Liquidity and Transparency in Bank Risk Managment

8/6/2019 Liquidity and Transparency in Bank Risk Managment

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Liquidity and Transparency

in Bank Risk Management

Lev Ratnovski

Bank of England and

University of Amsterdam

June 2007

Abstract

Liquidity risk is associated with uncertainty over solvency at the renancingstage. To insure, banks can accumulate liquid assets, or enhance transparency to

facilitate renancing. Both are important components of risk management. A liq-

uidity buer provides complete insurance against small liquidity needs, while trans-

parency oers partial insurance against large ones as well. Due to leverage, banks

can under-invest in both liquidity and transparency. While liquidity can be imposed,

transparency is not veriable. This multi-tasking problem complicates liquidity

regulation: liquidity requirements can compromise banks endogenous transparencychoices.


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1 Introduction

Banks perform maturity transformation and insure publics liquidity needs, but in

process become exposed to liquidity risk (Diamond and Dybvig, 1983). When re-

nancing frictions prevent a solvent bank from covering a liquidity shortage, it may go

bankrupt despite having valuable long-term assets.

There are two principal stylized facts about recent liquidity events in developed

countries. Firstly, most of them were associated with increased solvency concerns:

1991, Citibank and Standard Chartered (HK): rumors of technical insolvency;

1998, Lehman Brothers (US): rumors of severe losses on emerging markets;

2002, Commerzbank (Germany): rumors of insolvency due to trading losses.

Secondly, in contrast to traditional retail runs, the impact of liquidity events was

most acute in wholesale nance markets. There, a bank with uncertain solvency typically

has to cover all maturing (and demandable) outows without any access to new funds.

In contrast, retail outows were relatively modest, e.g. only 5% of depositor base during

the BAWAG episode in 2006.

Even when rumors turn out to be unsubstantiated, withdrawals and restricted access

to new funds impose signicant strain. To survive a liquidity shock, a bank must be able

to support itself with own funds for the duration of liquidity stress, and/or alleviate the

markets concerns over its solvency to regain access to funds as soon as possible.

This paper studies the options for bank liquidity risk management, when liquidity

risk is driven by asymmetric information, and in presence of active wholesale nance

markets. We suggest that there are two distinct ways in which a solvent bank can

insure against inability to renance. One is to accumulate liquidity form a precau-

tionary buer of short-term assets to cover possible outows internally. Another is to

adopt transparency establish a set of mechanisms that facilitate solvency information

transmission to the market and improve access to external funds Both investments


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tasking problem, which complicates optimal policy design. We show that liquidity re-

quirements can compromise banks endogenous transparency choices. This can damage

nancial stability and social welfare, particularly when transparency is an eective risk

management mechanism, and market access is important in managing liquidity shocks.

This paper builds on the notion of banks strategic endogenous transparency. We

believe that this is an important and topical dimension, particularly in the context of

recent debates on the role of market discipline pillar of Basel II, "principles-based" regu-

lation (which relies on sound processes rather than "rules-based" formal requirements),

and the importance of sound corporate governance.

Banking business is inherently opaque, because in the course of lending relationships

they obtain private and commonly not veriable information on borrowers. Banks can

alter the degree of asymmetric information by choosing more of less information-sensitive

loans (Boot and Thakor, 2000). Our interpretation of transparency is that, in addition

to asset choice, a bank can also make a specic investment, in transparency, which for

any given asset mix, will reduce ex-post information asymmetry over banks assets value.

It is instructive to compare transparency to disclosure (Perotti and Von Thadden,

2003). Disclosure is an ex-post action information release of uncertain reliability.

Disclosure can be not credible (when outsiders do not believe that information is truth-

ful) and not eective (when outsiders have no incentives to interpret information, Boot

and Thakor, 2001). In this context contrast, transparency can be regarded as an ex-ante

investment that enables credible and eective disclosure ex-post.

There are a number of examples of possible transparency investments. Banks can

issue subordinated debt (Calomiris, 1999) even when cheaper funds are available in

order to have market participants who specialize in assessing the bank available should

a genuine need for funds arise. Banks can create more robust risk management systems

that produce more veriable information on eects of possible shocks. Banks can invest

in establishing better external oversight. Transparency can also be improved by stream-

lining "large and complex nancial institutions" (LCFIs) so as to make their individual

businesses more comparable with specialized counterparts


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While transparency improves future communication, it cannot be perfect. In some

circumstances, ex-post communication channels fail, and even a transparent bank can

be unable to conrm its solvency. The eectiveness of transparency probability of

successful communication is at least partially determined by factors outside a single

banks control. The factors can be country-specic (more developed and liquid nancial

markets) or industry-specic (more transparent other banks, or location in the nan-

cial centre, when transparency is associated with positive externalities, Admati and

Peiderer, 2000).

