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Liquidity Risk
Chapter 6
Liquidity Risk “Everything that can be counted does not necessarily count; everything that counts cannot necessarily be counted.” Albert Einstein
GLOSSARY OF TERMS Duration Mismatching When the duration of the bank’s assets is not equal to the duration of its liabilities. Informational Frictions Includes both asymmetric information and moral hazard. Lender of Last Resort A central bank that stands ready to provide the bank with emergency liquidity in case it is needed. Wholesale Financing typically short-term funding coming from the interbank market or institutional investors (repos, FED funds, commercial paper, large denomination CDs, etc.); often alternative for deposits but not insured.
INTRODUCTION The purpose of this chapter is to examine liquidity risk in some detail. We begin by discussing the sources of liquidity risk. We then turn to the interaction between liquidity and default risks. Next we discuss the interaction between liquidity and interest rate risks, and provide some formal definitions of liquidity risk. Having established these basics, the chapter turns to how liquidity risk can be managed. In line with the Enterprise Risk Management (ERM) framework discussed in Chapter 4, a framework for the management and governance of liquidity risk is introduced. Following this, we consider various approaches for mitigating liquidity risk. These approaches include keeping liquid assets, reducing withdrawal risk in deposits, and preserving access to funding markets. Also, the role of the lender-of-last-resort in reducing liquidity risk is discussed. That discussion highlights the difficulty any lender-of-last-resort would have in distinguishing between a liquidity crisis and an insolvency crisis and hence in coming up with the appropriate policy response. In concluding, we comment on the systemic nature of liquidity risk.
WHAT, AFTER ALL, IS LIQUIDITY RISK? There are occasions on which the bank does not have ready access to funds that it needs, and is therefore forced to incur costs. These could be the costs associated with passing up investment opportunities. Alternatively, they could be distressfinancing costs. These are examples of situations in which the financial intermediary faces liquidity risk. We define liquidity risk as the risk of being unable to satisfy claims without impairment to its financial or reputational capital.1 It is important to distinguish between illiquidity and insolvency. The latter relates to a condition in which the value of the firm’s liabilities exceeds the value of its assets, and hence its net worth is negative. Illiquidity can be as damaging and costly as insolvency, but it is a form of distress rooted in the (non)marketability of assets rather than in their ultimate or full value. To be sure, this may be a vacuous distinction when addressed at close range. Nevertheless, in thin markets, time and marketing efforts often are essential to the realization of asset values. Liquidating assets on short notice often results in “distress” or “fire sale” prices which are below the assets’ true values in normal times. The relationship between time available for marketing and the realizable values of assets is central to the notion of liquidity. Informational frictions are at the heart of liquidity problems. To see how informational asymmetries interact with default and interest rate risks to create liquidity risk, let us imagine that you own a bank that has made loans of $1 million with a maturity of 2 years and financed them with uninsured demand deposits. As a banker, you know more about the default risk of your loans than outsiders do, that is, there is asymmetric information about loan quality. Now, suppose that 6 months down the road, $400,000 of deposits are withdrawn because your depositors suffer a “liquidity shock”, that is, they have an urgent need for funds to take care of some expenditures, such as medical care of paying for college. However,
1. The BIS comes with a very similar definition: “Liquidity is the ability of a bank to fund increases in assets and meet obligations as they come due, without incurring unacceptable losses” (BIS, 2008). S. I. Greenbaum, A. V. Thakor & A. W. A. Boot: Contemporary Financial Intermediation, Fourth edition. http://dx.doi.org/10.1016/B978-0-12-405208-6.00006-1 Copyright © 2019 Elsevier Inc. All rights reserved.
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your existing stock of cash assets is only $100,000. This means you need to raise $300,000 to fund the deposit withdrawal. If potential depositors’ perceptions about the quality of your loan portfolio are sufficiently favorable, you will not have any trouble acquitting new deposits in the amount of $300,000. But suppose that outsiders have received unfavorable information about your loans.2 If this information is sufficiently unfavorable, new deposits may simply not be forthcoming,3 or you might have to pay an excessively high interest rate – relative to the rate you consider “appropriate” – to attract the necessary deposits.4 The point is this can happen even though your loans are in good shape. Your problem is that you know this, but your potential new depositors do not. This is an example of liquidity risk. There are four points we should note about this example. First, the problem for your bank started with existing depositors experiencing their own “liquidity shock” or need for liquidity. Second, an informational asymmetry about asset quality plays a pivotal role in creating liquidity risk. If you know your loan quality is good and outsiders knew as much about your loan quality as you do, then you would be able to acquire the deposits you need at a price that you consider appropriate for the risk associated with the loan portfolio. This eliminates liquidity risk. Third, it is easy to confuse insolvency or credit risk with liquidity risk. That is, if the bank’s loan quality truly deteriorated and the credit risk of the bank for (uninsured) depositors went up, the bank would be faced with insolvency risk and new deposits would not be forthcoming even if there was no asymmetric information about loan quality between you and your potential new depositors. An outside observer would simply see the bank unable to raise new deposits and think this was a manifestation of liquidity risk when it is really an insolvency problem. Fourth, duration mismatching may be an important ingredient in creating liquidity risk, but it is not a necessary ingredient. To see the importance of duration mismatching, suppose your asset and liability portfolios were perfectly duration matched. Then the assets that were funded by a specific set of liabilities would pay off at the same time that the liabilities came due, and informational asymmetry about these assets that arises after these assets are on the bank’s books would not matter. Of course, if an informational asymmetry exists about the new loans you make, then a premium reflecting this asymmetry will show up in the interest rate on the deposits raised to fund these loans. However, you can pass this premium along to your borrowers in the way you price your loans, so that your capital is not impaired.
The Interaction Between Liquidity and Default Risks Liquidity risks and default risks are interrelated. If a sudden need for liquidity forces you to sell illiquid assets quickly, the value that is realized might be low and impair solvency in the sense that the proceeds from the sale of those assets may be insufficient to satisfy the claims of your creditors. So liquidity risk may trigger default risk. The opposite may happen too: concerns about credit risk (i.e., default risk) of existing assets may cause a freeze in funding markets, making it difficult or impossible for the institution to raise the financing it needs to invest in new loans, thereby triggering liquidity problems. What this means is that liquidity and default risks should not be looked at in isolation. Typically, we think that a big part of liquidity risk is withdrawal risk, which stems from a bank’s deposits being of shorter duration than its assets. Thus, the deposits used to finance loans come due before the loans mature, and if they are withdrawn but cannot be rolled over, we have liquidity risk.
The Interaction Between Liquidity and Interest Rate Risks We now turn to the interaction between interest rate risk and liquidity risk. There are two ways to explain this interaction. First, suppose we have deposit interest rate ceilings. Given this ceiling, a rise in market interest rates causes withdrawals because depositors can earn higher rates elsewhere. Hence, deposit interest rate ceilings transform interest rate risk into withdrawal risk. Another way to understand this interaction is by returning to the example we discussed in the section under interest rate risk. If the term structure receives a random shock that causes interest rates to rise, it is possible that you will experience a deposit outflow as your depositors will want to reinvest their money at the prevailing higher interest rates. You have two ways to finance these withdrawals. One way is for you to acquire new (partially insured) deposits. But this
2. This information may be different from what you know about your loans, that is, you may still know more than outsiders and may thus believe that your loan quality is good. 3. Indeed, it is possible that all of your existing deposits may be withdrawn. Observe that deposit insurance may mitigate this, but note banks do often depend on other (noninsured) funding sources like wholesale financing (see Huang and Ratnovski (2011), and Bouwman (2014). 4. In fact, your willingness to pay such a high rate of interest may be viewed as a signal of poor loan quality. Then, liquidity risk can be interpreted as the likelihood of incurring this signaling cost.
