Optimally harnessing inter‐day and intra‐day information for daily value‐at‐risk prediction

We make use of quantile regression theory to obtain a combination of individual potentially‐biased VaR forecasts that is optimal because, by construction, it meets the correct out‐of‐sample conditional coverage criterion ex post. This enables a Wald‐type conditional quantile forecast encompassing test to be used for any finite set of competing (semi/non)parametric models which can be nested. Two attractive properties of this backtesting approach are its robustness to both model risk and estimation uncertainty. We deploy the techniques to analyse inter‐day and high frequency intra‐day VaR models for equity, FOREX, fixed income and commodity trading desks. The forecast combination of both types of models is especially warranted for more extreme‐tail risks. Overall, our empirical analysis supports the use of high frequency 5 minute price information for daily risk management.