Joseph G. Haubrich is vice president of and an economist at the Federal Reserve Bank of Cleveland. Andrew W. Lo is the Charles E. and Susan T. Harris Group Professor of Finance and director of the Laboratory for Financial Engineering at the Massachusetts Institute of Technology.

Quantifying Systemic Risk Illustrated Edition

By Joseph G. Haubrich, Andrew W. Lo

THE UNIVERSITY OF CHICAGO PRESS

Copyright © 2013 National Bureau of Economic Research
All rights reserved.
ISBN: 978-0-226-31928-5

Contents

Acknowledgments……………………………………………………xiIntroduction Joseph G. Haubrich and Andrew W. Lo……………………..1Systemic Risk and Financial Innovation: Toward a “Unified” Approach Henry
T. C. Hu………………………………………………………….111. Liquidity Risk, Cash Flow Constraints, and Systemic Feedbacks Sujit
Kapadia, Mathias Drehmann, John Elliott, and Gabriel Sterne…………….292. Endogenous and Systemic Risk Jon Danielsson, Hyun Song Shin, and
Jean-Pierre Zigrand………………………………………………..733. Systemic Risks and the Macroeconomy Gianni De Nicolò and Marcella
Lucchetta…………………………………………………………1134. Hedge Fund Tail Risk Tobias Adrian, Markus K. Brunnermeier, and
Hoai-Luu Q. Nguyen…………………………………………………1555. How to Calculate Systemic Risk Surcharges Viral V. Acharya, Lasse H.
Pedersen, Thomas Philippon, and Matthew Richardson…………………….1756. The Quantification of Systemic Risk and Stability: New Methods and
Measures Romney B. Duffey………………………………………….223Contributors………………………………………………………265Author Index………………………………………………………267Subject Index……………………………………………………..271

Excerpt

CHAPTER 1

Liquidity Risk, Cash FlowConstraints, andSystemic Feedbacks

Sujit Kapadia, Mathias Drehmann, John Elliott,and Gabriel Sterne

1.1 Introduction

The global financial crisis has served to reiterate the central role of liquidityrisk in banking. Such a role has been understood at least since Bagehot(1873). This chapter develops a framework that promotes an understandingof the triggers and system dynamics of liquidity risk during periods offinancial instability and illustrates these effects in a quantitative model ofsystemic risk.

The starting point of our analysis is the observation that although thefailure of a financial institution may reflect solvency concerns, it often manifestsitself through a crystallization of funding liquidity risk. In a worldwith perfect information and capital markets, banks would only fail if theirunderlying fundamentals rendered them insolvent. In such a world, providedvaluations are appropriate (e.g., adjusted to reflect prospective losses), thenexamining the stock asset and liability positions would determine banks’health, and solvent banks would always be able to finance random liquiditydemands by borrowing, for example, from other financial institutions. Inreality, informational frictions and imperfections in capital markets meanthat banks may find it difficult to obtain funding if there are concerns abouttheir solvency, regardless of whether or not those concerns are substantiated.In such funding crises, the stock solvency constraint no longer fullydetermines survival; what matters is whether banks have sufficient cashinflows, including income from asset sales and new borrowing, to cover allcash outflows. In other words, the cash flow constraint becomes critical.

The lens of the cash flow constraint also makes it possible to assess howbanks’ defensive actions during a funding liquidity crisis may affect the restof the financial system. Figure 1.1 provides a stylized overview of the transmissionmechanisms. For simplicity, it is assumed that the crisis starts witha negative shock leading to funding problems at one bank (bank A). Thenature of the shock can be manifold—for example, it could be a negativeearnings shock leading to a deterioration of the bank’s solvency position ora reputational shock. After funding problems emerge, confidence in bankA may deteriorate further, either endogenously or linked to concerns aboutthe shock (channel 1 in figure 1.1).

In an attempt to stave off a liquidity crisis, the distressed bank may takedefensive actions, with possible systemic effects (channels 2 and 3). Forinstance, it may hoard liquidity. Initially, it may be likely to start hoarding(future) liquidity by shortening the maturities of the interbank marketloans it provides. This is advantageous to bank A as shorter-term loanscan be realized more quickly and hence may be used as a buffer to potentialliquidity shocks. More extremely, the distressed bank could also cutthe provision of interbank loans completely, raising liquidity directly. Boththese actions could create or intensify funding problems at other banks thatwere relying on the distressed bank for funding (channel 2). The distressedbank could also sell assets, which could depress market prices, potentiallycausing distress at other banks because of mark-to-market losses or margincalls (channel 3). In addition, funding problems could also spread viaconfidence contagion, whereby market participants decide to run on banksjust because they look similar to bank A (channel 4) and, in the event ofbank failure, through interbank market contagion via counterparty creditrisk (channel 5).

