Estimation of value at risk with ARMAX and GARCHX variation during COVID-19 pandemic period (Case study: IDX30 stock data in banking sub-sector on Indonesia stock exchange)

Investment is a term that has several definitions associated with finance and economics. The term is related to the accumulation of a form of asset with hope of obtaining future benefits. The GARCH model is used to design time series that have case of heteroscedasticity or variance that is not constant. The GARCHX model is a model that can be used to model time series data in the financial sector which has high volatility with the involvement of exogenous variables. Beside using GARCHX method to calculate return, there is also Value at Risk method. Value at Risk (VaR) is a market risk calculation method to determine the maximum risk of loss that can occur in a portfolio. Therefore, in this study, the ARMAX method and six GARCHX variations were proposed in the stock data on the IDX30 index in Banking sub-sector in the last six years, which were during 2015-2021. The data used in the study were from 2 January 2015 to 29 January 2021. The GARCHX variation methods used were GARCHX, EGARCHX, GJRGARCHX, APARCHX, FGARCHX, and CGARCHX. The exogenous variable used in this study was the Composite Stock Price Index (IHSG) data. Simulation study was also carried out in this study by generating data with a Normal distribution with various means and standard deviation with n as many as 1500. The data used as a reference in this simulation study were the IDX30 return data for the period of January 2015 to January 2021. The purpose of this simulation is to find out which GARCHX variation method is the best for dealing with heteroscedasticity case. Towards this study, VaR calculation result was compared to each GARCHX variation in all banking issuers, so that particular issuers having the least risk would be known and could be recommended to invest during COVID-19 pandemic period.