Value-at-Risk and Extreme Returns

Accurate prediction of the frequency of extreme events is of primary importance in many financialapplications such as Value-at-Risk (VaR) analysis. We propose a semi-parametric method for VaRevaluation. 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 historicalsimulation and the J.P. Morgan RiskMetrics technique on a portfolio of stock returns. For predictions oflow probability worst outcomes, RiskMetrics analysis underpredicts the VaR while historical simulationoverpredicts the VaR. However, the estimates obtained from applying the semi-parametric method aremore accurate in the VaR prediction. In addition, an option is used in the portfolio to lower downsiderisk. Finally, it is argued that current regulatory environment provides incentives to use the lowestquality VaR method available.