Risk in Emerging Stock Markets from Brazil and Mexico: Extreme Value Theory and Alternative Value at Risk Models

Conventional Value-at-risk (VaR) models tend to underestimate stock market losses, as they assume normality and fail to capture the frequency and severity of extreme fluctuations, Extreme value theory (EVT) overcomes this limitation by providing a framework in which to analyze the extreme behavior of stock-markets returns and by quantifying possible losses during financial turbulences. This study uses the c-quantile of a fat-tailed distribution for VaR analysis. An innovation in the present work is the application of EVT not only to the left tail of the returns distribution but also to its right tail, while assessing long and short positions. A generalized extreme value distribution (GEVD) is used to analyze the two largest stock markets from Latin America, Brazil and Mexico; a conditional VaR (CVaR) model is applied to determine risk exposure from investing in those markets, with daily index data for the period 1970-2004. The results confirm the presence of fat tails in both markets as a result of the excess of kurtosis; the empirical evidence shows that VaR and CVaR based on EVT yield more precise and robust information about financial risk than conventional parametric estimations.