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Estimating risk of foreign exchange portfolio: Using VaR and CVaR based on GARCH–EVT-Copula model

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  • Wang, Zong-Run
  • Chen, Xiao-Hong
  • Jin, Yan-Bo
  • Zhou, Yan-Ju

Abstract

This paper introduces GARCH–EVT-Copula model and applies it to study the risk of foreign exchange portfolio. Multivariate Copulas, including Gaussian, t and Clayton ones, were used to describe a portfolio risk structure, and to extend the analysis from a bivariate to an n-dimensional asset allocation problem. We apply this methodology to study the returns of a portfolio of four major foreign currencies in China, including USD, EUR, JPY and HKD. Our results suggest that the optimal investment allocations are similar across different Copulas and confidence levels. In addition, we find that the optimal investment concentrates on the USD investment. Generally speaking, t Copula and Clayton Copula better portray the correlation structure of multiple assets than Normal Copula.

Suggested Citation

  • Wang, Zong-Run & Chen, Xiao-Hong & Jin, Yan-Bo & Zhou, Yan-Ju, 2010. "Estimating risk of foreign exchange portfolio: Using VaR and CVaR based on GARCH–EVT-Copula model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(21), pages 4918-4928.
    • Handle: RePEc:eee:phsmap:v:389:y:2010:i:21:p:4918-4928
    DOI: 10.1016/j.physa.2010.07.012
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    2. Karmakar, Madhusudan, 2017. "Dependence structure and portfolio risk in Indian foreign exchange market: A GARCH-EVT-Copula approach," The Quarterly Review of Economics and Finance, Elsevier, vol. 64(C), pages 275-291.
    3. Zhichao Zhang & Li Ding & Fan Zhang & Zhuang Zhang, 2015. "Optimal Currency Composition for China's Foreign Reserves: A Copula Approach," The World Economy, Wiley Blackwell, vol. 38(12), pages 1947-1965, December.
    4. Florentina Paraschiv & Stine Marie Reese & Margrethe Ringkjøb Skjelstad, 2020. "Portfolio stress testing applied to commodity futures," Computational Management Science, Springer, vol. 17(2), pages 203-240, June.
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    6. Lin, Saiyan & Chen, Rongda & Lv, Zhihong & Zhou, Tianqing & Jin, Chenglu, 2019. "Integrated measurement of liquidity risk and market risk of company bonds based on the optimal Copula model," The North American Journal of Economics and Finance, Elsevier, vol. 50(C).
    7. Ahmet Akca & Ethem Çanakoğlu, 2021. "Adaptive stochastic risk estimation of firm operating profit," Economia e Politica Industriale: Journal of Industrial and Business Economics, Springer;Associazione Amici di Economia e Politica Industriale, vol. 48(3), pages 463-504, September.
    8. Kim, Dongwhan & Kang, Kyu Ho, 2021. "Conditional value-at-risk forecasts of an optimal foreign currency portfolio," International Journal of Forecasting, Elsevier, vol. 37(2), pages 838-861.
    9. Aloui, Chaker & Jammazi, Rania, 2015. "Dependence and risk assessment for oil prices and exchange rate portfolios: A wavelet based approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 436(C), pages 62-86.
    10. Akhtaruzzaman, Md & Banerjee, Ameet Kumar & Boubaker, Sabri & Moussa, Faten, 2023. "Does green improve portfolio optimisation?," Energy Economics, Elsevier, vol. 124(C).
    11. Aleš Kresta, 2015. "Application of Performance Ratios in Portfolio Optimization," Acta Universitatis Agriculturae et Silviculturae Mendelianae Brunensis, Mendel University Press, vol. 63(6), pages 1969-1977.
    12. Lahmiri, Salim, 2017. "Asymmetric and persistent responses in price volatility of fertilizers through stable and unstable periods," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 466(C), pages 405-414.
    13. Hong Qiu & Genhua Hu & Yuhong Yang & Jeffrey Zhang & Ting Zhang, 2020. "Modeling the Risk of Extreme Value Dependence in Chinese Regional Carbon Emission Markets," Sustainability, MDPI, vol. 12(19), pages 1-15, September.
    14. Wei, Yu, 2012. "Forecasting volatility of fuel oil futures in China: GARCH-type, SV or realized volatility models?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(22), pages 5546-5556.
    15. Mateusz Buczyński & Marcin Chlebus, 2021. "GARCHNet - Value-at-Risk forecasting with novel approach to GARCH models based on neural networks," Working Papers 2021-08, Faculty of Economic Sciences, University of Warsaw.

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