This study extends the Diebold-Yilmaz Connectedness Index (DYCI) methodology and, based on forecast error covariance decompositions, derives a network risk model for a portfolio of assets. As a normalized measure of the sum of variance contributions, system-wide connectedness averages out the information embedded in the covariance matrix in aggregating pairwise directional measures. This actually does matter, especially when there are large differences in asset variances. As a first step towards deriving the network risk model, the portfolio covariance matrix is decomposed to obtain the network-driven component of the portfolio variance using covariance decompositions. A second step shows that a common factor model can be estimated to obtain both the variance and covariance decompositions. In a third step, using quantile regressions, the proposed network risk model is estimated for different shock sizes. It is shown, in contrast to the DYCI model, the dynamic quantile estimation of the network risk model can differentiate even small shocks at both tails. This result is obtained because the network risk model makes full use of information embedded in the covariance matrix. Estimation results show that in two recent episodes of financial market turmoil, the proposed network risk model captures the responses to systemic events better than the system-wide index.