Optimasi Portofolio Saham Syariah Menggunakan Model Indeks Tunggal dan VaR Berbasis GUI Matlab

Lindrawati Abdjul; Resmawan Resmawan; Agusyarif Rezka Nuha; Nurwan Nurwan; Djihad Wungguli; La Ode Nashar

doi:10.34312/jjom.v5i1.18570

Optimasi Portofolio Saham Syariah Menggunakan Model Indeks Tunggal dan VaR Berbasis GUI Matlab

Lindrawati Abdjul, Resmawan Resmawan, Agusyarif Rezka Nuha, Nurwan Nurwan, Djihad Wungguli, La Ode Nashar

Abstract

Sharia-based investment is an investment by the community to obtain profits in accordance with Islamic principles and law. This study aims to calculate the optimal portfolio return value using the Single Index Model, calculate risk with VaR (Value at Risk), and then implement it with Matlab’s GUI (Graphical User Interface). The data used is closing stock price data on the JII (Jakarta Islamic Index) using 30 stocks for two consecutive years. Furthermore, these stocks are selected which have a positive average return value. The study results show that 14 stocks are candidates for optimal portfolios with positive return values, namely: ACES, ADRO, ANTM, BRPT, BTPS, CTRA, EXCL, INCO, MDKA, MNCN, SCMA, TPIA, UNTR, and WIKA. Then the optimal portfolio of the 14 stocks is determined using the Single Index Model considering the ERB (Excess Return to Beta) value ≥ cut-off point value (C*). Based on the value, 4 shares were obtained that belong to the optimal portfolio, namely: MDKA, BRPT, BTPS, and ANTM. Furthermore, VaR calculations are performed on the 4 optimal portfolios to obtain optimum VaR consistency values with 500 repetitions. The VaR calculation results with a 95% confidence level show that the average VaR result is in the range of -0.14704 to -0.3420 so that when investors invest in 4 optimal stocks, the losses experienced by investors are no more than 34%.

Keywords

Investation; Single Index Model; Value at Risk; Sharia Stock; Graphical User Interface

Full Text:

PDF

References

E. Tandelilin, Portofolio dan Investasi: Teori dan Aplikasi. Yogyakarta: Kanisius, 2010.

N. S. M. Mussafi, “Analisis Risk Asset Portfolio Berbasis Reward To Variability Pada Saham Syariah Di Indonesia Menggunakan Nonlinear Programming,” Jurnal Matematika ”MANTIK”, vol. 3, no. 2, pp. 57–64, oct 2017, doi: 10.15642/mantik.2017.3.2.57-64.

C. A. Chairunnisa, H. Yozza, and D. Devianto, “Pengukuran Nilai Risiko Portofolio Berdasarkan Mean-VaR,” J. Mat. UNAND, vol. 7, no. 1, pp. 24–32, 2018, doi: 10.25077/jmu.7.1.24-32.2018.

N. P. Iriani, M. S. Akbar, and H. Haryono, “Estimasi Value at Risk (VaR) pada Portofolio Saham dengan Copula,” J. Sains Dan Seni Pomits, vol. 2, no. 2, pp. D195–D200, 2013, doi: 10.12962/j23373520.v2i2.4653.

T. S. Nuryanto, A. Prahutama, and A. Hoyyi, “Historical Simulation Untuk Menghitung Value At Risk Pada Portofolio Optimal Berdasarkan Single Index Model Menggunakan Gui Matlab,” J. Gaussian, vol. 7, no. 4, pp. 408–418, 2018, doi: 10.14710/j.gauss.v7i4.28869.

A. K. Z. Bodie and A. J. Marcus, Investments, 10th ed. New York: McGraw-Hill Education, 2014.

G. Cornuejols, J. Pe'na, and R. Tutuncu, Optimization Methods in Finance, 2nd ed. Cambridge: Cambridge University Press, 2018, doi: https://doi.org/10.1017/9781107297340.

S. I. U. Chasanah, S. Abdullah, N. Valentika, U. Kiftiyani, and A. R. Nuha, “Analisis Pembentukan Portofolio Optimal Saham-Saham Jakarta Islamic Index (Jii) Pada Masa Pandemi Covid-19,” J. Saintika Unpam J. Sains dan Mat. Unpam, vol. 3, no. 1, pp. 52–67, 2020, doi: http://dx.doi.org/10.32493/jsmu.v3i1.5649.

A. Damayanti and R. Subekti, “Optimasi Portofolio Menggunakan Pendekatan Least Diskriminant Dengan Return Black Litterman,” Jurnal Kajian dan Terapan Matematika, vol. 6, no. 4, pp. 46–51, 2017.

I. R. Saputri and E. Arliani, “Optimasi Portofolio Saham Menggunkan Separable Programming,” Jurnal Kajian dan Terapan Matematika, vol. 7, no. 2, pp. 28–37, 2018.

L. Muzdalifah, “Optimasi Portofolio dengan Kendala Buy-In Threshold Menggunakan Metode Cuckoo Search,” Jurnal Riset dan Aplikasi Matematika (JRAM), vol. 2, no. 1, pp. 13–22, apr 2018, doi: 10.26740/jram.v2n1.p13-22.

E. K. Dewi, D. Ispriyanti, and A. Rusgiyono, “Expected Shortfall Pada Portofolio Optimal Dengan Metode Single Index Model (Studi Kasus pada Saham IDX30),” Jurnal Gaussian, vol. 10, no. 2, pp. 269–278, may 2021, doi: 10.14710/j.gauss.v10i2.30947.

H. Y. Astuti, N. I. Yuli, and T. Tarno, “Optimasi Value At Risk Return Aset Tunggal Dan Portofolio Menggunakan Simulasi Monte Carlo Dilengkapi Gui Matlab,” J. Gaussian, vol. 5, no. 4, pp. 695–704, 2016, doi: https://doi.org/10.14710/j.gauss.5.4.695-704.

S. B. Abdillah and S. Rahayu, “Analisis pembentukan portofolio optimal menggunakan model indeks tunggal untuk pengambilan keputusan investasi,” in e-Proceeding Manag., 2015, pp. 1–15.

S. A. Heryanti, “Perhitungan Value at Risk Pada Portfolio Optimal: Studi Perbandingan Saham Syariah dan Saham Konvensional,” IKONOMIKA, vol. 2, no. 1, pp. 75–84, may 2017, doi: 10.24042/febi.v2i1.958.

R. R. Margana and L. G. Sri Artini, “Pembentukan Portofolio Optimal Menggunakan Model Indeks Tunggal,” E-Jurnal Manajemen Universitas Udayana, vol. 6, no. 2, 2017.

DOI: https://doi.org/10.34312/jjom.v5i1.18570