The main innovation of this chapter is to provide a quantitative frameworkshowing how shocks to fundamentals may interact with fundingliquidity risk and potentially generate contagion that can spread across thefinancial system. In principle, one might wish to construct a formal forecastingframework for predicting funding crises and their spread. But it isdifficult to estimate the stochastic nature of cash flow constraints becauseof the binary, nonlinear nature of liquidity risk, and because liquidity crisesin developed countries have been (until recently) rare events, so data arelimited. Instead, we rely on a pragmatic approach and construct plausiblerules of thumb and heuristics. These are based on a range of sources, includingbehavior observed during crises. This carries the advantage that it providesfor a flexible framework that can capture a broad range of features andcontagion channels of interest. Such flexibility can help to make the modelmore relevant for practical risk assessment, as it can provide a benchmark forassessing overall systemic risk given a range of solvency and liquidity shocks.

Our modeling approach disentangles the problem into distinct steps. First,we introduce a “danger zone” approach to model how shocks affect individualbanks’ funding liquidity risk. This approach is simple and transparent(yet subjective) as we assume that certain funding markets close if the dangerzone score crosses particular thresholds. The danger zone score, in turn,summarizes various indicators of banks’ solvency and liquidity conditions.These include a bank’s similarity to other banks in distress (capturing confidencecontagion) and its short-term wholesale maturity mismatch—sincethe latter indicator worsens if banks lose access to long-term funding markets,the framework also captures “snowballing” effects, whereby banks areexposed to greater liquidity risk as the amount of short-term liabilities thathave to be refinanced in each period increases over time. Second, we combinethe danger zone approach with simple behavioral reactions to assess howliquidity crises can spread through the system. In particular, we demonstratehow liquidity hoarding and asset fire sales may improve one bank’s liquidityposition at the expense of others. Last, using the RAMSI (Risk AssessmentModel for Systemic Institutions) stress testing model presented in Aikmanet al. (2009), we generate illustrative distributions for bank profitability toshow how funding liquidity risk and associated contagion may exacerbateoverall systemic risk and amplify distress during financial crises. In particular,we demonstrate how liquidity effects may generate pronounced fat tailseven when the underlying shocks to fundamentals are Gaussian.

The feedback mechanisms embedded in the model all played an importantrole in the current and / or past financial crises. For example, the deteriorationin liquidity positions associated with snowballing effects was evident inJapan in the 1990s (see figures 14 and 15 in Nakaso 2001). And in this crisis,interbank lending collapsed from very early on. Spreads between interbankrates for term lending and expected policy rates in the major funding marketsrose sharply in August 2007, before spiking in September 2008 following thecollapse of Lehman Brothers (figure 1.2, panels A through C, thick blacklines). Throughout this period, banks substantially reduced their lendingto each other at long-term maturities, with institutions forced to roll overincreasingly large portions of their balance sheet at very short maturities.Figure 1.3 highlights these snowballing effects between 2007 and 2008. Atthe same time, the quantity of interbank lending also declined dramaticallyand there was an unprecedented increase in the amounts placed by banksas reserves at the major central banks, indicative of liquidity hoarding atthe system level.

In principle, the collapse in interbank lending could have arisen eitherbecause banks had concerns over counterparty credit risk, or over their ownfuture liquidity needs; it is hard to distinguish between these empirically.But anecdotal evidence suggests that, at least early in the crisis, banks werehoarding liquidity as a precautionary measure so that cash was available tofinance liquidity lines to off-balance sheet vehicles that they were committedto rescuing, or as an endogenous response to liquidity hoarding by othermarket participants. Interbank spread decompositions into contributionsfrom credit premia and noncredit premia (fig. 1.6, panels A through C), andrecent empirical work by Acharya and Merrouche (2012) and Christensen,Lopez, and Rudebusch (2009) all lend support to this view.

It is also clear that the reduction in asset prices after summer 2007 generatedmark-to-market losses that intensified funding problems in the system,particularly for those institutions reliant on the repo market who wereforced to post more collateral to retain the same level of funding (Gortonand Metrick 2010). While it is hard to identify the direct role of fire sales incontributing to the reduction in asset prices, it is evident that many assetswere carrying a large liquidity discount.

Finally, confidence contagion and counterparty credit losses came to thefore following the failure of Lehman Brothers. The former was evident inthe severe difficulties experienced by the other US securities houses in thefollowing days, including those that had previously been regarded as relativelysafe. Counterparty losses also contributed to the systemic impact ofits failure, with the fear of a further round of such losses via credit derivativecontracts being one of the reasons for the subsequent rescue of AmericanInternational Group (AIG).

There have been several important contributions in the theoretical literatureanalyzing how liquidity risk can affect banking systems, some of whichwe refer to when discussing the cash flow constraint in more detail in section1.2. But empirical papers in this area are rare. One of the few is van den End(2008), who simulates the effect of funding and market liquidity risk for theDutch banking system. The model builds on banks’ own liquidity risk models,integrates them to system-wide level, and then allows for banks’ reactions,as prescribed by rules of thumb. But the paper only analyzes shocksto fundamentals and therefore does not speak to overall systemic risk.

