S. Tian et al Jourmal of Banking 8 Finance 37(2013)2765-2778 Investment =B+S Shock Fig. 1. Investment and cash flow for Project G capital requirement after the banks take action such as liquidating or able to bailing out failed banks because it induces banks to differentiate taking over the assets associated with the failed bank. theirrisks. Kashyapet al (2008) propose replacing capital requirements Second, using the inventory buffer model of bank capital to study by mandatory capital insurance policy so that banks are forced to hoard contagion allows us to model banks' precautionary risk management liquidity Chari and Kehoe(2010) show that regulation in the form of behaviors before crisis happens. Banks' optimal capital holding prior ex-ante restrictions on private contracts can increase welfare while to the crisis is endogenously determined. Within the inventory ex-post bailouts trigger a bad continuation equilibrium of the policy framework, the bank manages inventory reserves in order to cope game. Farhi and Tirole(2012)propose a model that banks choose tocor vith uncertain outcomes. If the bank has sufficient inventory re- relate their risk exposures in anticipation of imperfectly targeted gov serves to take over the joint assets of other banks, the failure of ernment intervention to distressed institutions. one bank does not necessarily lead to contagion. So when the risk Our study is closely related to Philippon and Schnabl(2013) of failure of other banks is properly understood, the possibility of who analyze public intervention choices(buying equity, purchas contagion in the inventory setup becomes relatively remote Govern- ing assets, and providing debt guarantees) to alleviate debt over ment bailout is not always necessary if a bank can internally cope hang among private firms. They find that with asymmetric with potential contagion arising from asset linkages. information between firms and the govern buying equity An alternative is the conventional approach in which a bank cap dominates the two other interventions. we also consider bailou ital is a continuously binding constraint, similar to a household bud with equity injection, but our study further shows that common et or a firm s feasible production set. with this approach, one banks stock bailout is preferable ex ante to preferred equity bailout be- takeover of another bank,s assets is impossible because this would cause it induces banks to target for a higher level of capital holding violate the binding capital requirement. Liquidation of a joint project and thus reduces the government bailout budget. is the only possible outcome. If the bank invests a large share of assets in the project and the loss ratio is high, the failure of one bank leads Acharya et al. (2010)that government support to surviving banks directly to the failure of its partner banks in a joint project. In order conditional on their liquid asset holdings increases banks' incen- to prevent such interbank contagion, it is necessary for the govern- tive to hold liquidity, and that support to failed banks or uncondi- ity of continuing the joint project without government intervention. their study stresses the role of banks'asset composition, our focus Hence contagion becomes excessively mechanical in the conven- is the role of banks' capital holdings in anticipation of common tional set-up, which is inherently biased towards government bailout. stock or preferred equity bailout. Third, our paper adds to the bailout literature by explicitly examin- The rest of the paper is organized as follows. We ing how government bailout policy (injection of common equity versus benchmark model setup in Section 2 In Section 3, we provide the ba preferred equity)affects banks' ex ante capital buffer and possibilities sic accounting analysis to examine when interbank contagion may interbank contagion, and how banks' capital holding prior to the cri- emerge due to a failure of a partner bank In Section 4 we derive the is, in turn, affects the level of government bailout. Earlier studies have solution for a banks optimal capital-asset ratio prior to the crisis for addressed whether, when, and how to bail out a bank. Our study com- dealing with a partner banks potential failure in anticipation of gov- plements the literature by providing a case for why a bailout is not al- ernment intervention. Section 5 shows simulation results for the rela- ways necessary to help a healthy bank survive contagion. tionships between a number of public policy and banks' investment Spurred by the recent financial crisis, there is a growing literature parameters and the level of ex-ante capital holding, possibility of con- on bank bailouts. Acharya and Yorulmazer(2008)point out that tagion, and government bailout amounts. Section 6 concludes granting liquidity to surviving banks to take over failed banks is prefer 2. The model related to earlier work stu g bank behavior under ca uirement constraints. Diamond and Rajan(2000) argue that the optimal bank In this section, we set up a framework to describe how a bank pital structure reflects a tradeoff between the effects of bank capital on liquidity determines its optimal capital-ass that banks eation, the expected costs of bank distress, and the default risk of borrowers. Bolton maintain a buffer of capital that exce set ratIo and Freixas(2006)posit that bank lending is constrained by capital adequacy in order to reduce the potential future costs of ity and recap- hubbard et al.