Perbandingan Value at Risk dan Expected Shortfall pada Portofolio Optimal menggunakan Metode Downside Deviation

Indah Nugrahaeni; Hendra Perdana; Neva Satyahadewi

doi:10.37905/jjom.v6i2.24326

Perbandingan Value at Risk dan Expected Shortfall pada Portofolio Optimal menggunakan Metode Downside Deviation

Indah Nugrahaeni, Hendra Perdana, Neva Satyahadewi

Abstract

Portfolio formation is one of the strategies that investors can do to get the best results Portfolio formation can use the Downside Deviation method. The optimal portfolio with this method uses downside deviation and sets the return below the benchmark as a measure of risk. Every optimal portfolio certainly cannot be separated from risk. To measure risk, you can use the Value at Risk (VaR) and Expected Shortfall values. This study aims to form an optimal portfolio using the Downside Deviation method and continued by comparing the possible losses that occur from the formed portfolio using the VaR and Expected Shortfall values. The data used in this study is the daily closing price data of LQ-45 Index stocks in the banking sector in the period February-June 2023. From the stock data, data selection is carried out by selecting stocks that have a positive expected return and are normally distributed. Then, the optimal portfolio formation stage is continued using the Downside Deviation method and comparing the possible risks formed with the VaR and Expected Shortfall values. The results of this study show that the optimal portfolio with the Downside Deviation method consists of four stocks, namely with the stock codes BRIS.JK, BBRI.JK, BBNI.JK, and BBCA.JK. This study uses a case example by investing capital of Rp100,000,000 with a one-day time period and three levels of confidence, namely 90%, 95%, and 99%. Based on the comparison of the risk value of the portfolio formed using VaR and Expected Shortfall, it is shown that the possible risk with the Expected Shortfall method is greater than the VaR value. Therefore, Expected Shortfall is better in estimating the maximum risk.

Keywords

Portfolio; Downside Deviation; Value at Risk; Expected Shortfall

Full Text:

PDF

References

E. Tandelilin, “Dasar-dasar manajemen investasi,” Manajemen Investasi, vol. 34, pp. 117-121, 2010.

F. S. Mar’ati, “Mengenal Pasar Modal (Instrumen Pokok dan Proses

Go Public),” Among Makarti, vol. 3, no. 1, pp. 79–88, 2010. doi: 10.52353/ama.v3i1.19.

S. Hasbiah, Anwar, and B. Bado, “Model Markowitz dalam Keputusan Investasi Saham pada Index LQ45 di Bursa Efek Indonesia,” Jekpend, vol. 5, no. 1, pp. 69–77, 2022. doi: 10.26858/jekpend.

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, Dec. 2021. doi: 10.34312/euler.v9i2.11518.

E. P. Setiawan and D. Rosadi, “Model Pengoptimuman Portofolio MeanVariance dan Perkembangan Praktisnya,” Jurnal Optimasi Sistem Industri, vol. 18, no. 1, pp. 25–36, May 2019. doi: 10.25077/josi.v18.n1.p25-36.2019.

I. B. A. Darmayuda, K. Dharmawan, and K. Sari, “Estimasi Expected Shortfall dalam Optimalisasi Portofolio dengan Metode Downside Deviation pada Saham IDXHEALTH,” E-Jurnal Matematika, vol. 12, no. 2, pp. 114–120, 2023. doi: 10.24843/MTK.2023.v12.i02.p408.

Y. Konan, D. Kusnandar, and N. Imro’ah, “Penerapan Metode Exponentially Weighted Moving Average dan Metode Semi Varians dalam Perhitungan Risiko Portofolio Saham,” Bimaster: Buletin Ilmiah Matematika, Statistika dan Terapannya, vol. 11, no. 2, pp. 309–318, 2022. doi: 10.26418/bbimst.v11i02.53482.

H. J. Atmaja, “Analisis Pemilihan Portofolio Optimal pada 27 Saham LQ45 BEI,” Universitas Terbuka, 2011.

R. D. Ramadhan, S. R. Handayani, and M. G. W. Endang, “Analisis pemilihan Portofolio Optimal dengan Model dan Pengembangan dari Portofolio Markowitz (Studi pada Indeks BISNIS-27 di Bursa Efek Indonesia periode 2011-2013),” Jurnal Administrasi Bisnis, vol. 14, no. 1, pp. 1–10, 2014.

S. A. Heryanti, “Perhitungan Value at Risk pada Portofolio Optimal : Studi Perbandingan Saham Syariah dan Saham Konvensional,” IKONOMIKA, vol. 2, no. 1, pp. 75–84, May 2017. doi: 10.24042/febi.v2i1.943.

R. Rahmawati, A. Rusgiyono, A. Hoyyi, and D. A. I. Maruddani, “Expected Shortfall untuk Mengukur Risiko Kerugian Petani Jagung,” Media Statistika, vol. 12, no. 1, pp. 117–128, Jul. 2019. doi: 10.14710/medstat.12.1.117-128.

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.10.2.269-278.

R. T. M. C. Simorangkir, “Pengaruh Kinerja Keuangan terhadap Return Saham Perusahaan Pertambangan,” Jurnal Bisnis dan Akuntansimn, vol. 21, no. 2, pp. 155–164, Dec. 2019. doi: 10.34208/jba.v21i2.616.

A. Solihatun, L. Gubu, 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),” JMKS (Jurnal Matematika dan Statistika), vol. 3, no. 1, pp. 245–254, 2023.

Y. Saepudin, H. Yasin, and R. Santoso, “Analisis Risiko Investasi Saham Tunggal Syariah dengan Value at Risk (VaR) dan Expected Shortfall (ES),” Jurnal Gaussian, vol. 6, no. 2, pp. 271–280, 2017. doi: 10.14710/j.gauss.6.2.271-280.

DOI: https://doi.org/10.37905/jjom.v6i2.24326