Analysis of Optimal Portfolio Formation Using Multi-Objective Optimization Method and Nadir Compromise Programming

Randa Resvitasari Aliwu, Emli Rahmi, Agusyarif Rezka Nuha, Lailany Yahya, Djihad Wungguli, Armayani Arsal

Abstract


A portfolio is a collection of financial assets in the stocks owned by a company or individual. An optimal portfolio is a selected portfolio that aligns with the investor's preferences, drawn from a set of efficient portfolios that have been formed. This research aims to create an optimal portfolio using the Multi-Objective Optimization method and the Nadir Compromise Programming (NCP) method. Additionally, Value at Risk (VaR) analysis is applied to determine the maximum risk an investor will bear for the portfolio. The data used consists of closing stock prices on the IDX30 Index from February 2022 to July 2023. The findings indicate that the optimization approach produces portfolios that align with investor risk-return preferences. The comparison of Multi-Objective Optimization and NCP methods provides insights into their effectiveness in portfolio selection. Furthermore, the VaR analysis helps investors understand potential risk levels, offering a comprehensive perspective on portfolio performance.


Keywords


Multi-Objective Optimization Method; Optimal Portfolio; Value at Risk

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References


J. Avianti and M. Ratnasari, “Analisis Pembentukan Portofolio Optimal dengan Single Index Model dan Z-Score pada Emiten IDX BUMN 20,†Journal of Emerging Business Management and Entrepreneurship Studies, vol. 1, no. 1, pp. 21–38, 2021, doi: 10.34149/jebmes.v1i1.4.

A. W. Anggraeni, A. Ramli, and Anwar, “Optimasi Portofolio Pada Saham Indeks Idx80 Di Bursa Efek Indonesia Dengan Menggunakan Model Markowitz Sebagai Dasar Penetapan Investasi,†Edunomika, vol. 7, no. 1, pp. 1–13, 2023, doi: 10.29040/jie.v7i1.6610.

S. A. Mulya, A. Aziz, and T. Permadhy, “Pembentukan Portofolio Optimal Dengan Model Markowitz Sebagai Dasar Keputusan Investasi,†in PROSIDING BIEMA Business Management, Economic, and Accounting National Seminar, vol. 1, 2020, pp. 1242–1256.

K. I. Sari, K. Dharmawan, and L. P. I. Harini, “Penentuan Portofolio Optimal Saham Yang Tergolong Indeks Lq45 Menggunakan Fungsi Utilitas Bentuk Pangkat,†E-Jurnal Matematika, vol. 9, no. 1, p. 85, 2020, doi: 10.24843/mtk.2020.v09.i01.p283.

S. Handini and E. Astawinetu, Teori Portofolio dan Pasar Modal Indonesia. Scopindo Media Pustaka, 2020.

A. Rahman, “Pembentukan Portofolio Optimal Menggunakan Single Indeks Model pada Saham yang Terdaftar di Indeks LQ-45 (Periode 2016-2021),†Ph.D. dissertation, Universitas Pakuan, 2022.

N. P. Hartono, O. Rohaeni, and E. Kurniati, “Menentukan Portofolio Optimal Menggunakan Model Markowitz,†Jurnal Riset Matematika, vol. 1, no. 1, pp. 57–64, 2021, doi: 10.29313/jrm.v1i1.162.

M. Ermis, M. Rasuli, and A. Rokhmawati, “Analisis Perbandingan Kinerja Portofolio Optimal Markowitz Model dan Treynor Black Model pada Saham LQ45 di Bursa Efek Indonesia,†Jurnal Ekonomi KIAT, vol. 31, no. 1, pp. 29–35, 2020, doi: 10.25299/kiat.2020.vol31(1).2737.

M. R. Saputra and D. Saepudin, “Optimasi Portofolio Berbasis Prediksi Return Saham Menggunakan Hybrid XGBoost dan Improved Firefly Algorithm untuk Saham–Saham dalam Indeks LQ45,†in eProceedings of Engineering, vol. 10, no. 3, 2023, pp. 3505–3514. [Online]. Available: https://openlibrarypublications.telkomuniversity.ac.id/.

Y. C. Duan, “A Multi-objective Approach to Portfolio Optimization,†Undergraduate Mathematics Journal Rose-Hulman Undergraduate Mathematics Journal, vol. 8, no. 1, p. 12, 2007.

M. P. P. Pranata, “Optimalisasi Portofolio Saham Menggunakan Metode Multi Objektif Berdasarkan Indeks IDX-MES BUMN 17,†Skripsi, Universitas Islam Negeri Sultan Syarif Kasim Riau Pekanbaru, 2022. [Online]. Available: http://repository.uin-suska.ac.id/id/eprint/62375.

M. Amiri, M. Ekhtiari, and M. Yazdani, “Nadir compromise programming: A model for optimization of multi-objective portfolio problem,†Expert Systems with Applications, vol. 38, no. 6, pp. 7222–7226, 2011, doi: 10.1016/j.eswa.2010.12.061.

M. Mustafian, M. Mauliddin, and A. Abdal, “Penerapan Value at Risk dan Conditional Value at Risk dalam Pengukuran Risiko Portofolio Optimal Menggunakan Pendekatan Simulasi Monte Carlo,†Jurnal Riset dan Aplikasi Matematika (JRAM), vol. 08, no. 01, pp. 39–50, 2024, doi: 10.26740/jram.v8n1.p39-50.

I. W. E. Sultra, M. R. Katili, and M. R. F. Payu, “Metode Simulasi Historis Untuk Perhitungan Nilai Value At Risk Pada Portofolio Dengan Model Markowitz,†Euler : Jurnal Ilmiah Matematika, Sains dan Teknologi, vol. 9, no. 2, pp. 94–102, 2021, doi: 10.34312/euler.v9i2.11518.

E. D. Septyanto, “Analisis Portofolio Optimal Menggunakan Metode Multi Objektif pada Saham Jakarta Islamic Index,†Journal Of Mathematics UNP, vol. 4, no. 1, pp. 1–17, 2019.

R. Y. Indriani, D. Suhaedi, and F. H. Badruzzaman, “Penggunaan Metode Nadir Compromise Programming dalam Menyelesaikan Permasalahan Multi Objektif,†Jurnal Riset Matematika, vol. 1, no. 2, pp. 82–90, 2021, doi: 10.29313/jrm.v1i2.364.

A. Solihatun, L. Gubu, A. Aswani, E. Cahyono, and L. O. Saidi, “Perhitungan Value at Risk (VaR) Pada Portofolio Saham IDX Sektor Keuangan (IDXFINANCE) Menggunakan Metode Simulasi Historis (Historical Simulation Method),†Jurnal Matematika, Komputasi dan Statistika, vol. 3, no. April, pp. 245–254, 2023.

L. Abdjul, R. Resmawan, A. R. N. Nuha, N. Nurwan, D. Wungguli, and L. O. Nashar, “Optimasi Portofolio Saham Syariah Menggunakan Model Indeks Tunggal dan VaR Berbasis GUI Matlab,†Jambura Journal of Mathematics, vol. 5, no. 1, pp. 243–253, 2023, doi: 10.34312/jjom.v5i1.18570.

IDX, “IDX Channel,†2022. [Online]. Available: https://www.idx.co.id/id/datapasar/data-saham/indeks-saham/. [Accessed: Jan. 31, 2024].

Yahoo Finance, “Yahoo Finance,†2022. [Online]. Available: https://finance.yahoo.com. [Accessed: Feb. 5, 2024].




DOI: https://doi.org/10.37905/jjom.v7i1.29065



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