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may require you to pay a premium to depositors due to a possible informational asymmetry about your loan portfolio. Moreover, you must satisfy reserve and capital requirements on deposits. An alternative is to liquidate part of your asset portfolio to meet these unanticipated deposit withdrawals. You can do this by selling off marketable securities you hold or by selling off some of your loans.5 Due to an informational asymmetry about your loans, however, you may only be able to sell your loans for less than what you think they are worth. The loss you incur as a result is also a part of liquidity risk. Although this loss is precipitated by an unfavorable move in interest rates, note again the central role played by asymmetric information. Moreover, the greater the asymmetric information, the greater the potential for loss, and hence the lower the asset’s liquidity. This is why, despite an active secondary market, a corporation’s common stock is not as liquid as a U.S. Treasury bill.
SOME FORMAL DEFINITIONS OF LIQUIDITY Think of P* as the full-value price of an asset, that is, the highest price an owner can expect to realize by liquidating one unit, provided all useful preparations are made for the sale. If the asset is sold before all useful preparations can be made, a lesser price will be realized. Call this lesser price Pi, where i = 0, . . ., n indicates the time used for marketing, and n is the time needed to realize full value. The length of time used should be thought of as the interval between a decision to sell and the time at which a sales contract is consummated.6 Hence Pn = P* and for all values of i < n, the realized price of the asset, Pi, is less than full value. One way to think of liquidity is in terms of L1 =
Pi . P*
A limitation of this definition is that the liquidity of a particular asset depends on the value of i chosen. Thus, for low values of i, one asset may be more liquid than another, whereas for greater values of i, the liquidity comparison might be reversed. This impedes the consistent ranking of assets according to their liquidity. One way to mitigate, if not obviate, this problem of liquidity reversal among assets is to think in terms of an “average” value of i. Hence L2 =
1 n Pi ∑ . n i=0 P *
A still more appealing approach recognizes the inherent uncertainty regarding i, the time interval between the decision to sell, and the actual sale. Thus, we can view it as a random variable with a probability distribution, g(i), which stipulates the probability of each possible outcome (i = 0, . . ., n). The expected value of an asset, E(P), is then defined as n
E ( P) = ∑ g(i) Pi , i=0
and this leads to a third definition of liquidity, which is L3 =
E (P) . P*
The liquidity concept can be further generalized to account for marketing expenditures, say M. The more general view is that the realizable price of an asset depends on time, marketing expenditures, and full-value price, so that Pi = f (i, M , P*),
5. A bank can sell its loans to another bank just as a firm would sell its debt in a private placement. This practice, which is quite old, is known as “loan sales.” A more recent practice is securitization, which involves the bank selling the loan, typically as a component in a portfolio of loans, directly to investors in the capital market. This is usually done through an underwriter and is a process of converting a previously untraded security into a traded security. We will have a lot more to say about this in Chapter 11. 6. The terms of the transaction are fixed at the time the sales contract is consummated, but the transfer of property takes place at the “closing,” a date that may coincide with the date of the sales contract, but often occurs later.
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and if M is the optimally chosen marketing expenditure, n
E ( P ′) = ∑ g(i) f (i, M , P*) i=0
is the expected value of an asset, conditional to the owner’s spending optimally on marketing. This leads to our fourth definition of liquidity L4 =
E ( P ′) P*
and M/P* can be thought of as a measure of the market’s thinness, a measure akin to the bid–ask spread. Note that the positive relationship between available time for marketing and marketing effort on the one hand and realizable value on the other has nothing to do with changes in supply or demand for the asset; the realizable value increases in the context of given market conditions. Time is not used to await a more favorable market, but rather to do the marketing necessitated by costly information. For a depository institution, there are many ways to reduce liquidity risk. An obvious way is to simply keep more liquid assets on hand. The other is to reduce the deposit withdrawal risk that creates liquidity risk. A third way is to rely on a lender of last resort who stands ready to replenish the bank’s liquidity when needed. In what follows, we discuss each in turn.
THE MANAGEMENT OF LIQUIDITY RISK As part of its ERM, introduced in Chapter 4, a bank needs to put in place policies and actions to control and manage liquidity risk. These include the allocation of responsibilities, formulating procedures, setting limits, and the actual measurement and management of liquidity risk. In Table 6.1, we present a framework outlined by the Bank for International Settlements (BIS).
Reducing Liquidity Risk With Liquid Assets Think of the fractional reserve banking system described in Chapter 3. That bank can be thought of as holding two kinds of assets: cash and loans that mature in two or more periods (prior to maturity the loans are assumed to be worthless). The bank’s liabilities all mature in one period, and may or may not be renewed (withdrawn). If the fraction withdrawn after one period is equal to, or smaller than, the bank’s holding of cash assets, the bank will continue in business for two periods, at least. On the other hand, if withdrawals exceed the bank’s holding of cash assets, that bank will be unable to honor its liabilities – it has promised all depositors immediate access even though its own capacity to satisfy claims is strictly limited by its holding cash assets.7 Therein lies the liquidity conundrum of banking. Notice that an important role of a bank is the provision of liquidity services, and it provides this service by mismatching its balance sheet on the liquidity attribute, that is, it holds assets that are less liquid than its liabilities. This is one form of asset transformation. The quality of this liquidity service provided by the bank depends on three factors: the liquidity of its loan portfolio, the cash (or liquid assets) it has on hand, and the withdrawal risk in its deposit base. By investing in more liquid loans and/or keeping more cash on hand, the bank can improve its own liquidity. However, it does so at the expense of profits. An alternative would be to seek ways to dissipate withdrawal risk, which is what we turn to next.
Reducing Liquidity Risk by Dissipating Withdrawal Risk A depository institution can reduce the variance of its deposit flows by diversifying the sources of funding, that is, having many distinct and dissimilar depositors. This is formally demonstrated in Appendix 6.1. A diverse depositor base results in more predictable deposit flows; the improved predictability reduces the cash needed to service a deposit base to any arbitrary probabilistic standard. That is, the larger and more diverse the depositor base, the smaller the cash holding necessary to achieve any preselected probability of a stock-out (liquidity crisis). This is one way the depository institution produces liquidity. Nevertheless, withdrawals will sometimes exceed the institution’s capacity to service them, even though this may 7. This is the rationale behind the standard measure of liquidity in the savings industry, which is the ratio of cash and short-term U.S. government securities and other specified securities to deposits and borrowing due within 1 year. Following the 2007–2009 financial crisis the Dodd-Frank Act (see Chapter 15) has introduced a more extensive regulation of liquidity dictating the holdings of high quality liquid assets (HQLA). The – so called – liquidity coverage ratio (LCR) became active in the United States, and similar regulation was adopted in Europe (see Chapter 15).
