This paper proposes new dynamic component models of realized covariance (RCOV) matrices based on recent work in time-varying Wishart distributions. The specifications are linked to returns for a joint multivariate model of returns and covariance dynamics that is both easy to estimate and forecast… . Realized covariance matrices are constructed for 5 stocks using high-frequency intraday prices based on positive semi-definite realized kernel estimates. The models are compared based on a term-structure of density forecasts of returns for multiple forecast horizons. Relative to multivariate GARCH models that use only daily returns, the joint RCOV and return models provide significant improvements in density forecasts from forecast horizons of 1 day to 3 months ahead. Global minimum variance portfolio selection is improved for forecast horizons up to 3 weeks out.