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All Journal CAUCHY: Jurnal Matematika Murni dan Aplikasi International Journal of Quantitative Research and Modeling International Journal of Health, Medicine, and Sports
Yasmin, Arla Aglia
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Computer Science & IT Decision Sciences, Operations Research & Management Dentistry Engineering Environmental Science Health Professions Mathematics Medicine & Pharmacology Nursing Physics Public Health

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Journal : CAUCHY: Jurnal Matematika Murni dan Aplikasi

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Optimization Modeling of Investment Portfolios Using The Mean-VaR Method with Target Return and ARIMA-GARCH Yasmin, Arla Aglia; Riaman, Riaman; Sukono, Sukono
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 10, No 1 (2025): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v10i1.30042

Abstract

This research develops a portfolio optimization model using the Mean-Value at Risk (Mean-VaR) approach with a target return constraint, addressing the gap in models that specific return objectives. The ARIMA-GARCH model is utilized to predict stock returns and volatility, offering precise inputs for optimization. By applying the Lagrange method and Kuhn-Tucker conditions, the model determines optimal portfolio weights that balance risk and return. Using data from infrastructure stocks on the Indonesia Stock Exchange (January 2019-September 2024), the model’s effectiveness is validated through numerical simulations. The results illustrate efficient frontiers for target returns of 5x10^-6, 0.001, and 0.0019, revealing that higher return targets proportionally increase risk. ARIMA-GACRH’s advantage lies in its ability to capture both mean and variance dynamics, ensuring reliable volatility estimates for informed decision-making. This study contributes to portfolio optimization literature by emphasizing target return constraints and demonstrating the practical utility of volatility modeling. The findings provide a robust framework for investors to align portfolios with financial goals and risk tolerance. Future work could explore broader market contexts or integrated additional constraints for enhanced applicability.
Co-Authors Abdul Halim , Nurfadhlina Agung Prabowo Amal, Moh Alfi Azahra, Astrid Sulistya Pirdaus , Dede Irman Riaman Riaman, Riaman Suhaimi, Nurnisaa binti Abdullah Sukono .