Optimality of the RiskMetrics VaR model

Using different loss functions in estimation and forecast evaluation of econometric models can cause suboptimal parameter estimates and inaccurate assessment of predictive ability. Though there are not general guidelines on how to choose the loss function, the modeling of Value-at-Risk is a rare instance is which the loss function for forecasting evaluation is well defined. Within the context of the RiskMetrics™ methodology, which is the most popular to calculate Value-at-Risk, we investigate the implications of considering different loss functions in estimation and forecasting evaluation. Based on U.S. equity, exchange rates, and bond market data we find that there can be substantial differences on the estimates under alternative loss functions. On calculating the 99% VaR for a 10-day horizon, the RiskMetrics™ model for equity markets overestimates substantially the decay factor. However, the out-of-sample performance is not systematically superior by using the estimates under the correct loss function.