Fire Sales in a Model of Complexity

• Published date: 01 December 2013
• DOI: http://doi.org/10.1111/jofi.12087
• Author: ALP SIMSEK,RICARDO J. CABALLERO
• Date: 01 December 2013

THE JOURNAL OF FINANCE •VOL. LXVIII, NO. 6 •DECEMBER 2013

Fire Sales in a Model of Complexity

RICARDO J. CABALLERO and ALP SIMSEK∗

ABSTRACT

We present a model of financial crises that stem from endogenous complexity.We

conceptualize complexity as banks’ uncertainty about the financial network of cross

exposures. As conditions deteriorate, cross exposures generate the possibility of a

domino effect of bankruptcies. As this happens, banks face an increasingly complex

environment since they need to understand a greater fraction of the financial network

to assess their own financial health. Complexity dramatically amplifies banks’ per-

ceived counterparty risk, and makes relatively healthy banks reluctant to buy risky

assets. The model also features a novel complexity externality.

ONE OF THE MOST damaging aspects of financial crises is the enormous uncer-

tainty they generate, and a central factor behind this uncertainty is the com-

plexity of the linkages among modern financial institutions (banks, for short).

The concern for the uncertainty and complexity combination, and the perverse

fire sales that accompany it, influences private and public choices alike. Federal

Reserve Chairman Ben Bernanke, in his testimony to the Senate on April 3,

2008 following the Fed’s Bear Stearns intervention, captures this concern as

follows:

Our financial system is extremely complex and interconnected, and Bear

Stearns participated extensively in a range of critical markets. The sud-

den failure of Bear Stearns likely would have led to a chaotic unwinding

of positions in those markets and could have severely shaken confidence.

The company’s failure could also have cast doubt on the financial posi-

tions of some of Bear Stearns’ thousands of counterparties and perhaps of

companieswithsimilarbusinesses....Moreover, the adverse impact of a

default would not have been confined to the financial system but would

∗Both the authors are from MIT and NBER. We thank Jeff Campbell, John Geanakoplos,

Campbell Harvey, David Laibson, Fred Malherbe, Juan Ocampo, Katerina Smidkova, Fernando

Vega-Redondo, Adam Zawadowski, an anonymous referee, and an Associate Editor for valuable

comments. We also thank the seminar participants at Bilkent University, Boston College, The Fed-

eral Reserve Bank of Boston, Boston University, Harvard University, MIT, Middle East Technical

University, New York University, the University of Chicago, the University of Michigan; confer-

ence participants at the AEA meetings, Brown University, CIED-Tel Aviv University, Columbia

University,ECB, IRFMP, MFI, MNB-CEPR, PSU-Cornell, SAET,SED for their comments; and the

NSF for financial support. This paper covers and extends the substantive issues in (and hence,

replaces) “Complexity and Financial Panics,” NBER WP #14997.

DOI: 10.1111/jofi.12087

2549

2550 The Journal of Finance R

have been felt broadly in the real economy through its effects on asset

values and credit availability.1

Unfortunately, Chairman Bernanke’s testimony would prove prescient only

a few months later during the Lehman episode, when the demise of the invest-

ment bank wrecked havoc around the world. Moreover, the concern for a repeat

of such turmoil is the central reason behind the multiple recent attempts to

insulate the rest of Europe from the sovereign debt problems of its periphery.

In this paper, we present a model of crises that builds upon the idea that

complexity, a dormant factor during normal times, becomes acutely relevant

and self-reinforcing during crises. Complexity matters in our model not di-

rectly (and in this sense this is not a “networks” paper) but through the un-

certainty it generates and through the reactions of the economic agents to this

uncertainty.

The basic structure of our model is a network of cross exposures between

financial institutions that is susceptible to a domino effect of bankruptcies.

However, we make assumptions such that domino effects are of limited size

in the absence of our informational mechanism. In this context, we concep-

tualize complexity by banks’ uncertainty about cross exposures. In particular,

banks have only local knowledge of cross exposures: they understand their own

exposures, but they are increasingly uncertain about cross exposures of banks

that are farther away (in the network) from themselves.2During normal times,

banks only need to understand the financial health of their direct counterpar-

ties. In contrast, when a surprise liquidity shock hits parts of the network, a

domino effect of bankruptcies becomes possible, and banks become concerned

that they might be indirectly hit. Banks’ uncertainty about cross exposures,

a dormant factor in normal times, suddenly becomes relevant. In particular,

banks now need to understand the financial health of the counterparties of

their counterparties (and their counterparties). Since banks only have local

knowledge of the exposures, they cannot rule out an indirect hit. They now per-

ceive significant counterparty risk that leads them to retrench into a liquidity

conservation mode.