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TABLE 6.1 BIS Principles for the Management of Liquidity Risk Fundamental principle for the management and supervision of liquidity risk Principle 1: A bank is responsible for the sound management of liquidity risk. A bank should establish a robust liquidity risk management framework that ensures it maintains sufficient liquidity, including a cushion of unencumbered, high-quality liquid assets, to withstand a range of stress events, including those involving the loss or impairment of both unsecured and secured funding sources* Governance of liquidity risk management Principle 2: A bank should clearly articulate a liquidity risk tolerance that is appropriate for its business strategy and its role in the financial system Principle 3: Senior management should develop a strategy, policies, and practices to manage liquidity risk in accordance with the risk tolerance and to ensure that the bank maintains sufficient liquidity. Senior management should continuously review information on the bank’s liquidity developments and report to the board of directors on a regular basis. A bank’s board of directors should review and approve the strategy, policies, and practices related to the management of liquidity at least annually and ensure that senior management manages liquidity risk effectively Principle 4: A bank should incorporate liquidity costs, benefits, and risks in the internal pricing, performance measurement, and new product approval process for all significant business activities (both on- and off-balance sheet), thereby aligning the risk-taking incentives of individual business lines with the liquidity risk exposures their activities create for the bank as a whole Measurement and management of liquidity risk Principle 5: A bank should have a sound process for identifying, measuring, monitoring and controlling liquidity risk. This process should include a robust framework for comprehensively projecting cash flows arising from assets, liabilities, and off-balance sheet items over an appropriate set of time horizons Principle 6: A bank should actively monitor and control liquidity risk exposures and funding needs within and across legal entities, business lines, and currencies, taking into account legal, regulatory, and operational limitations to the transferability of liquidity Principle 7: A bank should establish a funding strategy that provides effective diversification in the sources and tenor of funding. It should maintain an ongoing presence in its chosen funding markets and strong relationships with funds providers to promote effective diversification of funding sources. A bank should regularly gauge its capacity to raise funds quickly from each source. It should identify the main factors that affect its ability to raise funds and monitor those factors closely to ensure that estimates of fund raising capacity remain valid Principle 8: A bank should actively manage its intraday liquidity positions and risks to meet payment and settlement obligations on a timely basis under both normal and stressed conditions and thus contribute to the smooth functioning of payment and settlement systems Principle 9: A bank should actively manage its collateral positions, differentiating between encumbered and unencumbered assets. A bank should monitor the legal entity and physical location where collateral is held and how it may be mobilized in a timely manner Principle 10: A bank should conduct stress tests on a regular basis for a variety of short-term and protracted institution-specific and market-wide stress scenarios (individually and in combination) to identify sources of potential liquidity strain and to ensure that current exposures remain in accordance with a bank’s established liquidity risk tolerance. A bank should use stress test outcomes to adjust its liquidity risk-management strategies, policies, and positions and to develop effective contingency plans Principle 11: A bank should have a formal contingency funding plan (CFP) that clearly sets out the strategies for addressing liquidity shortfalls in emergency situations. A CFP should outline policies to manage a range of stress environments, establish clear lines of responsibility, include clear invocation and escalation procedures, and be regularly tested and updated to ensure that it is operationally robust Principle 12: A bank should maintain a cushion of unencumbered, high-quality liquid assets to be held as insurance against a range of liquidity stress scenarios, including those that involve the loss or impairment of unsecured and typically available secured funding sources. There should be no legal, regulatory, or operational impediment to using these assets to obtain funding Public disclosure Principle 13: A bank should publicly disclose information on a regular basis that enables market participants to make an informed judgment about the soundness of its liquidity risk-management framework and liquidity position *In their “Principles for sound liquidity risk management and supervision” the BIS complements this principle with the following “instruction” to supervisors: “Supervisors should assess the adequacy of both a bank’s liquidity risk-management framework and its liquidity position and should take prompt action if a bank is deficient in either area in order to protect depositors and to limit potential damage to the financial system.” Source: BIS (2008).
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happen only with very small probability, and in that sense the system is imperfect. Indeed, this is the system’s Achilles’ heel. Bank runs are the trauma that illustrates this vulnerability of fractional reserve banking, a vulnerability caused by the illiquidity of bank assets.
Reducing Liquidity by Preserving Access to Funding Markets The management of liquidity is referred to as the treasury function, and it is usually entrusted to the chief financial officer (CFO). It is her responsibility to “fund the bank.” This requires a thorough understanding of the institution’s cash flows, as well as all potential sources of liquidity. Ultimately, protection comes from maintaining diverse, capacious, and reliable sources of funding against future contingencies. This explains why the typical bank will borrow from virtually all reasonably priced sources. To be sure, cost will be a consideration, but opportunities to reduce short-run funding costs by concentrating on fewer funding sources are commonly avoided. In “paying up” for funding diversity, the bank is purchasing lines of credit, and this reduces the likelihood of being rationed. It is common for funding sources to evaporate under stress; CFOs understand this only too well. Continental Illinois Bank and Trust found that holders of its large CDs (Certificates of Deposit) abandoned them in their hour of keenest need, and the high-yield bond market went into eclipse when Drexel Burnham Lambert was forced into insolvency because banks chose to withdraw their funding. And in the 2007–2009 financial crisis many commercial banks, including Northern Rock in the United Kingdom, and investment banks “discovered” that access to short-term wholesale financing could disappear overnight. The conventional protection against the trauma of being rationed is to accept the extra cost of participating in as many markets as possible, thereby diversifying funding sources. Liquidity is consciously purchased by banks as well as their borrowers, and it is the fragility of liquidity that makes this part of banking particularly challenging.
Reducing the Liquidity Risk of an Individual Bank with a Lender of Last Resort It was long ago discovered that the liquidity of a fractional reserve banking system can be ensured with a thoroughly credible “lender of last resort” (LLR). This was the major motivation for the creation of central banks, including the Federal Reserve System. With an institution capable of creating money limitlessly, it becomes possible to support banks facing the most extraordinary deposit outflows. Provided that the banks are sound (solvent, given reasonable time to liquidate their assets), this could be done by having the central bank lend to the banks using their illiquid loans as collateral. With such a lending facility, sound but illiquid banks could be protected and financial market disruptions avoided. This argument is developed more fully in Appendix 6.2. However, an inexpensive, readily available LLR faces the danger of inheriting the entire liquidity management problem of the banking industry. That is, the bank’s incentive to hold cash assets (or even diversify its deposit base) is weakened if borrowings from the central bank are inexpensive and readily available. This is a moral hazard associated with the introduction of the LLR, and it has two implications. First, it shifts deposit seigniorage from the public to privately owned banks. Second, the LLR is also exposed to the credit risk of the bank’s collateral. The moral hazard of lower, voluntarily held cash assets explains the consequent introduction of cash asset reserve requirements, and also why there are carefully administered detailed rules and informal restrictions governing access to the discount window. Thus, legal reserve requirements and LLR pricing and availability shift at least a portion of the liquidity management problem back to the banks. Other banks, without access to an LLR facility, own the liquidity problem outright.
THE DIFFICULTY OF DISTINGUISHING BETWEEN LIQUIDITY AND INSOLVENCY RISKS AND THE LLR’S CONUNDRUM In practice, it is not always easy to distinguish between liquidity risk and insolvency risk, as indicated earlier. This was true, for example, in the 2007–2009 subprime crisis. Financial institutions in the shadow banking system found that there was a sharp increase in the “haircuts” on the collateral used in repurchase transactions, which meant a substantial reduction in short-term liquidity. Similarly, mutual funds faced massive withdrawals by investors. These were the conditions prevailing during the 2007–2009 crisis; see Chapter 14 for more on this. Many interpreted these conditions as a liquidity crisis. Consequently, central banks undertook massive interventions in the capital market, infusing huge amounts of liquidity. However, in reality this was an insolvency crisis, and when this was recognized, the actions of central banks (especially the Federal Reserve) turned to the kinds of initiatives needed to deal with an insolvency crisis, for example, infusing more capital into banks.
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The reason why liquidity and insolvency risks are hard to distinguish in practice is simple.8 When a bank is faced with a liquidity crisis, it means that its financiers are pressed for funds and cannot make funding available to the bank because of their own “liquidity shock.” When a bank is faced with an insolvency crisis, it means it has experienced a deterioration in the quality of the assets on its balance sheet and its risk of insolvency has gone up, and as a result its financiers are unwilling to fund the bank. Since the outcome in both cases is the same – the drying up of funding for the bank – it is hard to tell what kind of crisis the bank is facing.10
CONCLUSION Liquidity risk is possibly the most important risk in banking. In their asset-transformation role, banks engage in liquidity transformation: banks typically have longer duration assets than liabilities, and offer via the liability side of the balance sheet liquidity services to their depositors. The effect is that banks might be confronted with roll-over risk and withdrawals of deposits that could cause funding gaps. The 2007–2009 financial crisis showed the systemic nature of liquidity risk as well as its close relationship to insolvency risk. Unexpectedly high subprime mortgage defaults elevated concerns about insolvency risk, leading to funding markets breaking down, and inducing institutions to engage in asset sales caused downward price spirals, putting enormous stress on the stability of the financial system.9 These effects related to how fundamental concerns about insolvency risk caused liquidity to shrink are discussed in Chapter 14, and the regulatory responses are covered in Chapters 15 and 16.
