metadata: authors: 0: author: Cordella,Tito
1: author: Dell'Ariccia,Giovanni
2: author: Marquez,Robert
count: World
docna: 0: docna: Government guarantees, transparency, and
            bank risk-taking
docty: Policy Research Working Paper
subtopic: Human Rights,Financial Crisis Management & Restructuring,International Trade and Trade Rules,Deposit Insurance,Financial Structures
teratopic: Finance and Financial Sector Development
abstracts: cdata!: This paper presents a model of bank risk
            taking and government guarantees. Levered banks take
            excessive risk, as their actions are not fully priced at the
            margin by debt holders. The impact of government guarantees
            on bank risk taking depends critically on the portion of
            bank investors that can observe bank behavior and hence
            price debt at the margin. Greater guarantees increase risk
            taking (moral hazard) when informed investors hold a
            sufficiently large fraction of liabilities. Otherwise,
            greater guarantees reduce risk taking by increasing the
            profits of the bank (franchise value effect). The results
            extend to the case in which information disclosure, and thus
            the portion of informed investors, is endogenous but costly.
            The model also shows that when bank capital is endogenous,
            public guarantees lead unequivocally to an increase in bank
            leverage and an associated increase in risk taking. The
            analysis points to a complex relationship between prudential
            policy and the institutional framework governing bank
            resolution and bailouts.
repnme: repnme: Government guarantees, transparency, and
            bank risk-taking
display_title: Government guarantees, transparency,
            and bank risk-taking
listing_relative_url: /research/2017/02/27192943/government-guarantees-transparency-bank-risk-taking
topicv3: Deposit Insurance m1326722 322,Market Discipline m1326726 1248,Trade m1326924 698,Credit Risk m1505083 3885,Discrimination m1505707 3379
publishtoextweb_dt: 2017-02-15T00:00:00Z
historic_topic: Finance and Financial Sector Development
no_of_pages: 38
author_keys: 0: author_key: 879396
fullavailablein: node_id: 27192943
node_id: 27192943
model_extractions: WPS7971 Policy Research Working Paper 7971 Government Guarantees, Transparency, and Bank Risk-Taking _Tito Cordella Giovanni Dell’Ariccia Robert Marquez_ Development Economics Vice Presidency Operations and Strategy Team February 2017
Policy Research Working Paper 7971

# **Abstract**

This paper presents a model of bank risk taking and government guarantees. Levered banks take excessive risk, as their actions are not fully priced at the margin by debt holders. The impact of government guarantees on bank risk taking depends critically on the portion of bank investors that can observe bank behavior and hence price debt at the margin. Greater guarantees increase risk taking (moral hazard) when informed investors hold a sufficiently large fraction of liabilities. Otherwise, greater guarantees reduce risk taking by increasing the profits of the bank (franchise value effect). The results extend to the case in which information disclosure, and thus the portion of informed investors, is endogenous but costly. The model also shows that when bank capital is endogenous, public guarantees lead unequivocally to an increase in bank leverage and an associated increase in risk taking. The analysis points to a complex relationship between prudential policy and the institutional framework governing bank resolution and bailouts.

This paper is a product of the Operations and Strategy Team, Development Economics Vice Presidency. It is part of a larger effort by the World Bank to provide open access to its research and make a contribution to development policy discussions around the world. Policy Research Working Papers are also posted on the Web at http://econ.worldbank.org. The authors may be contacted at tcordella@worldbank.org, gdellariccia@imf.org, and rsmarquez@ucdavis.edu.

_The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent._ Produced by the Research Support Team
Government Guarantees, Transparency, and Bank Risk-Taking<sup>�</sup> Tito Cordella Giovanni Dell ’Ariccia The World Bank International Monetary Fund and CEPR Robert Marquez University of California, Davis JEL Classi...cation Numbers: G1, G21, G28 Keywords: Bailouts, moral hazard, value e¤ect, transparency, leverage, risk pricing.

> �The views expressed in this paper are those of the authors and do not necessarily represent those of the IMF, the World Bank, or their Executive Boards. The authors would like to thank Oliver Masetti, Patricia Mosser, Pau Rabanal, Damiano Sandri, and two anonimous reviewers for useful comments. Tito Cordella is an Adviser at The World Bank (Development Economics), Giovanni Dell’Ariccia is Deputy Director of the Research Department at the IMF. Robert Marquez is a Professor of Finance at the University of California. Davis.
# 1 Introduction

The bailouts of banks and other ...nancial intermediaries during the Global Financial Crisis led to a regulatory backlash focused on limiting future public intervention in support of the ...nancial sector. In particular, the post-crisis regulatory debate has centered on how to eliminate too-big-too-fail subsidies and reduce the moral hazard associated with implicit or explicit government guarantees. With these objectives in mind, regulatory reforms have typically introduced new and higher hurdles for government support to banks during crises. Cases in point can be seen in the new restrictions on Federal Reserve Bank actions written into Dodd-Frank, or in the recently introduced bail-in requirements in the EU.

The primary rationale underpinning these reforms is that bailouts are inequitable and that the expectation of public support a¤ects the behavior of bankers. In particular, part of the argument is that public guarantees prevent the correct pricing of risk by market participants. This induces ine¢ ciently reckless behavior by bankers who become less concerned about risk taking since their actions are not re‡ected in their costs of ...nancing. Removing the expectation of bailouts is then expected to restore market discipline and thus prevent banks from taking socially excessive risk.

Yet, the notion that the expectation of bailouts and other forms of public guarantees lead to greater moral hazard relies on the assumption that banks are transparent and investors can price risk at the margin correctly, or that a bailout is likely to bene...t shareholders/managers in addition to creditors/depositors. Put di¤erently, the assumption is that, absent government guarantees, implicit or explicit, competitive forces will be able to discipline bank behavior early enough to prevent excessive risk taking, hence reducing the probability of ...nancial crises.

