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...