REVIEW QUESTIONS 1. What is liquidity risk and how is it linked to interest rate and credit risks? What is the role of asymmetric information in creating liquidity risk? 2. How can liquidity risk be managed? What are some of the impediments faced by banks in implementing an integrated risk-management system that managers credit risk, liquidity risk, and interest rate risk? 3. What factors lead to an increase in the bank’s liquidity risk and why is it important for the economy that banks take on liquidity risk?
APPENDIX 6.1 DISSIPATION OF WITHDRAWAL RISK THROUGH DIVERSIFICATION Suppose that a bank has n depositors, each of whom deposits $1. Each deposit is subject to withdrawal after one period, but may remain for two. Assume that the probability that a $1 deposit will be withdrawn after one period is one in ten, that is, p = 0.1, but whether a given deposit is actually withdrawn after one period cannot be known until that one period has passed. Deposits are used to fund loans that pay back in full in two periods, but are worthless until they mature. (There is no secondary market in loans.) This is a harmless simplifying assumption and does not affect the argument that follows. Of course, the bank will need to hold some fraction of its assets in cash in order to satisfy its one-period withdrawals. The question is how much cash the bank should prudently hold. If the bank has $1 or $1 million of deposits, the probability of withdrawal remains fixed at 10%, and the expected withdrawal is this probability multiplied by the amount of deposits. However, if the bank has only $1 in deposits, the withdrawal inevitably will be all or nothing at all, zero or one. Indeed, the expected value of $0.10 is unattainable, and the bank’s decision to hold 10 percent in cash, if feasible, is virtually pointless. However, as the bank’s depositors increase in number, assuming independence among them, the withdrawal of 10% becomes more predictable; in the limit, as depositors become more and more numerous, a 10% cash holding will “almost certainly” satisfy deposit withdrawals. This idea is apparent from the definition of the standard deviation of a binomial distribution where n is the number of depositors and q ≡ 1 – p; the standard deviation of the bank’s deposits will be σ = npq. Note that this measure of uncertainty varies with the square root of the number of depositors, and hence in the limit as the number of depositors increases to infinity, the standard deviation per dollar of deposit equals lim (σ / n) = 0. n →∞
This means that as the number of depositors becomes larger, the withdrawal uncertainty per loan diminishes, approaching zero in the limit, even though the withdrawal probability remains unchanged at p = 0.1. So, as the depositor population increases, the 10% withdrawal can be treated increasingly as a routine (almost fixed) cost, rather than as a potential 8. Farhi and Tirole (2012) provide a model in which the central bank cannot distinguish between a liquidity crisis and an insolvency crisis. 9. See Brunnermeier and Pedersen (2009). 10. In a recent paper, Thakor and Vuong (2018) develop a theoretical model of countercyclical capital buffers and show that having a sufficiently high capital buffer can not only address current insolvency risk, but also future illiquidity risk. Thus, by asking banks to keep sufficiently high capital buffers, regulators can minimize the severity of the problem of disentangling solvency and liquidity risks.
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catastrophe. The risk of ruin, the probability that withdrawals exceed the bank’s cash holding, never actually becomes zero since σ/n → 0 only in the limit. But the risk of ruin can be managed, and made indefinitely small by diversifying the bank’s sources of funding.
APPENDIX 6.2 LENDER-OF-LAST-RESORT MORAL HAZARD In a world of fiat money, value derives from an administered or artificial scarcity. That is, our money is money by fiat or legal mandate (hence legal tender) and is not convertible into gold or any other commodity at a fixed exchange rate, as in the case of commodity-backed money. The more money the government prints, or otherwise creates, the less its value, and this applies to bank deposits as well as to paper money. The administered scarcity of money also creates a monopoly profit referred to as “seigniorage.” This profit on the production of money is shared by the privately owned banks and the public, via its effective ownership of the central bank. The Federal Reserve is nominally owned by member commercial banks. However, the equity in the Federal Reserve banks pays a statutorily fixed rate of return, much like a bond, whereas the residual earnings of the Federal Reserve flow back to the U.S. Treasury via a special franchise tax. Given that neither central bank nor private bank deposits pay interest (any interest rates below competitive rates will sustain the point), the distribution of seigniorage between the banks and the public (or central bank) depends on the cash asset reserves the banks choose to hold. The more reserves banks hold, the smaller will be banks’ share of the seigniorage. Since the introduction of an LLR reduces the amount of reserves the banks will desire to hold, it effectively shifts seigniorage from the public to the banks. This is the moral hazard associated with the introduction of an LLR, and it explains that one rationale for legal reserve requirements (that stipulate the minimum cash assets that banks must hold) is to restore the “appropriate” sharing of seigniorage between banks and the public. This point is easily illustrated. Suppose we have a single commercial bank with $10 million in deposit liabilities, an amount consistent with the money supply the central bank wishes to maintain in consideration of monetary policy. There are no reserve requirements and no LLR facility. The commercial bank voluntarily holds 10% of its assets in cash against withdrawal risk. It makes no difference whether the bank’s cash assets are vault cash or deposits at the central bank, so for simplicity assume that these assets are all on deposit at the Federal Reserve where they earn nothing. The commercial bank’s balance sheet would then be Commercial Bank Cash assets
$1 million
Deposit liability
Loans or other earning assets
$9 million
$10 million
Total assets
$10 million
Total liabilities $10 million
The Federal Reserve’s balance sheet, to a first approximation, would show Federal Reserve Earning assets
$1 million
Deposit liability $1 million
Note that the Federal Reserve’s deposit liability corresponds to the bank’s cash assets. Now suppose the Federal Reserve introduces an LLR facility. It has no reason to change the money supply, but banks now have a new source of liquidity. Hence, they will feel less need to hold nonearning cash assets. Say they cut these holdings from 10% to 5%. The bank’s balance sheet now becomes Commercial Bank Cash assets
$0.5 million
Deposit liability
Loans or other earning assets
$9.5 million
$10 million
Total assets
$10 million
Total liabilities $10 million
$0.5 million
Deposit liabilities $0.5 million
and the Federal Reserve shrinks to Federal Reserve Earning assets
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In effect, $0.5 million in earning assets have been transferred from the Federal Reserve’s balance sheet to the bank’s balance sheet, and this occurs as a direct consequence of the introduction of the LLR. One could argue that if the LLR facility is properly priced, the moral hazard will be discouraged. However, note that before its introduction, the LLR interest rate was infinite, so that any finite interest rate will improve bank liquidity, and should therefore result in some reserve dissipation. As a historical matter, the LLR tends to price low for reasons that are not entirely clear. This generous pricing practice aggravates the moral hazard problem and heightens the need for legal reserve requirements. Thus, reserve requirements control the moral hazard of the LLR, and a lowering of reserve requirements transfers deposit seigniorage from the public to the banks. Raising reserve requirements has the reverse effect. One hundred percent reserve requirements shift all deposit seigniorage to the public. This is the basis for the conventional wisdom that the reserve requirement is a tax on the banks, but one could just as easily argue that any reserve requirement less than 100 percent is a subsidy to banks. The hard question here is: To whom should the monopoly rents associated with administered money belong?
REFERENCES BIS, 2008. Principles for Sound Liquidity Risk Management and Supervision. Basel Committee on Bank Supervision, Bank for International Settlement, Basel. Bouwman, C., 2014. Liquidity: how banks create it and how it should be regulated. In: Berger, A.N., Molyneux, P., Wilson, J.O.S. (Eds.), The Oxford Handbook of Banking, second ed, Oxford, UK. Brunnermeier, M.K., Pedersen, L.H., 2009. Market liquidity and funding liquidity. Rev. Finan. Stud. 22, 2201–2238. Farhi, E., Tirole, J., 2012. Collective moral hazard, maturity mismatch, and systemic bailouts. Am. Econ. Rev. 102, 60–93. Huang, R., Ratnovski, L., 2011. The dark side of bank wholesale funding. J. Finan. Intermed. 20, 248–263. Thakor, A.V., Vuong, T., 2018. Optimal Capital Buffers, working paper, Washington University in St. Louis.