In contrast, our model shows that when banks are su¢ ciently opaque, or when the pricing of liabilities cannot easily incorporate risk taking in interim periods (i.e., after the debt has been issued), a public insurance scheme can improve banks’incentives by reducing the cost of liabilities. While guarantees make the pricing of debt insensitive to risk, they also reduce the promised interest rate that banks must o¤er their investors and depositors. Since bankers (or bank shareholders) are residual claimants on the returns from loans on their portfolios, a reduced cost of funding increases a bank’s payo¤ conditional on success. This greater payo¤ increases the bank’s incentives to monitor its loans in order to guarantee repayment. Equivalently, it induces the bank to choose 1
safer portfolios than what would be individually optimal with higher deposit and bond rates. Thus, public guarantees can curb rather than exacerbate banks’risk-shifting tendencies.

It is important to note, however, that the force described above improves the bank’s incentives only when a large portion of the bank’s liabilities is already insensitive to risk at the margin. If all the bank’s liabilities re‡ected the bank’s risk choices at the margin, then risk taking would be fully internalized and guarantees would just create moral hazard.

A second important distinction is between the bailout of bondholders and that of shareholders/managers (that is, agents that have full control over a bank’s risk taking activity). The e¤ects discussed above pertain to the bailout of bondholders and depositors. In contrast, insuring an informed party (shareholders/managers) against a risk over which it has full control can only lead to worse incentives. Consistently, in the model we present in this paper, the promise or expectation of bailing out shareholders has an unequivocally detrimental impact on bank risk taking, irrespectively of the weight of shareholder claims in a bank’s liability structure.

Also note that saying that a bank’s risk is “priced at the margin”is not the same as saying that a bank portfolio is correctly priced in equilibrium. In the latter case, investors form conjectures about a bank’s behavior and price its liabilities accordingly. The bank takes the cost of its liabilities as given when it makes its risk taking choices. And, in equilibrium, deposit rates and yields on debt correctly re‡ect the bank’s risk taking decisions. In the former case, the cost of a bank’s liabilities is a function of its risk taking, and the bank takes it directly into account when it makes its choices.

Empirical evidence on whether investors can price bank risk correctly (and in particular, at the margin) is at best mixed. On the one hand, there is solid evidence that depositors and other security holders are able to identify banks that are at risk of failure, either by running or by demanding higher interest rates. On the other, this does not necessarily imply that depositors are able to discipline e¤ectively bank managers’behavior ex ante. Indeed, there is similarly solid evidence that events (such as regulatory audits) in which details about bank holdings are suddenly revealed lead to sharp repricing of banks’liabilities (see Section 8, for a survey of the literature and discussion).

If our benchmark model looks at the incentive e¤ects of guarantees for given levels of transparency/disclosure and leverage, we then relax such assumptions. First, we allow banks to exert some control over the fraction of their liabilities that is priced at the margin. Think about this as banks being able to make a (costly) investment in transparency/disclosure. Under these conditions, 2
bailouts may entail an additional form of moral hazard by reducing the bene...ts (to the bank) of transparency, and hence lead banks to be more opaque, which everything else equal will tend to increase their risk taking. Yet, even with this additional source of moral hazard, we show that if the cost of information disclosure is su¢ ciently high, the net e¤ect of bailouts may still be reduced risk taking.

The second extension deals with leverage. In our model, capital is costly (there is an equity premium) and observable; investors use it to infer a bank’s risk taking behavior (higher capital means less risk). When allowed to choose their level of leverage, banks will choose capital as to balance its higher cost with its bene...t in reducing the cost of debt and deposits in equilibrium. Under these conditions, the expectation of a bailout will reduce the bene...ts of capital and, hence, increase leverage. This, in turn, will unequivocally increase risk taking. This points to an important interaction between bailout policies and capital regulation. For intermediaries subject to su¢ ciently high capital requirements, our results with exogenous capital apply and the e¤ects of bailout on risk taking depend on the proportion of liabilities priced at the margin. For the rest, the expectation of bailouts leads to greater leverage and an excessive increase in risk taking.

Finally a couple of caveats. First, most of the issues we discuss are relevant for other sectors of the economy as well. Large non-...nancial corporations, which have sometimes been bailed out because of their systemic nature, are often opaque and investors may have di¢ culty in pricing their risk at the margin. Hence, to some extent, the model could apply beyond the ...nancial sector. Yet, there are obvious reasons to focus primarily on banks. First, the size and frequency of bailouts (and the explicit guarantees) for the ...nancial sector do not ...nd a counterpart in other industries. Second, by the very nature of their business, banks and other ...nancial intermediaries ...nd it easier than non-...nancial ...rms to modify their risk pro...le on a short-term basis. It is, then, likely more di¢ cult for investors to price their risk at the margin (see Morgan, 2002). Finally, as a consequence, the post-crisis reform debate has primarily focused on measures addressing issues related to the bailout of banks.

Second, in this paper, we abstract from the issue of whether a bank is systemic or not. This is obviously a relevant issue when deciding whether or not to bail out an institution. However, the issue is somewhat orthogonal to the point we are making in this paper. Most papers examine the trade-o¤ between the ex-post aggregate welfare bene...ts from bailing out a systemic bank in a crisis and the ine¢ ciencies (the increased risk taking) associated with the expectation or promise 3
of such action. Here we are interested in the conditions under which such a promise indeed leads to increased ine¢ ciency. That said, it is worth noting that, in a related model (modi...ed to admit contagion), the promise of bailout for systemic institutions may improve the incentives of banks subject to the risk of contagion (see Dell’Ariccia and Ratnovski, 2013), providing an additional counterbalance to standard moral hazard e¤ects.

The paper relates to the literature on bailouts, deposit insurance, and moral hazard in banking. Our model extends the simple framework used in Cordella and Levy Yeyati (2002), Dell’Ariccia and Marquez (2006), Allen, Carletti, and Marquez (2011), and Dell’Ariccia, Laeven, and Marquez (2014), where banks face quadratic monitoring costs, are protected by limited liabilities, and only repay depositors when the project succeeds. In addition, we allow for part of a bank’s debt liabilities to be priced at the margin and we consider government guarantees. The idea that insurance can have a pro-incentive e¤ect is studied in Cordella and Levy-Yeyati (2003) and Dell’Ariccia and Ratvnoski (2013). However, in both these papers insurance is provided against risks outside the control of the bank (macroeconomic risk in the ...rst case, and contagion risk in the second). The mechanism at work in our paper is then more akin to the e¤ect of lower deposit rates explored in Matutes and Vives (2000) and Hellman, Murdoch, and Stiglitz (2005). There a deposit rate ceiling or deposit insurance increases a bank’s charter value and hence reduces agency problems.

