Measuring Stock Investment Risk Using Expected Shortfall tith the Gramcharlier Expansion at PT. Energi Mega Persada Tbk

Abstract

Stock investment provides attractive return opportunities but is also accompanied by significant risks due to price volatility, especially in the energy sector. This study aims to measure the investment risk of PT Energi Mega Persada Tbk (ENRG) shares using the Expected Shortfall (ES) method with the Gram–Charlier Expansion approach. The research uses a quantitative approach based on secondary data consisting of daily closing prices of ENRG shares during the period January 2020 to December 2025, obtained from Investing.com. The analysis process included stock return calculation, descriptive statistical analysis, normality testing, and risk measurement using Value at Risk (VaR) and Expected Shortfall under both normal distribution assumptions and the Gram–Charlier Expansion approach. The results indicate that ENRG stock returns do not follow a normal distribution, characterized by positive skewness and high kurtosis, which reflects asymmetric behavior and heavy-tailed distribution. The risk measurement using normal distribution at a 95% confidence level produces an Expected Shortfall value of ?0.0771, while the Gram–Charlier Expansion approach generates a higher absolute Expected Shortfall value of ?0.2493. These findings demonstrate that the Gram–Charlier Expansion approach provides a more conservative and realistic estimation of extreme loss risks because it incorporates skewness and kurtosis characteristics of stock returns. Therefore, the application of Expected Shortfall based on Gram–Charlier Expansion is considered more appropriate for measuring investment risk in highly volatile energy sector stocks, particularly for investors requiring more accurate risk management information.