Model Pengoptimuman Portofolio Mean-Variance dan Perkembangan Praktisnya

Ezra Putranda Setiawan; Dedi Rosadi

doi:10.25077/josi.v18.n1.p25-36.2019

Ezra Putranda Setiawan

SMA Negeri 8 Yogyakarta

http://orcid.org/0000-0002-8869-6799

Dedi Rosadi

Universitas Gadjah Mada

Keywords

Abstract

Many research about portfolio optimization in Indonesia still uses the ‘original’ mean-variance model as proposed by Markowitz more than 60 years ago. This article reviews the development and modification of the Markowitz’s mean-variance model, especially that dealing with real stock-market features, which could help the investor to create their own portfolio. There were several real-stock market features that implemented in the modification of mean-variance portfolios optimization models, such as the minimum transaction lots, the transaction cost, the cardinality constraint, the weight constraint, and the sectoral constraint. To implement these features, several heuristic methods were used to obtain the optimal portfolio weight, such as genetic algorithm, Tabu search, bee colony algorithm, particle swarm algorithm, and simulated annealing. These methods become alternative to the mathematical programming method.

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References

[1] T. Darmadji, H. M. Fakhrudin, Pasar Modal di Indonesia - Pendekatan Tanya Jawab. Edisi 3. Jakarta: Salemba Empat, 2012.

[2] M. Samsul, Pasar Modal dan Manajemen Portofolio. Jakarta: Erlangga, 2015.

[3] H. M. Markowitz, “Portfolio Selection”. Journal of Finance. vol. 7, pp. 77-91, 1952. https://doi.org/10.1111/j.1540-6261.1952.tb01525.x.

[4] R. Ibnas, M. Irwan, and M. Al Ma'arif, “Implementasi Metode Markowitz dalam Pemilihan Portofolio Saham Optimal” Jurnal Matematika Dan Statistika Serta Aplikasinya, vol. 5(2), pp. 33-36, 2017.

https://doi.org/10.24252/jmsa.V5N1P14.

[5] K. A.Latulanit, M. Amin, and M. C. Mawardi, “Analisis Penentuan Portofolio Optimal dengan Menggunakan Model Markowitz pada Perusahaan Sektor Perbankan yang Terdaftar dalam Indeks LQ-45 di Bursa Efek Indonesia” Jurnal Riset Akuntansi, vol. 7(06), pp. 27-41, 2018.

[6] D. Septyanto and B. Kertopati, “Analisis pembentukan portofolio dengan menggunakan Model Markowitz dan Single Index Model pada saham yang masuk dalam Indeks Lq45 di Bursa Efek Indonesia tahun 2009-2013” Jurnal Keuangan dan Perbankan, vol. 16(2), pp. 140-156, 2017.

[7] I. Yunita, “Markowitz Model dalam Pembentukan Porto-folio Optimal (Studi kasus pada Jakarta Islamic Index)” Jurnal Manajemen Indonesia, vol. 18(1), pp. 77-85, 2018. https://doi.org/10.25124/jmi.v18i1.1262.

[8] E. J. Elton, M. J. Gruber, M. W. Padberg, “Simple Criteria for Optimal Portfolio Selection” Journal of Finance vol. 31(5), pp. 1341-1357, 1976. https://doi.org/10.1111/j.1540-6261.1976.tb03217.x.

[9] W. Sharpe, “A Simplified Model of Portfolio Analysis” Management Science vol. 13, pp. 277-293, 1967. https://doi.org/10.1287/mnsc.9.2.277.

[10] H. Soleimani, H. R. Golmakani, M. H. Salimi, “Markowitz-based portfolio selection with minimum transaction lots, cardinality constra-int and regarding sector capitali-zation using genetic algorithm”. Expert System with Applications vol. 36, pp. 5058-5063, 2009.

https://doi.org/10.1016/j.eswa.2008.06.007.

[11] M. Tuba and N. Bacanin, “Artificial bee colony algorithm hybridized with firefly algorithm for cardinality constrained mean-variance portfolio selection problem” Applied Mathe-matics and Information Sciences, vol. 8(6), pp. 2831-2844, 2014. https://doi.org/10.12785/amis/080619.

[12] H. R. Golmakani and M. Fazel, “Constrained portfolio selection using particle swarm algorithm”. Expert System with Application vol. 38, pp. 8327-8335, 2011.

https://doi.org/10.1016/j.eswa.2011.01.020.

[13] B. Kitchenham, Procedures for undertaking systematic reviews. Technical Report TR/SE-0401, Department of Computer Science, Keele University and National ICT, Australia Ltd, 2004.

