and Company LLC

In prediction of quantiles of daily S&P 500 returns we consider how we use high-frequency 5-minute data. We examine methods that incorporate the high frequency information either indirectly through combining forecasts (using forecasts generated from returns sampled at dif-ferent intra-day interval) or directly through combining high frequency information into one model. We consider subsample averaging, bootstrap averaging, forecast averaging methods for the indirect case, and factor models with principal component approach for both cases. We show, in forecasting daily S&P 500 index return quantile (VaR is simply the negative of it), us-ing high-frequency information is bene\u85cial, often substantially and particularly so in forecasting downside risk. Our empirical results show that the averaging methods (subsample averaging, bootstrap averaging, forecast averaging), which serve as di¤erent ways of forming the ensemble average from using high frequency intraday information, provide excellent forecasting perfor-mance compared to using just low frequency daily information