Mean-Variance Portfolio Optimization with Lot Size Constraints in Energy Stocks: A Monte CarloApproach

Willen Vimelia, Riaman Riaman, Sukono Sukono

Abstract


Stock investment requires portfolio optimization strategies that maximize returns and consider risks and practical constraints, such as target lot sizes. These constraints are crucial to ensuring the realistic implementation of portfolios in compliance with market regulations, particularly in Indonesia, where 1 lot equals 100 shares. However, existing research on the Mean-Variance model and Monte Carlo simulation has rarely incorporated target lot constraints, limiting the applicability of these models in real-world scenarios. To bridge this gap, this study conducts a systematic literature review (SLR) on portfolio optimization in Indonesia's energy sector stocks, focusing on the Mean-Variance model, risk aversion, Monte Carlo simulation, and target lot constraints. The PRISMA framework guides this SLR, with bibliometric analysis performed using RStudio. A rigorous selection process from Scopus and ScienceDirect databases yielded 13 relevant articles for in-depth analysis creates a more practical and effective approach to portfolio management. This advancement enables investors to achieve balanced portfolios that are both theoretically robust and feasible in practice. The study contributes significantly to optimizing investment strategies for Indonesia’s energy sector and opens avenues for further research into practical portfolio optimization methods.

Keywords


Portfolio optimization; Mean-Variance; Monte Carlo; Lot constraints; Energy Stock

Full Text:

PDF

References


[1] M. Purwantini, R. H. Yustrianthe, E. Grediani, and Handayani, “Determinan faktor yang mempengaruhi minat investasi,” Fair Value J. Ilm. Akunt. dan Keuang., vol. 5, no. 4, pp. 1577–1585, 2022, doi: 10.32670/fairvalue.v5i4.2623.

[2] S. Senthilnathan, “Risk, Return and Portfolio Theory A Contextual Note,” SSRN Electron. J., no. October, 2015, doi: 10.2139/ssrn.2627423.

[3] Z. Puspitaningtyas, Prediksi Risiko Investasi Saham. Yogyakarta: Griya Pandiva, 2015.

[4] Liestyowati, L. M. Possumah, R. M. Yadasang, and H. Ramadhani, “Pengaruh Diversifikasi Portofolio terhadap Pengelolaan Risiko dan Kinerja Investasi: Analisis pada Investor Individu,” J. Akunt. Dan Keuang. West Sci., vol. 2, no. 03, pp. 187–194, 2023, doi: 10.58812/jakws.v2i03.642.

[5] M. Ramadhan, T. Suharti, and I. Nurhayati, “Diversifikasi Saham Dalam Pembentukan Portofolio Untuk Meminimumkan Risiko,” Manag. J. Ilmu Manaj., vol. 3, no. 4, p. 450, 2020, doi: 10.32832/manager.v3i4.3914.

[6] Y. Priyatna and F. Sukono, “Optimasi Portofolio Investasi dengan Menggunakan Model Markowitz,” J. Mat. dan Komput., vol. 6, no. 1, pp. 1–10, 2003.

[7] I. G. A. G. N. Raditya, D. Saepudin, and I. Kurniawan, “Optimasi Portofolio Saham dengan Pendekatan Box Uncertainty Set Studi Kasus : IDX 30,” e-Proceeding Eng., vol. 8, no. 1, pp. 918–929, 2021.

[8] D. H. Bangun, S. P. Anantadjaya, and L. Lahindah, “Portofolio Optimal Menurut Markowitz Model Dan Single Index Model : Studi Kasus Pada Indeks Lq45,” JAMS - J. Manag. Stud., vol. 01, no. 01, pp. 70–93, 2012.

[9] M. Ivanova and L. Dospatliev, “Application of Markowitz Portfolio Optimization on Bulgarian Stock Market From 2013 To 2016,” Int. J. Pure Apllied Math., vol. 117, no. 2, Jan. 2018, doi: 10.12732/ijpam.v117i2.5.

[10] R. Robiyanto, “Performance Evaluation and Risk Aversion Rate for Several Stock Indices in Indonesia Stock Exchange,” J. Manaj. dan Kewirausahaan, vol. 19, no. 1, pp. 60–64, 2017, doi: 10.9744/jmk.19.1.60-64.

[11] A. Díaz and C. Esparcia, “Assessing Risk Aversion From the Investor’s Point of View,” Front. Psychol., vol. 10, 2019, doi: 10.3389/fpsyg.2019.01490.

[12] D. S. Lestari, “Analisis Pengaruh Program ‘Yuk Nabung Saham’ oleh PT Bursa Efek Indonesia terhadap Minat Mahasiswa untuk Berinvestasi di Pasar Modal,” J. Ilmu Sos. Manajemen, Akuntansi, dan Bisnis, vol. 2, no. 3, pp. 1–13, 2021, doi: 10.47747/jismab.v2i3.363.

[13] Megawati, Resmawan, B. R. Payu, and A. Adityaningrum, “Prediksi Pergerakan Saham Menggunakan Metode Simulasi Monte Carlo untuk Pembentukan Portofolio Optimal dengan Pendekatan Model Markowitz,” J. Stat. dan Apl., vol. 6, no. 1, pp. 86–95, 2022, doi: 10.21009/jsa.06108.