Transparency has many benetical eects2. For example, transparency can help

increase fundamental value by improving monitoring capabilities (Boot and Schmeits,

2000), or reduce overall funding costs by allowing better ex-ante screening. But in this

paper we focus on eects of transparency within response to shocks. The reason is that

since unforeseen shocks likely associated with an increase in asymmetric information,

the eects of thransaprency can be particularly pronounced during such such times.

This paper contributes to the literature on liquidity crises. The closest model of

liquidity events based on asymmetric information is Chari and Jagannathan (1987).

Chari and Jagannathan describe consumer-based panics. In their model, uninfored

depositors observe others withdrawals and make inferences over a banks solvency, but

are unable to distinguish whether withdrawals have information-based or liquidity-drivenreasons. This information friction amplies liquidity shocks, so that uninformed runs

can be a consequence of abnormal liquidity-based withdrawals in fundamentally solvent

bank.

In contrast, our paper has a wholesale nance perspective. We therefore focus on

dierent triggers and eects of liquidity events. The model purposefully downplays

the determinants of bank withdrawals. With ecient funding markets those should beunimportant, as a bank known to be solvent should be able to obtain renancing to

cover any of them3 (Goodfriend and King, 1988). We therefore focus on the renancing

problem itself. This problem, we suggest, is driven by imprecise solvency information if

informed investors. The bank may need to prove its solvency. This allows an immediate


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sheet, and funding problems are driven by moral hazard. In our model, liquidity needs

originate on the liabilities side of the balance sheet (consistent with the mainstream

view on bank fragility), and funding problems are driven by asymmetric information

(consistent with the well-documented "ight to quality" episodes, Bernanke et al., 1996).

There is so far scarce literature on the choice between cash in hand and borrowing

capacity. In a recent paper, Acharya et al. (2006) note that future risky borrowing

capacity depends on cash-ows. Therefore, when the correlation of future cash ows with

investment opportunities is positive, rms prefer reducing risky debt ("saving borrowing

capacity"), while if negative rms prefer accumulating cash. We oer an additional

perspective, emphasizing that the funding capacity of cash holdings is limited to small

liquidity needs but certain, while that of transparency (borrowing capacity) is unlimited

(can serve large needs as well) but uncertain when ex-post communication channels can

fail.

Empirical literature has demonstrated that both liquidity (Paravisini, 2006) and

transparency (access to nancial markets, Kashyap and Stein, 1990, Holod and Peek,

2004) determine bank nancial constraints. There is also evidence that banks can be

insuciently liquid (Gatev et al., 2004, Gonzalez-Eiras, 2003) and transparent (Mor-

gan, 2002). While empirical literature has mostly considered liquidity and transparency

separately, this paper brings them into the joint framework. This generates novel em-

pirical predictions for bank liquidity risk and its management. Our model suggests

that more liquid banks will be resilient to small shocks, while more transparent banks

(with higher borrowing capacity) will be able to withstand large shocks as well. In re-

sponse, banks will rely on liquidity to manage routine liquidity needs, but put emphasis

on transparency in anticipation of large shocks. The degree to which banks can rely

on transparency and market access (larger or listed banks, or those in more developed

nancial systems) should be negatively correlated to their liquidity choices.

Lastly, the paper contributes to topical regulatory debates. Is solvency enough?

when do you need liquidity? under asymmetric information


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2 Setup

2.1 Economy and Agents

Consider a risk-neutral economy with three dates: 0; 1; 2. The economy is populated by

multiple small investors and a single bank. Small investors are endowed with money.

They have access to a safe storage technology (cash), or can lend to the bank, charging

the gross interest rate of 1.

The bank has no initial capital, but has exclusive access to a protable investment

project. For each unit of nancing at date 0, the project returns at date 2 a high return

X with probability 1 s, but 0 with a small probability s (s for the probability of a

solvency problem). A bank operates under a leverage constraint (representing capital

requirements) and cannot borrow more than 1 at date 0. It is nanced by debt and

maximizes date 2 prot.

2.2 Solvency Uncertainty and Liquidity Risk

Two events happen at date 1. One is a random withdrawal of initial nancing. Another is

a signal on the banks solvency. The two events are independent withdrawals are made

by uninformed depositors or represent maturing term funding, and are not inuencedby the solvency signal.

