Value At Risk, Minimum Capital Requirement And The Use Of Extreme Value Distributions: An Application To BRICS Markets

Abstract

This paper uses closing prices of the BRICS (Brazil, Russia, India, China, and South Africa) financial markets to implement a risk model that generates point estimates of both Value at Risk (VaR); and Expected Shortfall (ES). The risk model is thereafter backtested using three techniques namely the Basel II green zone, the unconditional test, and the conditional test.

We first filter the log-return data using an Autoregressive Regression model (AR) of order one for the conditional mean and an Exponential Generalised Autoregressive Conditional Heteroscedasticity of order one (EGARCH 1,1) for the conditional variance. We thereafter fit the filtered returns by using the Generalised Pareto Distribution (GPD) model before we compute both VaR and ES estimates. We find that the use of the GPD is well suited to financial markets that are highly exposed to global financial risks.

Our results show that both VaR and ES estimates for South Africa are very low when compared with those of other BRICS financial markets. We argue that South Africa’s credit and loan regulations, pioneered by the National Credit Regulator (NCR), might have decreased its exposure to global financial risks. The resulting minimum capital requirement values are found to be significantly different depending on whether the Variance-Covariance or the GPD methodology is used. The backtesting methodologies show that the VaR model used in the paper is more robust and practically reliable.