CoVaR and ΔCoVaR — a bank's footprint on system risk
Turn the camera around: not the bank's own loss, but the system's loss when this bank is in trouble. CoVaR is the system VaR conditional on the bank in distress; ΔCoVaRis that minus the system VaR when the bank is at its median state. ΔCoVaR is the bank's marginal spillover, not the same as CoVaR. A bigger, more linked bank widens the gap.
ΔCoVaR (marginal system-risk contribution)+2.07 pp
CoVaR (distress) 6.36%CoVaR (median) 4.29%ΔCoVaR +2.07% pp
ΔCoVaR = CoVaR(distress) − CoVaR(median) — the marginal gap, not the level
Linkage / dependence ρ0.60
Bank size / system weight35%
Tail level q5.0%
CoVaR — a level: the system's VaR while the bank sits in distress (its own q-quantile loss).
ΔCoVaR — a difference: CoVaR(distress) − CoVaR(median). It nets out the system's baseline and isolates the bank's marginal spillover.
Not the same. A high CoVaR can be mostly baseline system stress; ΔCoVaR is the part the bank adds.
This bank's distress lifts system VaR only from 4.29% to 6.36%, a ΔCoVaR of 2.07%. A small or weakly linked bank adds little system risk even if its own VaR is large.
ΔCoVaR (Adrian & Brunnermeier, 2016) ranks systemic importance by a firm's marginal spillover. A sibling measure, SRISK, instead asks how big a capital hole the firm would open in a crisis.