Measuring systemic risk more broadly is in its infancy, in particular ifinformation from banks’ balance sheets is used (Borio and Drehmann 2009).Austrian National Bank (OeNB 2006) and Elsinger, Lehar, and Summer(2006) integrated balance-sheet based models of credit and market risk witha network model to evaluate the probability of bank default in Austria. Alessandriet al. (2009) introduced RAMSI and Aikman et al. (2009) extend theapproach in a number of dimensions. RAMSI is a comprehensive balance-sheetmodel for the largest UK banks, which projects the different itemson banks’ income statement via modules covering macro-credit risk, netinterest income, noninterest income, and operating expenses. Aikman et al.(2009) also incorporate a simplified version of the danger zone frameworkdeveloped more fully in this chapter. But in their model, contagion can onlyoccur upon bank failure due to confidence contagion, default in the networkof interbank exposures (counterparty risk), or from fire sales, which areassumed to depress asset prices at the point of default. In particular, theydo not allow for snowballing effects or incorporate banks’ cash flow constraints,and do not capture behavioral reactions such as liquidity hoardingor predefault fire sales, all of which are key to understanding the systemicimplications of funding liquidity crises.

The chapter is structured as follows. Section 1.2 provides the conceptualand theoretical framework for our analysis, focusing on the potential triggersand systemic implications of funding liquidity crises through the lens ofbanks’ cash flow constraints. Sections 1.3 and 1.4 focus on our quantitativemodeling. Section 1.3 provides details on how the danger zone approachcaptures the closure of funding markets to individual institutions, and section1.4 presents details and partial simulation results of how behavioralreactions and the danger zone approach interact to create systemic feedbacks.Section 1.5 integrates these effects into RAMSI to illustrate howshocks to fundamentals may be amplified by funding liquidity risk and systemicliquidity feedbacks. Section 1.6 concludes.

1.2 Funding Liquidity Risk in a System-Wide Context: Conceptual andTheoretical Issues

1.2.1 The Cash Flow Constraint

Liquidity risk arises because inflows and outlays are not synchronized(Holmström and Tirole 1998). This would not matter if agents could issuefinancial contracts to third parties, pledging their future income as collateral.But given asymmetric information and other frictions, this is not alwayspossible in reality. Hence, the timing of cash in-and outflows is the crucialdriver of funding liquidity risk, and a bank is liquid if it is able to settle allobligations with immediacy (see Drehmann and Nikolaou 2012). This is thecase if, in every period, cash outflows are smaller than cash inflows and thestock of cash held, along with any cash raised by selling (or repoing) assets:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Breaking down these components further:

(1) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where:

• WL are wholesale liabilities and WA are wholesale assets

• RL are retail liabilities and RA are retail assets

• LA^S are the proceeds from the sale of liquid assets such as cash orgovernment bonds,

• ILA^S_i is the volume of illiquid asset i sold or used as collateral to obtainsecured (repo) funding

• p_i is the market price of illiquid asset i, which may be below its fair valueand possibly even zero in the short run

• subscripts _{Due, New,} and _Ro refer to obligations that are contractually due,newly issued or bought, and rolled over, respectively.

We note several issues. First, assessing funding liquidity risk through a cashflow constraint is common in practice (for a recent overview see Matz andNeu 2007) and also forms the basis of elements of proposed new liquidityregulations (Basel Committee 2010). Nonetheless, the literature has tendedto model funding liquidity risk differently, even though most theoreticalmodels can be recast in the cash flow constraint as discussed later.

Second, the flow constraint is written in terms of contractual maturities asthese are the ultimate drivers of funding liquidity risk in crises. But in normaltimes, the constraint might reasonably be thought of in terms of behavioralmaturities that may differ from contractual ones. For example, many retaildeposits are available on demand. In normal conditions, a bank can expectthe majority of these loans to be rolled over continuously, so RL_Due mayroughly equal RL_Ro. But, in times of stress, depositors may choose to withdraw,so the behavioral maturity may collapse closer to the contractual one.

Third, equation (1) still makes some simplifying assumptions. For example,contingent claims are an important driver of funding liquidity risk.In particular, firms rely heavily on credit lines (see, e.g., Campello et al. 2010).Equally, banks negotiate contingent credit lines with other banks. We donot include off-balance sheet items separately because once drawn they arepart of new assets or liabilities. Repo transactions are also an importantcomponent of banks’ liquidity risk management. Even though technicallydifferent, we treat them as part of the asset sales category because in bothcases, the market price broadly determines the value that can be raised fromthe underlying asset, which may or may not be liquid. Transactions withthe central bank are also included under repo. These occur regularly, even innormal conditions, as banks obtain liquidity directly from the central bankduring open market operations.

Beyond this, different funding markets split into several submarkets suchas interbank borrowing, unsecured bonds, securitizations, commercialpaper, and so forth. And there is clearly also a distinction between foreignand domestic funding markets. These separate markets may have quitedifferent characteristics that make them more or less susceptible to illiquidity.Not all factors relevant to funding market dynamics can be easily incorporatedinto a model of systemic risk. But there are two that we judge tobe sufficiently important as well as empirically implementable to split themout separately. First, we differentiate retail funding, secured markets, andunsecured markets. Second, we split unsecured funding into longer-term andshorter-term markets. We discuss these in more detail later in the chapter.
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