Before revision:  While the common components, driven by market shocks, are related to the non-diversifiable or {\it systematic } components of risk, the idiosyncratic components show important interdependencies which are nicely described through network structures. Those networks shed some light on the contagion phenomenons associated with financial crises, and help assessing how {\it systemic} a given firm islikely to be.
After revision:  While the common components, driven by market shocks, are related to the non-diversifiable or {\it systematic } (LVDN), where the nodes are stocks, and the weight associated with edge (i,j) represents the proportion of h-step-ahead forecast error variance of variable i accounted for by variable j's innovations. To overcome the curse of dimensionality, we decompose the panel into a component driven by few global, market-wide, factors, and an idiosyncratic one modelled by means of a sparse vector autoregression (VAR) model. Inversion of the VAR together with suitable identification restrictions, produces the estimated network, by means of which we can assess how {\it systemic} a given firm islikely to be.