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All Journal CAUCHY: Jurnal Matematika Murni dan Aplikasi I-Finance Journal Jurnal Fourier Jurnal Ilmiah Ekonomi Islam JTAM (Jurnal Teori dan Aplikasi Matematika) Beta: Jurnal Tadris Matematika Jambura Journal of Mathematics JISKa (Jurnal Informatika Sunan Kalijaga) Jurnal Bakti Saintek: Jurnal Pengabdian Masyarakat Bidang Sains dan Teknologi Share: Jurnal Ekonomi dan Keuangan Islam MATHunesa: Jurnal Ilmiah Matematika Kaunia: Integration and Interconnection of Islam and Science Journal
Mohammad Farhan Qudratullah
Depertemen Matematika, Fakultas Sains Dan Teknologi, UIN Sunan Kalijaga Yogyakarta
Religion Biochemistry, Genetics & Molecular Biology Chemistry Computer Science & IT Economics, Econometrics & Finance Education Electrical & Electronics Engineering Library & Information Science Mathematics Physics Social Sciences Other

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Portfolio Optimization using Shariah-Compliant Asset Pricing Model in Indonesia Qudratullah, Mohammad Farhan; Hanafi, Syafiq Mahmadah; Sunaryati, Sunaryati
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 9, No 2 (2025): April
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v9i2.29168

Abstract

This paper develops portfolio optimization using the Shariah-Compliant Asset Pricing Model (SCAPM) which maximizes the Sharpe ratio by considering investors' prevention of risk. There are four approaches to developing portfolio optimization (SCAPM without interest rates, SCAPM with zakah rate, SCAPM with nominal gross domestic product growth (GDP), and SCAPM with inflation). This is a quantitative study that implements these models in the Islamic capital market in Indonesia, namely Islamic stocks included in the Jakarta Islamic Index (JII) for the period January 2011-December 2018. Based on the results of the Kendall W concordance test, this study found that the four SCAPM optimum portfolios have a very high level of conformity for return, risk, and performance at a 95% confidence level. In terms of the plot and ratio of return and risk, based on the investor's prevention of risk: the optimum portfolio 1 (risk-seeker) and the optimum portfolio 3 (risk-neutral) tend to give the same results and these portfolios were more efficient than the optimum portfolio 2 (risk-averter). This study contributes to the existing literature in the area of mathematics and the Islamic capital market, specifically in terms of the optimal Sharia-compliant portfolio. It is the first study developing, implementing, and testing the optimal portfolio with four approaches SCAPM based on the investors' prevention of risk in Indonesia.
ANALISIS RISIKO PORTOFOLIO OPTIMAL MENGGUNAKAN TREYNOR BLACK MODEL DAN EXPECTED SHORTFALL salsabila, Salsabila; Qudratullah, Mohammad Farhan
MATHunesa: Jurnal Ilmiah Matematika Vol. 13 No. 3 (2025)
Publisher : Universitas Negeri Surabaya

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.26740/mathunesa.v13n3.p466-474

Abstract

Perkembangan investasi syariah di Indonesia menunjukkan tren yang positif dan mendorong perlunya penerapan strategi manajemen risiko yang efektif. Penelitian ini bertujuan membentuk portofolio optimal berbasis saham syariah dengan menggabungkan model Treynor-Black dan metode Expected Shortfall (ES). Model Treynor-Black digunakan untuk mengidentifikasi saham-saham unggulan berdasarkan alpha dan beta, sedangkan ES dipilih karena mampu mengukur risiko ekstrem secara lebih akurat dibandingkan Value at Risk (VaR). Analisis dilakukan dengan menggunakan data harian saham yang tergabung dalam Jakarta Islamic Index (JII) untuk periode Juni 2023 hingga Mei 2024. Hasil analisis menunjukkan bahwa terdapat 10 saham yang layak dimasukkan ke dalam portofolio aktif. Bobot yang dihasilkan ADRO sebesar 26,42%, TPIA 16,19%, AKRA 12,46%, PTBA 9,07%, JPFA 8,54%, ACES sebesar 8,36%, EXCL sebesar 7,31%, MIKA sebesar 7,14%, CPIN sebesar 3,03%, dan CTRA 1,48%. Portofolio gabungan yang terbentuk dari portofolio aktif dan portofolio pasar menghasilkan expected return harian sebesar 0,025% dengan standar deviasi sebesar 1,11%, dan nilai Expected Shortfall 5,02%. Hal ini mencerminkan keseimbangan antara potensi keuntungan dan risiko yang terukur, sehingga kombinasi model Treynor Black dan Expected Shortfall efektif dalam membentuk portofolio syariah yang optimal dan responsif terhadap dinamika pasar.
Co-Authors Abdul Aziz Didik Krisdiyanto Hanafi, Syafiq Mahmadah Indah Puspita Sari Khurul Wardati Laeli Nurani Maria Ulfah Siregar Mr. Fitree Tahe Mr. Riyanto, Mr. Muhammad Safi’ Mulhan Muhammad Zakuan Muhammad Zakuan, Muhammad Muhtar Safi’i Mulat Arja’i, Mulat Mulat Arja’i Novia Amilatus Solekha Pipit Pratiwi Rahayu Rini Puspitaningtiyas Riyanto Riyanto Salsabila, Salsabila Slamet Haryono Sunaryati Sunaryati Syaeful Arief Syarif Hidayatullah Taufiq Aji Tri Anton Saputro Tutik Farihah