Determination of Optimal Portfolio by Calculating Transaction Costs using Genetic Algorithms on the  Jakarta Islamic Index

Sinta Oktavia Nur Fadhila; Agus Maman Abadi; Ezra Putranda Setiawan

doi:10.31764/jtam.v8i1.17469

Determination of Optimal Portfolio by Calculating Transaction Costs using Genetic Algorithms on the Jakarta Islamic Index

Sinta Oktavia Nur Fadhila, Agus Maman Abadi, Ezra Putranda Setiawan

Abstract

The optimal portfolio is a portfolio that can provide maximum returns at the same level of risk. In investing, the term "high return, high risk" is known, meaning that the higher the return, the higher the risk. Therefore, investors need to develop an optimal portfolio to obtain the maximum return on investment at the same level of risk. This study aims to determine the optimal formation of a stock portfolio by calculating transaction costs using the genetic algorithm method on stocks that are members of the Jakarta Islamic Index. This research uses data of daily return on stocks included in Jakarta Islamic Index from 1 August 2020-1 August 2022. The dataset consists of two variables: the date of observation and daily stock returns. The method used in this study is the minimum variance method and the genetic algorithm. Data analysis was divided into two stages: model formulation and model testing through case studies. The analysis of optimal portfolio formation using genetic algorithms shows that in terms of performance, the minimum variance portfolio is superior to the genetic algorithm portfolio, as indicated by the Sharpe ratio value. Meanwhile, the genetic algorithm portfolio is superior to the minimum variance portfolio regarding transaction costs. The genetic algorithm portfolio can provide a fairly high total return, small transaction costs, and good performance compared to the minimum portfolio. Hence, the genetic algorithm portfolio is worthy of recommendation to investors.

Keywords

Genetic Algorithm; Transaction Costs; Minimum Variance; Optimal Portfolio.

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References

Arnott, R. D., & Wagner, W. H. (1990). The measurement and control of trading costs. Financial Analysts Journal, 46(6), 73–80. https://doi.org/10.2469/faj.v46.n6.73

Azim, M. F., Azizah, & Anggraeni, D. (2021). Optimasi portofolio saham dengan pembobot menggunakan algoritma genetika. Jurnal Sains Matematika Dan Statistika, 7(1), 58. https://doi.org/10.24014/jsms.v7i1.12190

Baixauli-Soler, J. S., Alfaro-Cid, E., & Fernandez-Blanco, M. O. (2012). A naïve approach to speed up portfolio optimization problem using a multiobjective genetic algorithm. Investigaciones Europeas de Dirección y Economía de La Empresa, 18, 126–131. https://doi.org/10.1016/S1135-2523(12)70002-3

Chang, T.-J., Yang, S.-C., & Chang, K.-J. (2009). Portfolio optimization problems in different risk measures using genetic algorithm. Expert Systems with Applications, 36(7), 10529–10537. https://doi.org/10.1016/j.eswa.2009.02.062

Cheong, D., Kim, Y. M., Byun, H. W., Oh, K. J., & Kim, T. Y. (2017). Using genetic algorithm to support clustering-based portfolio optimization by investor information. Applied Soft Computing, 61, 593–602. https://doi.org/10.1016/j.asoc.2017.08.042

Darmadji, T., & Fakhruddin, H. M. (2012). Pasar modal di Indonesia: Pendekatan tanya jawab (3rd ed.). Salemba Empat. https://digilib.ukwk.ac.id/index.php?p=show_detail&id=5086

DeMiguel, V., Mei, X., & Nogales, F. J. (2016). Multiperiod portfolio optimization with multiple risky assets and general transaction costs. Journal of Banking & Finance. https://doi.org/10.1016/j.jbankfin.2016.04.002

Fahria, I., & Kustiawan, E. (2020). Algoritma genetika dalam pembentukan portofolio optimum perusahaan emiten. Jurnal Matematika Dan Statistika Serta Aplikasinya, 8(2), 70. https://doi.org/10.24252/msa.v8i2.16030

Fang, Y., Lai, K. K., & Wang, S. Y. (2005). Portfolio rebalancing model with transaction costs based on fuzzy decision theory. European Journal of Operational Research, 175(2), 879–893. https://doi.org/10.1016/j.ejor. 2005.05.020

Financial Services Authority. (2015). Buku saku Otoritas Jasa Keuangan (2nd ed.). Otoritas Jasa Keuangan. www.ojk.go.id

Grover, J., & Lavin, A. M. (2007). Modern portfolio optimization: A practical approach using an excel solver single-index model. The Journal of Wealth Management, 10(1), 60–72. www.iijournals.com

Liagkouras, K., & Metaxiotis, K. (2018). Multi-period mean–variance fuzzy portfolio optimization model with transaction costs. Engineering Applications of Artificial Intelligence, 67, 260–269. https://doi.org/10.1016/j.engappai.2017.10.010