Liquidity Risk “Everything that can be counted does not necessarily count; everything that counts cannot necessarily be counted.” Albert Einstein
GLOSSARY OF TERMS Duration Mismatching When the duration of the bank’s assets is not equal to the duration of its liabilities. Informational Frictions Includes both asymmetric information and moral hazard. Lender of Last Resort A central bank that stands ready to provide the bank with emergency liquidity in case it is needed. Wholesale Financing typically short-term funding coming from the interbank market or institutional investors (repos, FED funds, commercial paper, large denomination CDs, etc.); often alternative for deposits but not insured.
INTRODUCTION The purpose of this chapter is to examine liquidity risk in some detail. We begin by discussing the sources of liquidity risk. We then turn to the interaction between liquidity and default risks. Next we discuss the interaction between liquidity and interest rate risks, and provide some formal definitions of liquidity risk. Having established these basics, the chapter turns to how liquidity risk can be managed. In line with the Enterprise Risk Management (ERM) framework discussed in Chapter 4, a framework for the management and governance of liquidity risk is introduced. Following this, we consider various approaches for mitigating liquidity risk. These approaches include keeping liquid assets, reducing withdrawal risk in deposits, and preserving access to funding markets. Also, the role of the lender-of-last-resort in reducing liquidity risk is discussed. That discussion highlights the difficulty any lender-of-last-resort would have in distinguishing between a liquidity crisis and an insolvency crisis and hence in coming up with the appropriate policy response. In concluding, we comment on the systemic nature of liquidity risk.
WHAT, AFTER ALL, IS LIQUIDITY RISK? There are occasions on which the bank does not have ready access to funds that it needs, and is therefore forced to incur costs. These could be the costs associated with passing up investment opportunities. Alternatively, they could be distressfinancing costs. These are examples of situations in which the financial intermediary faces liquidity risk. We define liquidity risk as the risk of being unable to satisfy claims without impairment to its financial or reputational capital.1 It is important to distinguish between illiquidity and insolvency. The latter relates to a condition in which the value of the firm’s liabilities exceeds the value of its assets, and hence its net worth is negative. Illiquidity can be as damaging and costly as insolvency, but it is a form of distress rooted in the (non)marketability of assets rather than in their ultimate or full value. To be sure, this may be a vacuous distinction when addressed at close range. Nevertheless, in thin markets, time and marketing efforts often are essential to the realization of asset values. Liquidating assets on short notice often results in “distress” or “fire sale” prices which are below the assets’ true values in normal times. The relationship between time available for marketing and the realizable values of assets is central to the notion of liquidity. Informational frictions are at the heart of liquidity problems. To see how informational asymmetries interact with default and interest rate risks to create liquidity risk, let us imagine that you own a bank that has made loans of $1 million with a maturity of 2 years and financed them with uninsured demand deposits. As a banker, you know more about the default risk of your loans than outsiders do, that is, there is asymmetric information about loan quality. Now, suppose that 6 months down the road, $400,000 of deposits are withdrawn because your depositors suffer a “liquidity shock”, that is, they have an urgent need for funds to take care of some expenditures, such as medical care of paying for college. However,
1. The BIS comes with a very similar definition: “Liquidity is the ability of a bank to fund increases in assets and meet obligations as they come due, without incurring unacceptable losses” (BIS, 2008). S. I. Greenbaum, A. V. Thakor & A. W. A. Boot: Contemporary Financial Intermediation, Fourth edition. http://dx.doi.org/10.1016/B978-0-12-405208-6.00006-1 Copyright © 2019 Elsevier Inc. All rights reserved.
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your existing stock of cash assets is only $100,000. This means you need to raise $300,000 to fund the deposit withdrawal. If potential depositors’ perceptions about the quality of your loan portfolio are sufficiently favorable, you will not have any trouble acquitting new deposits in the amount of $300,000. But suppose that outsiders have received unfavorable information about your loans.2 If this information is sufficiently unfavorable, new deposits may simply not be forthcoming,3 or you might have to pay an excessively high interest rate – relative to the rate you consider “appropriate” – to attract the necessary deposits.4 The point is this can happen even though your loans are in good shape. Your problem is that you know this, but your potential new depositors do not. This is an example of liquidity risk. There are four points we should note about this example. First, the problem for your bank started with existing depositors experiencing their own “liquidity shock” or need for liquidity. Second, an informational asymmetry about asset quality plays a pivotal role in creating liquidity risk. If you know your loan quality is good and outsiders knew as much about your loan quality as you do, then you would be able to acquire the deposits you need at a price that you consider appropriate for the risk associated with the loan portfolio. This eliminates liquidity risk. Third, it is easy to confuse insolvency or credit risk with liquidity risk. That is, if the bank’s loan quality truly deteriorated and the credit risk of the bank for (uninsured) depositors went up, the bank would be faced with insolvency risk and new deposits would not be forthcoming even if there was no asymmetric information about loan quality between you and your potential new depositors. An outside observer would simply see the bank unable to raise new deposits and think this was a manifestation of liquidity risk when it is really an insolvency problem. Fourth, duration mismatching may be an important ingredient in creating liquidity risk, but it is not a necessary ingredient. To see the importance of duration mismatching, suppose your asset and liability portfolios were perfectly duration matched. Then the assets that were funded by a specific set of liabilities would pay off at the same time that the liabilities came due, and informational asymmetry about these assets that arises after these assets are on the bank’s books would not matter. Of course, if an informational asymmetry exists about the new loans you make, then a premium reflecting this asymmetry will show up in the interest rate on the deposits raised to fund these loans. However, you can pass this premium along to your borrowers in the way you price your loans, so that your capital is not impaired.
The Interaction Between Liquidity and Default Risks Liquidity risks and default risks are interrelated. If a sudden need for liquidity forces you to sell illiquid assets quickly, the value that is realized might be low and impair solvency in the sense that the proceeds from the sale of those assets may be insufficient to satisfy the claims of your creditors. So liquidity risk may trigger default risk. The opposite may happen too: concerns about credit risk (i.e., default risk) of existing assets may cause a freeze in funding markets, making it difficult or impossible for the institution to raise the financing it needs to invest in new loans, thereby triggering liquidity problems. What this means is that liquidity and default risks should not be looked at in isolation. Typically, we think that a big part of liquidity risk is withdrawal risk, which stems from a bank’s deposits being of shorter duration than its assets. Thus, the deposits used to finance loans come due before the loans mature, and if they are withdrawn but cannot be rolled over, we have liquidity risk.
The Interaction Between Liquidity and Interest Rate Risks We now turn to the interaction between interest rate risk and liquidity risk. There are two ways to explain this interaction. First, suppose we have deposit interest rate ceilings. Given this ceiling, a rise in market interest rates causes withdrawals because depositors can earn higher rates elsewhere. Hence, deposit interest rate ceilings transform interest rate risk into withdrawal risk. Another way to understand this interaction is by returning to the example we discussed in the section under interest rate risk. If the term structure receives a random shock that causes interest rates to rise, it is possible that you will experience a deposit outflow as your depositors will want to reinvest their money at the prevailing higher interest rates. You have two ways to finance these withdrawals. One way is for you to acquire new (partially insured) deposits. But this
2. This information may be different from what you know about your loans, that is, you may still know more than outsiders and may thus believe that your loan quality is good. 3. Indeed, it is possible that all of your existing deposits may be withdrawn. Observe that deposit insurance may mitigate this, but note banks do often depend on other (noninsured) funding sources like wholesale financing (see Huang and Ratnovski (2011), and Bouwman (2014). 4. In fact, your willingness to pay such a high rate of interest may be viewed as a signal of poor loan quality. Then, liquidity risk can be interpreted as the likelihood of incurring this signaling cost.
