Estimation of Tail Value at Risk for Bivariate Portfolio using Gumbel Copula

Investing in the stock market involves complex risks, especially under extreme and unpredictable conditions. While Value at Risk (VaR) is a widely used risk measure, it has limitations in capturing tail-end risks. This study employs Tail Value at Risk (TVaR) using the Gumbel Copula approach, which effectively models upper-tail dependence in return distributions—an aspect often overlooked by traditional linear correlation methods. This quantitative research utilizes copula-based Monte Carlo simulation. The data consists of daily closing prices of PT Adaro Energy Indonesia Tbk (ADRO) and PT Indo Tambangraya Megah Tbk (ITMG) from July 3, 2023, to July 30, 2024. The analysis begins with return calculation and tests for autocorrelation and homoskedasticity. The Gumbel Copula parameter is estimated using Kendall’s Tau, resulting in a dependence parameter of 1.7791. Based on this, 1,000 simulations are conducted to generate new return data that reflect extreme dependencies between the two stocks. An optimal portfolio is constructed using the Mean-Variance Efficient Portfolio (MVEP) method, assigning weights of 31.61% to ADRO and 68.39% to ITMG. TVaR is then calculated from the simulated portfolio returns. The results show increasing TVaR values at higher confidence levels: 2.08%, 2.64%, 3.14%, and 4.11% for 80%, 90%, 95%, and 99%, respectively. These findings demonstrate that TVaR provides more accurate insights into potential losses in extreme market conditions, supporting investors in developing more informed and risk-sensitive portfolio strategies.