The generalized Pareto distribution (GPD) approach for estimating the Value-at-Risk
(VaR) and the expected shortfall (ES) is compared to other methods for evaluating extreme
risk with normally distributed returns. When the market index returns have a fat-tailed
distribution, the risk measures computed from the normal distribution underestimate the
tail-related risk. We also compare the computation results of the VaR based on the GPD
approximations to those based on the RiskMetrics methodology and GARCH model
estimation. The estimates of the VaR are robust to a variety of threshold values. Contrary to
this, the VaR values based on the RiskMetrics methodology and the GARCH model are
extremely volatile. From a risk manager’s perspective, it would be difficult to adjust capital
requirement of a financial institution to conditional market risk. Due to concerns raised for
practical and statistical reasons, we can conclude that the GPD method for measuring
unconditional market risk is more appropriate for measuring and managing the tail-related
risk.