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Liquidity, capital requirements, and shadow banking
International Review of Economics and Finance xxx (xxxx) xxx
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International Review of Economics and Finance journal homepage: www.elsevier.com/locate/iref
Liquidity, capital requirements, and shadow banking Zehao Liu a, Chengbo Xie b, * a b
School of Finance, Renmin University of China, Beijing, China School of Finance, Southwestern University of Finance and Economics, Chengdu, China
A R T I C L E I N F O
A B S T R A C T
JEL classification: E58 G21 G28
We study the role of capital requirements in adjusting market liquidity. Liquidity is necessary as it prevents fire sales and suppresses the risk-shifting problem when a negative shock occurs. However, hoarding excessive liquidity is costly as it crowds out efficient investments. A capital requirement on commercial banks reduces deposit returns. This causes investors to allocate more resources to more efficient capital market investments, improving social welfare. However, an excessively high capital requirement is undesirable because the return from holding liquidity is so low that liquidity provision is insufficient to avoid risk-shifting behaviors. Shadow banks can bypass capital regulation, and strict capital regulation will drive money to shadow banks. Thus, a liquidity shortage emerges because shadow bank securities are less liquid than commercial bank deposits. Policy maker should implement lower capital requirements in the presence of shadow banks.
Keywords: Liquidity Capital requirements Shadow banking Inefficient liquidity hoarding Regulatory arbitrage
1. Introduction Capital requirements are an important policy instrument for the regulation of financial intermediaries. The argument as to whether capital requirements should be raised is persistent. After the global financial crisis, many economists and policy makers called for a substantial increase in bank capital requirements as capital requirements set upper bounds for bank leverage and reduce the probability of distress and insolvency. Basel III, which was agreed upon by the members of the Basel Committee on Banking Supervision and will be fully introduced in 2019, will significantly increase the capital requirements for banks. However, banks claim that the cost of capital requirements are high and oppose proposals to increase capital requirements (see, for example (American Bankers Association, 2012),). To determine optimal capital requirements, we need better knowledge concerning the benefits and costs of capital requirements. While existing literature mainly discusses the role of capital requirements in reducing the risk of bank investment portfolios, we show the role of capital requirements through the liquidity channel: capital requirements can suppress inefficient hoarding and reduce the excessive cost of liquidity. We extend the model in (Gorton & Huang, 2004). In an economy, there are two financial intermediaries — a commercial bank and a capital market — and many investors. Investors can deposit their money in the commercial bank, and the bank can then invest in risk-free assets that provide a non-zero fixed return.1 Investors can also invest in risky projects through the capital market. Bank debts (deposits) are more liquid than capital market securities. Then, only cash and deposits can be used to make payments. Similar to (Gorton & Huang, 2004), there is a moral hazard problem. When a negative shock to the project output occurs, the * Corresponding author. E-mail addresses: [email protected] (Z. Liu), [email protected] (C. Xie). 1 The assumption that commercial banks use deposits to buy risk-free assets is for simplicity. As long as bank assets are safer than capital market assets, all the results will hold. In reality, banks make loans to firms, which typically present less risk than stocks or derivative investments. https://doi.org/10.1016/j.iref.2019.11.019 Available online xxxx 1059-0560/© 2019 Published by Elsevier Inc.
Please cite this article as: Liu, Z., & Xie, C., Liquidity, capital requirements, and shadow banking, International Review of Economics and Finance, https://doi.org/10.1016/j.iref.2019.11.019
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investors who are managing the project cannot repay their loans. This motivates these investors to add risk to the project by gambling on a less likely high return. An inefficient risk-shifting problem emerges. In addition to adding risk, the investors whose projects suffered negative shocks can also sell their projects on the market. If these investors can obtain enough money to repay the loans from the transactions, they will not add risk. If risk is not added, the risky projects are ex ante more efficient than the risk-free assets. However, if risk is added, the risky projects are less efficient. On the condition that there is sufficient liquidity to prevent the addition of risk, a social planner will invest all the remaining money into risky projects. However, in this situation, if a negative shock occurs, the price of risky projects will be low, and the investors can obtain a high return from purchasing the projects in a fire sale. Thus, some investors are willing to hold more deposits at the beginning to exploit this possibility. This money hoarding behavior reduces allocation efficiency because, ex ante, liquidity that exceeds the necessary amount to prevent a moral hazard problem is less efficient than project investment. In this model, money invested in safe assets becomes the source of liquidity when the economic state is poor. Liquidity is necessary as it prevents fire sales and suppresses the risk-shifting problem when a negative shock occurs. However, hoarding excessive liquidity is costly as it crowds out efficient investments. Raising capital is expensive for commercial banks. Therefore, a capital requirement on commercial banks will reduce the return of deposits because banks are forced to raise more expensive capital and less money is allocated to depositors. Lower deposit rates will drive investors to make more capital market investments. Social welfare is thus increased. However, an excessively high capital requirement is also undesirable because the return on holding liquidity will be unduly low causing insufficient liquidity provision to avoid risk-shifting behaviors. This trade-off leads to an optimal capital requirement. The optimal capital requirement is achieved when project holders are indifferent between selling the projects and adding risk after the negative shock occurs. We then extend the model to consider shadow banking. Shadow banks perform a similar function as commercial banks by issuing safe assets to finance loans. Many previous studies agree that the growth of shadow banking has been largely driven by regulatory arbitrage, particularly the arbitrage of capital requirements (see, for example (Acharya, Schnabl, & Suarez, 2013; Gennaioli, Shleifer, & Vishny, 2013; Gorton & Metrick, 2010; Plantin, 2014; Pozsar, Adrian, Ashcraft, & Boesky, 2010),). In our model, shadow banks make the same type of investments as commercial banks; that is, buying risk-free assets, but shadow banks can circumvent the capital requirement regulation and thus can offer a higher return than commercial banks. However, shadow bank securities cannot be used to purchase risky projects. This assumption characterizes the fact that shadow bank securities are less liquid than commercial bank deposits. Money market mutual funds or wealth management products can be considered to be this type of shadow bank. These intermediaries raise money from investors and lend money to commercial banks through repo and other interbank lending instruments in a wholesale bank market. They conduct similar business to commercial banks but are largely not subject to capital requirements. By investing in shadow bank securities, investors enjoy a higher return compared to commercial banks, but they sacrifice liquidity.2 Then, if the capital requirement is moderate, the introduction of shadow banks will not change the allocation of the economy. This is because without shadow banks, the total return earned by the investors is higher than the return of shadow bank securities (risk-free rate); thus, investors will not deviate to invest in shadow banks. In contrast, if the capital requirement is high, commercial bank deposits and capital market investments will both shrink, which leads to a reduction in social welfare. The intuition is the following. Without shadow banks, the total return earned by investors is lower than the return from shadow bank securities (risk-free rate). This motivates investors to use shadow banks to bypass capital requirement regulations. Investors move money from commercial banks to shadow banks, and total market liquidity decreases. Lower amounts of liquidity reduces the fire sale price of risky assets leading to a reduction in capital market investment returns. Therefore, investors choose to invest less in the ex ante more efficient capital market investments, and social welfare decreases. Compared to the economy without shadow banks, policy maker should adopt a lower capital requirement when shadow banks exist. Otherwise, high capital requirements will drive money to the shadow banking sector. Commercial bank deposits are not attractive because they are subject to strict capital regulation. Capital market investments are not attractive either because liquidity is scarce and risk is added if negative shocks occur. In summary, the emergence of shadow banks undermines the role of capital requirements. In the absence of shadow banks, a large capital requirement is desirable. In contrast, in the presence of shadow banks, the same capital requirement may be detrimental because it causes the emergence of shadow banks. Therefore, policy maker should be more discreet and use large capital requirements in the presence of shadow banks. The contributions of the paper are as follows. First, we propose a new role for capital requirements; that is, to suppress costly liquidity hoarding and increase efficient investments. This role is persistent even in the absence of credit risks. Second, we show that shadow banks can undermine the role of capital requirements through liquidity. Shadow banks enable investors to obtain higher returns through regulatory arbitrage instead of taking efficient risks. Thus, efficient capital market investments decrease. Third, we show that in the presence of shadow banks, the optimal capital requirement should be reduced unless the shadow banks can be properly regulated. 1.1. Literature review Our paper is related to several strands of literature. The first strand addresses the role of capital regulations. The conventional role of capital requirements is to mitigate the moral hazard problem; that is, the excessive risk taking by equity holders. (See, for example
2 For example, when investors want to purchase other financial assets, they must first convert shadow bank securities to cash or deposits and then purchase other assets.
