Business Index 27 Stock Portfolio Optimization Using the Black Litterman Model Accompanied by Value At Risk Calculation
Bahasa Indonesia
DOI:
https://doi.org/10.20956/j.v21i1.36306Keywords:
Investment, Indeks Bisnis 27, Black Litterman Model, Value at RiskAbstract
An investment can provide a profit with a certain level of risk for an investor both now and in the future. This indicates that investments are important in both financial and asset management. Finance investments can be made on several stocks or portfolios. To profit from an investment, you need a tool to optimize profit and risk, which is a portfolio. This research uses the Black Litterman Model in portfolio optimization along with Value at Risk (VaR) calculations to determine the risk of each stock. The data used is close price data on the Business Index 27 for the period January-December 2023. Next, selected 9 shares in the formation of an optimal portfolio namely, AKRA, AMRT, ASII, BBCA, BBNI, BBRI, INKP, KLBF and TLKM. Based on the calculations, the rate of profit achieved on the portfolio is 5.48% with a risk of 0.40%. Then use the Historical Method and the Monte Carlo Simulation Method to calculate the VaR using nine optimal stocks, with a 95% confidence rate. In the Monte Carlo simulation, 300 repetitions of VaR calculations are performed. Different results on both methods are due to different approaches to risk calculation
References
Abdjul, L., Resmawan, Nuha, A.R., Nurwan, Wungguli, D. & Nashar, L.O., 2023. Optimasi Portofolio Saham Syariah Menggunakan Model Indeks Tunggal dan VaR Berbasis GUI Matlab. Jambura J. Math., Vol.5, No. 1, 243-253.
Abdullaevich, M.M., 2020. The Basic Concepts Of Investment And Its Importance JournalNX- A Multidiscip. Peer Rev. J., Vol. 6, No. 6, 193-196.
Arisena, A. & Sugiyanto, I., 2019. Return Portofolio Optimal Menggunakan Single View Black-litterman Model dengan Pendekatan ARIMA (Autoregressive Integrated Moving Average). J. Co Manag., Vol. 2, No. 2, 258–264.
Atmaja, M.Z.E., Prahutama, A. & Ispriyanti, D., 2021. Pembentukan Dan Pengukuran Kinerja Portofolio Efisien Dengan Metode Correlation Model Menggunakan GUI Matlab (Studi Kasus: Kelompok Saham pada Indeks JII, LQ45, dan INFOBANK15). J. Gaussian, Vol. 10, No. 2, 180–189.
Azis, I., Syazali, M. & Manurung, E.N., 2023. The Optimal Portfolio Of Islamic Stocks Using The Markowitz And Black-Litterman Models. Desimal J. Mat., Vol. 6, No. 1, 1–6.
Elton, E.J., Gruber, M.J., Brown, S.J. & Goetzmann, W.N., 2014. Modern Portfolio Theory and Investment Analysis, 9th Edition. John Wiley & Sons Inc.
Ermiati, P. & Sari, D.P., 2022. Analisis Sensitivitas Model Black-Litterman Menggunakan Treynor Ratio pada Portofolio Saham. J. Math. UNP., Vol. 7, No. 1, 52–60.
Finance, Y., 2023. Yahoo Finance https://finance.yahoo.com/. [25 Februari 2024]
Härdle, W.K. & Simar, L., 2015. Applied Multivariate Statistical Analysis, 4th Edition. J Springer.
Hasan, N., Pelleng, F.A.O. & Mangindaan, J.V., 2019. Analisis Capital Asset Pricing Model (CAPM) Sebagai Dasar Pengambilan Keputusan Berinvestasi Saham (Studi pada Indeks Bisnis-27 di Bursa Efek Indonesia). J. Adm. Bisnis, Vol. 8, No. 1, 36–43.
Indonesia, B., 2023. Bank Indonesia https://www.bi.go.id/. [26 Februari 2024]
Litterman, B., 2003. Modern Investment Management - An Equilibrium Approach. John Wiley & Sons, Inc., USA: Wiley.
Medika, A.N. & Sari, D.P., 2023. Penerapan Model Black Litterman Dalam Pembentukan Portofolio Saham Indeks LQ-45. MATHunesa, Vol. 11, No. 3, 551–559.
Murtadina, U.A. & Saputro, D.R.S., 2019. Optimalisasi Portofolio dengan Metode Black-Litterman Melalui Pendekatan Bayes. Prosiding Sendika, Vol.5 thn 2019, 236-240. Fakultas Keguruan dan Ilmu Pendidikan Universitas Muhammadiyah, Purworejo.
Muthohiroh, U., Rahmawati, R. & Ispriyanti, D., 2021. Pendekatan Metode Markowitz Untuk Optimalisasi Portofolio Dengan Risiko Expected Shortfall (Es) Pada Saham Syariah Dilengkapi GUI Matlab. J. Gaussian, Vol. 10, No. 3, 445–454.
Nainggolan, Y.T., Juliana, A. & Alantina, C.A., 2020. Analisis Value At Risk Dalam Pembentukan Portofolio Optimal (Studi Kasus Perusahaan Perbankan Di Indonesia). J. Manaj., Vol. 10, No. 2, 124–136.
Roman, S., 2014. Introduction To The Mathematics Of Finance. Spinger Science+Business Media. New York.
Solihatun, A., Gubu, L., Aswani, Cahyono, E. & Saidi, L.O., 2023. 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. 1, 245-254.
Subekti, R., 2008. Aplikasi Model Black Litterman dengan Pendekatan Bayes (Studi kasus : portofolio dengan 4 saham dari S&P500). Seminar Nasional Matematika FMIPA UNY thn 2008, 1-12. Fakultas Matematika dan Ilmu Pengetahuan Alam Universitas Negeri Yogyakarta, Yogyakarta.
Tandelilin, E., 2010. Portofolio dan Investasi Teori dan Aplikasi, 1st Edition. Penerbit Kanisus. Yogyakarta.
Wagafir, Y., Rasjid, H. & Pongoliu, Y.I., 2022. Analisis Penerapan Metode Single Index Model dan Constant Correlation Model dalam Optimalisasi Portofolio Saham Indeks LQ-45 di Bursa Efek Indonesia ( BEI ) Periode 2019-2021. Islam. Econ. Financ. Journal, Vol. 1, No. 2, 93–114.
Zhao, Y. & Xu, W., 2023. Risk Measurement Of China’s Green Financial Market Based On B-Spline Quantile Regression. Heliyon, Vol. 9, No. 6, 1–8.
Downloads
Published
Issue
Section
License
Copyright (c) 2024 Jurnal Matematika, Statistika dan Komputasi
This work is licensed under a Creative Commons Attribution 4.0 International License.
This work is licensed under a Creative Commons Attribution 4.0 International License.
Jurnal Matematika, Statistika dan Komputasi is an Open Access journal, all articles are distributed under the terms of the Creative Commons Attribution License, allowing third parties to copy and redistribute the material in any medium or format, transform, and build upon the material, provided the original work is properly cited and states its license. This license allows authors and readers to use all articles, data sets, graphics and appendices in data mining applications, search engines, web sites, blogs and other platforms by providing appropriate reference.
