Comparison of Historical Simulation and Variance-Covariance Methods for Value at Risk Estimation of BBRI Stock
Keywords:
BBRI Stock, Kupiec Backtesting, Historical Simulation, Value at Risk, Variance-Covariance.Abstract
Stock investment is exposed to market risk arising from fluctuations in stock prices. Therefore, accurate risk measurement is essential for investors and risk managers. Among the various tools available for quantifying investment risk, Value at Risk (VaR) has gained widespread adoption as a method for determining the worst expected loss under a given probability threshold. This study compares the Historical Simulation and Variance-Covariance methods in estimating the Value at Risk of PT Bank Rakyat Indonesia (Persero) Tbk (BBRI) stock using daily closing price data from January 2, 2024, to December 31, 2025. The Jarque-Bera normality test indicated that the return data were not normally distributed, suggesting the presence of non-normal characteristics in the return distribution. Based on an assumed investment value of IDR 10,000,000, the VaR estimates at the 95% confidence level were IDR 334,739 and IDR 356,444 using Historical Simulation and Variance-Covariance, respectively. At the 99% confidence level, the estimated VaR values were IDR 534,695 and IDR 500,158, respectively. Kupiec Proportion of Failures (POF) backtesting showed that both methods produced statistically valid VaR estimates. However, Historical Simulation generated a more conservative risk estimate at the 99% confidence level, indicating a greater ability to capture extreme losses under non-normal return distributions. Therefore, Historical Simulation is recommended as the preferred method for measuring the market risk of BBRI stock.
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Kiswah Institute