COMPARISON BETWEEN VALUE AT RISK AND ADJUSTED EXPECTED SHORTFALL: A NUMERICAL ANALYSIS
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.
Edriani, T. S., "The Geometric Brownian Motion of Indosat Telecommunications Daily Stock Price During the Covid-19 Pandemic in Indonesia," in J. Phys.: Conf. Ser., Jakarta, 2021.
KSEI, Statistik Pasar Modal Indonesia April 2017, Jakarta: KSEI Publisher, 2017.
KSEI, Statistik Pasar Modal Indonesia April 2022, Jakarta: KSEI Publisher, 2022.
T. Trimono, D. A. I. Maruddani and D. Ispriyanti, "Pemodelan Harga Saham dengan Geometric Brownian Motion dan Value at Risk PT Ciputra Development Tbk," Jurnal Gaussian, vol. 6, no. 1, pp. 261-270, 2017.
A. Nayak, M. M. M. Pai and R. M. Pai, "Prediction Models for Indian Stock Market," Procedia Computer Science, vol. 89, pp. 441-449, 2016.
I. Indonesia, "Tutup Tahun 2021 dengan Optimisme Pasar Modal Indonesia Lebih Baik," 30 12 2021. [Online]. Available: https://www.idx.co.id/id/berita/siaran-pers/1632. [Accessed 20 11 2022].
E. T. Widyarti, D. A. I. Maruddani, T. Trimono and H. Hersugondo, "Blue Chip Stocks Valuation and Risk Prediction on The Indonesia Stock Exchange," Academy of Accounting and Financial Studies Journal, vol. 25, no. 6, pp. 1-14, 2021.
H. Basri and V. Mayasari, "Perbandingan Kinerja Saham Syariah di Bursa Efek Indonesia dan Bursa Malaysia," Jurnal Ilmiah Ekonomi Global Masa Kini, vol. 10, no. 2, pp. 82-92, 2019.
Trimono and D. A. I. Maruddani, "Valuasi Harga Saham PT Aneka Tambang Tbk sebagai Peraih IDX Best Blue 2016," Statistika, vol. 17, no. 1, pp. 33-43, 2017.
N. Pinasthika and B. A. Surya, "Optimal Portfolio Analysis With Risk-Free Assets Using Index-Tracking and Markowitz Mean-Variance Portfolio Optimization Model," Journal of Business and Management, vol. 3, no. 7, pp. 737-751, 2014.
T. Aven, "Risk assessment and risk management: Review of recent advances on their foundation," European Journal of Operational Research, vol. 253, pp. 1-13, 2016.
Y. Lina, W. Saputra and V. Pricila, "Risk Analysis of Jakarta Composite Index Using Value at Risk and Expected Shortfall Based on Principal Component Regression," AIP Conference Proceedings, vol. 2633, pp. 1-18, 2022.
S. Fanelli and L. Straub, "A Theory of Foreign Exchange Interventions," The Review of Economic Studies, vol. 88, no. 6, pp. 2857-2885, 2021.
J. Xiang, S. R. Velu and S. Zygiaris, "Monte Carlo Simulation Prediction of Stock Prices," in 14th International Conference on Developments in eSystems Engineering (DeSE), Sharjah, 2021.
T. H. D. Trimono, A. W. A. Susilo and K. I. A. Syuhada, "Bounds of Adj-TVaR Prediction for Aggregate Risk," Inprime Journal, vol. 1, no. 1, pp. 1-7, 2019.
N. Juliarini, I. Sumarjaya and K. Sari, "Peramalan Volatilitas dan Estimasi Value at Risk (VaR) Saham Blue Chip Pada Sektor Perbankan," E-Jurnal Matematika, vol. 10, no. 4, pp. 198-208, 2021.
G. A. Saputri, A. Suharsono and Haryono, "Analisis Value at Risk (VaR) pada Investasi Saham Blue Chips dengan Pendekatan Copula," Jurnal Sains dan Seni ITS, vol. 8, no. 2, pp. 200-205, 2019.
J. Kim and I. Choi, "Unit Roots in Economic and Financial Time Series: A Re-Evaluation at the Decision-Based Significance Levels," Econometrics, , vol. 5, no. 41, pp. 1-23, 2017.
S. Nadarajah, B. Zhang and S. Chan, "Estimation methods for expected shortfall," Quantitative Finance, vol. 14, no. 2, pp. 1-12, 2014.
D. A. I. Maruddani, Value at Risk untuk Pengukuran Risiko Investasi Saham: Aplikasi dengan Program R, Yogyakarta: Wade Group, 2019.
A. J. Patton, J. F. Ziegel and R. Chen, "Dynamic semiparametric models for expected shortfall (and Value-at-Risk)," Journal of Econometrics, vol. 211, pp. 388-413, 2019.
P. Astuti and T. Gunarsih, "Value-at-Risk Analysis In Risk Measurement And Formation Of Optimal Portfolio In Banking Share," JBTI, vol. 12, no. 2, pp. 103-114, 2021.
D. A. I. Maruddani and Trimono, "Valuation of Portfolio Risk and Performance of Several Blue Chip Stocks in Indonesia using Value-at-Risk based on n-Dimensional Geometric Brownian Motion," Thailand Statistician, vol. 19, no. 2, pp. 501-510, 2021.
T. Tarno, D. A. I. R. R. Maruddani, A. Hoyyi, T. Trimono and M. Munawar, "ARIMA-GARCH Model and ARIMA-GARCH Ensemble for Value-at-Risk Prediction on Stocks Portfolio," Preprints, pp. 1-13, 2020.
H. Hersugondo, "Price Index Modeling and Risk Prediction of Sharia Stocks in Indonesia," Economies, , vol. 10, no. 17, pp. 1-13, 2022.
D. Jadhav, T. Ramanathan and U. Naik-Nimbakar, "Modified Expected Shortfall: A New Robust Coherent Risk Measure," Journal of Risk, vol. 16, no. 1, pp. 69-83, 2013.
Y. Zhang and S. Nadarajah, "A review of backtesting for value at risk," Communications in Statistics - Theory and Methods, pp. 1-24, 2017.
T. Mrkvicka, "Backtesting the Evaluation of Value-at-Risk Methods for Exchange Rates," Studies in Economics and Finance, vol. 40, no. 1, pp. 171-191, 2023.
D. A. I. Maruddani and T. Trimono, Microsoft Excel untuk Pengukuran Value at Risk : Aplikasi Pada Risiko Investasi Saham., Semarang: UNDIP Press, 2020.
T. Tarno, T. Trimono, D. A. I. Maruddani, Y. Wilandari and R. S. Utami, "Risk Assessment of STOCks Portfolio Through Ensemble ARMA-GARCH and Value at Risk (Case Study: INDF.JK and ICBP.JK Stock Price)," Media Statistika, vol. 14, no. 2, pp. 125-136, 2021.
Copyright (c) 2023 Trimono Trimono, Di Asih Maruddani
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
Authors who publish with this Journal agree to the following terms:
- Author retain copyright and grant the journal right of first publication with the work simultaneously licensed under a creative commons attribution license that allow others to share the work within an acknowledgement of the work’s authorship and initial publication of this journal.
- Authors are able to enter into separate, additional contractual arrangement for the non-exclusive distribution of the journal’s published version of the work (e.g. acknowledgement of its initial publication in this journal).
- Authors are permitted and encouraged to post their work online (e.g. in institutional repositories or on their websites) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published works.