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(Hellmann, Murdock, & Stiglitz, 2000; Keeley, 1990),). However (Allen, Carletti, & Marquez, 2011), argues that banks are willing to hold capital in excess of regulatory minimums because costly capital financing serves as a better commitment device for monitoring than interest rate on loans (Kara & Ozsoy, 2016). studies a model in which banks with higher liquidity holdings lead to less severe decreases in asset prices during times of distress. This externality is not internalized by individual banks and, as a consequence, regulators must raise the minimum capital ratio requirement to inefficiently high levels. The role of the capital ratio in our view is similar to (Diamond & Rajan, 2000) and (Gorton & Winton, 2017) who posit that greater capital reduces the liquidity provision. However, in our model, this reduction improves social welfare since there is excess liquidity in private market equilibrium (the hoarding problem in (Gorton & Huang, 2004)). Our paper is also related to the literature on bank’s reaction to a change in capital regulation (Harris, Opp, & Opp, 2014). develops a model in which capital requirements for banks may be counterproductive. The authors show that under some conditions, increased competition may imply that increases in capital requirements cause more banks in the economy to engage in value-destroying risk-shifting (Plantin, 2014). shows that tightening capital requirements may spur a surge in shadow banking activity that leads to overall greater risk on the money-type liabilities of formal and shadow banking institutions. Our paper shows similar results as (Plantin, 2014) and that shadow banking activities will arise endogenously if capital requirements are too high. Empirically (Kisin & Manela, 2016), estimates the shadow cost of capital requirements using data on a costly loophole that allowed banks to relax these constraints. The authors find that increasing capital requirements would impose a modest cost (Gropp, Mosk, Ongena, & Wix, 2019). studies the impact of higher capital requirements and find that the banks that have stricter capital requirements imposed on them increase their capital ratios by reducing their risk-weighted assets, not by raising their levels of equity. The third strand discusses the benefits and costs of the shadow banking system. Shadow banks create money-type liabilities, which are useful in normal times but may lead to a serious crisis when a negative shock occurs (see (Gorton & Metrick, 2012; Krishnamurthy & Vissing-Jorgensen, 2012; Sunderam, 2015; Moreira & Savov, 2017; Gorton & Metrick, 2010)). We model the rise of shadow banks as a means of regulatory arbitrage documented by (Acharya et al., 2013; Plantin, 2014) and (Harris et al., 2014). (Plantin, 2014) shows that if shadow banks can bypass capital regulation, a higher capital requirement may drive more money to the shadow banking sector and lead to greater overall risk. In the author’s paper, capital regulation mainly takes effect through bank leverage while, in our paper, capital regulation mainly takes effect through liquidity provision (Moreira & Savov, 2017). also proves the negative macroeconomic consequences of the shadow banking sector. The authors emphasize the potential liquidity risk of shadow banking securities. However, in their paper, the risk exists because the market investors may produce information on the real value of shadow banking securities. In our paper, the liquidity risk originates from the fact that the shadow bank securities are a weaker medium of exchange than the commercial bank deposits. In (Gennaioli et al., 2013), shadow banks are welfare-reducing when investors neglect tail risks. In our paper, assets in shadow banks are safe but less liquid. Moreover, (Cai, García-Herrero, Li, & Le, 2019; Chen, Ren, & Zha, 2018; Hachem & Song, 2016) provide empirical evidence of regulatory arbitrage on loan-to-deposit regulation as the origin of the shadow banking sector in China. The remainder of paper is organized as follows. Section 2 sets up the model and examines the private market allocation. Section 3 introduces capital requirements and explores its role in improving welfare. Section 4 studies the endogenous emergence of the shadow banking system and how it affects social welfare. Section 5 concludes. 2. The model 2.1. Model setup Consider an economy with three dates, date 0, date 1, and date 2. The economy has a single consumption good. At date 0, there are three types of agents: a continuum of investors, a continuum of firms in the capital market, and a continuum of banks. All agents in the economy are risk-neutral. Every investor is endowed with wealth W, and other agents have no endowments. An investor must invest in short-term safe assets at both date 0 and date 1 through banks or invest in long-term risky projects by lending to firms through the capital market.3 We assume only banks have access to safe projects, which characterizes the scarcity of safe assets. The safe project between date 0 and 1 provides a gross return of R0f , and the safe project between date 1 and 2 provides a gross return of R1f . Banks fund their investment by issuing short-term deposits. The gross interest rate for date 0 deposits is R0 , and the gross interest rate for date 1 deposits is R1 . The cash flows of the risky project depends on the state of the economy: in state H with probability q, the cash flow is H while in state L with probability 1 q, the cash flow is L < H. For simplicity, we assume that the banking sector and the capital market are both competitive, and the investor gets all the surplus.4 We assume that ex ante, the risky project is more efficient. Assumption 1. qH þ ð1 qÞL > R0f R1f . In other words, the expected payoff of the risky project is higher than that of the safe asset. While the actual payoff of the risky project is realized at date 2, the information arrives at date 1. Similar to (Gorton & Huang, 2004), we assume that a moral hazard problem arises between firms and investors. Firms have access to a risky project at date 1, which
3 We thank an anonymous referee for advice on a more general setting in which short-term safe assets exist in both periods. Another way to set up the model is to assume that there is a short-term safe asset and a long-term safe asset. The no-arbitrage condition assures the equivalence of the two settings. 4 This is essentially the same as the assumption that investors are the equity holders and all the profits will be paid out as dividends.
