Estimation of Value-at-Risk Adjusted under the Capital Asset Pricing Model Based on ARMAX-GARCH Approach

Abstract

Investors having an understanding of investment statistics are important. Especially quantitative tools related to investment risk measurement. Value-at-Risk Adjusted is one of the investment risk measurement tools, which assumes that returns are not normally distributed.This paper intends to measure investment risk based onValue-at-Risk Adjustedor called Modified Value-at-Risk under the Capital Asset Pricing Model. It is assumed that the return of the market index has a non-constant average and there is a long memory effect. The average of the return of the market index is estimated using ARFIMA models.It is also assumed that the stock risk premium correlates with market risk premiums, and stock risk premiums some time before. The correlation will be analyzed using the ARMAX-GARCH model approach. The Modified Value-at-Risk was then formulated based on the Capital asset Pricing Model with the ARMAX-GARCH model approach.To measure the performance of Modified Value-at-Risk that has been formulated is done with back testing. Back testing is carried out based on the Lopez II method. As a case study, analyzed some data on 10 stocks traded on the capital market in Indonesia.The results of the analysis show that the market index return risk premium significantly follows the ARFIMA model, and the 10 share risk premium significantly follows the ARMAX-GARCH model. Based on the results of back testing calculations indicate that the Value-at-Risk Adjustedor Modified Value-at-Risk is very suitable to be used to measure investment risk in the 10 stocks analyzed.