VALUE AT RISK ESTIMATION FOR STOCK PORTFOLIO USING THE ARCHIMEDEAN COPULA APPROACH

  • Mohammad Dicky Saifullah Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Brawijaya, Indonesia
  • Umu Sa'adah Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Brawijaya, Indonesia https://orcid.org/0009-0007-3350-4896
  • Kwardiniya Andawaningtyas Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Brawijaya, Indonesia
  • Endang Wahyu Handamari Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Brawijaya, Indonesia https://orcid.org/0009-0004-0268-022X
DOI: https://doi.org/10.30598/barekengvol18iss3pp1779-1790
Keywords: Archimedean Copula, Investment, Return, Stock, Value at Risk

Abstract

Investment is one of the many ways to achieve future profits. One form of investment that is widely made is stocks. The return obtained in investing in stocks is potentially higher than other investment alternatives, but the risks borne are amplified, so it is necessary to analyze these risks that may occur. In this study, the Archimedean copula method is used to estimate the Value at Risk on shares of PT Bank Rakyat Indonesia Tbk (BBRI) and PT Telekomunikasi Indonesia Tbk (TLKM) for the period September 1, 2021, to August 31, 2023. The stock data is used to determine the Archimedean copula model and calculate the estimated value of Value at Risk (VaR) on the stock return portfolio using the Archimedean copula approach. The Archimedean copula models used are the Clayton copula model, Gumbel copula, and Frank copula. Of the three Archimedean copula models, the best model was selected by looking at the largest Maximum Likelihood Estimation (MLE) value. In this study, the log-likelihood value of Clayton copula is 7.958, Gumbel copula is 6.663, and Frank copula is 8.398. Therefore, Frank copula is the best Archimedean copula model with the largest log-likelihood value of 8.398 for the said data. Then the VaR estimation is done with the Frank copula model. The Value at Risk estimation results based on the Frank copula model show maximum loss rates of -0.0277 at the 90% confidence level, -0.0363 at the 95% confidence level, and -0.0516 at the 99% confidence level.

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Published
2024-08-02
How to Cite
[1]
M. Saifullah, U. Sa’adah, K. Andawaningtyas, and E. Handamari, “VALUE AT RISK ESTIMATION FOR STOCK PORTFOLIO USING THE ARCHIMEDEAN COPULA APPROACH”, BAREKENG: J. Math. & App., vol. 18, no. 3, pp. 1779-1790, Aug. 2024.
Issue
Vol 18 No 3 (2024): BAREKENG: Journal of Mathematics and Its Application
Section
Articles

Copyright (c) 2024 Mohammad Dicky Saifullah, Umu Sa'adah, Kwardiniya Andawaningtyas, Endang Wahyu Handamari

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