ANALISIS RISIKO PORTOFOLIO OPTIMAL GLOBAL MINIMUM VARIANCE (GMV) MENGGUNAKAN VALUE AT RISK (VAR) – EXPONENTIALLY WEIGHTED MOVING AVERAGE (EWMA) (STUDI KASUS: JAKARTA ISLAMIC INDEX (JII) PERIODE JANUARI 2021 – DESEMBER 2025)NIM.: 22106010026Nadiva Freya DanellaauthorThe rapid growth of Islamic investment in Indonesia necessitates adaptive risk management strategies, particularly for stocks included in the Jakarta Islamic Index (JII). This study aims to analyze the optimal portfolio formation process using Global Minimum Variance (GMV), determine optimal portfolio weights, and analyze portfolio returns and risks using Value at Risk (VaR) using Exponentially Weighted Moving Average (EWMA) volatility estimation for JII stocks. This study uses monthly data from the Jakarta Islamic Index (JII) for the period January 2021– December 2025. The GMV model is used to determine portfolio weights with nonnegative constraints (without short selling) in accordance with sharia principles, while VaR–EWMA is used to estimate volatility and measure portfolio risk more responsive to market changes. The results show that the optimal portfolio weights are dominated by INDF (18.92%), TLKM (13.23%), SIDO (12.98%), and EXCL (12.01%), with no negative weights. The GMV portfolio generated an expected annual return of 15.21% with an annual volatility of 8.45%. The risk level, measured using the 95% VaR normal method, yielded an average VaR of 2.92% per month, so that for an investment of IDR 100 million, the maximum loss is estimated to be around IDR 2.9 million per month. Kupiec backtesting results showed that the VaR-EWMA model has good accuracy with a p-value of 0.9762 and an actual breach rate of 5.08%, which is close to the expected breach rate of 5.00%. These results indicate that the GMV and VaR-EWMA models are effective in forming an optimal portfolio with measurable risk and sensitivity to market changes.515.6 Metode Analitik - Matematika2026-05-26UIN SUNAN KALIJAGA YOGYAKARTA;FAKULTAS SAINS DAN TEKNOLOGIThesis