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Submitted
November 12, 2025
Accepted
January 30, 2026
Published
February 3, 2025
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Abstract

Stock investment has become increasingly popular in Indonesia, and the construction of an optimal portfolio is essential for effective risk and return management. This study integrates the Capital Asset Pricing Model (CAPM) with the Simulated Annealing algorithm to optimize stock portfolios. The Simulated Annealing algorithm enables flexible and realistic portfolio management by addressing non-linear complexities and market constraints. In addition, this study develops a Graphical User Interface (GUI)-based application using Python to assist investors in calculating and determining optimal portfolio allocations. The application utilizes stock data and investment parameters as inputs and produces optimal allocation outputs based on CAPM and heuristic solutions generated by the Simulated Annealing algorithm. This research offers an efficient and adaptive solution for portfolio optimization in a fluctuating market environment.

Keywords

stock investement, portofolio optimization, capital asset pricing model, simulated annealing, graphical user interface

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Copyright (c) 2025 Rizky Akhmad Subagja, Kartika Yulianti, Fitriani Agustina

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

How to Cite
Subagja, R. A., Yulianti, K., & Agustina, F. (2025). Pengoptimalan Portofolio Saham dengan Capital Asset Pricing Model dan Algoritma Simulated Annealing. Diophantine Journal of Mathematics and Its Applications, 4(2), 85–91. https://doi.org/10.33369/diophantine.v4i2.45880
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References

  1. Putra, I. R. N., & Moelyani, I. A. (2021). Analisis Metode Dollar Cost Averaging Sebagai Strategi Investasi Paling Efektif Untuk Investor Pemula. In Prosiding Seminar Nasional Riset Pasar Modal (Vol. 1, No. 1).
  2. Bodie, Z., Kane, A., & Marcus, A. J. (2018). Investments (11th ed.). McGraw-Hill Education.
  3. Parendra, A., Firmansyah, A., & Prakosa, D. K. (2020). Ukuran perusahaan, leverage, risiko saham di perusahaan perbankan. Dinamika Akuntansi Keuangan dan Perbankan, 9(2), 119-132.
  4. Silalahi, P. R. (2023). Teori Portofolio Dan Analisis Investasi: Integrasi Syariah.
  5. Markowitz, H. (1952). Portfolio Selection. The Journal of Finance, 7(1), 77-91.
  6. Sudarsana, I. M. B., Sedana, I. B. P., & Artini, L. G. S. (2014). Pembentukan Portofolio Optimal Pada Saham-Saham Indeks IDX30 Di PT Bursa Efek Indonesia. E-Jurnal Ekonomi Dan Bisnis Universitas Udayana, 3(2), 81-89.
  7. Adnyana, I. M. (2020). Buku: Manajemen Investasi dan Portofolio.
  8. Treynor, J. L. (1961). Market value, time, and risk. Time, and Risk (August 8, 1961).
  9. Sharpe, W. F. (1964). Capital asset prices: A theory of market equilibrium under conditions of risk. The journal of finance, 19(3), 425-442.
  10. Lintner, J. (1969). The valuation of risk assets and the selection of risky investments in stock portfolios and capital budgets: A reply. The review of economics and statistics, 222-224.
  11. Hidayati, R. S. (2018). Analisis Portofolio Optimal Perusahaan Terdaftar di IHSG dengan Metode CAPM dan Markowitz. Academica: Journal of Multidisciplinary Studies, 2(2), 269-279.
  12. Jayaprana, O. (2014). Perbandingan Return Saham LQ45 Di Bursa Efek Indonesia Dengan Menggunakan Capital Asset Pricing Model (CAPM) dan Arbitrage Pricing Theory (APT) (Doctoral dissertation, Universitas Pendidikan Indonesia).
  13. Busetti, F. (2005). Metaheuristic approaches to realistic portfolio optimization. arXiv preprint cond-mat/0501057.
  14. Kirkpatrick, S., Gelatt, C. D., & Vecchi, M. P. (1983). Optimization by Simulated Annealing. Science, 220(4598), 671-680.
  15. Zhu, H., Wang, Y., Wang, K., & Chen, Y. (2011). Particle Swarm Optimization (PSO) for the constrained portfolio optimization problem. Expert Systems with Applications, 38(8), 10161-10169.
  16. Doerner, K., Gutjahr, W. J., Hartl, R. F., Strauss, C., & Stummer, C. (2004). Pareto ant colony optimization: A metaheuristic approach to multiobjective portfolio selection. Annals of operations research, 131, 79-99.
  17. Gao, W., Sheng, H., Wang, J., & Wang, S. (2018). Artificial bee colony algorithm based on novel mechanism for fuzzy portfolio selection. IEEE Transactions on Fuzzy Systems, 27(5), 966-978.
  18. Crama, Y., & Schyns, M. (2003). Simulated Annealing for complex portfolio selection problems. European Journal of operational research, 150(3), 546-571.
  19. Liadi, E., Dharmawan, K., & Nilakusmawati, DPE (2020). Determining Efficient Stocks Using the Capital Asset Pricing Model (Capm) Method. E-Journal of Mathematics, 9(1), 23.
  20. Husen, M., Masudin, I., & Utama, D. M. (2015). Penjadwalan job shop statik dengan metode simulated annealing untuk meminimasi waktu makespan. Spektrum Industri, 13(2), 115.
  21. Setiawan, E. P., & Rosadi, D. (2019). Model Pengoptimuman Portofolio Mean-Variance dan Perkembangan Praktisnya. Jurnal Optimasi Sistem Industri, 18(1), 25-36.