Withdrawals and liquidity need. While the project is long-term, some debt matures

earlier and must be renanced. In reality there may be multiple renancing events

through the course of the project, but for the analysis we collapse them into a single

"intermediate" date 1. The amount of funds maturing at date 1 liquidity need is

random. With probability 1=2, the liquidity need is low the bank has to repay someL < 1. With additional probability 1=2, the liquidity need is high the bank has to

repay 1. If the bank cannot repay, it fails and goes bankrupt with no liquidation value.

Information and liquidity risk. Because investors always oer an elastic supply of

funds, a bank known to be solvent is able to renance itself by new borrowing and


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With the residual probability s + q, the signal indicates that the bank is likely to be

insolvent. This represents a probability q that a solvent bank is pooled with insolvent

banks. The posterior probability of insolvency in such a case, s=(s + q), is higher then

the ex-ante probability of insolvency, s. This higher uncertainty over banks value may

prevent external renancing. We therefore call such event a "liquidity shock". The

informational structure of the game is illustrated on Figure 1.

>

We impose the following restrictions on parameter values:

1. A bank has a positive NPV, even if it always failed in a liquidity shock.

X >1

1

(s + q)

(A1)

This assures that a bank is always nanced at date 0.

2. A bank in a liquidity shock has a negative posterior expected NPV at date 1.

X 2 (A3)


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2.3 Liquidity Risk Management

We consider two distinct ways in which a bank can hedge its liquidity risk.

1. Accumulate liquidity. A bank can invest L units in the short-term asset (cash).

This allows to fully cover small withdrawals at date 1, and therefore insure against

small liquidity shocks that happen with probability 1=2.

2. Adopt transparency. A bank can invest T to establish transparency. We think

of transparency as a strategic ex-ante investment, such as credible disclosure, that

allows a bank to better communicate solvency information to the market. In par-

ticular, this may enable the bank to publicly conrm its solvency in the event of

liquidity shock. We assume that, since transparency relies on ex-post informa-

tion communication, it is eective (enables a bank to prove its solvency) with a

probability t < 1. The eectiveness of transparency may be determined by factorsoutside a single banks control, such as the level of nancial market development

in a country. Notice that transparency allows to insure against both small and

large liquidity shocks.

Both liquidity and transparency have costs. We consider two sources of liquidity

costs. Firstly, given maximum date 0 leverage, liquidity crowds out investment in aprotable project. This reduces the return to a successful liquid bank from X to X(1

L) + L, a loss of(X 1)L.

Secondly, we assume that when a liquid bank fails (e.g., due to inability to renance

a large liquidity shock or insolvency), the value of its liquidity buer is lost. It may be

spent in costly bankruptcy proceedings, or appropriated by the bankers and transformed

into marginal private benets (as in Myers and Rajan; we model such moral hazard inmore detail in Section 6). This makes the return to a failing liquid bank 0.

The cost of transparency is the value of associated investment, T, which is, rstly,

a direct expense and, secondly, crowds out investment in a protable project. Trans-

parency reduces return to a successful bank from X to X(1 T), a loss ofT X.


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Liquidity and transparency are therefore costly hedges against liquidity risk. The

decisions on whether and how to hedge are made by the bankers, and, we assume here,

are not contractible. In the presence of leverage, this gives rise to a risk-shifting problem

(Jensen and Meckling, 1976) that may lead to insucient hedging. This basic conict

of interest is the principal distortion of our model.

The timeline of the game is as follows.

Date 0. Banks attract deposits. They divide assets between the protable project,the precautionary liquidity buer, and the investment in transparency;

Date 1 . A bank may be hit by a liquidity shock and require renancing. A bank

that is unable to cover withdrawals from the precautionary buer or by borrowing from

the market, is liquidated;

Date 2. Project returns realize; successful banks repay debts and consume prots.

The game tree with payos depending on banks strategic choicesis shown on

Figure 2.

>

3 First Best

In this section, we derive socially optimal levels of bank liquidity and transparency.

We show that, for low enough costs of hedging, banks can optimally combine them in

liquidity risk management. A precautionary liquidity buer completely insures a solvent

bank against small withdrawals in a liquidity shock. Transparency partically insures

against against large withdrawals as well, by possibly enabling external renancing.

3.1 Risk Management Options

We rst derive the social payos depending on the banks liquidity management choices.