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may require you to pay a premium to depositors due to a possible informational asymmetry about your loan portfolio. Moreover, you must satisfy reserve and capital requirements on deposits. An alternative is to liquidate part of your asset portfolio to meet these unanticipated deposit withdrawals. You can do this by selling off marketable securities you hold or by selling off some of your loans.5 Due to an informational asymmetry about your loans, however, you may only be able to sell your loans for less than what you think they are worth. The loss you incur as a result is also a part of liquidity risk. Although this loss is precipitated by an unfavorable move in interest rates, note again the central role played by asymmetric information. Moreover, the greater the asymmetric information, the greater the potential for loss, and hence the lower the asset’s liquidity. This is why, despite an active secondary market, a corporation’s common stock is not as liquid as a U.S. Treasury bill.
SOME FORMAL DEFINITIONS OF LIQUIDITY Think of P* as the full-value price of an asset, that is, the highest price an owner can expect to realize by liquidating one unit, provided all useful preparations are made for the sale. If the asset is sold before all useful preparations can be made, a lesser price will be realized. Call this lesser price Pi, where i = 0, . . ., n indicates the time used for marketing, and n is the time needed to realize full value. The length of time used should be thought of as the interval between a decision to sell and the time at which a sales contract is consummated.6 Hence Pn = P* and for all values of i < n, the realized price of the asset, Pi, is less than full value. One way to think of liquidity is in terms of L1 =
Pi . P*
A limitation of this definition is that the liquidity of a particular asset depends on the value of i chosen. Thus, for low values of i, one asset may be more liquid than another, whereas for greater values of i, the liquidity comparison might be reversed. This impedes the consistent ranking of assets according to their liquidity. One way to mitigate, if not obviate, this problem of liquidity reversal among assets is to think in terms of an “average” value of i. Hence L2 =
1 n Pi ∑ . n i=0 P *
A still more appealing approach recognizes the inherent uncertainty regarding i, the time interval between the decision to sell, and the actual sale. Thus, we can view it as a random variable with a probability distribution, g(i), which stipulates the probability of each possible outcome (i = 0, . . ., n). The expected value of an asset, E(P), is then defined as n
E ( P) = ∑ g(i) Pi , i=0
and this leads to a third definition of liquidity, which is L3 =
E (P) . P*
The liquidity concept can be further generalized to account for marketing expenditures, say M. The more general view is that the realizable price of an asset depends on time, marketing expenditures, and full-value price, so that Pi = f (i, M , P*),
5. A bank can sell its loans to another bank just as a firm would sell its debt in a private placement. This practice, which is quite old, is known as “loan sales.” A more recent practice is securitization, which involves the bank selling the loan, typically as a component in a portfolio of loans, directly to investors in the capital market. This is usually done through an underwriter and is a process of converting a previously untraded security into a traded security. We will have a lot more to say about this in Chapter 11. 6. The terms of the transaction are fixed at the time the sales contract is consummated, but the transfer of property takes place at the “closing,” a date that may coincide with the date of the sales contract, but often occurs later.
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and if M is the optimally chosen marketing expenditure, n
E ( P ′) = ∑ g(i) f (i, M , P*) i=0
is the expected value of an asset, conditional to the owner’s spending optimally on marketing. This leads to our fourth definition of liquidity L4 =
E ( P ′) P*
and M/P* can be thought of as a measure of the market’s thinness, a measure akin to the bid–ask spread. Note that the positive relationship between available time for marketing and marketing effort on the one hand and realizable value on the other has nothing to do with changes in supply or demand for the asset; the realizable value increases in the context of given market conditions. Time is not used to await a more favorable market, but rather to do the marketing necessitated by costly information. For a depository institution, there are many ways to reduce liquidity risk. An obvious way is to simply keep more liquid assets on hand. The other is to reduce the deposit withdrawal risk that creates liquidity risk. A third way is to rely on a lender of last resort who stands ready to replenish the bank’s liquidity when needed. In what follows, we discuss each in turn.
THE MANAGEMENT OF LIQUIDITY RISK As part of its ERM, introduced in Chapter 4, a bank needs to put in place policies and actions to control and manage liquidity risk. These include the allocation of responsibilities, formulating procedures, setting limits, and the actual measurement and management of liquidity risk. In Table 6.1, we present a framework outlined by the Bank for International Settlements (BIS).
Reducing Liquidity Risk With Liquid Assets Think of the fractional reserve banking system described in Chapter 3. That bank can be thought of as holding two kinds of assets: cash and loans that mature in two or more periods (prior to maturity the loans are assumed to be worthless). The bank’s liabilities all mature in one period, and may or may not be renewed (withdrawn). If the fraction withdrawn after one period is equal to, or smaller than, the bank’s holding of cash assets, the bank will continue in business for two periods, at least. On the other hand, if withdrawals exceed the bank’s holding of cash assets, that bank will be unable to honor its liabilities – it has promised all depositors immediate access even though its own capacity to satisfy claims is strictly limited by its holding cash assets.7 Therein lies the liquidity conundrum of banking. Notice that an important role of a bank is the provision of liquidity services, and it provides this service by mismatching its balance sheet on the liquidity attribute, that is, it holds assets that are less liquid than its liabilities. This is one form of asset transformation. The quality of this liquidity service provided by the bank depends on three factors: the liquidity of its loan portfolio, the cash (or liquid assets) it has on hand, and the withdrawal risk in its deposit base. By investing in more liquid loans and/or keeping more cash on hand, the bank can improve its own liquidity. However, it does so at the expense of profits. An alternative would be to seek ways to dissipate withdrawal risk, which is what we turn to next.
Reducing Liquidity Risk by Dissipating Withdrawal Risk A depository institution can reduce the variance of its deposit flows by diversifying the sources of funding, that is, having many distinct and dissimilar depositors. This is formally demonstrated in Appendix 6.1. A diverse depositor base results in more predictable deposit flows; the improved predictability reduces the cash needed to service a deposit base to any arbitrary probabilistic standard. That is, the larger and more diverse the depositor base, the smaller the cash holding necessary to achieve any preselected probability of a stock-out (liquidity crisis). This is one way the depository institution produces liquidity. Nevertheless, withdrawals will sometimes exceed the institution’s capacity to service them, even though this may 7. This is the rationale behind the standard measure of liquidity in the savings industry, which is the ratio of cash and short-term U.S. government securities and other specified securities to deposits and borrowing due within 1 year. Following the 2007–2009 financial crisis the Dodd-Frank Act (see Chapter 15) has introduced a more extensive regulation of liquidity dictating the holdings of high quality liquid assets (HQLA). The – so called – liquidity coverage ratio (LCR) became active in the United States, and similar regulation was adopted in Europe (see Chapter 15).