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generates a large gross return with small chance, and nothing otherwise. This project has negative NPV, but firms may find it profitable because they can transfer the additional risk to the investor, particularly in state L. The following assumption is made to account for the effect of the moral hazard problem. Assumption 2. If a firm engages in the inefficient project, the gross return becomes δS for state S, δ < 1. We assume H is large enough that the firm will not engage in unnecessary risky investments at date 1 if the state is H. We also assume that although the information on the realization of the risky project arrives at date 1, it is not feasible to design a contract based on the state at date 0. Thus, the firm will offer a non-state-contingent contract to the investors. A market opens at date 1, and firms can sell the projects on the market. Due to the information transparency required by the market, firms cannot add risk through the inefficient risky project to the assets if they are sold. This assumption simplifies the analysis while keeping the benefit of holding liquidity. Otherwise, we have to assume heterogeneity among the available investor funds.5 The existence of this liquidation market gives the safe assets a role, which is providing liquidity in the market when the negative shock hits. Investors are willing to hold some deposits if the project is sold at a discount as it prevents the detrimental moral hazard problem. Finally, if the state is L and the assets are not sold, the firm will add risk to the assets in place. Although the provision of liquidity at date 1 can prevent firms from adding risk, it is costly since by Assumption 1, the first-best allocation is putting all money into the risky project and no risk is added. The following assumption assures that liquidity provision improves social welfare. Assumption 3. qH þ ð1 qÞδL < R0f R1f . That is, the project is ex ante inefficient if risk is added. By Assumption 3, if there is no liquidation market, then the return of the long-term risky project is lower than the compound return of the safe asset between date 0 and 1 and the safe asset between date 1 and 2. Combined with Assumption 1, we conclude that liquidity provision indeed improves social welfare. Particularly, the second-best allocation is providing the minimum amount of liquidity that prevents risk-adding activity and risky project investments as much as possible. We summarize the timeline of the model below. 1. At date 0, an investor invests D in date 0 deposits offered by banks and receives R0 D at date 1; the investor invests W D in the risky project through the capital market. 2. At the beginning of date 1, news about the state (H or L) arrives and becomes public. 3. The cash flows of the deposits are repaid to the investors. 4. The liquidation market opens, and investors decide the amount of assets to buy in the market given the price of one unit of date 2 project output PS where S is the state of the economy. 5. Firms decide whether to add risk to the unsold assets; investors purchase date 1 deposits with the proceeds from the sale of risky projects. 6. At date 2, the cash flows of the risky project are realized. 2.2. Private market allocation We focus on the case where banks and capital markets coexist in equilibrium and solve the model backwards from date 1. At date 1, given price, after receiving cash flows from deposits, investors determine the amount of assets to buy based on the state since all uncertainly has been resolved. If the state is H, then no one is willing to sell its assets since, by assumption, no risk will be added. If the state is L, however, investors may want to sell their assets. Define P ¼ PL R1 as the total cash flows at date 2 from selling one unit of output of the project in state L and then depositing it in the bank at date 1. P is crucial for the investor’s decision in the liquidation market since it measures the benefit of selling risky projects in the bad state. On the demand side, an investor will spend all their money if P < 1 and spend nothing if P > 1. In the case of P < 1, market demand is determined by the total liquidity available at date 1, which depends on the total amount of deposits invested at date 0. On the supply side, if P > δ, then selling the asset is better than adding risk for the investor. The investor will ask the firm to sell all the assets, and the amount depends on the wealth that is not invested in the deposits. Lemma 1. If δ < P < 1, the price in state L is determined by the following equation, P¼
R0 R1 D : ðW DÞL
(1)
PROOF. See Appendix. AT DATE 0, the investor decides how to allocate their wealth W Between Date 0 deposits and risky assets. If the asset is sold at a discount; that is, P < 1, investing in deposits (hoarding liquidity) will pay back if the state is L, and the risky asset is also less attractive since it must be sold at a discount. In equilibrium, the investor must be indifferent between investing through either banks or the capital market since they coexist. In other words, the expected returns are the same.
5 We can also rationalize the assumption by assuming that the whole firm is sold to the investor who does not have access to the risk-adding technology.
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Lemma 2. In any equilibrium, given price P, the expected returns of investing in deposits and risky assets are the same. qH þ ð1 qÞPL ¼ qR0 R1 þ ð1 qÞ
R0 R1 : P
(2)
PROOF. See Appendix. The left-hand side of equation (2) is the expected return on risky projects. If the state is H, investors will hold the risky project. If the state is L, then investors will sell at price PL and invest in the second-period safe asset with the proceeds earning PL R1 ¼ P. On the righthand side, an investor must hold the deposits in state H and would like to purchase the risky projects in state L, which gives the investor a total gross return of RPL0 ¼ R0PR1 . Note that the equilibrium depends on the long-term return of the deposits R0 R1 as a whole, and term structure has less relevance within the framework. Thus, without loss of generosity, we can assume that R ¼ R0 R1 and Rf ¼ R0f R1f . Particularly, we let R1 ¼ R1f ¼ 1 so that P ¼ PL also measures the price in the liquidation market. By equations (1) and (2), we can mutually solve the equilibrium price P and the deposit amounts D. Proposition 1. In equilibrium, R ¼ Rf . The equilibrium amount of liquidity D always exists and is uniquely determined by the solution of the following equation. LðW DÞ DR ¼ qðH RÞ; ð1 qÞ D W D
(3)
the equilibrium price at date 1 in state L is determined by RD ¼ P¼ ðW DÞL
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi q2 ðH RÞ2 þ 4ð1 qÞ2 RL qðH RÞ 2ð1 qÞL
:
(4)
Furthermore, equilibrium price indeed satisfies the condition δ < P < 1.
PROOF. See Appendix.
The fact that δ < P < 1 implies that the allocation of the equilibrium is inferior to the second-best allocation. In fact, the second-best allocation requires a minimum amount of liquidity provision and putting money into risky projects as much as possible. By equation (1), the price is increasing with liquidity provision. Therefore, optimal allocation asks for a minimum price at which the firm is willing to sell; that is, P ¼ δ. However, this price is attractive to investors and will encourage them to invest more in deposits at date 0 to exploit this chance. This money hoarding behavior reduces allocation efficiency because, ex ante, liquidity that exceeds the necessary amount to prevent the moral hazard problem is less efficient than project investment. We are interested in the comparative statics of the model. First, the increase in cash flows at different states have asymmetric impacts on the equilibrium. When the gross return H increases, it directly increases the demand for risky assets resulting in a lower amount of liquidity D. However, the increase in gross return L, while also increasing the expected return, will increase the amount of liquidity. This is because the revenue of selling assets in the liquidation market is constrained by the total amount of liquidity. Thus, the increase in L has no direct impact on the demand for risky assets. However, the increase in L will lower the liquidation price P, which increases the demand for hoarding. Therefore, the equilibrium amount of liquidity will increase. Second, the impact on the liquidity provision in response to the increase in R is ambiguous. On the one hand, the increase in the short-term cash flow will increase the demand for deposits. On the other hand, however, it will increase the total amount of liquidity available in the liquidation market, which pulls the liquidation price up and also increases the demand for risky assets. Nonetheless, we can show that the provision for liquidity will increase R as long as the economy is more likely to be in the H state. We summarize all the results in the following corollary. Corollary 1.
The amount of social liquidity provision D is
(i) increasing with L and decreasing with H; (ii) increasing with R if q 12. PROOF. See Appendix. In later sections, we assume that q > 12 to make sure that the liquidity provision is increasing with R. Assumption 4. q > 12. That is, the economy is more likely to be in a good state. Based on the change in liquidity provision, we can also study the change in liquidation price in response to changes in the parameters. In our model, the price is less than the face value in the bad state. In other words, there is a fire sale problem due to the lack of liquidity. The following corollary demonstrates how returns affect the fire sale price. Corollary 2.
The liquidation price P is
(i) decreasing with L and H. (ii) increasing with R if q 12.
