”, Journal of Empirical Finance, 38.590-622. (2016)
[19] Bosi, S.  Ha-Huy, T.  Le Van, C.  Pham, C.-T.  Pham, N.-S. “Financial bubbles and capital accumulation in altruistic economies”, Journal of Mathematical Economics, 75.125-139. (2018)
[20] Maynard, A.  Ren, D. “The finite sample power of long-horizon predictive tests in models with financial bubbles”, International Review of Financial Analysis, (2016).
[21] Michaelides, P.G.  Tsionas, E.G.  Konstantakis, K.N.  “Non-linearities in financial bubbles: Theory and Bayesian evidence from S&P500”, Journal of Financial Stability, 24.61-70. (2016)
[22] Miao, J.  Wang, P.  “Banking bubbles and financial crises”, Journal of Economic Theory, 157.763-792. (2015)
[23] Wigniolle, B. “Optimism, pessimism and financial bubbles”, Journal of Economic Dynamics and Control, 41.188-208. (2014)
[24] Harvey, D.I.  Leybourne, S.J.  Sollis, R.  Taylor, A.R.  “Tests for explosive financial bubbles in the presence of non-stationary volatility”, Journal of Empirical Finance, 38.548-574. (2016)
[25] Kunieda, T.  Shibata, A.  “Asset bubbles, economic growth, and a self-fulfilling financial crisis”, Journal of Monetary Economics, 82.70-84. (2016)
[26] Gong, B.  Pan, D.  Shi, D.  “New investors and bubbles: an analysis of the baosteel call warrant bubble”, Management Science, 63.2493-2508. (2016)
[27] Obayashi, Y.  Protter, P.  Yang, S.  “The lifetime of a financial bubble”, Mathematics and Financial Economics, 11.45-62. (2017)
[28] Fry, J.  Cheah, E.-T.  “Negative bubbles and shocks in cryptocurrency markets”, International Review of Financial Analysis, 47.343-352. (2016)
[29] Sornette, D.  Cauwels, P.  “Financial bubbles: mechanisms and diagnostics”, Swiss Finance Institute Research Paper, (2014).
[30] Hirota, S.  Sunder, S.  “Price bubbles sans dividend anchors: Evidence from laboratory stock markets”, Behavioral Interactions, Markets, and Economic Dynamics, Springer, pp. 357-395. (2016)
[31] Guastaroba, G.  Mansini, R.  Ogryczak, W.  Speranza, M.G.  “Linear programming models based on Omega ratio for the enhanced index tracking problem”, European Journal of Operational Research, 251.938-956. (2016)
[32] Mansini, R.  Ogryczak, W.  Speranza, M.G.  “On LP solvable models for portfolio selection”, Informatica, 14.37-62. (2003)
[33] Ghahtarani, A.  Sheikhmohammady, M.  Najafi, A.A. “Development of Robust Random Variable for Portfolio Selection Problem”, Industrial Engineering & Management Systems, 17.632-641. (2018)
[34] Barak, S.  Arjmand, A. Ortobelli, S. “Fusion of multiple diverse predictors in stock market”, Information Fusion, 36.90-102. (2017)
[35] Chong, E.  Han, C.  Park, F.C.  “Deep learning networks for stock market analysis and prediction: Methodology, data representations, and case studies”, Expert Systems with Applications, 83.187-205. (2017)
[36] de Oliveira, F.A.  Nobre, C.N.  Zarate, L.E.  “Applying Artificial Neural Networks to prediction of stock price and improvement of the directional prediction index–Case study of PETR4, Petrobras, Brazil”, Expert Systems with Applications, 40.7596-7606. (2013)
[37] Krauss, C.  Do, X.A.  Huck, N.  “Deep neural networks, gradient-boosted trees, random forests: Statistical arbitrage on the S&P 500”, European Journal of Operational Research, 259.689-702. (2017)
[38] Maroco, J.  Silva, D. Rodrigues, A.  Guerreiro, M.  Santana, I.  Mendonça, A. de “Data mining methods in the prediction of Dementia: A real-data comparison of the accuracy, sensitivity and specificity of linear discriminant analysis, logistic regression, neural networks, support vector machines, classification trees and random forests”, BMC research notes, 4.299. (2011)
[39] Weng, B.  Ahmed, M.A.  Megahed, F.M.  “Stock market one-day ahead movement prediction using disparate data sources”, Expert Systems with Applications, 79.153-163. (2017)
[40] Kohavi, R.  Quinlan, J.R.  “Data mining tasks and methods: Classification: decision-tree discovery, in:  Handbook of data mining and knowledge discovery”, Oxford University Press, Inc., 267-276. (2002)
[41] Verikas, A.  Gelzinis, A.  Bacauskiene, M.  “Mining data with random forests: A survey and results of new tests”, Pattern recognition, 44.330-349. (2011)
[42] Lin, C.-T.  Lee, C.G.  Lin, C.-T.  Lin, C.  “Neural fuzzy systems: a neuro-fuzzy synergism to intelligent systems”, Prentice hall PTR Upper Saddle River NJ, (1996).
Scientia Iranica
Volume 28, Issue 5
Transactions on Industrial Engineering (E)
September and October 2021
Pages 2812-2829

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History

  • Receive Date: 08 August 2018
  • Revise Date: 30 October 2019
  • Accept Date: 18 November 2019

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