Visualized Portfolio Optimization of stock market: Case of TSE
الموضوعات :
Fatemeh Lakzaie
1
(Department of Mathematics, Semnan University, Semnan, Iran)
Alireza Bahiraie
2
(Department of Mathematics, Semnan University, Semnan, Iran)
saeed mohammadian
3
(Department of Mathematics, Semnan University, Semnan, Iran)
الکلمات المفتاحية: Portfolio optimization, Mean-variance theory, Minimum spanning tree,
ملخص المقالة :
An investment portfolio is a collection of financial assets consisting of investment tools such as stocks, bonds, and bank deposits, among others, which are held by a person or a group of persons. In this research, we use the Markowitz model to optimize the stock portfolio and identify the minimum spanning tree (MST) structure in the portfolio consisting of 50 stocks traded in the TSE. The observable which is used to detect the minimum spanning tree (MST) of the stocks of a given portfolio is the synchronous correlation coefficient of the daily difference of logarithm of closure price of stocks. The correlation coefficient is calculated between all the possible pairs of stocks present in the portfolio in a given time course. The goal of the present study is to obtain the taxonomy of a portfolio of stocks traded in the TSE by using the information of time series of stock prices only. In this research, report results obtained by investigating the portfolio of the stocks used to compute 50 stocks of the Iran Stock Exchange in the time period from January 2012 to October 2022.
[1] Deng, G. F., Lin, W. T., and Lo, C. C., Markowitz-based portfolio selection with cardinality constraints using
improved particle swarm optimization, Expert Systems with Applications, 2012; 39(4): 4558–4566. doi: 10.1016/j.eswa.2011.09.129
[2] Engels, M., Portfolio Optimization : Beyond Markowitz, A master thesis in University of Leiden, 2004.
[3] Hernandez, J. A., Are oil and gas stocks from the Australian market riskier than coal and uranium stocks ?
Dependence risk analysis and portfolio optimization, Energy Econ., 2014; 45:528–536. doi: 10.1016/j.eneco.2014.08.015
[4] Palczewski, J., Poulsen, R., Schenk-Hoppé, K. R., and Wang, H., Dynamic portfolio optimization with
transaction costs and state-dependent drift, European Journal of operational research, 2015; 243(3): 921–931.
doi: 10.1016/j.ejor.2014.12.040
[5] Logubayom, A. I., and Victor, T. A., Portfolio Optimization of Some Stocks on the Ghana Stock Exchange
Using the Markowitz Mean-Variance Approach, Journal of Financial Risk Management, 2019; 8(01): 29–
41.doi: 10.4236/jfrm.2019.81003
[6] Hali, N. A., and Yuliati, A., Markowitz Model Investment Portfolio Optimization : a Review Theory,
International Journal of Research in Community Services, 2020; 1(3):14–18.doi: https: 10.46336/ijrcs.v1i3.104
[7] Li, B., and Zhang, R., A new mean-variance-entropy model for uncertain portfolio optimization with liquidity
and diversifica-tion, Chaos, Solitons & Fractals, 2021; 146: 110842.doi: 10.1016/j.chaos.2021.110842
[8] Barbi, A. Q., and Prataviera, G. A., Nonlinear dependencies on Brazilian equity network from mutual
information minimum spanning trees, Physica A: Statistical Mechanics and its Applications, 2019 ; 523: 876–
885.doi: 10.1016/j.physa.2019.04.147
[9] Kumar, S., Kumar, S., and Kumar, P., Diffusion entropy analysis and random matrix analysis of the Indian
stock market, Physica A: Statistical Mechanics and its Applications, 2020; 560:125122.doi: 10.1016/j.physa.2020.125122
[10] Coletti, P., Comparing minimum spanning trees of the Italian stock market using returns and volumes,
Physica A: Statistical Mechanics and its Applications, 2016; 463: 246–261.doi: 10.1016/j.physa.2016.07.029
[11] Bonanno, G., Caldarelli, G., Lillo, F., and Mantegna, R. N., Topology of correlation-based minimal
spanning trees in real and model markets, Physical Review E, 2003; 68(4): 4–7.doi: 10.1103/PhysRevE.68.046130
[12] Wang, J., Zhao, L., and Huang, R., A network analysis of the Chinese stock market, Physica A: Statist.
