Portfolio Risk Assessment Using VaR and CVaR: A Comparative Study of Variance–Covariance Method and Monte Carlo Simulation

Abstract

This study examines portfolio risk in Indonesia’s energy sector by applying Value at Risk (VaR) and Conditional Value at Risk (CVaR) under the Variance–Covariance and Monte Carlo Simulation approaches. The analysis focuses on ten stocks from the oil and gas as well as coal subsectors listed on the Indonesia Stock Exchange (IDX), using monthly closing price data from January 2020 to December 2024. A Weighted Scoring Method (WSM) is first employed to select stocks with superior fundamentals and liquidity, based on market capitalization, return on equity, debt-to-equity ratio, net profit margin, trading volume, and dividend yield. An optimal portfolio is then constructed using the Maximum Sharpe Ratio (MSR) framework, resulting in a portfolio dominated by PTBA, MEDC, and MBAP. Portfolio risk is subsequently estimated using VaR and CVaR at the 95% and 99% confidence levels under both the Variance–Covariance and Monte Carlo approaches. The empirical results indicate that CVaR consistently produces higher risk estimates than VaR, highlighting its superior ability to capture tail risk. Furthermore, the Variance–Covariance method yields slightly more conservative CVaR estimates compared to Monte Carlo Simulation, which is attributed to the near-normal distribution of portfolio returns during the observation period. Model validity is confirmed through backtesting using the Kupiec test, which shows that the VaR estimates satisfy statistical adequacy criteria. Overall, the findings suggest that while the Variance–Covariance approach remains effective under normality assumptions, Monte Carlo Simulation offers greater flexibility in modeling extreme market conditions. This study contributes to the literature by providing empirical evidence on comparative risk estimation methods in Indonesia’s highly volatile energy sector.