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For a strategy "L" when a bank is liquid but not transparent:

SL = (1 s q=2) (X C) 1

A solvent bank is able to survive a small liquidity shock by covering it from the pre-

cautionary buer (probability q=2), but fails in a large liquidity shock that is above the

buer size. The probability of a solvency shock is s; and of a large liquidity shock q=2.

Therefore the probability of survival is 1

s

q=2; the return in that case is X

C (Cis the hedging cost), and the initial investment is 1.

For a strategy "T" when a bank is transparent but not liquid:

ST = (1 s q(1 t)) (X C) 1

A solvent bank is able to survive a liquidity shock (either small or large) when it is

successful in communicating solvency information to the market, with probability t. The

probability of a solvency shock is s, and that of a solvent bank being unable to prove its

solvency to the market q(1 t). Therefore the probability of survival is 1 s q(1 t);

the return in that case is X C, and the initial investment is 1.

Lastly, for a strategy "LT", when a bank is both liquid and transparent:

SLT = (1 s q(1 t)=2) (X 2C) 1

A solvent bank is able to survive a small liquidity shock always by covering it from a

precautionary buer, and a large liquidity shock with probability t when it is successful

in communicating solvency information. The probability of a solvency shock is s, and

of a large liquidity shock when a bank is unable to prove its solvency to the market

q=2 (1 t). Therefore the probability of survival is 1sq(1 t)=2, the return in that

case is X 2C (note double hedging cost), and the initial investment 1.

3.2 Optimal Risk Management


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hedge (liquidity or transparency whichever more eective), or have both hedges. Note

that the marginal benet of the second hedge is lower than that of the rst hedge. This

is because the rst hedge is a more eective one (liquidity for t < 1=2 and transparency

for t > 1=2), and moreover already protects a bank from a range of liquidity shocks.

We analyze the optimal depth of hedging, as a function of the cost of hedging C, in two

cases:

Case 1: Liquidity more eective, t < 1=2. It is optimal that a bank:

Has no hedge, "N", for SN

> SL

, corresponding to high costs of hedging:

C >q=2

1 s q=2 X

Is only liquid, "L", for SL

> SN

and SL

> SLT

, corresponding to intermediate

costs of hedging:

qt=2

1 s q(1=2 t) X < C SL

, corresponding to low costs

of hedging:

C 1=2. Analogously, it is optimal that

a bank:

Has no hedge, "N", for SN

> ST

, corresponding to:

C >qt

1 s q(1 t) X

Is only transparent, "T", for ST

> SN

and ST

> SLT

, corresponding to:


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having both hedges is socially optimal:

We can formulate the rst main result.

Proposition 1 Banks can combine liquidity and transparency in their risk manage-

ment. There exist parameter values (1) or (2), such that it is optimal that a bank is both

liquid and transparent.

Proposition 1 establishes that when costs of hedging are suciently low, it is optimal

that banks use both liquidity (to fully hedge small withdrawals) and transparency (to

partially hedge large withdrawals) as mechanisms to mitigate liquidity risk. It implies

that that both are important dimensions of liquidity risk management, which may need

to be combined in a socially optimal outcome.

In the following analysis we will focus on the case when conditions (1) or (2) are

satised.

4 Suboptimal Liquidity Risk Management

We now turn to banks private liquidity and transparency choices. They may deviate

from the social optimum due to leverage. The presence of debt creates risk-shiftingincentives, revealed as lower private incentives to hedge. The reason is that the bankers

incur the costs of hedging as a reduced payo in the good state, but do not carry the

burden of failure in the bad state thanks to limited liability. The losses in case of default

are born by debtholders. We study how leverage can distort hedging incentives and bias

banks liquidity risk management choices away from the socially optimal ones.

In this section, we treat liquidity and transparency choices as not contractible (e.g.because depositors are small). We introduce the possibility of contracting on liquidity

choices in the next section, which deals with scope for regulation.

4 1 Private Payos


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We can now derive the private payos. They are similar to the social payos, with

the dierence that the bankers repay initial investment only if the project succeeds. The

payos are:

For a strategy "N" when a bank is not liquid and not transparent:

N = (1 s q) (X 1)

For a strategy "L" when a bank is liquid but not transparent:

L = (1 s q=2) (X C 1)

For a strategy "T" when a bank is transparent but not liquid:

T = (1

s

q(1

t))

(X

C

1)

Lastly, for a strategy "LT", when a bank is both liquid and transparent:

LT = (1 s q(1 t)=2) (X 2C 1)

4.2 Risk Management Choices

Since liquidity and transparency have the same costs, and the bankers benet from the

eectiveness of hedge they adopt, the private choice between liquidity and transparency

is not distorted by leverage. As in the social optimum, liquidity is preferred L > T

for t < 1=2, and transparency is preferred T > L for t > 1=2.

