Extreme conditional value at risk: a coherent scenario for risk management

This paper empirically compares the static unconditional Value-at-Risk (VaR) and conditional Value-at-Risk (CVaR) estimates based on two extreme value theory (EVT) distributions: the generalized extreme value distribution (GEV) and the generalized Pareto distribution (GPD); and two other traditional methodologies: the historical simulation and the variance covariance method as a benchmark models. Using daily equity and exchange rate data from the United States, Japan, Europe, Brazil, Hong-Kong and South Africa covering the pre-crisis period (2004 to 2006), the crisis period (2007 to 2008) and the recovery period (2009 to 2011), we consider both the downside and upside risk to evaluate extreme losses for both long and short positions held by investors. The paper has several findings. Firstly, we find that the conditional GEV model outperforms all the other models at all the quantiles; however it overestimates risk especially the upside risk. Secondly, the conditional GPD does not perform significantly different from the unconditional historical simulation. Thirdly, as expected of models that ignore the fact that returns are fat tailed by assuming normally distributed returns, the unconditional variance-covariance model underestimates risk in both directions and at all quantiles. Fourthly, risk levels were highest during the crisis period, and decreased significantly in the recovery period however to levels still above the pre-crisis period. Lastly, regarding risk levels in advanced economies compared to emerging economies, a reverse of the pre- crisis period scenario occurred since the onset of the financial crisis, advanced economies are now riskier than emerging economies.