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PROOF. See Appendix. Corollary 2 shows that the increase in risky cash flows will lower the fire sale price. However, just as Corollary 1 shows, while the increase in cash flows in state L will enlarge the discount and worsen the fire sale problem, the increase in cash flows in state H actually reduces the liquidity provision. The corollary also shows that the increase in return on deposits will lower the discount and mitigate the fire sale problem. 3. Capital requirements Recall that the second-best allocation requires the minimum amount of liquidity provision as long as it is still beneficial to sell all the assets in the market. We have shown that liquidity provision decreases if R decreases. If the bank only finances through issuing safe securities, then R ¼ Rf , which is determined by the real factors in the economy. However, based on the scarcity assumption, only banks have access to the safe asset technology. Therefore, it is possible that the gross return on safe security R is lower than Rf , and the provision of social liquidity will decrease and social welfare will be improved. One way to reach this goal is to set a capital requirement because raising capital is expensive for banks compared to issuing deposits and may reduce the return of deposits if they are forced to raise equity capital. In this section, we assume policy makers can announce a regulation at date 0 that the proportion of equity must be no less than C for every bank. For simplicity, we assume the cost of capital for issuing equity is γ > Rf and is exogenously given. In this framework, the capital requirement is a useful policy instrument as it effectively reduces the deposit rate R offered by the bank. To see this, notice that since the bank only has access to the risk-free Project, and banks are perfectly competitive, for any bank, a zero-profit condition implies that Rf ¼ ð1 CÞR þ Cγ;
(5)
where the left-hand side is the cash flow from assets, and the right-hand side is the cash flow owed to outsiders. By equation (5) we can solve the gross return of investors. Lemma 3. For capital requirement C, the gross return on safe securities issued by banks is R¼
Rf γC : 1C
(6)
Furthermore, R < Rf and is decreasing with C. PROOF. See Appendix. The reduced deposit rate will increase the investor’s incentive to invest in the risky projects, as we have seen in Corollary 1. Thus, we immediately find that at least some capital requirement will improve the social welfare because it leads to less liquidity provision. Lemma 4. Total amount of liquidity D is decreasing with C. PROOF.See Appendix. Although a higher capital requirement reduces the amount of liquidity in the economy, it is also disruptive because the constrained liquidity provision will lower the liquidation price P, as shown in Corollary 2. If the price falls to δ, it is indifferent for the firm between selling assets in the market or adding risk. This further increase in capital requirements will not change the expected return on investing in risky projects. However, the expected return on investing in bank-issued security continues to decrease by Lemma 3. As a result, if capital requirement increases further, the unduly low return of holding liquidity will make investing in the bank strictly inferior to investing in the capital market. Moreover, since there is no liquidity offered in the market, there is no asset sold, and risk will be added. This trade-off implies that the optimal capital requirement is such that the price is just equal to δ. The following proposition examines the optimal capital requirement policy. Proposition 2.
C ¼
The optimal capital requirement is
8 R R f > > < γ R
if qH þ ð1 qÞδL >
δq þ 1 q δ
> > : Rf 1 γ1
if qH þ ð1 qÞδL
δq þ 1 q δ
;
(7)
where R is defined as R ¼
δ ðqH þ ð1 qÞδLÞ: δq þ 1 q
PROOF. See Appendix. If the welfare loss of risk-adding behavior is mild, then capital requirements can attain the optimal allocation. On the other hand, if the moral hazard problem is too severe, then optimal allocation would require a negative return on deposits, which is infeasible. In this 6
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case, the optimal capital requirement is restricted by a zero interest rate on deposits. Proposition 2 gives us a new role for capital requirements in addition to regulating the conventional moral hazard problem. The new role is improving social welfare by reducing the unnecessary hoarding activities at date 0 in order to buy discounted assets when the economy is in a bad state. In the next section, we examine the possibility that a shadow banking system arises as regulatory arbitrage. 4. Shadow banking Since capital requirements constrain banks’ activities, banks may try to find some channels to circumvent the regulation. In this section, we consider the possibility that a bank can establish a shadow bank that can bypass the capital requirements. To focus on the role of regulatory arbitrage only, we assume that even if the shadow bank is not subject to capital requirements, it cannot invest in the capital market. This assumption captures the fact that shadow banking institutions, such as money market mutual funds and wealth management products, usually invest through money markets such as repos and offer similar products as traditional banks. To differentiate shadow banks from commercial banks without capital requirements, we make the following assumption. Assumption 5. The assets in the shadow banking system cannot be used as a medium of exchange in the liquidation market. This assumption describes the disadvantages of investing in shadow banking assets. By Assumption 4, the return on investing in shadow banking assets is just Rf . In reality, the assets created by the shadow banking system are often less liquid than deposits, particularly when the economy is in a bad state. Moreover, when making investments, investors need to first convert shadow bank securities to cash or deposits and then purchase other assets. We also assume that before the emergence of shadow banks, the social welfare is second best. Assumption 6. qH þ ð1 qÞδL > δqþ1q . δ , then the liquidity provision is minimized given that all assets are sold in the liquidation By Proposition 2, if qH þ ð1 qÞδL > δqþ1q δ market. The following result shows that the emergence of shadow banks will indeed be detrimental to social welfare. Proposition 3.
The allocation with the optimal capital requirement cannot be sustained if there is a shadow banking system.
PROOF. See Appendix. Proposition 3 shows that the shadow banking system will arise endogenously in the economy if the capital requirement regulation on commercial banks is optimal without shadow banks. The intuition is as follows. According to the previous section, we know that the interest rate on commercial bank deposits, R, is less than Rf when the economy attains the second-best allocation. This motivates investors to use shadow banks to bypass capital requirement regulation because they can offer a higher expected return (Rf ) than other investment channels. As a result, investors move money from commercial banks to shadow banks, and the total market liquidity decreases. Lower liquidity reduces the fire sale price of risky assets leading to a reduction in capital market investment returns. Therefore, investors choose to invest less in the ex ante more efficient capital market investments, and social welfare decreases. This result is consistent with the regulatory arbitrage view of the shadow banking system. (For instance (Acharya et al., 2013; Harris et al., 2014; Plantin, 2014),). The result also implies that the regulator is restricted in the sense that they cannot set the capital requirement as high as they would like, which is demonstrated in the next proposition. Proposition 4.
b < C defined by There is a threshold value for capital requirements C
b b ¼ Rf R ; C b γR
(8)
where b¼ R
Rf L q þ ð1 qÞ2 Rf qH
;
such that: b then there is no shadow banking system, and the allocation is the same as in Proposition 1 but with R ¼ Rf γC. (i) If C C, 1C b then all wealth is invested in the shadow banking system. (ii) If C > C, PROOF. See Appendix. Proposition 4 shows that introducing shadow banks in an environment with strict capital requirements will exhaust the liquidity provision offered by commercial banks, lower the expected return on risky projects, and exacerbate the fire sale problem. As a result, there will be less resources allocated to more efficient risky projects, and social welfare will decrease. On the other hand, if capital requirements are moderate, without shadow banks, the total return earned by the investors is higher than the return from shadow bank securities (risk-free rate). Thus, investors will not deviate to invest in shadow banks. Consequently, the optimal capital requirement is one whereby shadow banks are just about to emerge, which is lower than the capital requirement in the case with no shadow banks.
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Corollary 3.
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b The optimal capital requirement with shadow banking system is C.
