Analysis of Value at Risk (VaR) on Stock Portofolios using The T-Student Copula Method
Abstract
This study aims to estimate the portfolio risk of PT Bank Rakyat Indonesia (BBRI) and PT Bank Central Asia (BBCA) stocks using the t-Student Copula approach, and to compare Value at Risk (VaR) between the two assets. This method is utilized due to the characteristics of financial data, which are non-normally distributed and exhibit extreme dependence (tail dependence). The methodology integrates the GARCH(1,1) model to account for marginal volatility and the t-Student Copula to capture the dependency structure through Monte Carlo simulation with 10,000 iterations. The results indicate a significant positive correlation, with a Kendall’s Tau of 0.3242 and a Copula correlation parameter of 0.4886. Furthermore, the degree of freedom of 12.9364 confirms the presence of tail dependence. From the portfolio risk estimation, the Value at Risk (VaR) at a 95% confidence level is 1.9774% and at a 99% confidence level is 3.1301%, with Expected Shortfall (ES) values of 2.7571% and 4.0775%, respectively. By comparing the estimation results, this study identifies differences in the risk profiles of BBRI and BBCA, driven by the individual volatility of each asset. In conclusion, the t-Student Copula provides more accurate and conservative risk estimates as it is capable of anticipating simultaneous extreme loss potential, making it a highly relevant instrument for investors in portfolio risk management within the Indonesian capital market.
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