The study of volatility and covariation has become one of the most active and successful areas of research in time series econometrics and economic forecasting in recent years. Thanks to the increasing availability of daily and intra-daily information on the returns of financial assets as well as computing power, different kinds of models have been proposed over the last two decades. In this work we deeply focus on two different classes of models, namely the Multivariate GARCH models, based on daily observed returns, and the Realized Covariance models, based on intra-daily data recorded at higher frequency. The reason behind this choice is due to the evidence that many researchers are currently interested in pointing out which class could be preferable in realistic financial settings and if using high-frequency information could really lead to significant estimation and forecasting improvements. We face this issue by analyzing a set of selected models and evaluating their profitability for portfolio optimization.