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TABLE 6.1 BIS Principles for the Management of Liquidity Risk Fundamental principle for the management and supervision of liquidity risk Principle 1: A bank is responsible for the sound management of liquidity risk. A bank should establish a robust liquidity risk management framework that ensures it maintains sufficient liquidity, including a cushion of unencumbered, high-quality liquid assets, to withstand a range of stress events, including those involving the loss or impairment of both unsecured and secured funding sources* Governance of liquidity risk management Principle 2: A bank should clearly articulate a liquidity risk tolerance that is appropriate for its business strategy and its role in the financial system Principle 3: Senior management should develop a strategy, policies, and practices to manage liquidity risk in accordance with the risk tolerance and to ensure that the bank maintains sufficient liquidity. Senior management should continuously review information on the bank’s liquidity developments and report to the board of directors on a regular basis. A bank’s board of directors should review and approve the strategy, policies, and practices related to the management of liquidity at least annually and ensure that senior management manages liquidity risk effectively Principle 4: A bank should incorporate liquidity costs, benefits, and risks in the internal pricing, performance measurement, and new product approval process for all significant business activities (both on- and off-balance sheet), thereby aligning the risk-taking incentives of individual business lines with the liquidity risk exposures their activities create for the bank as a whole Measurement and management of liquidity risk Principle 5: A bank should have a sound process for identifying, measuring, monitoring and controlling liquidity risk. This process should include a robust framework for comprehensively projecting cash flows arising from assets, liabilities, and off-balance sheet items over an appropriate set of time horizons Principle 6: A bank should actively monitor and control liquidity risk exposures and funding needs within and across legal entities, business lines, and currencies, taking into account legal, regulatory, and operational limitations to the transferability of liquidity Principle 7: A bank should establish a funding strategy that provides effective diversification in the sources and tenor of funding. It should maintain an ongoing presence in its chosen funding markets and strong relationships with funds providers to promote effective diversification of funding sources. A bank should regularly gauge its capacity to raise funds quickly from each source. It should identify the main factors that affect its ability to raise funds and monitor those factors closely to ensure that estimates of fund raising capacity remain valid Principle 8: A bank should actively manage its intraday liquidity positions and risks to meet payment and settlement obligations on a timely basis under both normal and stressed conditions and thus contribute to the smooth functioning of payment and settlement systems Principle 9: A bank should actively manage its collateral positions, differentiating between encumbered and unencumbered assets. A bank should monitor the legal entity and physical location where collateral is held and how it may be mobilized in a timely manner Principle 10: A bank should conduct stress tests on a regular basis for a variety of short-term and protracted institution-specific and market-wide stress scenarios (individually and in combination) to identify sources of potential liquidity strain and to ensure that current exposures remain in accordance with a bank’s established liquidity risk tolerance. A bank should use stress test outcomes to adjust its liquidity risk-management strategies, policies, and positions and to develop effective contingency plans Principle 11: A bank should have a formal contingency funding plan (CFP) that clearly sets out the strategies for addressing liquidity shortfalls in emergency situations. A CFP should outline policies to manage a range of stress environments, establish clear lines of responsibility, include clear invocation and escalation procedures, and be regularly tested and updated to ensure that it is operationally robust Principle 12: A bank should maintain a cushion of unencumbered, high-quality liquid assets to be held as insurance against a range of liquidity stress scenarios, including those that involve the loss or impairment of unsecured and typically available secured funding sources. There should be no legal, regulatory, or operational impediment to using these assets to obtain funding Public disclosure Principle 13: A bank should publicly disclose information on a regular basis that enables market participants to make an informed judgment about the soundness of its liquidity risk-management framework and liquidity position *In their “Principles for sound liquidity risk management and supervision” the BIS complements this principle with the following “instruction” to supervisors: “Supervisors should assess the adequacy of both a bank’s liquidity risk-management framework and its liquidity position and should take prompt action if a bank is deficient in either area in order to protect depositors and to limit potential damage to the financial system.” Source: BIS (2008).
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happen only with very small probability, and in that sense the system is imperfect. Indeed, this is the system’s Achilles’ heel. Bank runs are the trauma that illustrates this vulnerability of fractional reserve banking, a vulnerability caused by the illiquidity of bank assets.
Reducing Liquidity by Preserving Access to Funding Markets The management of liquidity is referred to as the treasury function, and it is usually entrusted to the chief financial officer (CFO). It is her responsibility to “fund the bank.” This requires a thorough understanding of the institution’s cash flows, as well as all potential sources of liquidity. Ultimately, protection comes from maintaining diverse, capacious, and reliable sources of funding against future contingencies. This explains why the typical bank will borrow from virtually all reasonably priced sources. To be sure, cost will be a consideration, but opportunities to reduce short-run funding costs by concentrating on fewer funding sources are commonly avoided. In “paying up” for funding diversity, the bank is purchasing lines of credit, and this reduces the likelihood of being rationed. It is common for funding sources to evaporate under stress; CFOs understand this only too well. Continental Illinois Bank and Trust found that holders of its large CDs (Certificates of Deposit) abandoned them in their hour of keenest need, and the high-yield bond market went into eclipse when Drexel Burnham Lambert was forced into insolvency because banks chose to withdraw their funding. And in the 2007–2009 financial crisis many commercial banks, including Northern Rock in the United Kingdom, and investment banks “discovered” that access to short-term wholesale financing could disappear overnight. The conventional protection against the trauma of being rationed is to accept the extra cost of participating in as many markets as possible, thereby diversifying funding sources. Liquidity is consciously purchased by banks as well as their borrowers, and it is the fragility of liquidity that makes this part of banking particularly challenging.
Reducing the Liquidity Risk of an Individual Bank with a Lender of Last Resort It was long ago discovered that the liquidity of a fractional reserve banking system can be ensured with a thoroughly credible “lender of last resort” (LLR). This was the major motivation for the creation of central banks, including the Federal Reserve System. With an institution capable of creating money limitlessly, it becomes possible to support banks facing the most extraordinary deposit outflows. Provided that the banks are sound (solvent, given reasonable time to liquidate their assets), this could be done by having the central bank lend to the banks using their illiquid loans as collateral. With such a lending facility, sound but illiquid banks could be protected and financial market disruptions avoided. This argument is developed more fully in Appendix 6.2. However, an inexpensive, readily available LLR faces the danger of inheriting the entire liquidity management problem of the banking industry. That is, the bank’s incentive to hold cash assets (or even diversify its deposit base) is weakened if borrowings from the central bank are inexpensive and readily available. This is a moral hazard associated with the introduction of the LLR, and it has two implications. First, it shifts deposit seigniorage from the public to privately owned banks. Second, the LLR is also exposed to the credit risk of the bank’s collateral. The moral hazard of lower, voluntarily held cash assets explains the consequent introduction of cash asset reserve requirements, and also why there are carefully administered detailed rules and informal restrictions governing access to the discount window. Thus, legal reserve requirements and LLR pricing and availability shift at least a portion of the liquidity management problem back to the banks. Other banks, without access to an LLR facility, own the liquidity problem outright.
THE DIFFICULTY OF DISTINGUISHING BETWEEN LIQUIDITY AND INSOLVENCY RISKS AND THE LLR’S CONUNDRUM In practice, it is not always easy to distinguish between liquidity risk and insolvency risk, as indicated earlier. This was true, for example, in the 2007–2009 subprime crisis. Financial institutions in the shadow banking system found that there was a sharp increase in the “haircuts” on the collateral used in repurchase transactions, which meant a substantial reduction in short-term liquidity. Similarly, mutual funds faced massive withdrawals by investors. These were the conditions prevailing during the 2007–2009 crisis; see Chapter 14 for more on this. Many interpreted these conditions as a liquidity crisis. Consequently, central banks undertook massive interventions in the capital market, infusing huge amounts of liquidity. However, in reality this was an insolvency crisis, and when this was recognized, the actions of central banks (especially the Federal Reserve) turned to the kinds of initiatives needed to deal with an insolvency crisis, for example, infusing more capital into banks.
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The reason why liquidity and insolvency risks are hard to distinguish in practice is simple.8 When a bank is faced with a liquidity crisis, it means that its financiers are pressed for funds and cannot make funding available to the bank because of their own “liquidity shock.” When a bank is faced with an insolvency crisis, it means it has experienced a deterioration in the quality of the assets on its balance sheet and its risk of insolvency has gone up, and as a result its financiers are unwilling to fund the bank. Since the outcome in both cases is the same – the drying up of funding for the bank – it is hard to tell what kind of crisis the bank is facing.10
CONCLUSION Liquidity risk is possibly the most important risk in banking. In their asset-transformation role, banks engage in liquidity transformation: banks typically have longer duration assets than liabilities, and offer via the liability side of the balance sheet liquidity services to their depositors. The effect is that banks might be confronted with roll-over risk and withdrawals of deposits that could cause funding gaps. The 2007–2009 financial crisis showed the systemic nature of liquidity risk as well as its close relationship to insolvency risk. Unexpectedly high subprime mortgage defaults elevated concerns about insolvency risk, leading to funding markets breaking down, and inducing institutions to engage in asset sales caused downward price spirals, putting enormous stress on the stability of the financial system.9 These effects related to how fundamental concerns about insolvency risk caused liquidity to shrink are discussed in Chapter 14, and the regulatory responses are covered in Chapters 15 and 16.
