Extreme Value Theory-Based Value at Risk for Stock Portfolio Risk Estimation: A Comparative Study of GEV and GPD Models in Indonesian Banking Stocks
Keywords:
Block Maxima, Extreme Value, Investment, Peak Over Threshold, Value at RiskAbstract
Risk management is a crucial element in stock investment activities to minimize the negative impacts of market uncertainty, particularly during periods of extreme price fluctuations. One effective statistical approach for measuring maximum potential loss in return distributions characterized by fat tails is Value at Risk (VaR) integrated with Extreme Value Theory (EVT). This study aims to analyze stock portfolio risk, estimate potential losses, and evaluate the comparative accuracy of the Block Maxima and Peak Over Threshold methods. The Block Maxima method models maximum extreme values within specific time blocks using the Generalized Extreme Value (GEV) distribution, whereas the Peak Over Threshold method models data exceeding a predefined threshold (u) using the Generalized Pareto Distribution (GPD). The research sample consists of five banking subsector stocks with the largest market capitalization, BBCA, BBRI, BMRI, BBNI, and BRIS for the period from May 1, 2019, to May 31, 2025. Results indicate that VaR estimation at a 95% confidence level using the VaR-GEV method yields a potential loss of 6.64%, while the VaR-GPD method yields 3.13%. Evaluation via the Kupiec backtesting test reveals that the VaR-GEV model is invalid due to being overly conservative with an excessively low violation rate. Conversely, the VaR-GPD model is proven valid, with an actual violation rate of 5.49% that closely aligns with expected values. Given its superior validity and accuracy, the Value at Risk Generalized Pareto Distribution approach is determined to be the optimal model for estimating market risk under extreme conditions.
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