Institutional Repository UIN Sunan Kalijaga YogyakartaANALISIS RISIKO PORTOFOLIO OPTIMAL BERBASIS SINGLE INDEX MODEL MENGGUNAKAN VALUE AT RISK (VAR) DENGAN METODE HISTORICAL SIMULATION (STUDI KASUS: SAHAM IDX30 PERIODE JANUARI 2025 – DESEMBER 2025)NIM.: 22106010061Dinda Kusuma SariauthorA portfolio is a collection of assets used to diversify and manage investment risk. An optimal portfolio is needed to obtain a combination of stocks that maximizes returns while minimizing risk. This study aims to analyze optimal portfolio formation using the Single Index Model (SIM), determine stock investment weights, and measure portfolio risk using Value at Risk (VaR) with the Historical Simulation approach. The data consist of daily closing prices of IDX30 stocks and the IHSG from January to December 2025. Stocks were initially selected based on an expected return greater than the risk-free rate (E(Ri) > Rf ), followed by selecting stocks with Excess Return to Beta (ERB) greater than or equal to the cut-off point (ERB ≥ C∗). The results show that eight stocks were selected to form the optimal portfolio namely BRPT, ANTM, ASII, UNVR, INCO, MDKA, MBMA, and MEDC. The two largest investment weights were BRPT at 38.59%, with an expected return of 0.6174%, and ANTM at 30.98%, with an expected return of 0.3595%. SIM simplifies parameter estimation while considering market factors, but is limited to a single market factor. Historical Simulation requires no specific distributional assumption but depends on historical data quality. VaR increases with the investment horizon due to the square-root-of-time rule. At a 95% confidence level, one-day VaR was Rp3,184,844 and was valid based on the Kupiec POF test.510 Mathematics (Matematika)2026-08-03UIN SUNAN KALIJAGA YOGYAKARTA;FAKULTAS SAINS DAN TEKNOLOGIThesis

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