Source: Adrian & Brunnermeier (2016) · American Economic Review 106(7), 1705–1741 · doi:10.1257/aer.20120555
TL;DR
Proposes CoVaR, a measure of systemic risk: the Value-at-Risk of the whole financial system conditional on a particular institution being in distress. An institution's contribution to systemic risk is ΔCoVaR — the difference between system VaR when the institution is at its VaR (distress) level versus when it is at its median state. Institutions with similar own VaR can contribute very differently to systemic risk; ΔCoVaR is predictable from leverage, size, and maturity mismatch, enabling a countercyclical, forward-looking measure.
Problem it solves
The standard risk measure, VaR, gauges an institution in isolation and ignores externalities, interconnectedness, and tail comovement. It also tends to be procyclical (risk looks low precisely when imbalances build — the "volatility paradox"). CoVaR reframes measurement around an institution's contribution to system-wide tail risk.
The method
Definition. CoVaR_q^{system|i} is the q-quantile (VaR) of the financial system's returns conditional on institution i being at its own q-VaR. The institution's marginal contribution is
ΔCoVaR_i = CoVaR(system | i at VaR) − CoVaR(system | i at median state).
Estimation: quantile regression of system returns on institution returns (and controls) at the 1% (and 50%) quantiles; CoVaR is read off the fitted quantile. Authors note Engle-Manganelli CAViaR uses related quantile-regression ideas.
Time-varying / forward ΔCoVaR. Quantile regressions conditioned on lagged state variables capturing tail-risk dependence: VIX (implied equity volatility), the slope of the yield curve, the aggregate credit spread, a short-term liquidity/TED-type spread, and market returns. Combining with institution characteristics yields a "forward-ΔCoVaR" that is forward-looking and countercyclical.
Assumptions & inputs
Data: weekly equity returns for the universe of publicly traded U.S. financial institutions (banks, broker-dealers, insurers, real estate), 1986Q1–2010Q4, a total of 1,226 institutions, merged with Compustat balance-sheet data. Returns are weekly changes in market-valued total assets.
Tail dependence is assumed estimable via quantiles; conditioning relationship assumed stable enough to forecast.
How to use it
Rank institutions by ΔCoVaR (not own VaR) to identify systemic importance, including "systemic-as-part-of-a-herd" exposures.
Predict future ΔCoVaR from lagged characteristics (leverage, size, maturity mismatch) for countercyclical, pre-emptive regulation/capital surcharges.
The paper shows the 2006Q4 value of the forward measure would have predicted more than half of realized cross-sectional covariances during the 2007–09 crisis.
Limitations & pitfalls
An institution's own VaR is shown to be a poor guide to ΔCoVaR — using the wrong measure misranks risk.
Estimates are sensitive to the conditioning method and the choice of state variables; conditional tail quantities are imprecise and can be unstable in crises.
Captures comovement, not the direction of causation/contagion; complements network-based measures.
Key references
Adrian & Brunnermeier (2016) — CoVaR — American Economic Review
