Optimization Modeling of Investment Portfolios Using The Mean-VaR Method with Target Return and ARIMA-GARCH

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...

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Main Authors: Arla Aglia Yasmin, Riaman Riaman, Sukono Sukono
Format: Article
Language:English
Published: Mathematics Department UIN Maulana Malik Ibrahim Malang 2025-03-01
Series:Cauchy: Jurnal Matematika Murni dan Aplikasi
Subjects:
Online Access:https://ejournal.uin-malang.ac.id/index.php/Math/article/view/30042
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author Arla Aglia Yasmin
Riaman Riaman
Sukono Sukono
author_facet Arla Aglia Yasmin
Riaman Riaman
Sukono Sukono
author_sort Arla Aglia Yasmin
collection DOAJ
description 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.
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spelling doaj-art-c6d4df0cd799479496c7d4921c1bf3692025-08-20T02:13:45ZengMathematics Department UIN Maulana Malik Ibrahim MalangCauchy: Jurnal Matematika Murni dan Aplikasi2086-03822477-33442025-03-0110114716510.18860/cauchy.v10i1.300428645Optimization Modeling of Investment Portfolios Using The Mean-VaR Method with Target Return and ARIMA-GARCHArla Aglia Yasmin0Riaman Riaman1Sukono Sukono2Master Program of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Padjadjaran, Sumedang 45363, IndonesiaDepartment of Mathematics, Universitas Padjadjaran, Sumedang 45363, Indonesia.Department of Mathematics, Universitas Padjadjaran, Sumedang 45363, Indonesia.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.https://ejournal.uin-malang.ac.id/index.php/Math/article/view/30042stocksportfolio optimizationmean-vartarget returnarima-garch
spellingShingle Arla Aglia Yasmin
Riaman Riaman
Sukono Sukono
Optimization Modeling of Investment Portfolios Using The Mean-VaR Method with Target Return and ARIMA-GARCH
Cauchy: Jurnal Matematika Murni dan Aplikasi
stocks
portfolio optimization
mean-var
target return
arima-garch
title Optimization Modeling of Investment Portfolios Using The Mean-VaR Method with Target Return and ARIMA-GARCH
title_full Optimization Modeling of Investment Portfolios Using The Mean-VaR Method with Target Return and ARIMA-GARCH
title_fullStr Optimization Modeling of Investment Portfolios Using The Mean-VaR Method with Target Return and ARIMA-GARCH
title_full_unstemmed Optimization Modeling of Investment Portfolios Using The Mean-VaR Method with Target Return and ARIMA-GARCH
title_short Optimization Modeling of Investment Portfolios Using The Mean-VaR Method with Target Return and ARIMA-GARCH
title_sort optimization modeling of investment portfolios using the mean var method with target return and arima garch
topic stocks
portfolio optimization
mean-var
target return
arima-garch
url https://ejournal.uin-malang.ac.id/index.php/Math/article/view/30042
work_keys_str_mv AT arlaagliayasmin optimizationmodelingofinvestmentportfoliosusingthemeanvarmethodwithtargetreturnandarimagarch
AT riamanriaman optimizationmodelingofinvestmentportfoliosusingthemeanvarmethodwithtargetreturnandarimagarch
AT sukonosukono optimizationmodelingofinvestmentportfoliosusingthemeanvarmethodwithtargetreturnandarimagarch