[14] D. Budgen and P. Brereton, Performing systematic literature reviews in software engineering. In Proceedings of the 28th international conference on Software engineering, ACM, pp. 1051-1052, 2006.

https://doi.org/10.1145/1134285.1134500.

[15] R. Mansini and M. G. Speranza, “Heuristic algorithms for the portfolio selection problem with minimum transaction lots” European Journal of Operational Research, vol. 114, pp. 219-233, 1999. https://doi.org/10.1016/S0377-2217(98)00252-5.

[16] H. Konno and H. Yamazaki, “Mean absolute deviation portfolio optimization model and its application to Tokyo Stock Market” Management Science vol. 7(5), pp. 519-531, 1991. https://doi.org/10.1287/mnsc.37.5.519.

[17] Afnaria. “Algoritma Heuristik untuk Problema Pemilihan Portofolio dengan Adanya Transaksi Lot Minimum”. Bulletin of Mathematics. Vol 3(2), pp. 161-174, 2011.

[18] F. Streichert, H. Ulmer, and A. Zell, Evolutionary algo-rithms and the cardinality constrained portfolio optimization problem. In Operations Research Proceedings, 2003, pp. 253-260). Springer, Berlin, Heidelberg.

https://doi.org/10.1007/978-3-642-17022-5_33.

[19] C. C. Lin, Y-T. Liu, “Genetic algorithms for portfolio selec-tion problems with minimum transaction lots” European Journal of Operational Research. vol. 185, pp. 393-404, 2008. https://doi.org/10.1016/j.ejor.2006.12.024.

[20] L. Chin, E. Chendra, and A. Sukmana, “Analysis of portfolio optimization with lot of stocks amount constraint: case study index LQ45”. In IOP Conference Series: Materials Science and Engineering, 300(1), p. 012004, 2018. https://doi.org/10.1088/1757-899X/300/1/012004.

[21] R. Mansini, W. Ogryczak, M. G. Speranza, “Twenty years of linear programming based portfolio optimization” European Journal of Operational Research vol. 234, pp. 518-535, 2014. https://doi.org/10.1016/j.ejor.2013.08.035.

[22] Z. Bodie, A. Kane, A. J. Marcus, Investment, sixth edition. New York: McGraw-Hill Companies Inc, 2005.

[23] R. D. Arnott and W. H. Wagner, “The measurement and control of trading costs" Financial Analysts Journal. Vol 46, pp. 73-80, 1990. https://doi.org/10.2469/faj.v46.n6.73.

[24] A. F. Perold, “Large-Scale Portfolio Optimization”. Manage-ment science, vol. 30(10), pp. 1143-1160, 1984. https://doi.org/10.1287/mnsc.30.10.1143.

[25] A. Yoshimoto, “The mean-variance approach to portfolio optimization subject to transaction cost” Journal of the Operational Research - Society of Japan. vol. 39(1), pp. 99-117, 1996. https://doi.org/10.15807/jorsj.39.99.

[26] Best, M.J., dan Hlouskova, “An algorithm for portfolio optimizati-on with transaction cost” Management Science. Vol. 51, pp. 1676-1688, 2005.

https://doi.org/10.1287/mnsc.1050.0418.

[27] Kellerer, H., Mansini, R., Speranza, M.G. “Selecting Portfo-lios with Fixed Cost and Minimum Transaction Lots” Annals of Operations Research, vol. 99, pp. 287-304, 2001. https://doi.org/10.1023/A:1019279918596.

[28] R. Mansini, W. Ogryczak, and M. G. Speranza, Linear and Mixed Integer Programming for Portfolio Optimization. New York: Springer, 2015. https://doi.org/10.1007/978-3-319-18482-1.

[29] A. Sofariah, D. Saepudin, R. F. Umbara, Optimasi Portofo-lio Saham dengan Memperhitungkan Biaya Transaksi menggunakan Algoritma Genetika Multi-Objective. e-Proceeding of Engineering. vol. 1, pp. 1156-1168, 2016.

[30] E. J. Elton, M. J. Gruber, S. J. Brown, W. N. Goetzmann, Modern Portfolio Theory and Investment Analysis. Ninth edition. New Jersey: Wiley, 2014.

[31] E. F. Fama, Foundations of Finance: Portfolio Decision and Securities Prices. New York: Basic Books Inc, 1976.

[32] H. Benjelloun, “The Evolution of Risk Diversification” Insurance Markets and Companies: Analyses and Actuarial Computations, vol. 2(2), pp. 94-106, 2011.