The paper contributes to the policy debate on bank resolution and intervention. Most of the narrative of the post-crisis reform e¤ort has been on making crisis resolution more equitable and in avoiding creating conditions conducive to moral hazard. From that standpoint, a trade-o¤ emerges between the need to minimize the macroeconomic e¤ects of bank distress ex post (including through generous bailouts) and avoiding policies that distort risk-taking incentives ex-ante. Here, we focus on what conditions that have to be in place for such a trade-o¤ to exist; in the process we identify an important relationship between capital regulation and bank resolution policies.

The paper is organized as follows: Section 2 presents a stylized model of bank risk taking highlighting the forces discussed above. Sections 3 and 4 explore under what conditions bailouts can improve rather than worsen a bank’s risk pro...le, when the fraction of liabilities with risk priced at the margin is exogenously speci...ed or is endogenously determined, respectively. Section 5 presents a brief discussion of additional e¤ects that may arise if government guarantees (in the form of a possible bailout) also have the potential to bene...t shareholders. Section 6 examines the case with endogenous bank leverage and discusses the role of capital regulation. Section 7 presents 4
illustrative numerical simulations of the model. Section 8 summarizes the evidence on debtholder discipline and bank risk taking. Finally, Section 9 concludes.

# 2 A model of bank risk taking

Consider a risk-neutral, pro...t-maximizing bank with a loan portfolio of size 1. The portfolio is ...nanced by equity, k, and a mass 1 � k of debt (bonds and deposits). Risk-neutral debt holders will invest in the bank as long as they are compensated for risk (i.e., as long as they break even relative to the risk free rate). Further, we assume that a fraction � of debt holders is able to observe the true riskiness of the bank’s portfolio, which, in turn, depends on the bank’s monitoring e¤orts; consequently, they can price bank risk at the margin. The rest either cannot observe risk taking or cannot easily condition the pricing on the actual, realized degree of risk, and hence it will price debt based on the expected riskiness. These latter investors must break even in equilibrium, but they do not adjust the pricing of their claims to the bank’s marginal portfolio choices.<sup>1</sup> Finally, we assume, that, with probability �, the government will intervene in case of bank failure and bail out debt holders. One alternative interpretation is that a fraction � of debt is protected by government guarantees such as deposit insurance, so that � can be viewed as caps on the amount of deposits that are insured.

In our model, we assume that the bank is protected by limited liability and it repays depositors only when successful. If the bank fails, the bank’s owners/managers lose the invested capital. More precisely, we assume that the portfolio of the bank returns R with probability q 2 [0; 1] and zero otherwise, where q is the bank’s choice of monitoring e¤ort, which entails a cost<sup><u>1</u></sup> 2<sup>cq2.Note that one</sup> can write an essentially identical model based on project screening/portfolio allocation.<sup>2</sup> Denoting by <u>r</u> the risk free rate, by rD the gross interest rate on bank debt, and by rE � <u>r</u> the opportunity cost of equity, the bank’s expected pro...ts can be written as:

> 1 This is equivalent to saying that for the fraction � of debt holders, bank portfolio risk is contractible, so that the pricing of their debt claim can be made contingent on the bank’s choice of risk. Instead, for other debt holders, the pricing of their claims cannot be made explicitly contingent on the bank’s chosen level of risk, even if the risk is correctly priced in equilibrium.

> 2 Equivalently, the framework can be seen as a portfolio choice problem for the bank: the bank chooses a portfolio on the e¢ cient frontier that repays R � 2<sup><u>c</u>qwithprobabilityq,andthusmusttradeo¤ greaterreturnswithgreater</sup> risk.

5
The ...rst term re‡ects the bank’s limited liability, which implies that the bank only repays debt holders (bond holders and depositors) when its project succeeds, which occurs with probability q. The cost of bank debt is a weighted average of interest rates that re‡ects the assumptions above: given the expectation of government bailout of debt holders, �, investors put the same weight on the risk-free rate. Yet, with probability 1 � � debt is subject to default and needs to be priced accordingly. A fraction � is priced in a way that perfectly re‡ects the bank’s actual risk taking at the margin, ( qr<sup>),withtheremainingportion,1 ��,re‡ectingtheexpectedrisktakingrD=</sup> Er[q]<sup>.</sup> The required return to equity, rE, is taken here as exogenous - all that matters for our purposes is that rE � <u>r.</u><sup>3</sup>

# 3 Equilibrium with exogenous priced-at-the-margin liabilities

For the moment, assume that �, the fraction of debt that is correctly priced at the margin, is exogenously given. Di¤erentiating (1) with respect to q, the ...rst order condition of the bank’s problem can be written as so that where First, note from (3) that a bank funded entirely with equity (thus without an agency problem) e would choose q = q �<sup><u>R</u></sup> c<sup>,whichhencerepresentsthesociallyoptimalmonitoringe¤ort.Itisalso</sup> immediate from (3) that generally we will have qb < q:e Second, the bank’s monitoring e¤ort, qb, is increasing in its gross return R and its capitalization, as is common in models that incorporate a moral hazard on the bank’s side. Note further, however, that qb is also increasing in �: the greater the fraction of liabilities the price of which is risk-sensitive, the more discipline is imposed on the bank through this channel. This e¤ect represents the depositor discipline channel discussed above, which leads the bank to exert more e¤ort and choose a safer portfolio. Finally, note that whether

> 3 Since investors are all risk neutral, there is no risk premium associated with equity and hence rE need not be a¤ected by leverage changes within the bank. Nevertheless, rE may be strictly greater than <u>r</u> to the extent that banks face di¢ culties in raising capital due to asymmetric information, issuance costs, dilution of existing shareholders, etc.

