# COMPARISON BETWEEN VALUE AT RISK AND ADJUSTED EXPECTED SHORTFALL: A NUMERICAL ANALYSIS

• Trimono Trimono Data Sicence Study Program, Faculty of Computer Science, UPN “Veteran”, Indonesia
• Di Asih Maruddani Department of Statistics, Faculty of Science and Mathematics, Diponegoro University, Indonesia
Keywords: Stock Investment, Loss Risk, Value at Risk, Adjusted Expected Shortfall, Backtesting

### Abstract

Loss risk is one of the variable that always appears in every kind of investment. On stock asset investments, the characteristics of the risk of loss is uncertain, this means that losses can occur at any time with a value that cannot be determined certainly. From this condition, investors must manage the loss risk appropriately in order to retain investment stability and get optimal profits. One of the important processes in risk management is loss risk forecast. Risk forecast can be done using risk measures. In stock investment, Value at Risk (VaR) is the most widely used risk measure because has a simple model and can be applied to many types of stocks. However, VaR does not satisfy the axiom of subadditivity, thus VaR is not a coherent risk measure. Another risk measure that is coherent and can be used as an alternative to predict loss risk is the Adjusted-Expected Shortfall (Adj-ES). This study aims to compare VaR and Adj-ES through numerical analysis and backtesting test. So we can get reference to conclude the best risk measure for predicting losses on stock investments. The data used in this study are 2022 IDX blue chip i. e EXCL.JK and ICBP.JK from 09/01/21 to 09/09/22. Based on the backtesting test, the violation ratio value for Adj-ES in every violation probability is less than 1 is less than 1. Then, for VaR at 1% violation probability, the violation ratio value is > 1.

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Published
2023-09-30
How to Cite
[1]
T. Trimono and D. Maruddani, “COMPARISON BETWEEN VALUE AT RISK AND ADJUSTED EXPECTED SHORTFALL: A NUMERICAL ANALYSIS”, BAREKENG: J. Math. & App., vol. 17, no. 3, pp. 1347-1358, Sep. 2023.
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Articles