[33] J. Y. Campbell, M. Lettau, B. G. Malkiel, Y. Xu, “Have Individual Stocks Become More Volatile? An Empirical Exploration of Idiosyncratic Risk” The Journal of Finance. Vol. 56 (1), pp. 1-43, 2001. https://doi.org/10.1111/0022-1082.00318.

[34] D. Bienstock, “Computational study of a family of mixed integer quadratic programming problems” Mathematical Programming, vol. 74, pp. 121-140, 1996.

https://doi.org/10.1007/BF02592208.

[35] M. Woodside-Oriakhi, C. Lucas, J. E. Beasley, “Heuristic algorithm for the cardinality constrained efficient frontier” European Journal of Operational Research, vol. 213, pp. 538-550, 2011. https://doi.org/10.1016/j.ejor.2011.03.030.

[36] D. Li, X. Sun, J. Wang, “Optimal lot solution to cardinality constrained mean-variance formulation for portfolio selection” Mathematical finance vol. 16, pp. 83-101, 2006. https://doi.org/10.1111/j.1467-9965.2006.00262.x.

[37] J. P. Vielma, S. Ahmed, G. L. Nemhauser, “A lifted linear programming branch-and-bound algorithm for mixed integer conic quadratic programs” INFORMS Journal on Computing vol. 20, pp. 438-450, 2008.

https://doi.org/10.1287/ijoc.1070.0256.

[38] N. Gulpinar, L. T. H. An, M. Moeini, “Robust investment strategies with discrete asset choice constraints using DC programming”. Optimization vol. 59, pp. 45-62, 2010. https://doi.org/10.1080/02331930903500274.

[39] T-J. Chang, N. Meade, J. E. Beasley, Y. M. Sharaiha, “Heuristics for cardinality constrained portfolio optimization” Computer & Operations Research vol. 27, pp. 1271-1302, 2000. https://doi.org/10.1016/S0305-0548(99)00074-X.

[40] A. Fernandez and S. Gomez, “Portfolio selection using neural networks” Computers & Operations Research vol. 34, pp. 1177–1191, 2007.

https://doi.org/10.1016/j.cor.2005.06.017.

[41] S. C. Chiam, K. C. Tan, A. Al-Mamum, “Evolutionary mul-tiobjective portfolio optimization in practical context” International Journal of Automation and Computing vol. 5, pp. 67–80, 2008. https://doi.org/10.1007/s11633-008-0067-2.

[42] J. Branke, B. Scheckenbach, M. Stein, K. Deb, H. Schmeck, “Portfolio optimization with an envelope-based multi-objective evolutionary algorithm” European Journal of Operational Research vol. 199, pp. 684–693, 2009. https://doi.org/10.1016/j.ejor.2008.01.054.

[43] M. C. Bartholomew-Biggs and S. J., “A global optimization pro-blem in portfolio selection”. Compu-tational Management Science, Vol. 6, pp. 329-345, 2009. https://doi.org/10.1007/s10287-006-0038-4.

[44] E.P. Setiawan and D. Rosadi, “Pengoptimuman Portofolio dengan Kendala Karakteristik Perusahaan Emiten” Jurnal Teknik Industri, vol. 19(2), pp. 93-102, 2017. https://doi.org/10.9744/jti.19.2.93-102.

[45] Y. Crama and M. Schyns, “Simulated annealing for complex portfolio optimization problem” European Journal of Operational Research. Vol. 150, pp. 546-571, 2003. https://doi.org/10.1016/S0377-2217(02)00784-1.

[46] R. Bronson, Teori dan Soal-Soal Operations Research (diterjemahkan H.J. Wospakrik), Jakarta: Erlangga, 1991.

[47] F. J. Fabozzi, P. N. Kolm, D. A. Pachamanova, S. M. Focardi, Robust Portfolio Optimization and Management. New Jersey: Wiley, 2007.

https://doi.org/10.3905/jpm.2007.684751.

[48] R. L. Haupt and S. E. Haupt, Practical Genetic Algorithm, 2nd edition. New Jersey: John Wiley and Sons, 2004. https://doi.org/10.1002/0471671746.

[49] Z. Zukhri, Algoritma Genetika: Metode Komputasi Evolu-sioner untuk Menyelesaikan Masalah Optimasi. Yogyakarta: Penerbit Andi, 2014.

[50] S. Arnone, A. Loraschi, A. Tettamanzi, “A genetic approach to portfolio selection”. Neural Network World, vol. 6, pp. 597-604, 1997.

[51] J. Shoaf and J. A. Foster, The efficient set GA for stock portfolios. In Proceedings of the Decision Science Institute, Orlando, pp. 571–573, 1996.

[52] W. Taufiq and S. Rostianingsih, “Penggunaan Algoritma Gene-tika untuk Pemilihan Portofolio Saham dalam Model Markowitz” Jurnal Informatika vol. 6(2), pp. 105-109, 2005.