REVIEW QUESTIONS 1. What is liquidity risk and how is it linked to interest rate and credit risks? What is the role of asymmetric information in creating liquidity risk? 2. How can liquidity risk be managed? What are some of the impediments faced by banks in implementing an integrated risk-management system that managers credit risk, liquidity risk, and interest rate risk? 3. What factors lead to an increase in the bank’s liquidity risk and why is it important for the economy that banks take on liquidity risk?
APPENDIX 6.1 DISSIPATION OF WITHDRAWAL RISK THROUGH DIVERSIFICATION Suppose that a bank has n depositors, each of whom deposits $1. Each deposit is subject to withdrawal after one period, but may remain for two. Assume that the probability that a $1 deposit will be withdrawn after one period is one in ten, that is, p = 0.1, but whether a given deposit is actually withdrawn after one period cannot be known until that one period has passed. Deposits are used to fund loans that pay back in full in two periods, but are worthless until they mature. (There is no secondary market in loans.) This is a harmless simplifying assumption and does not affect the argument that follows. Of course, the bank will need to hold some fraction of its assets in cash in order to satisfy its one-period withdrawals. The question is how much cash the bank should prudently hold. If the bank has $1 or $1 million of deposits, the probability of withdrawal remains fixed at 10%, and the expected withdrawal is this probability multiplied by the amount of deposits. However, if the bank has only $1 in deposits, the withdrawal inevitably will be all or nothing at all, zero or one. Indeed, the expected value of $0.10 is unattainable, and the bank’s decision to hold 10 percent in cash, if feasible, is virtually pointless. However, as the bank’s depositors increase in number, assuming independence among them, the withdrawal of 10% becomes more predictable; in the limit, as depositors become more and more numerous, a 10% cash holding will “almost certainly” satisfy deposit withdrawals. This idea is apparent from the definition of the standard deviation of a binomial distribution where n is the number of depositors and q ≡ 1 – p; the standard deviation of the bank’s deposits will be σ = npq. Note that this measure of uncertainty varies with the square root of the number of depositors, and hence in the limit as the number of depositors increases to infinity, the standard deviation per dollar of deposit equals lim (σ / n) = 0. n →∞
This means that as the number of depositors becomes larger, the withdrawal uncertainty per loan diminishes, approaching zero in the limit, even though the withdrawal probability remains unchanged at p = 0.1. So, as the depositor population increases, the 10% withdrawal can be treated increasingly as a routine (almost fixed) cost, rather than as a potential 8. Farhi and Tirole (2012) provide a model in which the central bank cannot distinguish between a liquidity crisis and an insolvency crisis. 9. See Brunnermeier and Pedersen (2009). 10. In a recent paper, Thakor and Vuong (2018) develop a theoretical model of countercyclical capital buffers and show that having a sufficiently high capital buffer can not only address current insolvency risk, but also future illiquidity risk. Thus, by asking banks to keep sufficiently high capital buffers, regulators can minimize the severity of the problem of disentangling solvency and liquidity risks.
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catastrophe. The risk of ruin, the probability that withdrawals exceed the bank’s cash holding, never actually becomes zero since σ/n → 0 only in the limit. But the risk of ruin can be managed, and made indefinitely small by diversifying the bank’s sources of funding.
APPENDIX 6.2 LENDER-OF-LAST-RESORT MORAL HAZARD In a world of fiat money, value derives from an administered or artificial scarcity. That is, our money is money by fiat or legal mandate (hence legal tender) and is not convertible into gold or any other commodity at a fixed exchange rate, as in the case of commodity-backed money. The more money the government prints, or otherwise creates, the less its value, and this applies to bank deposits as well as to paper money. The administered scarcity of money also creates a monopoly profit referred to as “seigniorage.” This profit on the production of money is shared by the privately owned banks and the public, via its effective ownership of the central bank. The Federal Reserve is nominally owned by member commercial banks. However, the equity in the Federal Reserve banks pays a statutorily fixed rate of return, much like a bond, whereas the residual earnings of the Federal Reserve flow back to the U.S. Treasury via a special franchise tax. Given that neither central bank nor private bank deposits pay interest (any interest rates below competitive rates will sustain the point), the distribution of seigniorage between the banks and the public (or central bank) depends on the cash asset reserves the banks choose to hold. The more reserves banks hold, the smaller will be banks’ share of the seigniorage. Since the introduction of an LLR reduces the amount of reserves the banks will desire to hold, it effectively shifts seigniorage from the public to the banks. This is the moral hazard associated with the introduction of an LLR, and it explains that one rationale for legal reserve requirements (that stipulate the minimum cash assets that banks must hold) is to restore the “appropriate” sharing of seigniorage between banks and the public. This point is easily illustrated. Suppose we have a single commercial bank with $10 million in deposit liabilities, an amount consistent with the money supply the central bank wishes to maintain in consideration of monetary policy. There are no reserve requirements and no LLR facility. The commercial bank voluntarily holds 10% of its assets in cash against withdrawal risk. It makes no difference whether the bank’s cash assets are vault cash or deposits at the central bank, so for simplicity assume that these assets are all on deposit at the Federal Reserve where they earn nothing. The commercial bank’s balance sheet would then be Commercial Bank Cash assets
$1 million
Deposit liability
Loans or other earning assets
$9 million
$10 million
Total assets
$10 million
Total liabilities $10 million
The Federal Reserve’s balance sheet, to a first approximation, would show Federal Reserve Earning assets
$1 million
Deposit liability $1 million
Note that the Federal Reserve’s deposit liability corresponds to the bank’s cash assets. Now suppose the Federal Reserve introduces an LLR facility. It has no reason to change the money supply, but banks now have a new source of liquidity. Hence, they will feel less need to hold nonearning cash assets. Say they cut these holdings from 10% to 5%. The bank’s balance sheet now becomes Commercial Bank Cash assets
$0.5 million
Deposit liability
Loans or other earning assets
$9.5 million
$10 million
Total assets
$10 million
Total liabilities $10 million
$0.5 million
Deposit liabilities $0.5 million
and the Federal Reserve shrinks to Federal Reserve Earning assets
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In effect, $0.5 million in earning assets have been transferred from the Federal Reserve’s balance sheet to the bank’s balance sheet, and this occurs as a direct consequence of the introduction of the LLR. One could argue that if the LLR facility is properly priced, the moral hazard will be discouraged. However, note that before its introduction, the LLR interest rate was infinite, so that any finite interest rate will improve bank liquidity, and should therefore result in some reserve dissipation. As a historical matter, the LLR tends to price low for reasons that are not entirely clear. This generous pricing practice aggravates the moral hazard problem and heightens the need for legal reserve requirements. Thus, reserve requirements control the moral hazard of the LLR, and a lowering of reserve requirements transfers deposit seigniorage from the public to the banks. Raising reserve requirements has the reverse effect. One hundred percent reserve requirements shift all deposit seigniorage to the public. This is the basis for the conventional wisdom that the reserve requirement is a tax on the banks, but one could just as easily argue that any reserve requirement less than 100 percent is a subsidy to banks. The hard question here is: To whom should the monopoly rents associated with administered money belong?
REFERENCES BIS, 2008. Principles for Sound Liquidity Risk Management and Supervision. Basel Committee on Bank Supervision, Bank for International Settlement, Basel. Bouwman, C., 2014. Liquidity: how banks create it and how it should be regulated. In: Berger, A.N., Molyneux, P., Wilson, J.O.S. (Eds.), The Oxford Handbook of Banking, second ed, Oxford, UK. Brunnermeier, M.K., Pedersen, L.H., 2009. Market liquidity and funding liquidity. Rev. Finan. Stud. 22, 2201–2238. Farhi, E., Tirole, J., 2012. Collective moral hazard, maturity mismatch, and systemic bailouts. Am. Econ. Rev. 102, 60–93. Huang, R., Ratnovski, L., 2011. The dark side of bank wholesale funding. J. Finan. Intermed. 20, 248–263. Thakor, A.V., Vuong, T., 2018. Optimal Capital Buffers, working paper, Washington University in St. Louis.