Journal of Risk Model Validation

Risk model validation for BRICS countries: a value-at-risk, expected shortfall and extreme value theory approach

Jean Paul Chung Wing and Preethee Nunkoo Gonpot

  • Expected Shortfall and VaR as risk measures have been used as compared to the usual VaR approach in literature.
  • Expected shortfall being a coherent risk measure is the appropriate tool to be used by practitioners as it prompts diversity in portfolio.
  • The analysis of the data set identifies specific features such as extreme values and change in volatility which ultimately determines the appropriateness of a risk model: symmetric/ asymmetric GARCH depends on the characteristics of the in-sample and out-of-sample data set.
  • EVT or dynamic models are appropriate when there are extreme values in the original data.
  • It is possible to single out various common models with a shift from frontier countries to emerging coutries. This statement can be extrapolated to developed economies where a few familiar risk models have been identified.


In this paper, we employ value-at-risk (VaR) and expected shortfall (ES) as risk measures to assess the competency of several volatility models, based on the stock indexes of the BRICS countries (Brazil, Russia, India, China and South Africa) after the financial crisis. The aim is to determine the most appropriate model for each country and identify a set of common models for the BRICS countries. A family of generalized autoregressive conditional heteroscedasticity (GARCH) models, extreme value theory (EVT) and a dynamic bivariate technique are considered to demonstrate different volatility dynamics. Some models are ruled out under the presented backtesting operations, while the nonrejected models are ranked using two loss functions. In spite of returns displaying large kurtosis, the models with normal innovation generally prove to have better estimates ofVaR and ES. GARCH and fractionally integrated GARCH are preferred by Brazil and Russia, while India favors dual models and the Student t distribution. The Glosten, Jagannathan and Runkle GARCH-N is the best model for South Africa, which is the only country that rejects the stationary EVT approach. Despite these contrasting results, we find that it is possible to obtain more than one model that can be used to model all of the BRICS countries: these are the integrated GARCH-N and exponential GARCH-EVT approaches.

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