Covar

Federal Reserve Bank of New York

Staff Reports

CoVaR

Tobias Adrian

Markus K. Brunnermeier

Staff Report no. 348

September 2008

Revised September 2011

This paper presents preliminary findings and is being distributed to economists

and other interested readers solely to stimulate discussion and elicit comments.

The views expressed in the paper are those of the authors and are not necessarily

reflective of views at the Federal Reserve Bank of New York or the Federal

Reserve System. Any errors or omissions are the responsibility of the authors.

CoVaR

Tobias Adrian and Markus K. Brunnermeier

Federal Reserve Bank of New York Staff Reports, no. 348

September 2008; revised September 2011

JEL classification: G01, G10, G18, G20, G28, G32, G38

Abstract

We propose a measure for systemic risk: CoVaR, the value at risk (VaR) of the financial

system conditional on institutions being in distress. We define an institution’s contribution

to systemic risk as the difference between CoVaR conditional on the institution being in

distress and CoVaR in the median state of the institution. From our estimates of CoVaR

for the universe of publicly traded financial institutions, we quantify the extent to which

characteristics such as leverage, size, and maturity mismatch predict systemic risk

contribution. We also provide out-of-sample forecasts of a countercyclical, forwardlooking

measure of systemic risk and show that the 2006:Q4 value of this measure would

have predicted more than half of realized covariances during the financial crisis.

Key words: value at risk, systemic risk, risk spillovers, financial architecture

Adrian: Federal Reserve Bank of New York (e-mail: tobias.adrian@ny.frb.org). Brunnermeier:

Princeton University, NBER, CEPR, CESifo (e-mail: markus@princeton.edu). Special thanks

go to Daniel Green and Hoai-Luu Nguyen for outstanding research assistance. The authors

also thank Paolo Angelini, Gadi Barlevy, Stephen Brown, René Carmona, Jon...