Application of ARIMA-GARCH Model to Estimating Expected Shortfall in BMRI Stocks

Abstract

Stocks are one of the best-known forms of investment and are still used today. In stock investment, it is necessary to know the movement and risk of loss that may be obtained from the stock investment so that investors can consider the possibility of profit. One way of calculating risk is to use the Expected Shortfall (ES). Because the stock movement is in the form of a time series, a model can be formed to predict the movement of the stock which can then be used for ES calculations using time series analysis. The purpose of the study was to determine the expected shortfall value of BMRI shares using time series analysis. The data used for this research is the daily closing price of shares for three years. In the time series analysis stage, the models used in predicting stock movements are Autoregressive Integrated Moving Average (ARIMA) for the mean model and Generalized Autoregressive Conditional Heteroscedasticity (GARCH) for the volatility model. The average value and variance obtained from the model are then used in calculating the ES on BMRI stock. Based on the results of the study, it was obtained that BMRI's stock had an ES of 0.008116. This means if an investment is made for BMRI shares of IDR 1,000,000.00 for 37 days (5% of 751 days) for an investment period with a 95% confidence level, the expected loss to be borne by the investor is IDR 8,116.00.