[14] R. D. Putra, Y. Apridiansyah, and E. Sahputra, “Penerapan Metode Monte Carlo pada Simulasi Prediksi Jumlah Calon Mahasiswa Baru Universitas Muhammadiyah Bengkulu,” PROCESSOR, vol. 17, no. 2, pp. 74–81, 2022, doi: 10.33998/processor.2022.17.2.1224.

[15] H. Manurung, “Analisis Kinerja Portofolio Saham dengan Menggunakan Metode Sharpe, Jensen dan Treyno,” J. Bus. Stud., vol. 04, no. 1, pp. 1–16, 2019, [Online]. Available: http://etd.ugm.ac.id/index.php?mod=penelitian_detail&sub=PenelitianDetail&act=view&typ=html&buku_id=9923

[16] C. Mari, “Hedging electricity price volatility using nuclear power,” Appl. Energy, vol. 113, pp. 615–621, 2014, doi: 10.1016/j.apenergy.2013.08.016.

[17] T. Petropoulos, K. Liapis, and E. Thalassinos, “Optimal Structure of Real Estate Portfolio Using EVA: A Stochastic Markowitz Model Using Data from Greek Real Estate Market,” Risks, vol. 11, no. 2, 2023, doi: 10.3390/risks11020043.

[18] S. Wang, G. Cai, P. Yu, G. Liu, and J. Luo, “Mean-Variance Portfolio Optimization with Nonlinear Derivative Securities,” Proc. - Winter Simul. Conf., pp. 576–587, 2023, doi: 10.1109/WSC60868.2023.10407819.

[19] R. Mallieswari, V. Palanisamy, A. T. Senthilnathan, S. Gurumurthy, J. J. Selvakumar, and S. Pachiyappan, “A Stochastic Method for Optimizing Portfolios Using a Combined Monte Carlo and Markowitz Model: Approach on Python,” Econ. - Innov. Econ. Res. J., vol. 12, no. 2, pp. 113–127, 2024, doi: 10.2478/eoik-2024-0014.

[20] M. J. Page et al., “The PRISMA 2020 statement: An updated guideline for reporting systematic reviews,” Br. Med. J., vol. 372, 2021, doi: 10.1136/bmj.n71.

[21] E. Bikas and E. Bikas, “Towards sustainable financial markets: Impact of structured securities on portfolio management,” J. Secur. Sustain. Issues, vol. 6, no. 2, pp. 275–288, 2016, doi: 10.9770/jssi.2016.6.2(7).

[22] D. P. Neto, E. G. Domingues, A. P. Coimbra, A. T. de Almeida, A. J. Alves, and W. P. Calixto, “Portfolio optimization of renewable energy assets: Hydro, wind, and photovoltaic energy in the regulated market in Brazil,” Energy Econ., vol. 64, pp. 238–250, 2017, doi: 10.1016/j.eneco.2017.03.020.

[23] C. Zhang, R. Hu, and L. Wei, “Uncertain portfolio selection model considering transaction costs and minimum transaction lots requirement,” J. Intell. Fuzzy Syst., vol. 32, no. 6, pp. 4543–4554, 2017, doi: 10.3233/JIFS-169218.

[24] M. Shadabfar and L. Cheng, “Probabilistic approach for optimal portfolio selection using a hybrid Monte Carlo simulation and Markowitz model,” Alexandria Eng. J., vol. 59, no. 5, pp. 3381–3393, 2020, doi: 10.1016/j.aej.2020.05.006.

[25] R. S. Lubis, H. Mawengkang, O. Darnius, and Mardiningsih, “A novel approach based on active constraint for minimizing var in the portofolio optimization problem,” J. Theor. Appl. Inf. Technol., vol. 99, no. 15, pp. 3703–3712, 2021.

[26] M.-F. Leung and J. Wang, “Cardinality-constrained portfolio selection based on collaborative neurodynamic optimization,” Neural Networks, vol. 145, pp. 68–79, 2022, doi: 10.1016/j.neunet.2021.10.007.

[27] A. Mukherjee, A. K. Singh, P. K. Mallick, and S. R. Samanta, “Portfolio Optimization for US-Based Equity Instruments Using Monte-Carlo Simulation,” 2022, pp. 691–701. doi: 10.1007/978-981-16-8763-1_57.

[28] L. Lv, B. Zhang, and H. Li, “An uncertain bi-objective mean-entropy model for portfolio selection with realistic factors,” Math. Comput. Simul., vol. 225, pp. 216–231, 2024, doi: 10.1016/j.matcom.2024.05.013.

[29] R. A. E. Mäkinen and J. Toivanen, “Short Communication: Monte Carlo Expected Wealth and Risk Measure Trade-Off Portfolio Optimization,” SIAM J. Financ. Math., vol. 15, no. 2, pp. SC41–SC53, 2024, doi: 10.1137/23M1624439.




DOI: https://doi.org/10.18860/cauchy.v10i1.32159

Refbacks

  • There are currently no refbacks.


Copyright (c) 2025 Willen Vimelia, Riaman Riaman, Sukono Sukono

Creative Commons License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

Editorial Office
Mathematics Department,
Universitas Islam Negeri Maulana Malik Ibrahim Malang
Gajayana Street 50 Malang, East Java, Indonesia 65144
Faximile (+62) 341 558933
e-mail: cauchy@uin-malang.ac.id

Creative Commons License
CAUCHY: Jurnal Matematika Murni dan Aplikasi is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.