(2002)find that banks that maintain more capital charge italization and the contagion effects of failure of its partner bank. nterest rate on loans. Jokipii and Milne(2008)show that capital buffers of the banks in the eu15 have a significant negative Co-movement with the cycle, which exacerbates the pro-cyclical impact of Basel cation as a capable monitor could distort bank closure policy. dreyfus assume that a banking group enter into a syndicated loan surance coverage is optimal. Rochet and Tirole(1996)derive the optimal prudential agreement to finance part of an investment, B, in an indivisible Pro- conducting undesired rescue opera- ject G Financing for the rest of the project, S, is obtained by issuing ons. Gale and vives(2002)argue that a bail out should be restricted ex ant equity or debt, or comes from other sourc oral hazard concerns. Gorton and Huang(2004 )show that the government bailout Ject G is bein rovides more effective liquidity than private investors. Diamond See the review of theoretical literature by philippon and Schnabl(2013),w that the market is perfect and that the financing metho al work on bailouts such as giannetti and simonov ailable for rest of the investment do not affect the cash flow of project g or the 011 Glasserman and Wang(2011). returns on investment B that the banking group receives.capital requirement after the banks take action such as liquidating or taking over the assets associated with the failed bank. Second, using the inventory buffer model of bank capital to study contagion allows us to model banks’ precautionary risk management behaviors before crisis happens. Banks’ optimal capital holding prior to the crisis is endogenously determined. Within the inventory framework, the bank manages inventory reserves in order to cope with uncertain outcomes. If the bank has sufficient inventory re￾serves to take over the joint assets of other banks, the failure of one bank does not necessarily lead to contagion. So when the risk of failure of other banks is properly understood, the possibility of contagion in the inventory setup becomes relatively remote. Govern￾ment bailout is not always necessary if a bank can internally cope with potential contagion arising from asset linkages.5 An alternative is the conventional approach in which a bank’ cap￾ital is a continuously binding constraint, similar to a household bud￾get or a firm’s feasible production set. With this approach, one bank’s takeover of another bank’s assets is impossible because this would violate the binding capital requirement. Liquidation of a joint project is the only possible outcome. If the bank invests a large share of assets in the project and the loss ratio is high, the failure of one bank leads directly to the failure of its partner banks in a joint project. In order to prevent such interbank contagion, it is necessary for the govern￾ment to inject equity in other banks. However, this omits any possibil￾ity of continuing the joint project without government intervention. Hence contagion becomes excessively mechanical in the conven￾tional set-up, which is inherently biased towards government bailout. Third, our paper adds to the bailout literature by explicitly examin￾ing how government bailout policy (injection of common equity versus preferred equity) affects banks’ ex ante capital buffer and possibilities of interbank contagion, and how banks’ capital holding prior to the cri￾sis, in turn, affects the level of government bailout. Earlier studies have addressed whether, when, and how to bail out a bank.6 Our study com￾plements the literature by providing a case for why a bailout is not al￾ways necessary to help a healthy bank survive contagion. Spurred by the recent financial crisis, there is a growing literature on bank bailouts.7 Acharya and Yorulmazer (2008) point out that granting liquidity to surviving banks to take over failed banks is prefer￾able to bailing out failed banks because it induces banks to differentiate their risks.Kashyap et al. (2008)propose replacing capital requirements by mandatory capital insurance policy so that banks are forced to hoard liquidity. Chari and Kehoe (2010) show that regulation in the form of