In modelling and forecasting volatility, two main trade-offs emerge: mathematical tractability versus economic interpretation and accuracy versus speed. The authors attempt to reconcile, at least partially, both trade-offs. The former trade-off is crucial for many financial applications, including portfolio and risk management. The speed/accuracy trade-off is becoming more and more relevant in an environment of large portfolios, prolonged periods of high volatility (as in the current financial crisis), and the burgeoning phenomenon of algorithmic trading in which computer-based trading rules are automatically implemented. The increased availability of high-frequency data provides new tools for forecasting variances and covariances between assets. However, there is scant literature on forecasting more than one realised volatility. Following Gourieroux, Jasiak and Sufana (Journal of Econometrics, forthcoming), the authors propose a methodology to model and forecast realised covariances without any restriction on the parameters while maintaining economic interpretability. An empirical application based on variance forecasting and risk evaluation of a portfolio of two US treasury bills and two exchange rates is presented. The authors compare their model with several alternative specifications proposed in the literature. Empirical findings suggest that the model can be efficiently used in large portfolios.