PENENTUAN VALUE AT RISK (VAR) PADA PORTOFOLIO BIVARIAT DENGAN PENDEKATAN COPULA GUMBEL - Febriani, Karina; Tarno, Tarno; Fakhriyana, Deby (Department of Statistics, Faculty of Science and Mathematics, Universitas Diponegoro, 2024)
One way to minimize risk in stock investment is stock portfolio. Value at Risk (VaR) is a calculation method that can be used to estimate the risk of a stock portfolio. VaR can be measured by parametric and non-parametric approaches. Calculation of VaR with Monte Carlo simulation assumes the data is normally distributed. Stock return data generally has high volatility so that the residual variance of the model is not constant (heteroscedasticity) and not normally distributed. The ARIMA-GARCH model can be used to solve heteroscedasticity problems. Copula is a tool used to model the combined distribution of residuals from the ARIMA-GARCH model which does not require normality assumptions. Gumbel's copula is copula that has the best sensitivity to high risk. This study uses stock data of PT Bukit Asam Tbk (PTBA) and PT Chandra Asri Petrochemical Tbk (TPIA) for the period April 1 2020 – December 1 2022. The initial step of this research is model stock returns using the ARIMA-GARCH method and then calculate portfolio VaR using the Gumbel’s copula. The results showed that the best model for PTBA is ARIMA(2,0,2) GARCH(1,1) and for TPIA is ARIMA(1,0,0) GARCH (1,1). At the 95% confidence level, the portfolio risk is 2,41%.