This structure exhibits strong interactions with secondary markets for banks’

assets. Banks in distress can sell their legacy assets to meet the surprise

liquidity shock. The natural buyers of the legacy assets are other banks in the

financial network, which may also receive an indirect hit. When the surprise

shock is small, the domino effect is small and buyers can rule out an indirect

hit. In this case, buyers purchase the distressed banks’ legacy assets at their

“fair” prices (which reflect the fundamental value of the assets). In contrast,

when the surprise shock is large, larger domino effects become possible and

buyers cannot rule out an indirect hit. As a precautionary measure, they hoard

liquidity and turn into sellers. The price of legacy assets plummets to fire

1Available at http://www.federalreserve.gov/newsevents/testimony/bernanke20080y03a.htm.

2In practice, banks also face many other sources of complexity (e.g., asset payoffs). Our modest

goal in this paper is to focus on one source of complexity (about the structure of cross exposures),

and to understand the role that this type of complexity plays during crises.

Fire Sales in a Model of Complexity 2551

sale levels (i.e., below fundamentals), which in turn exacerbates the domino

effect.

This feedback mechanism can generate multiple equilibria for intermediate

levels of the surprise shock. When legacy assets garner a fair price in the

secondary market, the banks in distress have access to more liquidity, and

the surprise shock is contained after fewer bankruptcies. When the domino

effect is smaller, the natural buyers rule out an indirect hit and demand legacy

assets, which ensures that these assets trade at their fair prices. Set against

this benign scenario is the possibility of a fire sale equilibrium, where the price

of legacy assets collapses to fire sale levels. This leads to a greater number

of bankruptcies and a larger domino effect. With a larger domino effect, the

natural buyers become worried about an indirect hit and they sell their own

legacy assets, which reinforces the collapse of asset prices.

Our model features a distinct complexity externality, which stems from the

dependence of banks’ counterparty risk on the endogenous size of the domino

effect. In particular, any action that increases the size of the domino effect in-

creases the counterparty risk perceived by banks that are uncertain about the

financial network, and banks dislike this effect. Our model features two vari-

ants of this complexity externality (one nonpecuniary, one pecuniary), each of

which supports different government policies. First, a bailout of the distressed

banks financed by small lump-sum taxes on all banks may lead to a Pareto

improvement. The market equilibrium is unable to replicate this allocation

because each bank fails to take into account that its contribution to a bailout

will reduce the counterparty risk faced by all other banks. Second, in the range

of multiple equilibria, policies that increase asset prices may lead to a Pareto

improvement by coordinating the banks on the fair price equilibrium. In this

range, the fire sale equilibrium is Pareto inefficient because a bank that sells

assets does not take into account the effect of its decision on other banks’ coun-

terparty risk. In particular, this bank generates a (small) reduction in asset

prices, which in turn leads to a larger domino effect and greater counterparty

risk, real and perceived, for all other banks.

Our paper is related to several strands of the literature. An extensive liter-

ature highlights the possibility of network failures and contagion in financial

markets. An incomplete list includes Rochet and Tirole (1996), Kiyotaki and

Moore (1997a), Allen and Gale (2000), Freixas, Parigi, and Rochet (2000), Eisen-

berg and Noe (2001), Lagunoff and Schreft (2001), Dasgupta (2004), Leitner

(2005), Cifuentes, Ferrucci, and Shin (2005), Rotemberg (2008), Allen, Babus,

and Carletti (2010), Acemoglu et al. (2012), and Zawadowski (2013) (see Allen

and Babus (2009) for a survey). Many of these papers focus on the mechanisms

through which solvency and liquidity shocks may generate a domino effect in

the financial network. In contrast, we take these phenomena as the reason for

the rise in banks’ uncertainty and we focus on the effect of this uncertainty

on banks’ prudential actions. It is also worth pointing out that the uncertainty

mechanism we emphasize in this paper is operational even for a relatively small

amount of network contagion. The contagion literature is sometimes criticized

because it appears unlikely that many financial institutions would be caught