PROOF. Omitted. In summary, the emergence of shadow banks undermines the effect of capital requirements. After introducing shadow banks, a large capital requirement may induce shadow banks, which reduces social welfare instead of improving it. The capital requirement regulation should be more discreet in the presence of shadow banks as the shadow banking system might exhaust the liquidity in the liquidation market, and the maximal social welfare that can be achieved through capital requirement decreases. 5. Conclusion Commercial banks are subject to many regulations among which capital requirements are the most prominent. We extend the model in (Gorton & Huang, 2004) to consider the role of capital requirements. Liquidity is necessary as it can promote transactions and prevent the detrimental moral hazard problem by transferring projects from distressed agents to normal agents. However, liquidity is also costly as it reduces the amount of investment in more efficient risky projects. Capital requirements reduce the cost of liquidity and improve social welfare. However, excessively high capital requirements are also not desirable as liquidity becomes so expensive that no investors are willing to hold, which leads to a drying up of liquidity. The optimal capital requirement is achieved when the price of risky projects makes the project holders indifferent between selling them and adding risk when the negative shock occurs. Shadow banks perform a similar function to commercial banks by issuing money-like securities to finance loans. The emergence of shadow banks undermines the effect of capital requirements. Before introducing shadow banks, a large capital requirement is desirable while, after introducing shadow banks, a large capital requirement may induce shadow banks, which reduces social welfare instead of increasing it. Therefore, the capital requirement regulation should be more discreet in the presence of shadow banks, and the maximal social welfare that can be achieved through capital requirement decreases. Our model has several empirical implications. First, the scale of shadow banks increases with an increase in capital requirements. Second, deposit returns decrease with an increase in capital requirements. Third, the holding of cash and deposits in the economy decreases with an increase in capital requirements. These issues can be further explored in future research. Acknowledgements This research was supported by the Fundamental Research Funds for the Central Universities and the Research Funds of Renmin University of China (Grant No. 19XNF001). We thank seminar participants of the Fifth Chinese Economy Symposium and an anonymous referee for helpful comments. Appendix A. Proofs Proof of Lemma 1.
The result is obvious from the market clearing condition
PL LðW DÞ ¼ R0 D:
Proof of Lemma 2. Investing one dollar in deposits will pay R0 R1 in state H and R0 =PL ¼ R0 R1 =P in state L. Investing in one dollar in risky projects will pay H in state H and PL R1 L ¼ PL in state L. Taking the expectation gives the result immediately. Proof of Proposition 1. Combine equation (1) with (2) and we obtain the result. Note that the left-hand side of (3) is decreasing with D, and it is þ∞ when D ¼ 0 and ∞ when D ¼ W. Therefore, the solution always exists and is unique since the right-hand side is a constant. To prove the last argument, note that if P 1, then the left-hand side of (2) is always larger than the right-hand side by Assumption 1. On the other hand, if P δ, then the left-hand side is always smaller than the right-hand side by Assumption 3. Thus, we conclude that δ < P < 1. Proof of Corollary 1. Define f ðDÞ WD D and gðDÞ 1=f ðDÞ, and take differentials on both sides with respect to D and L: ð1 qÞ½f ðDÞdL þ Lf ’ðDÞdD Rg’ðDÞdD ¼ 0; since f ’ðDÞ < 0 and g’ðDÞ > 0, we can conclude that dD Rg’ðDÞ Lf ’ðDÞ ¼ > 0: dL f ðDÞ with a similar approach, we can prove that dD ð1 qÞðLf ’ðDÞ Rg’ðDÞÞ ¼ < 0; dH q 8
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and dD ð1 qÞðLf ’ðDÞ Rg’ðDÞÞ : ¼ ð1 qÞgðDÞ q dR we now prove that gðDÞ 1. If gðDÞ > 1; then f ðDÞ < 1, the left-hand side of equation (3) will be negative since L < R ¼ Rf . Then, as long as q > 12, then 1 q < q, which implies that ð1 qÞgðDÞ < q, and we can conclude that dD dR > 0. Proof of Corollary 2. By equation (2), if L increases, then P has to decrease because, otherwise, the left-hand side will be larger than the right-hand side. Similarly, if R increases, then the price has to be higher because, otherwise, the left-hand side will be smaller than dD dP the right-hand side. According to the fact that dH < 0, we can infer that dH < 0 by equation (1). Proof of Lemma 3. The first part is derived from equation (5). The second part is obvious by noting that R Rf ¼ decreasing with C by (6). Proof of Lemma 4.
CðRf γÞ 1C
< 0, and R is
Combining Corollary 1 with Lemma 3, we can immediately get the result.
Proof of Proposition 2. At the optimal capital requirement, the liquidation price is just δ. By equation (2), we immediately solve the R . However, if qH þ ð1 qÞδL δqþ1q , then R 1, in which case investors will choose not to invest in deposits and will store the δ goods that are not invested in risky assets instead. In this case, the optimal capital requirement is such that R ¼ 1. Proof of Proposition 3. We prove the proposition by showing that at the optimal capital requirement, the expected return on investing in bank or capital markets is lower than the expected return on investing in shadow banks. To see this, note that the expected return when the capital requirement is C is actually qH þ ð1 qÞδL. By Assumption 3, this is lower than Rf , which is the expected return on investing in shadow banks. Thus, if the capital requirement is set at C , then investors will spend all their money purchasing shadow bank assets, implying that the original allocation cannot be an outcome of an equilibrium in the presence of the shadow banking system. Proof of Proposition 4. When C ¼ 0, the allocation is the same as in Proposition 1, with an equilibrium expected return larger than Rf . This implies that there are no shadow banks at all. As C increases, the expected return on investing in the capital market decreases because of the decrease in price by Corollary 2 (see the left-hand side of equation (2)). Due to Proposition 3, there must exist a threshold b At the threshold, the price is at which the expected return on investing in the capital market is equal to Rf . We denote the threshold by C. determined by the following equation: R qH þ ð1 qÞPL ¼ qR þ ð1 qÞ ¼ Rf : P b based on equation (5): b by the equation above. Therefore, we can calculate C Moreover, R ¼ R b b ¼ Rf R : C b γR b then the gross return R determined by equation (6) is lower than R. b However, this means the expected return on investing in If C > C, commercial banks is lower than investing in shadow banks. Thus, there will be no liquidity in the market, which implies that risk will be added to all risky assets making the expected return on investing in risky assets lower than Rf also. As a result, no one will invest in risky assets nor commercial bank deposits. Investors only invest in shadow banking assets. b < C since R is decreasing with b is apparently larger than R since the liquidation price is larger than δ. As a consequence, C Finally, R C.