[53] T-J Chang, S-C Yang, and K-J. Chang, “Portfolio optimiza-tion problems in different risk measures using genetic algorithm” Expert Systems with Applications vol. 36, pp. 10529-10537, 2009.

https://doi.org/10.1016/j.eswa.2009.02.062.

[54] S. Kirkpatrick, C. D. Gelatt, M. P. Vecchi, “Optimization by simulated annealing”. Science vol. 220, pp. 671-680, 1983. https://doi.org/10.1126/science.220.4598.671.

[55] D. T. Pham and D. Karaboga, Intelligent Optimisation Techniques. London: Springer-Verlag, 2000. https://doi.org/10.1007/978-1-4471-0721-7.

[56] I. Lazulfa and P. H. Saputro, Portfolio optimization with buy-in treshold constraint using simulated annealing algorithm. Prosiding Semi-nar Nasional Integrasi Matematika dan Nilai Islami, pp. 370-377, 2011.

[57] M. Gendreau, J-Y. Potvin, Tabu Search. In Burke, K.E., Kendall, G. (ed.) Search Methodologies. 2nd edition. New York: Springer, 2014. pp 243-264.

https://doi.org/10.1007/978-1-4614-6940-7_9.

[58] E. Rolland, “A tabu search method for constrained real-number search: Applications to portfolio selection". Technical report, 1997.

[59] J. Kennedy and R. C. Eberhart, Particle swarm optimization. In Proceedings of the 1995 IEEE International Conference on Neural Networks, 1995, pp. 1942–1948.

[60] M. Reyes-Sierra and C. A. Collo, “Multi-objective particle swarm optimizers: a survey of the state-of-the-art” International Journal of Computational Intelligence Research, vol. 2(3), pp. 287-308, 2006.

https://doi.org/10.5019/j.ijcir.2006.68.

[61] T. Cui, S. Cheng, and R. Bai, “A combinatorial algorithm for the cardinality-constrained portfolio optimization problem” Proceeding of the IEEE Congress on Evolutionary Computation pp. 491-498, 2014.

https://doi.org/10.1109/CEC.2014.6900357.

[62] T. Cura, “Particle swarm optimi-zation approach to portfolio optimization” Nonlinear analysis: Real world applications, vol. 10(4), pp. 2396-2406, 2009.

https://doi.org/10.1016/j.nonrwa.2008.04.023.

[63] O. Ertelince and C. B. Kalayci, “A survey of swarm intelligence for portfolio optimization: algorithms and applications” Swarm and Evolutionary Computation vol. 39, pp. 36-52, 2018.

https://doi.org/10.1016/j.swevo.2018.01.009.

[64] D. T. Pham, A. Ghanbarzadeh, E. Koç, S. Otri, S. Rahim, and M. Zaidi, “The Bees Algorithm-A Novel Tool for Complex Optimisation Problems” Intelligent Production Machines and Systems, pp. 454-459, 2006.

https://doi.org/10.1016/B978-008045157-2/50081-X.

[65] D. Karaboga and B. Basturk, “On the performance of the artificial bee colony (ABC) algorithm” Applied Soft Computing, vol. 8, pp. 687-697, 2008.

https://doi.org/10.1016/j.asoc.2007.05.007.

[66] D. Karaboga and B. Akay, “A comparative study of Artificial Bee Colony Algorithm” Applied Mathematics and Computation. Vol. 214, pp. 108-132, 2009.

https://doi.org/10.1016/j.amc.2009.03.090.

[67] A. Chen, Y. C. Liang, C. C. Liu, “An artificial bee colony algorithm for the cardinality-constrained portfolio optimization problems” In Evolutionary Computa-tion (CEC), 2012 IEEE Congress on pp. 1-8. IEEE, 2012. https://doi.org/10.1109/CEC.2012.6252920.

[68] Z. Wang, S. Liu, and X. Kong, “Artificial bee colony algorithm for portfolio optimization problems” International Journal of Advancements in Computing Technology, vol. 4(4), pp. 8-16, 2012.

https://doi.org/10.4156/ijact.vol4.issue4.2.

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Published

May 16, 2019

https://doi.org/10.25077/josi.v18.n1.p25-36.2019

How to Cite

[1]

E. P. Setiawan and D. Rosadi, “Model Pengoptimuman Portofolio Mean-Variance dan Perkembangan Praktisnya”, J. Optimasi Sist. Ind., vol. 18, no. 1, pp. 25–36, May 2019.

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Vol. 18 No. 1 (2019): Published in May 2019

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