Value-at-Risk and Extreme Returns

Accurate prediction of the frequency of extreme events is of primary importance in many financial applications such as Value-at-Risk (VaR) analysis. We propose a semi-parametric method for VaR evaluation. The largest risks are modelled parametrically, while smaller risks are captured by the non- parametric empirical distribution function. The semi-parametric method is compared with historical simulation and the J.P. Morgan RiskMetrics technique on a portfolio of stock returns. For predictions of low probability worst outcomes, RiskMetrics analysis underpredicts the VaR while historical simulation overpredicts the VaR. However, the estimates obtained from applying the semi-parametric method are more accurate in the VaR prediction. In addition, an option is used in the portfolio to lower downside risk. Finally, it is argued that current regulatory environment provides incentives to use the lowest quality VaR method available.