USE OF GLUE VALUE AT RISK FOR OPTIMAL PORTFOLIO RISK MEASUREMENT WITH THE SINGLE INDEX MODEL METHOD

  • Turnika Afdatul Rafni Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Negeri Padang, Indonesia https://orcid.org/0009-0009-2004-0353
  • Dina Agustina Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Negeri Padang, Indonesia https://orcid.org/0009-0007-0904-0024
Keywords: Backtesting, Glue Value at Risk, IDX30, Investment, Single Index Model, Stocks

Abstract

Creating an optimal portfolio and measuring risk are ways that can be used to reduce losses and maximize returns in an investment. In this study, the optimal portfolio is formed using the Single Index Model method, which assumes stock returns are influenced only by market returns. The stocks used are stocks that are consistently included in the IDX30 index during the period October 24, 2022-October 25, 2024 and provide positive expected returns, so that based on the Single Index Model method, 5 stocks are included in the optimal portfolio with the proportion of each stock as follows, PT Indofood Sukses Makmur Tbk (INDF) 30%, PT Barito Pacific Tbk (BRPT) 8%, PT Bank Mandiri Tbk (BMRI) 35%, PT Bank Central Asia Tbk (BBCA)17%, and PT Bank Negara Indonesia Tbk (BBNI) 10%. The risk of the optimal portfolio can be calculated using the Glue Value at Risk method, which provides a more accurate and coherent measure of risk. In this study with a confidence level of  and  and used a high distortion function   and , the Glue Value at Risk amount for the optimal portfolio was obtained at Rp1,996,926. The backtesting results show that Glue Value at Risk provides valid and accurate results for measuring risk at this level of confidence.

Downloads

Download data is not yet available.

References

Bursa Efek Indonesia, “INVESTOR PASAR MODAL TEMBUS 13 JUTA, KOLABORASI DENGAN KOMUNITAS DAN IDX MOBILE JADI ANDALAN,” Bursa Efek Indonesia. Accessed: Oct. 28, 2024. [Online]. Available: https://www.idx.co.id/id/berita/siaran-pers/2166

S. Huda and P. Sihombing, “ANALYSIS OF OPTIMAL PORTFOLIO FORMATION USING SINGLE INDEX MODEL AND STOCHASTIC DOMINANCE ON SRI-KEHATI INDEX,” European Journal of Business and Management Research, vol. 7, no. 1, pp. 160–165, Feb. 2022. doi: https://doi.org/10.24018/ejbmr.2022.7.1.1264.

A. Halim, ANALISIS INVESTASI DAN APLIKASINYA DALAM ASET KEUANGAN DAN ASET RILL, 2nd ed. Jln. Raya Lenteng Agung No. 101 Jagakarsa Jakarta Selatan : Penerbit Salemba Empat, 2018.

Bursa Efek Indonesia, “INDEKS.” Accessed: Oct. 28, 2024. [Online]. Available: https://www.idx.co.id/id/produk/indeks/

N. Khofifah, A. Rusgiyono, and D. A. I. Maruddani, “GLUE VALUE AT RISK UNTUK MENGUKUR RISIKO PADA PORTOFOLIO OPTIMAL DENGAN METODE MULTI INDEX MODEL,” Jurnal Gaussian, vol. 12, no. 1, pp. 116–125, May 2023. doi: https://doi.org/10.14710/j.gauss.12.1.116-125

P. Suseno, “KONSEP DASAR MANAJEMEN RISIKO,” 2014.

A. Solihatun, L. Gubu, E. Cahyono, and L. Ode Saidi, “PERHITUNGAN VALUE AT RISK (VAR) PADA PORTOFOLIO SAHAM IDX SEKTOR KEUANGAN (IDXFINANCE) MENGGUNAKAN METODE SIMULASI HISTORIS(HISTORICAL SIMULATION METHOD),” 2023. https://doi.org/10.33772/jmks.v3i1.32

N. F. Rizani, Mustafid, and Suparti, “PENERAPAN METODE EXPECTED SHORTFALL PADA PENGUKURAN RISIKO INVESTASI SAHAM DENGAN VOLATILITAS MODEL GARCH,” Jurnal Gaussian, vol. 8, no. 2, pp. 184–193, 2019. doi: https://doi.org/10.14710/j.gauss.v8i1.26644

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, p. 117, Jul. 2019. doi: https://doi.org/10.14710/medstat.12.1.117-128

