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 extremerisk with normally distributed returns. When the market index returns have a fat-taileddistribution, the risk measures computed from the normal distribution underestimate thetail-related risk. We also compare the computation results of the VaR based on the GPDapproximations to those based on the RiskMetrics methodology and GARCH modelestimation. The estimates of the VaR are robust to a variety of threshold values. Contrary tothis, the VaR values based on the RiskMetrics methodology and the GARCH model areextremely volatile. From a risk manager’s perspective, it would be difficult to adjust capitalrequirement of a financial institution to conditional market risk. Due to concerns raised forpractical and statistical reasons, we can conclude that the GPD method for measuringunconditional market risk is more appropriate for measuring and managing the tail-relatedrisk.