6
qb is increasing or decreasing in �, the fraction of deposits that are insured, depends on how large � is. To see this, note that @�<sup>@qb=</sup><sup><u>(�</u></sup> <u>r+rD(1c��))(1�k)</u> . For � large and close to 1, the bank’s level of monitoring qb is decreasing in �, while the opposite is true for � close to 0. We discuss this issue further below given it represents one of the main aspects of the paper.

b We now impose rational expectations, that is, E[q] = q, and use (3) and (4) to explicitly characterize the equilibrium values (denoted by an asterisk) of monitoring e¤ort and the interest rate on debt (i.e., deposits): To ensure the existence of an internal solution, q<sup>�</sup> 2 (0; 1), we further assume that<sup>4</sup> and, for the interval to be non empty, that<sup>5</sup> Having computed the equilibrium values for the monitoring e¤ort and the debt rate, we are now in a position to study how changes in the institutional setting a¤ect the bank’s risk taking incentives. Since, in our framework, the bank tends to take on excessive risk because is a levered institution, which operates under limited liability and partial pricing at the margin, an increase in equity necessarily makes the bank more prudent. Similarly, an increase in the fraction � of the risk sensitive non-insured debt also increases the equilibrium monitoring e¤ort of the bank. In both cases, the force at work is greater market discipline through a larger share of the bank liabilities priced at the margin. Put di¤erently, the bank’s behavior will re‡ect more directly on its cost of funding.

In contrast, the e¤ect of an increase in the probability of bailout has an ambiguous e¤ect on bank risk taking. On the one hand, it increases bank pro...ts conditional on success by reducing the average interest rate on debt; this makes the bank more prudent. On the other, it reduces the

> 4 The ...rst condition ensures that q� > 1; the second that the radicand in (5) and (6) is positive, and thus that a rational expectations equilibrium exists.

> 5 This condition is, of course, a su¢ cient one.

7
weight of debt priced at the margin, thus, diminishing the bank’s incentive to “behave”to reduce the cost of its funding.

In order to better understand the di¤erent forces in action, we study the link between government guarantees on the bank’s liabilities and risk taking incentives depending on how large the fraction of the bank’s debt is risk sensitive. More precisely, we can show that: Proposition 1 An increase in the share of debt liabilities covered by guarantees, �; decreases the bank’s monitoring e¤ort q if, and only if, the fraction � of risk sensitive uninsured deposits is large enough.

# Proof : See Appendix.

The proposition establishes that o¤ering a guarantee on deposits and/or debt as a way of increasing the bank’s return conditional on project success leads to greater moral hazard and more risk taking only when a signi...cant portion of the bank’s liabilities is priced at the margin. In other words, when most debt is priced in a way that re‡ects the bank’s risk taking decisions, we have the classic moral hazard result: increases in government guarantees reduce the bank’s incentives to monitor since it makes the interest it has to pay on debt less sensitive to its risk-taking decisions.

Conversely, when most of the bank’s liabilities earn a return that is ...xed relative to the bank’s risk choices (even if they are correctly priced in equilibrium), providing greater government guarantees, such as by increasing limits in the deposit insurance ceiling or extending coverage to uninsured debtholders, is a way of improving incentives for the bank to exert e¤ort since it raises the margin between its payo¤ conditional on success and its repayment to depositors, thus making it more willing to exert more e¤ort in monitoring. The overall e¤ect of government guarantees on bank’s monitoring e¤ort thus depends on the fraction of debt that is priced at the margin. The proposition also highlights that the “mortal sin” that has been ascribed to the introduction of deposit insurance, namely greater moral hazard, is highly dependent on the fact that, in the absence of deposit insurance, bank creditors can price their claims in a way that is responsive and reacts to the bank’s risk choices. Otherwise, even if these claims are priced correctly to re‡ect risk taking, o¤ering a government guarantee does not introduce a distortion, and indeed it helps alleviate those moral hazard problems that stem from limited liability.

Given much of the recent discussion concerning the role of bank capital in controlling risk taking and absorbing losses when those materialize, it is useful to study how the degree of capitalization 8
a¤ects a bank’s optimal reaction to greater deposit insurance coverage. Since the focus here is on controlling risk taking that may be induced by the introduction of a government guarantee, we consider the case where � = 1, so that the distortion in favor of great risk taking induced by deposit insurance is maximized. Given the equilibrium level of monitoring q<sup>�</sup> speci...ed in (5), for � = 1, that is, when all depositors price risk correctly at the margin, we have q<sup>�</sup> =<sup>R�(1</sup> c<sup>�k)</sup> <u>r�</u> , so that increases in � clearly decrease monitoring, or in other words lead to more risk taking:<sup>d</sup> d�<sup><u>q�</u>=�(1�</sup> c<sup>k)</sup> <u>r</u> < 0. Consider now an increase in bank capital k. This will have two e¤ects. First, more bank capital will reduce risk-taking, by increasing the bankers’“skin in the game,”<sup>d</sup> dk<sup><u>q�</u>> 0.Second,it will have</sup> d<sup>2</sup> <u>q</u><sup>�</sup> <u>r</u> the following marginal e¤ect: dkd�<sup>=</sup> c<sup>> 0.Inotherwords,anincreaseinkattenuatesthee¤ect</sup> of an increase in �, and helps control the moral hazard problem induced by the introduction of deposit insurance. It bears emphasizing, however, that capital is only needed to play this role when large guarantees, such as a comprehensive deposit insurance, lead bank to take on too much risk. Instead, when �, the fraction of uninsured deposits that price risk at the margin, is lower, deposit insurance leads to better incentives for the bank and thus to lower risk taking, so that there is less need to use capital to provide a countervailing e¤ect.

Other instruments: it is useful to note that the e¤ects identi...ed here, which stem from the “pricing at the margin” of debt instruments, are distinct from other mechanisms, which have also been recently proposed as e¤ective ways to reduce bank risk taking and protect other claimholders at the bank. A salient example is the use of contingent convertible bonds–“cocos”–that has been much discussed recently, and which has been touted as an e¤ective way of dealing with undercapitalized banks that may need additional capital exactly when they are in a downturn, having amassed losses (or potential losses) that reduced their capitalization. In our model, introducing cocos would have little e¤ect unless the bond part of the coco, to be repaid in “good times,”when the bank’s project is successful (i.e., with probability q), has an interest rate which itself prices the bank’s risk correctly at the margin. If the interest rate is ...xed up-front however, as for the fraction 1 � � of uninsured debt in our base model, then the same risk taking incentives as above arise. In the bad state, when the bank’s projects fail to pay o¤, the cocos would convert into equity, but since the bank is defaulting anyway in that case, such conversion would also have no incentive e¤ects.<sup>6</sup>

> 6 It would, however, reduce the burden on the deposit insurance fund.

