Tail-Value-at-Risk Estimation in Optimal Stock Portfolio Formation in Indonesia Using GFGM Type II-GARCH Copula - Abubakar, Rahmah; Apriyanto; Ekawati, Darma (Journal of Mathematics, Computations and Statistics, 2025)
Banking disintermediation encourages people to switch to investing in the capital market. Investors always hope to get capital gains and dividends from traded stocks. LQ45 stocks tend to be in demand because they promise good growth prospects. Stock investment has a high risk with a high-profit offer. One way to deal with risk is to determine the optimal portfolio composition by looking at the TVaR value. This study focuses on estimating the Tail-Value-at-Risk (TVaR) in forming an optimal portfolio of LQ45 stocks using the Copula GFGM Type II-GARCH model. The objectives of this study are (1) to estimate the TVaR of the LQ45 stock portfolio using the Copula GFGM Type II-GARCH model; (2) to apply the copula concept in measuring the dependence of the marginal distribution of LQ45 stocks; and (3) to determine the optimal portfolio of LQ45 stocks. The steps in this research method are to start by determining the return of each LQ45 stock and then testing its stationarity using ADF. Furthermore, heteroscedasticity testing is carried out to determine the best GARCH model. Next, the Copula GFGM-Type II function is used to measure the dependency of each stock. In the end, the TVaR of the portfolio formed from the Copula-GARCH model generation data is calculated. This study uses daily closing price data of stocks listed in the LQ45 index for the period 2017 to 2023. From the available data, there are 14 companies with complete data. based on the results of the data analysis obtained only. After data analysis, only 8 stocks met the assumptions. The best ARMA-GARCH model was obtained from these stocks. The results of the TVaR calculation were obtained from portfolios with different weight compositions. The best model for BBRI.JK stocks is the ARMA(2,2)- GARCH(1,1) model. The best model for BBTN.JK stocks is the ARMA(2,2)- GARCH(1,2) model. The best model for KLBF.JK stocks is the ARMA(1,1)- GARCH(1,2) model. The best model for AMRT.JK stocks is the MA(1)- GARCH(1,1) model. The best model for BRPT.JK stock is the AR(1)- GARCH(1,2) model. The best model for EXCL.JK stock is the ARMA(1,2)- GARCH(1,1) model. The best model for INDF.JK stock is the ARMA(1,1)- GARCH(1,2) model. The correlation value does not provide a significant difference to the TVaR in this portfolio.