However, leverage aects the choice of the depth of hedging. Since the incentives to

hedge are lower, the same depth is chosen only for lower costs of hedging. As before, we

distinguish two cases:

Case 1: Liquidity more eective, t < 1=2. The bank:

Chooses not to hedge "N" for > corresponding to high costs of hedging:


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Chooses to be both liquid and transparent, "LT", for LT > L, corresponding

to low costs of hedging:

C 1=2. The bank:

Chooses not to hedge, "N", for N > T, corresponding to:

C >qt

1 s q(1 t) (X 1)

Chooses to be transparent, "T", for T > N and T > LT, corresponding to:

q(1

t)=21 s (X 1) < C < qt1 s q(1 t)

(X 1) (4)

Chooses to be both liquid and transparent, "LT", for LT > T, corresponding

to:

C ST

but LT < T, is:

q(1 t)=2

1 s (X 1) < C L (3) as determined by low C and high t:

C qt=2

1 s q(1=2 t) (X 1) (9)

Observe that there exist parameters such that this interval is nonempty:

qt=2

1 s q(1=2 t) (X 1) 1=2) in countries with de-

veloped nancial markets, where banks can better rely on external renancing. There,

ill-designed liquidity requirements may have adverse eects. Developing countries are

likely to gain less from transparency (t < 1=2), and may have to rely on liquidity in-

stead. (This corresponds to the evidence that banks in developed countries are typically

highly liquid, and face more binding reserve requirements.) Therefore, there may be

heterogeneity in optimal liquidity-transparency outcomes across countries of dierent

nancial development, and this has to be borne in mind during possible internationalconvergence of liquidity regulation.

6 Discussion

6.1 Liquidity Risk and Solvency Regulation

Solvency regulation alone cannot prevent liquidity risk. Liquidity risk and welfare losses

in liquidity events can be signicant for any given solvency (1 s)X. This implies that,

in the presence of asymmetric information, a second regulatory mechanism liquidity

regulation cum transparency incentives is desirable.

6.2 Implications for Liquidity Regulation

Incorrect liquidity requirements can compromise banks transparency choices. There-

fore, it is important that liquidity regulation is thoroughly designed. Sole reliance on

stock liquidity is likely suboptimal, particularly when market access plays a large role

in managing liquidity risks. Then, an additional emphasis on transparency would be

benecial.

Our results are consistent with the evidence of dierent stock liquidity and liquidity

regulation across countries with varying nancial development. Bennet and Peristiani

(2002) for the US and Chaplin et al. (2000) for the UK, show that liquidity regulation is

not binding in advanced market economies (where banks have superior market access).


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6.4 Liquidity shocks

Can be positive (e.g. Barclays cash for ABN-AMRO take-over)

Buer: all tradeable (or collateralizeable) assets

6.5 Other eects of liquidity

Liquidity bias

Liquidity as signalling

Liquidity to hide losses

6.6 Empirical Implications

To add

7 Conclusion

This paper studied the roles of liquidity and transparency in bank risk management. Liq-

uidity risk was modelled as solvency uncertainty at the renancing stage. We showed

that both liquidity and transparency are important hedges, and moreover can be com-

bined in risk management. However, banks private choices can be distorted by leverage,

and policy response is complicated by multi-tasking. Reserve requirements may com-

promise banks transparency incentives, and target the lesser distortion altogether. The

paper has identied a number of empirical implications.

A Proofs

Lemma 1 Proof. For t < 1=2 we have to show that


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Indeed, in the nominator, X 1 < (1 t)X since X > 2 and (1 t) > 1=2; and in the

denominator, 1 s q(1 t) < 1 s.

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Figure 1: Information structure

1sq sq

InsolventSolvent 1s

Positive signal, known solvent

Solvent,

but unable

to refinance

Negative signal,pooled together

s


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EX-ANTE

HEDGING

DECISIONS

BANK

probability q

UNKNOWN SOLVENT=>LIQUIDITY SHOCK

probability sINSOLVENT

probability 1-s-qKNOWN SOLVENT

HIGH LIQUIDITY NEED

(withdrawals 1)

LOW LIQUIDITY NEED

(withdrawalsL

Liquidity and Transparency in Bank Risk Managment

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