9
This discussion suggests that the use of such instruments as cocos may be particularly valuable when the primary purpose of capital is to create a bu¤er that acts as a ...rst backstop against losses. But, in order to be useful when the primary concern is bank moral hazard, cocos are subject to the same conditions as standard bonds: they need to be priced at the margin. When this does not happen, the solution may require increasing the payo¤ of the bank in the good states of the world, rather than decreasing it in the bad states.

# 4 Endogenous information disclosure

In the previous section, we assumed that an exogenous fraction � of uninsured debt was priced at the margin. However, given its importance, a bank may like to exert some control over this fraction, if at all possible. In that case, the existence of government guarantees is likely to a¤ect also this aspect of a bank’s behavior. For instance, if debt pricing relies on information disclosure and information disclosure is costly, government guarantees will reduce the bene...ts (to the bank) from disclosure. Put di¤erently, when information disclosure is endogenous, a greater probability of bailouts may entail an additional form of moral hazard. In this section, we examine this issue.

We allow the bank to choose � by paying a cost<sup><u>1</u></sup> 2<sup>'�2beforedecidingonthemonitoringe¤ort</sup> q. One may therefore interpret � as the degree of transparency of the bank’s balance sheet, with greater transparency being more costly for the bank. � may also represent the fraction of debt to which the bank agrees to o¤er pricing that is risk sensitive, and thus it is contingent on how much risk is actually chosen.

Note that it need not be that the bank faces an actual cost associated with transparency, but rather that more transparent investments may earn lower returns than those the bank could earn by investing in more specialized but also more opaque projects.<sup>7</sup> Solving by backward induction, the problem of the bank can be written as:

> 7 One could also imagine that investors/depositors can make investments in information acquisition about the bank, or in monitoring the bank, and such decisions may well interact with the bank’s decision of how much transparent to make its balance sheet. We abstract from such considerations here in order to focus purely on the bank’s incentives to both disclose and monitor its portfolio.

10
where q<sup>�</sup> is given by expression (5). Such a set-up allows us to study how an increase in the cost of transparency ' a¤ects the relation between the degree of government guarantees and the bank’s monitoring e¤ort. Now consider the following Lemma: Lemma 1 The individually optimal proportion of debt liabilities priced at the margin, �<sup>b</sup> , is decreasing in the degree of government guarantees, �.

# Proof : See Appendix.

This lemma establishes that once the fraction � of liabilities priced at the margin is under the control of the bank, the promise of government guarantees entails an additional moral hazard problem. Since, in our setup, information disclosure is costly, banks will choose a lower level of disclosure when the bene...ts associated with pricing risk at the margin are reduced. Indeed, it is immediate that when � = 1, the ...rst order conditions from (7) will imply �<sup>b</sup> = 0. Note, however, that this does not mean that with � endogenous an increase in government guarantees always implies an increase in bank risk taking (a decline in q<sup>�</sup> ). As for the case with � exogenous, the e¤ect of greater guarantees on risk taking will depend on the balance of their moral hazard (now including their impact on �<sup>b</sup> ) and their “charter value”e¤ects. We demonstrate this in the following proposition.

Proposition 2 There exists a <u>'</u> such that for ' > <u>'</u> a bank’s monitoring e¤ort is always increasing in the degree of government guarantees, �:

# Proof : See Appendix.

The proposition establishes that more generous government guarantees (e.g., a comprehensive deposit insurance) decrease bank monitoring and lead to more risk taking, as it has often been argued, only when the cost of disclosure, or transparency, is relatively low. The intuition is similar to that for Proposition 1: when the cost of transparency ' is low, the bank will optimally choose to disclose a lot of information, implying that � will be high. In that case, as shown in Proposition 1, increases in � will lead to a reduction in monitoring e¤ort by the bank. Conversely, when ' is relatively high, the bank ...nds disclosure too onerous and will choose a low level of transparency �. In that case, increasing government guarantees is good for incentives and leads the bank to exert more monitoring e¤ort. Put di¤erently, since there is little pricing at the margin anyway, the 11
promise of bailout does not entail much moral hazard and the value e¤ect through bank pro...tability prevails.

The threshold level of the cost of transparency below which risk taking increases in � can be solved for explicitly, and is given by It is useful to study how such a threshold varies with di¤erent characteristics of the market, such as the level of capital for a bank, the marginal cost of bank e¤ort/reduced risk taking. We state the comparative statics of the threshold <u>'</u> as the following corollary, which follows directly from di¤erentiating (8) with respect to the c, k, and <u>r:</u> Corollary 1 Comparative statics: The threshold level of the cost of transparency to the bank, <u>',</u> is decreasing:

1. in the bank’s marginal cost of monitoring, c:

2. and in the bank’s degree of capitalization, k: From (9), it follows that the condition for government guarantees to reduce the riskiness of the bank’s portfolio get less stringent when agency problems become more severe (the cost of bank monitoring c increases). This re‡ects the fact that, when e¤ort by the bank to control risk taking is more costly, in equilibrium, the bank will exert less e¤ort and take more risk, all things equal. As a result, there is greater value in aligning the bank’s incentives with what is socially bene...cial, hence the threshold value <u>'</u> decreases.

The second part of the corollary, (10), implies that<sup>8</sup> the higher the bank capital is, the more likely it is that guarantees such as deposit insurance reduce risk taking incentives. The intuition here is that �<sup>�</sup> is decreasing in k, as the bene...ts from disclosure decrease with the proportion of liabilities that is priced at the margin (with and without disclosure). This means that, for higher

> 8 Remember that from (A.1), c > R.

12
values of k, the decrease in � caused by higher guarantees is smaller, and thus the moral hazard e¤ect is also smaller.

# 5 Insuring debt versus bailing out shareholders

In our analysis so far, we have focused on government guarantees that bene...t debt holders (e.g., depositors) but do not extend to shareholders. The primary reason for doing so has been to narrow our analysis to the debate concerning how policies like deposit insurance or the extension of guarantees to other (subordinated) bondholders may distort bank incentives and lead to increased risk taking by attenuating the channel of “debtholder discipline.” In practice, however, concerns have also been voiced that government intervention to provide funds to investors may also accrue to the bene...t of shareholders, bailing them out along with depositors when the bank su¤ers losses. For instance, by preventing a bank from going into liquidation, a rescue package may preserve its long term charter value. Essentially, the concern is that often rescue packages end up leaving signi...cant “crumbs on the table”for banks’shareholders and management.

