Value-at-Risk and Extreme Returns

We propose a semi-parametric method for unconditional Value-at-Risk (VaR) evaluation. The largest risks are modelled parametrically, while smaller risks are captured by the non-parametric empirical distribution function. A comparison of methods on a portfolio of stock and option returns reveals that at the 5% level the RiskMetrics analysis is best, but for predictions of low probability worst outcomes, it strongly underpredicts the VaR while the semi-parametric method is the most accurate.