Lin, C.-C., & Liu, Y.-T. (2008). Genetic algorithms for portfolio selection problems with minimum transaction lots. European Journal of Operational Research 185 (1), 393–404. https://doi.org/10.1016/j.ejor.2006.12.024

Mahayani, N. P. M., & Suarjaya, A. A. G. (2019). Penentuan portofolio optimal berdasarkan model markowitz pada perusahaan infrastruktur di Bursa Efek Indonesia. E-Jurnal Manajemen Universitas Udayana, 8(5), 3057. https://doi.org/10.24843/ejmunud.2019.v08.i05.p17

Markowitz, H. (1952). Portfolio selection. The Journal of Finance, 7(1). https://doi.org/10.1111/j.1540-6261.1952.tb01525

Parker, F. J. (2016). Goal-based portfolio optimization. The Journal of Wealth Management, 19(3), 22–30. https://doi.org/10.3905/jwm.2016.19.3.022

Peterson, B. G., & Carl, P. (2020). PerformanceAnalytics: Econometric Tools for Performance and Risk Analysis (R package version 2.0.4). https://doi.org/10.1016/j.heliyon.2022.e092921

Peterson, S. (2012). Investment theory and risk management. John Wiley & Sons. https://books.google.co.id/books?hl=id&lr=&id=yrA9Wj3A8d4C&oi=fnd&pg=PP15&dq=Peterson,+S.+(2012).+Investment+theory+and+risk+management.+John+Wiley+%26+Sons.&ots=1kjEtMK_Og&sig=5SExUxyeOJYELb0dVUB35LuCXas&redir_esc=y#v=onepage&q=Peterson%2C%20S.%20(2012).%20Investment%20theory%20and%20risk%20management.%20John%20Wiley%20%26%20Sons.&f=false

R Core Team. (2021). R: A language and environment for statistical computing. R Foundation for Statistical Computing. https://cir.nii.ac.jp/crid/1370294721063650048

Rudiawarni, F. A., Sulistiawan, D., & Sergi, B. S. (2022). Is conservatism good news? The case of stocks of Jakarta Islamic index. Heliyon, 8(4). https://www.cell.com/heliyon/pdf/S2405-8440(22)00580-1.pdf

Ruiz-Torrubiano, R., & Su´arez, A. (2015). A memetic algorithm for cardinality-constrained portfolio optimization with transaction costs. Applied Soft Computing, 36, 125–142. https://doi.org/10.1016/j.asoc.2015.06.053

Scrucca, L. (2017). On some extensions to GA package: hybrid optimisation, parallelisation and islands evolution. The R Journal, 9(1), 187–206. https://doi.org/10.32614/RJ-2017-008

Setiawan, E. P., & Rosadi, D. (2019). Model pengoptimuman portofolio mean-variance dan perkembangan praktisnya. Jurnal Optimasi Sistem Industri, 18(1), 25–36. https://doi.org/10.25077/josi.v18.n1.p25-36.2019

Sofariah, A., Saepudin, D., & Umbara, R. F. (2016). Optimasi portofolio saham dengan memperhitungkan biaya transaksi menggunakan algoritma genetika multi-objective. https://openlibrarypublications.telkomuniversity.ac.id/index.php/engineering/article/view/3730

Suksonghong, K., Boonlong, K., & Goh, K.-L. (2014). Multi-objective genetic algorithms for solving portfolio optimization problems in the electricity market. Electrical Power and Energy Systems, 58, 150–159. https://doi.org/10.1016/j.ijepes.2014.01.014

Vazhayil, J. P., & Balasubramanian, R. (2014). Optimization of India’s electricity generation portfolio using intelligent Pareto-search genetic algorithm. Electrical Power and Energy Systems, 55, 13–20. https://doi.org/10.1016/j.ijepes.2013.08.024

Wang, Z., Zhang, X., Zhang, Z., & Sheng, D. (2022). Credit portfolio optimization: A multi-objective genetic algorithm approach. Borsa Istanbul Review, 22(1), 69–76. https://doi.org/10.1016/j.bir.2021.01.004

Woodside-Oriakhi, M. (2011). Portfolio optimisation with transaction cost. School of Information Systems, Computing and Mathematics, Brunel University. http://bura.brunel.ac.uk/handle/2438/5839

Yahoo Finance. (2022). Yahoo Finance. Https://Finance.Yahoo.Com/Quote/ADRO.JK/History?Ltr=1& guccounter=1.

Yang, X. (2006). Improving portfolio efficiency: A genetic algorithm approach. Computational Economics, 28(1), 1–14. https://doi.org/10.1007/s10614-006-9021-y

Yoshimoto, A. (1996). The mean-variance approach to portfolio optimization subject to transaction costs. Journal of the Operations Research Society of Japan, 39(1), 99-117. https://doi.org/10.15807/jorsj.39.99

DOI: https://doi.org/10.31764/jtam.v8i1.17469