Such a bailout can be easily incorporated into the current framework and it is easy to show that this kind of component of a rescue package is unequivocally bad for incentives.

Consider the case where shareholders/managers also obtain some bene...t whenever government guarantees protect debt holders and depositors. This means that in default states there is the same probability � that shareholders will receive a payo¤ A. For instance, a bailout may allow bank shareholders to recover a fraction of their equity, so that A = �rEk, with � � 1. In that case, pro...ts are Maximizing (11), we obtain and, as usual, after imposing rD = Er[<sup>�</sup> qb]<sup>,weget</sup> 13
Comparing equation (13) with (5), it is immediate to verify that bailing out management/ shareholders is bad for incentives, for any �> 0. Note, however, that if government guarantees cannot easily be targeted to depositors/debt-holders only (so it is more like a bailout for political reasons rather than a pure guarantee on deposits), then there are two o¤setting e¤ects: the bailout probability � reduces rD, which is good for incentives, but increases the payo¤ to shareholders in the default state, which is bad for incentives. If A is small, then the pro incentive e¤ect will still dominate, whereas if A is large, the moral hazard e¤ect will.

The result in this section is not surprising: A bailout of shareholders/managers amount to insuring the informed party against a risk that it fully controls.<sup>9</sup> The implication is that rescue packages should be designed in a way that minimizes this e¤ect (with small A). Provisions to wipe out existing shareholders and replace a bank’s top management and board following a bailout would go in this direction.

# 6 Endogenous leverage

So far, we have treated the bank’s liability structure (its debt/equity mix) as exogenous. In this section, we relax that assumption and consider how government guarantees a¤ect a bank’s leverage. We add to the model an initial stage in which banks choose their level of capital, k, which is then observed by debtholders/depositors. Then, capital functions as a commitment device. Since k is observable, it informs debtholders/depositors’expectations about a bank’s risk taking and debt is priced accordingly. Formally, rD = E[rqb<sup>�</sup> jk]<sup>; and sinceqb decreases with leverage, higher capital implies</sup> a lower interest rate on uninsured debt liabilities. This e¤ect is countered by the fact that, as in most of the literature, we assume that capital is expensive (that is it requires a premium over debt). Formally, we assume a risk-adjusted constant equity premium so that rE = <u>r+q �</u><sup>:Forsimplicity,in</sup> this section, we will treat the proportion of debt priced at the margin, �, as exogenous. Expected pro...ts can be written as:

> 9 This is di¤erent from what happens when public guarantees insure banks against risks that they cannot control. In that case, strengthening the charter value of a bank can be bene...cial for incentives (see Cordella and Levy-Yeyati, 2003, and Dell’Ariccia and Ratvnoski, 2015).

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We solve the model by backward induction. The second stage remains identical to what we discussed in section 3. The equilibrium values of q and rD can be expressed as a function of k as in equations (5) and (6); from which it is immediate that<sup>@</sup> @k<sup><u>q�</u>>0and@r</sup> @kD<sup>�<0:Ifwesubstitute</sup> these equilibrium values into the expected pro...ts expression and take the ...rst order conditions with respect to k; we obtain: where<sup><u>@</u></sup> @q<sup><u>�</u></sup> @k@q<sup>= 0fromtheenvelopetheorem.Aftersomeplumbing,thiscanbewrittenas</sup> the solution to this equation gives<sup>b</sup> k: We can now state the following result.

Proposition 3 An increase in the share of debt liabilities priced at the margin, �; decreases a bank’s individually optimal level of capital,<sup>b</sup> k .

# Proof : See Appendix.

The intuition for this result is straightforward. In this model capital is costly, but it provides the bank with a commitment/signalling device to show that it behaves “prudently.”More capital increases a bank’s equilibrium monitoring, since shareholders price risk at the margin. Formally, a higher k means higher E[qbjk]; and thus a lower cost of debt. As � increases, a greater portion of the mass 1 � k of debtholders also prices risk at the margin, reducing the pro monitoring e¤ect of replacing debt with equity. Put di¤erently, since a larger portion of debtholders/depositors observes b b q directly, the bene...t from being able to a¤ect E[qjk] decreases. Indeed, note that for � = 1; the bank obtains no bene...t from holding capital and the model only admits a corner solution with b k = 0: Government guarantees have a similar e¤ect, although for slightly di¤erent reasons.

Proposition 4 An increase in the share of debt liabilities covered by guarantees, �; decreases a bank’s individually optimal level of capital,<sup>b</sup> k .

Proof : See Appendix.

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The proposition establishes that, irrespectively of the portion of debt liabilities priced at the margin, an increase in government guarantees will lead banks to increase leverage (decrease k). The intuition for this result is similar to that for the result above. The bene...t to the bank from holding more capital is that, by increasing the expected probability of bank solvency, E[qbjk]; it reduces the rate paid on liabilities that are not priced at the margin, rD. More government guarantees imply that a larger proportion of those liabilities pays the ...xed risk-free rate independently from the level of bank capital; this reduces the incentive to hold capital.

The question that arises from this proposition is whether the impact of bailout expectations on bank leverage is su¢ ciently strong to imply an unequivocal net e¤ect on bank risk taking. Remember that, in this model, more levered banks take more risk, since limited liability is at the core of our agency problem. Indeed, it is immediate from equation 3 that, for any �< 1; @k<sup>@qb>0.</sup> Finally, numerical simulations suggest that: Claim 1 When a bank’s capital,<sup>b</sup> k; is endogenous, an increase in the share of debt liabilities covered by guarantees, �; unequivocally decreases the bank’s monitoring e¤ort q:b Proof : See Appendix.

This ...nding means that, when leverage is endogenous, more pervasive guarantees always lead to higher risk taking. Essentially, the additional channel of bank leverage tilts the balance of the e¤ects against bank monitoring.

The results in this section have important implications as they highlight the relationship between prudential regulation and resolution policies. First, note that when bank leverage is constrained by capital (or leverage) requirements, the result here applies only to the extent that banks hold capital well in excess of regulation. Once the constraint binds, the relevant framework is that with exogenous k: It follows that by imposing higher capital requirements regulators can extend the region for which bailouts improve bank incentives. At the same time, this means that the promise of bailouts is more detrimental to incentives for unregulated ...nancial intermediaries.

