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CoVaR



Tobias Adrian

Federal Reserve Bank of New York

Markus K. Brunnermeier

Princeton University

This Version: November 1, 2010

Abstract

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

…nancial system conditional on institutions being under distress. We de…ne an insti-

tution’s contribution to systemic risk as the di¤erence between CoVaR conditional

on the institution being under distress and the CoVaR in the median state of the

institution. From our estimates of CoVaR f or the universe of publicly traded …nan-

cial institutions, we quantify the extent to which characteristics such as leverage,

size, and maturity mismatch predict systemic risk contribution. We show that pre-

dicted systemic risk contribution is countercyclical, and argue for macroprudential

regulation based on the degree to which such characteristics predict systemic risk

contribution.

Keywords: Value at Risk, Systemic Risk, Adverse Feedback Loop, E ndogen ous

Risk, Risk Spillovers, Financial Architecture, Capital Requirements

JEL classi…cation: G01, G10, G18, G20, G28, G32, G38



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

authors also thank Paolo Angelini, Gadi Barlevy, René Carmona, Stephen Brown, Robert Engle, Mark

Flannery, Xavier Gabaix, Paul Glasserman, Beverly Hirtle, Jon Danielson, John Kambhu, Arvind Kr-

ishnamurthy, Bu rton Malkiel, Maureen O’Hara, Andrew Patton, Matt Pritsker, Matt Richardson, Jean-

Charles Rochet, José Scheinkman, Jeremy Stein, Kevin Stiroh, and Skander Van den Heuvel for feedback,

as well as seminar participants at numerous universities, c entral banks, and conferences. We are grateful

for support from the Institute f or Quantitative Investment Research Europe. Brunnermeier also acknowl-

edges …nancial support from the Alfred P. Sloan Foundation. An earlier version of this paper with the

de…nition of CoVaR was presented at the NBER Summer Institute under the title “Risk Spillovers of

Financial Institutions”in July 2008.

Federal Reserve Bank of New York, Capital Markets, 33 Liberty Street, New York, NY 10045,

http://nyfedeconomists.org/adrian, e-mail: tobias.adrian@ny.frb.org.

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

the Federal Reserve Bank of New York or the Federal Reserve System.

Princeton University, Department of Economics, Bendheim Center for Finance, Princeton, NJ 08540-

5296, NBER, CEPR, CESIfo, http://www.princeton.edu/~markus, e-mail: markus@princeton.edu.

1 Introduction

During times of …nancial crises, losses tend to spread across …nancial institutions, threat-

ening the …nancial system as a whole.

While comovement of …nancial institutions’assets

and liabilities is primarily driven by fundamentals in normal times, comovement tends

to increase during times of crisis. Such increases of comovement give rise to systemic

risk— the risk that institutional distress spreads widely and distorts the supply of credit

and capital to the real economy. Negative spillover e¤ects can be direct, because of di-

rect contractual links and heightened counterparty credit risk, or indirect through price

e¤ects via liquidity spirals. Measures of systemic risk that capture the increase in tail

comovement during …nancial crises should become supervisory tools and form the basis

of any macroprudential regulation.

The most common measure of risk used by …nancial institutions— the value at risk

(VaR)— focuses on the risk of an individual institution in isolation. The q%-VaR is

the maximum dollar loss within the q%-con…dence interval; see the overviews by Kupiec

(2002) and Jorion (2006). However, a single institution’s risk measure does not necessarily

re‡ect systemic risk— the risk that the stability of the …nancial system as a whole is

threatened. First, according to the classi…cation in Brunnermeier, Crocket, Goodhart,

Perssaud, and Shin (2009), a systemic risk measure should identify the risk on the system

by “individually systemic”institutions, which are so interconnected and large that they

can cause negative risk spillover e¤ects on others, as well as by institutions that are

“systemic as part of a herd.” A group of 100 institutions that act like clones can be as

precarious and dangerous to the system as the large merged identity. The S&L crisis in the

1980s is a prominent example of many small institutions being systemic as part of herd.

Examples include the 1987 equity market crash, which was started by portfolio hedging of pension

funds and led to substantial losses of investment banks; the 1998 crisis, which was started with losses of

hedge funds and spilled over to the trading ‡oors of commercial and investment banks; and the 2007-09

crisis, which spread from SIVs to commercial banks and on to investment banks and hedge funds. See

Brady (1988), Rubin, Greenspan, Levitt, and Born (1999), Brunnermeier (2009), and Adrian and Shin

(2010a).

Second, risk measures should recognize that risk typically builds up in the background in

the form of imbalances and bubbles and materializes only during a crisis. Hence, high-

frequency risk measures that rely primarily on contemporaneous price movements are

misleading and procyclical. Regulation based on such contemporaneous measures tends

to be procyclical and potentially ampli…es business cycles (see Adrian and Shin (2010b)).

The objective of this paper is twofold: First, we propose a measure for systemic risk.

Second, we outline a method that allows for a countercyclical implementation of macro-

prudential policy by predicting future systemic risk using current institutional character-

istics such as size, leverage, and maturity mismatch. To emphasize the systemic nature

of our risk measure, we add to existing risk measures the pre…x “Co,” which stands for

conditional, comovement, contagion, or contributing. We focus primarily on CoVaR,

where institution i’s CoVaR relative to the system is de…ned as the VaR of the whole

…nancial sector conditional on institution i being in distress.

The di¤erence between

the CoVaR conditional on the distress of an institution and the CoVaR conditional on

the “normal”state of the institution, CoVaR, captures the marginal contribution of a

particular institution (in a non-causal sense) to the overall systemic risk.

There are several advantages to our CoVaR measure. First, while CoVaR focuses

on the contribution of each institution to overall system risk, current prudential regulation

focuses on the risk of individual institutions. Regulation based on the risk of institutions in

isolation can lead, in the aggregate, to excessive risk-taking along systemic risk dimensions.

To see this more explicitly, consider two institutions, A and B, which report the same VaR,

but for institution A the CoVaR= 0, while for institution B the CoVaR is large (in

absolute value). Based on their VaRs, both institutions appear equally risky. However,

the high CoVaR of institution B indicates that it contributes more to system risk. Since

Just as VaR sounds like variance, CoVaR sounds like covariance. This analogy is no coincidence.

In fact, under many distributional assumptions (such as the assumption that shocks are conditionally

Gaussian), the VaR of an institution is indeed proportional to the variance of the institution, and the

CoVaR of an institution is proportional to the covariance of the …nancial system and the individual

institution.

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