ex-ante restrictions on private contracts can increase welfare while ex-post bailouts trigger a bad continuation equilibrium of the policy game. Farhi and Tirole (2012) propose amodel that banks choose to cor￾relate their risk exposures in anticipation of imperfectly targeted gov￾ernment intervention to distressed institutions. Our study is closely related to Philippon and Schnabl (2013), who analyze public intervention choices (buying equity, purchas￾ing assets, and providing debt guarantees) to alleviate debt over￾hang among private firms. They find that with asymmetric information between firms and the government, buying equity dominates the two other interventions. We also consider bailout with equity injection, but our study further shows that common stock bailout is preferable ex ante to preferred equity bailout be￾cause it induces banks to target for a higher level of capital holding and thus reduces the government bailout budget. Our results on bailout policy also complement the findings of Acharya et al. (2010) that government support to surviving banks conditional on their liquid asset holdings increases banks’ incen￾tive to hold liquidity, and that support to failed banks or uncondi￾tional support to surviving banks has the opposite effect. While their study stresses the role of banks’ asset composition, our focus is the role of banks’ capital holdings in anticipation of common stock or preferred equity bailout. The rest of the paper is organized as follows. We introduce our benchmark model setup in Section 2. In Section 3, we provide the ba￾sic accounting analysis to examine when interbank contagion may emerge due to a failure of a partner bank. In Section 4 we derive the solution for a bank’s optimal capital-asset ratio prior to the crisis for dealing with a partner bank’s potential failure in anticipation of gov￾ernment intervention. Section5 shows simulation results for the rela￾tionships between a number of public policy and banks’ investment parameters and the level of ex-ante capital holding, possibility of con￾tagion, and government bailout amounts. Section 6 concludes. 2. The model In this section, we set up a framework to describe how a bank determines its optimal capital-asset ratio, assuming that banks maintain a buffer of capital that exceeds the regulatory requirement in order to reduce the potential future costs of illiquidity and recap￾italization and the contagion effects of failure of its partner bank. 2.1. One project We assume that a banking group enter into a syndicated loan agreement to finance part of an investment, B, in an indivisible Pro￾ject G. Financing for the rest of the project, S, is obtained by issuing equity or debt, or comes from other sources.8 Project G is being Cash flow t = 0 t =∞ Shock t =T Investment =B+S Fig. 1. Investment and cash flow for Project G. 5 Our paper is also related to earlier work studying bank behavior under capital requirement constraints. Diamond and Rajan (2000) argue that the optimal bank capital structure reflects a tradeoff between the effects of bank capital on liquidity creation, the expected costs of bank distress, and the default risk of borrowers. Bolton and Freixas (2006) posit that bank lending is constrained by capital adequacy requirements. Hubbard et al. (2002) find that banks that maintain more capital charge a lower interest rate on loans. Jokipii and Milne (2008) show that capital buffers of the banks in the EU15 have a significant negative co-movement with the cycle, which exacerbates the pro-cyclical impact of Basel II. 6 For example, Boot and Thakor (1993) model that a desire for the regulator to acquire a reputation as a capable monitor could distort bank closure policy. Dreyfus et al. (1994) discuss whether the setting of ceilings on the amount of deposit insurance coverage is optimal. Rochet and Tirole (1996) derive the optimal prudential rules while protecting the central banks from conducting undesired rescue opera￾tions. Gale and Vives (2002) argue that a bail out should be restricted ex ante due to moral hazard concerns. Gorton and Huang (2004) show that the government bailout for banks in distress provides more effective liquidity than private investors. Diamond and Rajan (2005) propose a robust sequence of intervention. 7 See the review of theoretical literature by Philippon and Schnabl (2013), who also discuss several recent empirical work on bailouts such as Giannetti and Simonov (2011), Glasserman and Wang (2011). 8 Given that our main research objective is not designing the capital structure for Project G, we assume that the market is perfect and that the financing methods available for rest of the investment do not affect the cash flow of Project G or the returns on investment B that the banking group receives. S. Tian et al. / Journal of Banking & Finance 37 (2013) 2765–2778 2767