References Acharya, V. V., Schnabl, P., & Suarez, G. (2013). Securitization without risk transfer. Journal of Financial Economics, 107(3), 515–536. Allen, F., Carletti, E., & Marquez, R. (2011). Credit market competition and capital regulation. Review of Financial Studies, 24(4), 983–1018. American Bankers Association. (2012). Comment letter on proposals to comprehensively revise the regulatory capital framework for u.s. banking organizations. Technical report. American Bankers Association. Cai, J., García-Herrero, A., Li, F., & Le, X. (2019). The regulatory arbitrage and window dressing in shadow banking: The example of Chinese wealth management product. Economic and Political Studies, 7(3), 314–336. https://doi.org/10.1080/20954816.2019.1633825. Chen, K., Ren, J., & Zha, T. (2018). The nexus of monetary policy and shadow banking in China. American Economic Review, 108(12), 3891–3936. Diamond, D. W., & Rajan, R. G. (2000). A theory of bank capital. The Journal of Finance, 55(6), 2431–2465. Gennaioli, N., Shleifer, A., & Vishny, R. W. (2013). A model of shadow banking. The Journal of Finance, 68(4), 1331–1363. Gorton, G., & Huang, L. (2004). Liquidity, efficiency, and bank bailouts. The American Economic Review, 94(3), 455–483. Gorton, G., & Metrick, A. (2010). Regulating the shadow banking system. Brookings Papers on Economic Activity, 2010(2), 261–297. Gorton, G., & Metrick, A. (2012). Securitized banking and the run on repo. Journal of Financial Economics, 104(3), 425–451. Gorton, G., & Winton, A. (2017). Liquidity provision, bank capital, and the macroeconomy. Journal of Money, Credit, and Banking, 49(1), 5–37. Gropp, R., Mosk, T., Ongena, S., & Wix, C. (2019). Banks response to higher capital requirements: Evidence from a quasi-natural experiment. The Review of Financial Studies, 32(1), 266–299. 9
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Hachem, K., & Song, Z. M. (2016). Liquidity regulation and unintended financial transformation in China. Rochester, NY: Social Science Research Network. SSRN Scholarly Paper ID 2717291. Harris, M., Opp, C. C., & Opp, M. M. (2014). Higher capital requirements, safer banks? Macroprudential regulation in a competitive financial system. Rochester, NY: Social Science Research Network. SSRN Scholarly Paper ID 2181436. Hellmann, T. F., Murdock, K. C., & Stiglitz, J. E. (2000). Liberalization, moral hazard in banking, and prudential regulation: Are capital requirements enough? The American Economic Review, 90(1), 147–165. Kara, G., & Ozsoy, S. (2016). Bank regulation under fire sale externalities. Technical report. SSRN. Keeley, M. C. (1990). Deposit insurance, risk, and market power in banking. The American Economic Review, 80(5), 1183–1200. Kisin, R., & Manela, A. (2016). The shadow cost of bank capital requirements. Review of Financial Studies, 29(7), 1780–1820. Krishnamurthy, A., & Vissing-Jorgensen, A. (2012). The aggregate demand for treasury debt. Journal of Political Economy, 120(2), 233–267. Moreira, A., & Savov, A. (2017). The macroeconomics of shadow banking. The Journal of Finance, 72(6), 2381–2432. Plantin, G. (2014). Shadow banking and bank capital regulation. Review of Financial Studies, 28(1), 146–175. Pozsar, Z., Adrian, T., Ashcraft, A. B., & Boesky, H. (2010). Shadow banking. Rochester, NY: Social Science Research Network. SSRN Scholarly Paper ID 1645337. Sunderam, A. (2015). Money creation and the shadow banking system. Review of Financial Studies, 28(4), 939–977.
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Contents lists available at ScienceDirect
International Review of Economics and Finance journal homepage: www.elsevier.com/locate/iref
Liquidity, capital requirements, and shadow banking Zehao Liu a, Chengbo Xie b, * a b
School of Finance, Renmin University of China, Beijing, China School of Finance, Southwestern University of Finance and Economics, Chengdu, China
A R T I C L E I N F O
A B S T R A C T
JEL classification: E58 G21 G28
We study the role of capital requirements in adjusting market liquidity. Liquidity is necessary as it prevents fire sales and suppresses the risk-shifting problem when a negative shock occurs. However, hoarding excessive liquidity is costly as it crowds out efficient investments. A capital requirement on commercial banks reduces deposit returns. This causes investors to allocate more resources to more efficient capital market investments, improving social welfare. However, an excessively high capital requirement is undesirable because the return from holding liquidity is so low that liquidity provision is insufficient to avoid risk-shifting behaviors. Shadow banks can bypass capital regulation, and strict capital regulation will drive money to shadow banks. Thus, a liquidity shortage emerges because shadow bank securities are less liquid than commercial bank deposits. Policy maker should implement lower capital requirements in the presence of shadow banks.
Keywords: Liquidity Capital requirements Shadow banking Inefficient liquidity hoarding Regulatory arbitrage
1. Introduction Capital requirements are an important policy instrument for the regulation of financial intermediaries. The argument as to whether capital requirements should be raised is persistent. After the global financial crisis, many economists and policy makers called for a substantial increase in bank capital requirements as capital requirements set upper bounds for bank leverage and reduce the probability of distress and insolvency. Basel III, which was agreed upon by the members of the Basel Committee on Banking Supervision and will be fully introduced in 2019, will significantly increase the capital requirements for banks. However, banks claim that the cost of capital requirements are high and oppose proposals to increase capital requirements (see, for example (American Bankers Association, 2012),). To determine optimal capital requirements, we need better knowledge concerning the benefits and costs of capital requirements. While existing literature mainly discusses the role of capital requirements in reducing the risk of bank investment portfolios, we show the role of capital requirements through the liquidity channel: capital requirements can suppress inefficient hoarding and reduce the excessive cost of liquidity. We extend the model in (Gorton & Huang, 2004). In an economy, there are two financial intermediaries — a commercial bank and a capital market — and many investors. Investors can deposit their money in the commercial bank, and the bank can then invest in risk-free assets that provide a non-zero fixed return.1 Investors can also invest in risky projects through the capital market. Bank debts (deposits) are more liquid than capital market securities. Then, only cash and deposits can be used to make payments. Similar to (Gorton & Huang, 2004), there is a moral hazard problem. When a negative shock to the project output occurs, the * Corresponding author. E-mail addresses: [email protected] (Z. Liu), [email protected] (C. Xie). 1 The assumption that commercial banks use deposits to buy risk-free assets is for simplicity. As long as bank assets are safer than capital market assets, all the results will hold. In reality, banks make loans to firms, which typically present less risk than stocks or derivative investments. https://doi.org/10.1016/j.iref.2019.11.019 Available online xxxx 1059-0560/© 2019 Published by Elsevier Inc.
Please cite this article as: Liu, Z., & Xie, C., Liquidity, capital requirements, and shadow banking, International Review of Economics and Finance, https://doi.org/10.1016/j.iref.2019.11.019
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investors who are managing the project cannot repay their loans. This motivates these investors to add risk to the project by gambling on a less likely high return. An inefficient risk-shifting problem emerges. In addition to adding risk, the investors whose projects suffered negative shocks can also sell their projects on the market. If these investors can obtain enough money to repay the loans from the transactions, they will not add risk. If risk is not added, the risky projects are ex ante more efficient than the risk-free assets. However, if risk is added, the risky projects are less efficient. On the condition that there is sufficient liquidity to prevent the addition of risk, a social planner will invest all the remaining money into risky projects. However, in this situation, if a negative shock occurs, the price of risky projects will be low, and the investors can obtain a high return from purchasing the projects in a fire sale. Thus, some investors are willing to hold more deposits at the beginning to exploit this possibility. This money hoarding behavior reduces allocation efficiency because, ex ante, liquidity that exceeds the necessary amount to prevent a moral hazard problem is less efficient than project investment. In this model, money invested in safe assets becomes the source of liquidity when the economic state is poor. Liquidity is necessary as it prevents fire sales and suppresses the risk-shifting problem when a negative shock occurs. However, hoarding excessive liquidity is costly as it crowds out efficient investments. Raising capital is expensive for commercial banks. Therefore, a capital requirement on commercial banks will reduce the return of deposits because banks are forced to raise more expensive capital and less money is allocated to depositors. Lower deposit rates will drive investors to make more capital market investments. Social welfare is thus increased. However, an excessively high capital requirement is also undesirable because the return on holding liquidity will be unduly low causing insufficient liquidity provision to avoid risk-shifting behaviors. This trade-off leads to an optimal capital requirement. The optimal capital requirement is achieved when project holders are indifferent between selling the projects and adding risk after the negative shock occurs. We then extend the model to consider shadow banking. Shadow banks perform a similar function as commercial banks by issuing safe assets to finance loans. Many previous studies agree that the growth of shadow banking has been largely driven by regulatory arbitrage, particularly the arbitrage of capital requirements (see, for example (Acharya, Schnabl, & Suarez, 2013; Gennaioli, Shleifer, & Vishny, 2013; Gorton & Metrick, 2010; Plantin, 2014; Pozsar, Adrian, Ashcraft, & Boesky, 2010),). In our model, shadow banks make the same type of investments as commercial banks; that is, buying risk-free assets, but shadow banks can circumvent the capital requirement regulation and thus can offer a higher return than commercial banks. However, shadow bank securities cannot be used to purchase risky projects. This assumption characterizes the fact that shadow bank securities are less liquid than commercial bank deposits. Money market mutual funds or wealth management products can be considered to be this type of shadow bank. These intermediaries raise money from investors and lend money to commercial banks through repo and other interbank lending instruments in a wholesale bank market. They conduct similar business to commercial banks but are largely not subject to capital requirements. By investing in shadow bank securities, investors enjoy a higher return compared to commercial banks, but they sacrifice liquidity.2 Then, if the capital requirement is moderate, the introduction of shadow banks will not change the allocation of the economy. This is because without shadow banks, the total return earned by the investors is higher than the return of shadow bank securities (risk-free rate); thus, investors will not deviate to invest in shadow banks. In contrast, if the capital requirement is high, commercial bank deposits and capital market investments will both shrink, which leads to a reduction in social welfare. The intuition is the following. Without shadow banks, the total return earned by investors is lower than the return from shadow bank securities (risk-free rate). This motivates investors to use shadow banks to bypass capital requirement regulations. Investors move money from commercial banks to shadow banks, and total market liquidity decreases. Lower amounts of liquidity reduces the fire sale price of risky assets leading to a reduction in capital market investment returns. Therefore, investors choose to invest less in the ex ante more efficient capital market investments, and social welfare decreases. Compared to the economy without shadow banks, policy maker should adopt a lower capital requirement when shadow banks exist. Otherwise, high capital requirements will drive money to the shadow banking sector. Commercial bank deposits are not attractive because they are subject to strict capital regulation. Capital market investments are not attractive either because liquidity is scarce and risk is added if negative shocks occur. In summary, the emergence of shadow banks undermines the role of capital requirements. In the absence of shadow banks, a large capital requirement is desirable. In contrast, in the presence of shadow banks, the same capital requirement may be detrimental because it causes the emergence of shadow banks. Therefore, policy maker should be more discreet and use large capital requirements in the presence of shadow banks. The contributions of the paper are as follows. First, we propose a new role for capital requirements; that is, to suppress costly liquidity hoarding and increase efficient investments. This role is persistent even in the absence of credit risks. Second, we show that shadow banks can undermine the role of capital requirements through liquidity. Shadow banks enable investors to obtain higher returns through regulatory arbitrage instead of taking efficient risks. Thus, efficient capital market investments decrease. Third, we show that in the presence of shadow banks, the optimal capital requirement should be reduced unless the shadow banks can be properly regulated. 1.1. Literature review Our paper is related to several strands of literature. The first strand addresses the role of capital regulations. The conventional role of capital requirements is to mitigate the moral hazard problem; that is, the excessive risk taking by equity holders. (See, for example
2 For example, when investors want to purchase other financial assets, they must first convert shadow bank securities to cash or deposits and then purchase other assets.
2
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(Hellmann, Murdock, & Stiglitz, 2000; Keeley, 1990),). However (Allen, Carletti, & Marquez, 2011), argues that banks are willing to hold capital in excess of regulatory minimums because costly capital financing serves as a better commitment device for monitoring than interest rate on loans (Kara & Ozsoy, 2016). studies a model in which banks with higher liquidity holdings lead to less severe decreases in asset prices during times of distress. This externality is not internalized by individual banks and, as a consequence, regulators must raise the minimum capital ratio requirement to inefficiently high levels. The role of the capital ratio in our view is similar to (Diamond & Rajan, 2000) and (Gorton & Winton, 2017) who posit that greater capital reduces the liquidity provision. However, in our model, this reduction improves social welfare since there is excess liquidity in private market equilibrium (the hoarding problem in (Gorton & Huang, 2004)). Our paper is also related to the literature on bank’s reaction to a change in capital regulation (Harris, Opp, & Opp, 2014). develops a model in which capital requirements for banks may be counterproductive. The authors show that under some conditions, increased competition may imply that increases in capital requirements cause more banks in the economy to engage in value-destroying risk-shifting (Plantin, 2014). shows that tightening capital requirements may spur a surge in shadow banking activity that leads to overall greater risk on the money-type liabilities of formal and shadow banking institutions. Our paper shows similar results as (Plantin, 2014) and that shadow banking activities will arise endogenously if capital requirements are too high. Empirically (Kisin & Manela, 2016), estimates the shadow cost of capital requirements using data on a costly loophole that allowed banks to relax these constraints. The authors find that increasing capital requirements would impose a modest cost (Gropp, Mosk, Ongena, & Wix, 2019). studies the impact of higher capital requirements and find that the banks that have stricter capital requirements imposed on them increase their capital ratios by reducing their risk-weighted assets, not by raising their levels of equity. The third strand discusses the benefits and costs of the shadow banking system. Shadow banks create money-type liabilities, which are useful in normal times but may lead to a serious crisis when a negative shock occurs (see (Gorton & Metrick, 2012; Krishnamurthy & Vissing-Jorgensen, 2012; Sunderam, 2015; Moreira & Savov, 2017; Gorton & Metrick, 2010)). We model the rise of shadow banks as a means of regulatory arbitrage documented by (Acharya et al., 2013; Plantin, 2014) and (Harris et al., 2014). (Plantin, 2014) shows that if shadow banks can bypass capital regulation, a higher capital requirement may drive more money to the shadow banking sector and lead to greater overall risk. In the author’s paper, capital regulation mainly takes effect through bank leverage while, in our paper, capital regulation mainly takes effect through liquidity provision (Moreira & Savov, 2017). also proves the negative macroeconomic consequences of the shadow banking sector. The authors emphasize the potential liquidity risk of shadow banking securities. However, in their paper, the risk exists because the market investors may produce information on the real value of shadow banking securities. In our paper, the liquidity risk originates from the fact that the shadow bank securities are a weaker medium of exchange than the commercial bank deposits. In (Gennaioli et al., 2013), shadow banks are welfare-reducing when investors neglect tail risks. In our paper, assets in shadow banks are safe but less liquid. Moreover, (Cai, García-Herrero, Li, & Le, 2019; Chen, Ren, & Zha, 2018; Hachem & Song, 2016) provide empirical evidence of regulatory arbitrage on loan-to-deposit regulation as the origin of the shadow banking sector in China. The remainder of paper is organized as follows. Section 2 sets up the model and examines the private market allocation. Section 3 introduces capital requirements and explores its role in improving welfare. Section 4 studies the endogenous emergence of the shadow banking system and how it affects social welfare. Section 5 concludes. 2. The model 2.1. Model setup Consider an economy with three dates, date 0, date 1, and date 2. The economy has a single consumption good. At date 0, there are three types of agents: a continuum of investors, a continuum of firms in the capital market, and a continuum of banks. All agents in the economy are risk-neutral. Every investor is endowed with wealth W, and other agents have no endowments. An investor must invest in short-term safe assets at both date 0 and date 1 through banks or invest in long-term risky projects by lending to firms through the capital market.3 We assume only banks have access to safe projects, which characterizes the scarcity of safe assets. The safe project between date 0 and 1 provides a gross return of R0f , and the safe project between date 1 and 2 provides a gross return of R1f . Banks fund their investment by issuing short-term deposits. The gross interest rate for date 0 deposits is R0 , and the gross interest rate for date 1 deposits is R1 . The cash flows of the risky project depends on the state of the economy: in state H with probability q, the cash flow is H while in state L with probability 1 q, the cash flow is L < H. For simplicity, we assume that the banking sector and the capital market are both competitive, and the investor gets all the surplus.4 We assume that ex ante, the risky project is more efficient. Assumption 1. qH þ ð1 qÞL > R0f R1f . In other words, the expected payoff of the risky project is higher than that of the safe asset. While the actual payoff of the risky project is realized at date 2, the information arrives at date 1. Similar to (Gorton & Huang, 2004), we assume that a moral hazard problem arises between firms and investors. Firms have access to a risky project at date 1, which
3 We thank an anonymous referee for advice on a more general setting in which short-term safe assets exist in both periods. Another way to set up the model is to assume that there is a short-term safe asset and a long-term safe asset. The no-arbitrage condition assures the equivalence of the two settings. 4 This is essentially the same as the assumption that investors are the equity holders and all the profits will be paid out as dividends.
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generates a large gross return with small chance, and nothing otherwise. This project has negative NPV, but firms may find it profitable because they can transfer the additional risk to the investor, particularly in state L. The following assumption is made to account for the effect of the moral hazard problem. Assumption 2. If a firm engages in the inefficient project, the gross return becomes δS for state S, δ < 1. We assume H is large enough that the firm will not engage in unnecessary risky investments at date 1 if the state is H. We also assume that although the information on the realization of the risky project arrives at date 1, it is not feasible to design a contract based on the state at date 0. Thus, the firm will offer a non-state-contingent contract to the investors. A market opens at date 1, and firms can sell the projects on the market. Due to the information transparency required by the market, firms cannot add risk through the inefficient risky project to the assets if they are sold. This assumption simplifies the analysis while keeping the benefit of holding liquidity. Otherwise, we have to assume heterogeneity among the available investor funds.5 The existence of this liquidation market gives the safe assets a role, which is providing liquidity in the market when the negative shock hits. Investors are willing to hold some deposits if the project is sold at a discount as it prevents the detrimental moral hazard problem. Finally, if the state is L and the assets are not sold, the firm will add risk to the assets in place. Although the provision of liquidity at date 1 can prevent firms from adding risk, it is costly since by Assumption 1, the first-best allocation is putting all money into the risky project and no risk is added. The following assumption assures that liquidity provision improves social welfare. Assumption 3. qH þ ð1 qÞδL < R0f R1f . That is, the project is ex ante inefficient if risk is added. By Assumption 3, if there is no liquidation market, then the return of the long-term risky project is lower than the compound return of the safe asset between date 0 and 1 and the safe asset between date 1 and 2. Combined with Assumption 1, we conclude that liquidity provision indeed improves social welfare. Particularly, the second-best allocation is providing the minimum amount of liquidity that prevents risk-adding activity and risky project investments as much as possible. We summarize the timeline of the model below. 1. At date 0, an investor invests D in date 0 deposits offered by banks and receives R0 D at date 1; the investor invests W D in the risky project through the capital market. 2. At the beginning of date 1, news about the state (H or L) arrives and becomes public. 3. The cash flows of the deposits are repaid to the investors. 4. The liquidation market opens, and investors decide the amount of assets to buy in the market given the price of one unit of date 2 project output PS where S is the state of the economy. 5. Firms decide whether to add risk to the unsold assets; investors purchase date 1 deposits with the proceeds from the sale of risky projects. 6. At date 2, the cash flows of the risky project are realized. 2.2. Private market allocation We focus on the case where banks and capital markets coexist in equilibrium and solve the model backwards from date 1. At date 1, given price, after receiving cash flows from deposits, investors determine the amount of assets to buy based on the state since all uncertainly has been resolved. If the state is H, then no one is willing to sell its assets since, by assumption, no risk will be added. If the state is L, however, investors may want to sell their assets. Define P ¼ PL R1 as the total cash flows at date 2 from selling one unit of output of the project in state L and then depositing it in the bank at date 1. P is crucial for the investor’s decision in the liquidation market since it measures the benefit of selling risky projects in the bad state. On the demand side, an investor will spend all their money if P < 1 and spend nothing if P > 1. In the case of P < 1, market demand is determined by the total liquidity available at date 1, which depends on the total amount of deposits invested at date 0. On the supply side, if P > δ, then selling the asset is better than adding risk for the investor. The investor will ask the firm to sell all the assets, and the amount depends on the wealth that is not invested in the deposits. Lemma 1. If δ < P < 1, the price in state L is determined by the following equation, P¼
R0 R1 D : ðW DÞL
(1)
PROOF. See Appendix. AT DATE 0, the investor decides how to allocate their wealth W Between Date 0 deposits and risky assets. If the asset is sold at a discount; that is, P < 1, investing in deposits (hoarding liquidity) will pay back if the state is L, and the risky asset is also less attractive since it must be sold at a discount. In equilibrium, the investor must be indifferent between investing through either banks or the capital market since they coexist. In other words, the expected returns are the same.
5 We can also rationalize the assumption by assuming that the whole firm is sold to the investor who does not have access to the risk-adding technology.
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Lemma 2. In any equilibrium, given price P, the expected returns of investing in deposits and risky assets are the same. qH þ ð1 qÞPL ¼ qR0 R1 þ ð1 qÞ
R0 R1 : P
(2)
PROOF. See Appendix. The left-hand side of equation (2) is the expected return on risky projects. If the state is H, investors will hold the risky project. If the state is L, then investors will sell at price PL and invest in the second-period safe asset with the proceeds earning PL R1 ¼ P. On the righthand side, an investor must hold the deposits in state H and would like to purchase the risky projects in state L, which gives the investor a total gross return of RPL0 ¼ R0PR1 . Note that the equilibrium depends on the long-term return of the deposits R0 R1 as a whole, and term structure has less relevance within the framework. Thus, without loss of generosity, we can assume that R ¼ R0 R1 and Rf ¼ R0f R1f . Particularly, we let R1 ¼ R1f ¼ 1 so that P ¼ PL also measures the price in the liquidation market. By equations (1) and (2), we can mutually solve the equilibrium price P and the deposit amounts D. Proposition 1. In equilibrium, R ¼ Rf . The equilibrium amount of liquidity D always exists and is uniquely determined by the solution of the following equation. LðW DÞ DR ