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All Journal Journal of Mathematics, Computation and Statistics (JMATHCOS)
Nunung Kusdaniyama
Department of Mathematics, Pamulang University, Banten, Indonesia
Mathematics

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A Markowitz–ARMA–GARCH–Copula Overlay for Jakarta Islamic Index Portfolios: A Complexity–Benefit Comparison with the Markowitz Model Irfani Azis; Nina Valentika; Nunung Kusdaniyama; Euis Aprianti; Tegar Aji Sukma Bestari
Journal of Mathematics, Computations and Statistics Vol. 9 No. 2 (2026): Volume 09 Issue 02 (June 2026)
Publisher : Jurusan Matematika FMIPA UNM

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.35580/Jmathcos12760

Abstract

This study develops and evaluates a Markowitz–ARMA–GARCH–Copula (MAGC) overlay for Islamic stock portfolios constructed from constituents of the Jakarta Islamic Index (JII) over the period May 2020–April 2025. The Markowitz mean–variance model is used as the baseline allocation approach to form an initial buy-and-hold portfolio. The MAGC overlay is then applied to incorporate daily volatility dynamics and copula-based dependence modeling into the evaluation and refinement of portfolio risk. ARMA–GARCH models are used to capture autocorrelation and time-varying volatility in stock returns, while the copula approach is employed to model cross-asset dependence without relying on the assumption of multivariate normality. Portfolio performance is assessed using expected return, total risk, Value at Risk (VaR), and Expected Shortfall (ES). The results show that the MAGC portfolio is broadly comparable to the Markowitz portfolio, with a slightly higher expected return (0.000350 vs. 0.000346), marginally lower volatility (0.011717 vs. 0.011721), and modest reductions in VaR (0.017890 vs. 0.018080) and ES (0.025380 vs. 0.025430). However, the bootstrap comparison indicates that these differences are not statistically significant. Therefore, the MAGC overlay provides only modest risk refinement rather than clear superiority over Markowitz. Overall, the findings suggest that the conventional Markowitz model remains a competitive and parsimonious baseline for buy-and-hold JII portfolio construction, while MAGC may serve as an additional tail-risk diagnostic tool for investment managers.
Co-Authors Euis Aprianti Irfani Azis Nina Valentika Tegar Aji Sukma Bestari