Second (and possibly more relevant in practice), the result that the individually optimal capital is decreasing in the probability of bailout suggests that banks will have greater incentives to circumvent capital regulation when bailout policies become more generous. In contrast, when the expectation of bailouts is low (such as, for instance, for hedge funds) intermediaries will tend to operate with lower levels of leverage.

16
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Baer and Brewer, 1986, Goldberg and Hudgins, 1996, Calomiris and Wilson, 1998, Flannery and Sorescu, 1996; for Argentina, Chile and Mexico, see Martinez Peria and Schmukler, 2001).

Yet, the fact that depositors tend to leave troubled banks and/or demand higher risk premia when a bank is in distress does not necessarily imply that depositors are able to discipline e¤ectively bank managers’behavior. This important point was raised ...rst by Bliss and Flannery (2001), who distinguish between the monitoring and the in‡uence aspect of market discipline. When they refer to (market) monitoring, they point to investors’ability to understand the ...nancial condition of a ...rm; when they refer to (market) in‡uence they point to investors’ability to a¤ect managerial actions and, ultimately, to align them with their own interests. With this important distinction in mind, they then look at a panel of large US bank holding companies, those for which one expects market discipline to hold, and they ...nd scant evidence of investors’in‡uence.

Actually, the distinction between the monitoring and the in‡uencing aspects of market discipline can be better understood as a distinction between ex-post and ex-ante discipline (Bliss, 2004). Expost discipline comes as a response to a managerial action, such as the withdrawal of deposits from a bank in a situation of ...nancial distress; ex-ante discipline, instead, constrains managers’action by making it costly to act in a way that is not aligned with (in our case) debtholders’objectives. In our model, when depositors observe the bank’s portfolio choice, risk is priced directly in the deposit rate and we have ex-ante discipline; when risk is non observable or, for various reasons, not contractible, discipline is necessarily ex-post. Such a distinction is very useful when interpreting some of the recent ...nancial crises.

Stephanou (2010), for instance, looks at the price of di¤erent instruments issued by some of the banks more exposed to mortgage instruments (Citigroup, Bear Stearns, and Lehman Brothers) in the period preceding the explosion of the sub-prime crisis in the US. His main ...nding is that the prices of these instruments only began to decline (vis-à-vis a market benchmark) in the second half of 2007, and went deep south only after Bearn Stearns’collapse. In other words, the market started to price in exposure to risky asset well after banks undertook such investments. Figure 6 plots the CDS spreads for ...ve major US banks in the run-up to the global ...nancial crisis. It is evident that until late 2007 markets did not discriminate across banks which then performed very di¤erently during the crisis. Further, while one could argue that the absence of discrimination may have been the result of an expected bailout, this hypothesis seems contradicted by the fact that late in 2007 and more in 2008 bank CDS started diverging dramatically.

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It is also important to notice that information disclosure is not enough to guarantee market discipline. Freixas and Laux (2012) argue that the latter requires that information e¤ectively reaches the market and is adequately processed and used. In their view, in the period that preceded the global ...nancial crisis, the lack of market discipline was not the consequence of insu¢ cient disclosure but of market participants’lack of incentives to process it.

With such distinctions clear in mind, we are now in a position to look at the recent literature on the e¤ects of government guarantees on bank risk taking behavior. Not surprising, this evidence is mixed, too. In Germany, Gropp et al. (2014) show that the unanticipated removal of saving banks’ government guarantees, because of a court decision, led to a reduction in credit risk; Dam and Koetter (2012), using political factors to identify the causal e¤ect of bank bailouts on risk taking, also ...nd economically signi...cant positive e¤ects. Conversely, looking at the bailout of distressed banks, Berger et al. (2016a) ...nd that capital support was conducive to a reduction both in lending and in risk taking.

There is also a large and growing literature trying to ascertain whether the Troubled Asset Relief Program (TARP) in the US was successful in reducing systemic risk by providing, among other things, an “upside” to banks, or whether it increased risk taking incentive because of the moral hazard it generated. Again, the evidence is mixed: Duchin and Sosyura (2014) show that bailedout banks tend to be riskier, even if such an increase in risk may not be perceived by regulators;<sup>12</sup> Schenk and Thornton (2016), instead, indicate that TARP bailouts are likely to increase risktaking in “weak”institutions (low charter values and high leverage) and to decrease it in “strong” institutions (high charter values and low leverage). Finally, using a di¤-in-di¤ strategy, Berger et al. (2016b) also show that TARP contributed to the reduction in systemic risk and that such a reduction has been stronger for larger, safer banks, in states with better economic situations.

The crisis also o¤ered natural experiments to look into the pricing behavior of bank investors. Data on banks’sovereign debt holdings disaggregated by bond issuer are not generally available. However, the EBA released detailed bank-level information when it announced the results of its stress tests. And evidence suggests that this had an impact on banks’CDS spreads. The table below (from Dell’Ariccia et al. 2016) shows that banks that were found to hold larger amounts of distress sovereign bonds on their balance sheets experienced a sharper increase in CDS spreads and drop in stock returns. This evidence is not consistent with the notion that investors price risk at

> 12 Because it occurs in the same asset classes and thus does not a¤ect the CAR.