Mech, Appl, 2009; 388(14): 2956–2964.doi: 10.1016/j.physa.2009.03.028
[13] Peng, C.K., Buldyrev, S.V., Havlin, S., Simons, M., Stanley, H.E. and Goldberger, A.L., Mosaic organization of DNA nucleotides, Physical review e, 1994; 49(2):1685.doi: 10.1103/PhysRevE.49.1685
[14] Huang, C.F., A hybrid stock selection model using genetic algorithms and support vector regression,
Applied Soft Computing, 2012; 12(2): 807-818.doi: 10.1016/j.asoc.2011.10.009
[15] Li, T., Zhang, W. and Xu, W., A fuzzy portfolio selection model with background risk, Applied
Mathematics and Computation, 2015; 256: 505–513.doi: 10.1016/j.amc.2015.01.007
[16] Tumminello, M., Aste, T., Di Matteo, T. and Mantegna, R.N., A tool for filtering information in complex
systems, Proceedings of the National Academy of Sciences, 2005; 102(30):10421–10426.doi.org/10.1073/pnas.0500298102
[17] Onnela, J. P., Chakraborti, A., Kaski, K., and Kertesz, J., Dynamic asset trees and Black Monday, PhysicaA:
Statistical Mechanics and its Applications, 2003; 324(1-2) :247–252.doi: 10.1016/S0378-4371(02)01882-4
[18] Heimo, T., Saramäki, J., Onnela, J. P., and Kaski, K., Spectral and network methods in the analysis of
correlation matrices of stock returns, Physica A: Statistical Mechanics and its Applications, 2007; 383(1):
147–151.doi: 10.1016/j.physa.2007.04.124
[19] Mangram, M. E., A simplified perspective of the Markowitz portfolio theory, Global journal of business
research, 2013; 7(1)P59–70.
[20] Gasser, S. M., Rammerstorfer, M., and Weinmayer, K., Markowitz revisited: Social portfolio engineering,
European Journal of Operational Research., 2016; 258(3):1181-1190.doi: 10.1016/j.ejor.2016.10.043
[21] Zanjirdar, M., Overview of portfolio optimization models, Advances in mathematical finance and
applications, 2020 ; 5(4):419–435.doi: 10.22034/amfa.2020.1897346.1407
[22] Fabozzi, F.J., Markowitz, H.M. and Gupta, F., 2008. Portfolio selection. Handbook of finance, 2.
[23] Kalayci, C. B., Ertenlice, O., and Akbay, M. A., A comprehensive review of deterministic models and
applications for mean-variance portfolio optimi-zation, Expert Systems with Applications, 2019; 125:345–
368.doi: 10.1016/j.eswa.2019.02.011
[24] Ozyesil, M., Markowitz Portfolio Optimization Model: An Application On Listed Firm On Borsa Istanbul-
30 National Stock Index (Bist-30), no. February, 2021.
[25] Chen, W., Zhang, H., Mehlawat, M. K., and Jia, L., Mean–variance portfolio optimization using machine
learning-based stock price prediction, Appl. Soft Comput, 2021; 100, p.106943.doi: 10.1016/j.asoc.2020.106943
[26] Kolm, P. N., Tütüncü, R., and Fabozzi, F. J., 60 Years of portfolio optimization: Practical Challenges and
current trends, European Journal of Operational Research, 2013;234(2):356-371.doi: 10.1016/j.ejor.2013.10.060
[27] Li, H., Mao, W., Zhang, A., and Li, C., An improved distribution network reconfiguration method based on
minimum spanning tree algorithm and heuristic rules, International Journal of Electrical Power & Energy
Systems, 2016; 82: 466–473.doi: 10.1016/j.ijepes.2016.04.017
[28] Xue, L., Chen, F., Guo, S., Fu, G., Li, T., and Yang, Y., Time-varying correlation structure of Chinese stock
market of crude oil-related companies greatly influenced by external factors, Physica a: Statistical Mechanics
and Its Applications, 2019; 530:121086.doi: 10.1016/j.physa.2019.121086
[29] Bonanno, G., Caldarelli, G., Lillo, F., Micciche, S., Vandewalle, N., and Mantegna, R. N., Networks of
equities in financial markets, The European Physical Journal B, 2004; 38(2): 363–371.doi: 10.1140/epjb/e2004-00129-6
[30] Bonanno, G., Lillo, F., and Mantegna, R. N., High-frequency cross-correlation in a set of stocks,
Quantitative Finance, 2001; 1:1469-7688. doi: 10.1080/713665554