D. Adrianto, D. A. I. Maruddani, and Tarno, “PENGUKURAN RISIKO GLUE-VALUE-AT-RISK PADA DATA DISTRIBUSI ELLIPTICAL,” Jurnal Gaussian , vol. 9, no. 1, pp. 75–86, 2020. doi: https://doi.org/10.14710/j.gauss.v9i1.27525

J. Belles-Sampera, M. Guillén, and M. Santolino, “BEYOND VALUE-AT-RISK: GLUEVAR DISTORTION RISK MEASURES,” 2013. doi: https://doi.org/10.1111/risa.12080

J. M. Prof. , Dr. , MBA. , Ak. , CMA. , CA. Hartono, TEORI DAN PRAKTIK PORTOFOLIO DENGAN EXCEL . Jln. Raya Lenteng Agung No. 101 Jagakarsa Jakarta Selatan : Penerbit Salemba Empat, 2013.

A. Gunawan, R. Fajriyah, M. A. Bimakasa, and S. N. Untari, “ANALYSIS OF PORTFOLIO FORMATION ON THE LQ45 STOCKS INDEX, USING THE MARKOWITZ AND SINGLE INDEX MODELS,” Barekeng, vol. 18, no. 4, pp. 2363–2374, Dec. 2024. doi: https://doi.org/10.30598/barekengvol18iss4pp2363-2374.

T. Trimono and D. A. Maruddani, “COMPARISON BETWEEN VALUE AT RISK AND ADJUSTED EXPECTED SHORTFALL: A NUMERICAL ANALYSIS,” Barekeng: Jurnal Ilmu Matematika dan Terapan, vol. 17, no. 3, pp. 1347–1358, Sep. 2023. doi: https://doi.org/10.30598/barekengvol17iss3pp1347-1358.

E. J. Elton, M. J. Gruber, S. J. Brown, and W. N. Goetzmann, MODERN PORTFOLIO THEORY AND INVESTMENT ANALYSIS NINTH EDITION, 9th ed. United States of America: John Wiley & Sons, Inc., 2014.

B. Kunni Fauziyyah and A. Prahutama, “ANALISIS PORTOFOLIO OPTIMAL MENGGUNAKAN MULTI INDEX MODEL (STUDI KASUS: KELOMPOK SAHAM IDX30 PERIODE JANUARI 2014-DESEMBER 2018),” vol. 8, no. 1, pp. 58–67, 2019. doi: https://doi.org/10.14710/j.gauss.v8i1.26622

E. Tandelilin, PASAR MODAL MANAJEMEN PORTOFOLIO & INVESTASI. Daerah Istimewa Yogyakarta: Penerbit PT Kanisius, 2017.

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 (STUDI KASUS: KELOMPOK SAHAM JII PERIODE JUNI-NOVEMBER 2017),” Jurnal Gaussian, vol. 7, no. 4, pp. 408–418, 2018. doi: https://doi.org/10.14710/j.gauss.v7i4.28869

P. Jorion, VALUE AT RISK: THE NEW BENCHMARK FOR MANAGING FINANCIAL RISK, 2nd ed. USA: McGraw-Hill, 2001.

D. A. I. Maruddani and T. D. Astuti, “RISIKO INVESTASI SAHAM SECOND LINER DENGAN TAIL VALUE AT RISK,” Jurnal Ilmiah Manajemen, vol. 11, no. 2, 2021.

S. A. Klugman, H. H. Panjer, and G. E. Willmot, LOSS MODELS FROM DATA TO DECISIONS, 5th ed. USA: John Wiley and Sons, Inc., 2019. doi: https://doi.org/10.1017/s1357321700000672

S. Halilbegovic and M. Vehabovic, “BACKTESTING VALUE AT RISK FORECAST: THE CASE OF KUPIEC POF-TEST,” European Journal of Economic Studies, vol. 17, no. 3, Sep. 2016. doi: https://doi.org/10.13187/es.2016.17.393

Published
2026-01-26
How to Cite
[1]
T. A. Rafni and D. Agustina, “USE OF GLUE VALUE AT RISK FOR OPTIMAL PORTFOLIO RISK MEASUREMENT WITH THE SINGLE INDEX MODEL METHOD”, BAREKENG: J. Math. & App., vol. 20, no. 2, pp. 1251–1262, Jan. 2026.