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the margin; in particular, since the stress tests revealed new information about bank holding, but little news about the underlying quality of those securities.

|**Impact of banks’ exposure togovern**|**ment debt**<br>|**on stock**<br>|**and CDS**<br>|**marketpe**<br>|**rformance**<br>|
|---|---|---|---|---|---|
||(1)|(2)|(3)|(4)|(5)|
|*|Banks'|stock market|returns|***<br>Banks' CD|***<br>S spreads|
|Sovereign CDSDomestic sovereign exposure|-1.664***|-1.782***|-1.690***|0.159|0.115|
||(0.396)|(0.425)|(0.401)|(0.062)|(0.047)|
|Domestic sovereign exposure (% assets)|-0.009||0.003|0.443*|0.596***|
||(0.038)||(0.040)|(0.266)|(0.183)|
|Sovereign CDS|-0.177***|-0.182***|-0.186***|0.041***||
||(0.035)|(0.037)|(0.035)|(0.005)||
|Bank FE|Yes||Yes|Yes|Yes|
|Country FE|Yes|Yes||Yes||
|Year||||Yes||
|Year-month FE|Yes|||||
|Bank-year-month FE||Yes||||
|Country-year-month FE|||Yes||Yes|
|Number of countries|12|12|12|5|5|
|Number of banks|33|33|33|29|29|
|Observations|1,468|1,468|1,468|1,849|1,849|
|R-squared|0.234|0.305|0.273|0.60|0.66|

Notes: In columns 1-3 the dependent variable is the bank’s stock market return and the sample contains 33 domestic banks from 12 euro area countries. The data are pooled over EBA stress test release periods, where each period includes the day of data release and the subsequent 10 trading days, during Mar 2010-Dec 2013. Regressions are run at the bank-trading day level. “Domestic exposure” is the ratio of the bank’s total holdings of domestic sovereign bonds to the bank’s total assets. “Sovereign CDS” is the log-difference of daily CDS spreads on a 5-year government bond. In columns 4-5 the dependent variable is the bank’s CDS spread and the sample includes 29 domestic banks in Greece, Ireland, Italy, Portugal, and Spain. Regressions are run at the bank-month level. The time period is Aug 2007-Jun 2013. “Sovereign CDS” is the maximum CDS spread on a 10-year sovereign bond during the month. “Domestic exposure” is the ratio of the bank’s total holdings of domestic sovereign bonds to the bank’s total assets (divided by 1000). A constant term is included (coefficient not shown). Standard errors clustered at the bank level appear in parentheses, where *** indicates significance at the 1% level, ** at the 5% level, and * at the 10% level. Sources: ECB Individual MFI Balance Sheet Statistics, European Banking Authority, Bankscope, Bloomberg, SNL Financial, and Datastream.

# 9 Discussion and conclusions

This paper reexamines the theoretical relationship between the expectation of a government bailout of bank debtholders (depositors and bondholders) and bank risk taking. After the Global Financial Crises, the regulatory policy debate has centered on how to make ...nancial institutions safer and more resilient to shocks. Within that debate, the classical argument that explicit (typically deposit insurance) or implicit (typically the expectation of a public bailout of bondholders) government guarantees on bank liabilities entail a moral hazard e¤ect that increases bank risk taking has played a prominent role. Yet, this argument critically relies on debtholders and depositors’ability to price bank risk at the margin. Put di¤erently, it requires the cost of bank liabilities to re‡ect changes in bank behavior. In contrast, absent this ability, the presence of government guarantees improves bank incentives by reducing the cost of their liabilities and hence increasing their charter value.

24
The simple model in this paper highlights these e¤ects. It shows that, when the proportion of bank debt-holders that can price risk at the margin is su¢ ciently high, the classical moral hazard argument holds. But when it is relatively low, the charter value e¤ect dominates. The model also shows that when banks can choose (at some cost) how much information to disclose and, hence, the proportion of liabilities priced at the margin, government guarantees entail an additional form of moral hazard. They tend to reduce the degree of disclosure. This tilts the balance in favor of the classical moral hazard e¤ect. Yet, when the cost of disclosure is su¢ ciently high, the charter value e¤ect still prevails. The model also ...nds that the balance between the moral hazard and charter value e¤ects is likely to vary across banks and with economic conditions.

Finally, the model shows that when bank capital is endogenous, public guarantees may lead to an increase in bank leverage and an associated increase in risk taking, an additional form of moral hazard. In that context, the model suggests that e¤ective capital regulation and limits on leverage may avoid some of the negative e¤ects of government guarantees and bailout expectations and increase the policy space on that front. This also means that government guarantees are much more problematic for institutions without leverage regulation.

The model of course has limitations. First, a multi-period could provide a more complex view of information disclosure. For instance, over time, investors could infer a bank’s portfolio position from its pro...tability and price its debt accordingly. Yet, as long as banks where able to adjust their portfolio “often enough,”absent information disclosure, investors would not be able to price risk at the margin (exactly as in our one-period model). From this perspective, our parameter capturing the proportion of a bank’s liabilities that are priced at the margin could be reinterpreted in a multiperiod setting to capture the portion of a bank portfolio that cannot be easily readjusted.

Second, the model does not make a distinction between deposits and other debt-like liabilities. Yet, we believe our distinction between informed and uninformed investors captures some of the characteristics of deposits versus debt. Indeed, in practice, the way government guarantees are designed can be seen as somewhat re‡ecting the ...ndings in our model. For instance, deposits are generally more protected than bonds, and small deposits are more protected than large ones. This partly re‡ect the desire to protect more vulnerable individuals, but it is also justi...ed with the assumption that informed bondholders and large depositors are more able to penalize excessive bank risk taking than less wealthy households.

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Recent regulatory reforms have aimed at minimizing the exposure of taxpayers to losses stemming from public interventions into banking systems and reducing the implicit subsidies associated with too-big-too-fail. New regulation has signi...cantly increased banks’loss absorption capacity by raising minimum capital requirements and imposing additional bu¤ers on systemic institutions. More critically (from this paper’s standpoint) reforms have aimed at tying the government’s hands in case of a crisis. In the US, the Dodd-Frank act included norms aimed at curbing the authorities’ability to inject public money into troubled ...nancial institutions. In the EU, the recently implemented BRRD (Bank Resolution and Recovery Directive) requires a bail-in of junior and subordinated debt of at least 8 percent of a bank’s total liabilities before public funds can be used.

These restrictions aim primarily at protecting taxpayers’ money, but were also informed, at least in part, by the desire to contain moral hazard associated with the expectation of government assistance. In light of the ...ndings in this paper, whether or not these measures will succeed in the latter objective depends on the degree with which bank risk is priced at the margin. From this standpoint, as discussed in the previous section, the empirical evidence on the matter is mixed. The paper also suggests that post-crisis reforms by reducing bank leverage have already reduced the moral hazard concerns associated with the expectation of government assistance, and have created policy space for more “generous” guarantees. However, our ...ndings also stress that providing (implicit or explicit) guarantees to unregulated entities is likely to result in moral hazard through the e¤ect they will have on agents’ability to lever up. A coherent design of prudential regulation, resolution policies, and the ...nancial safety net is, then, critical.

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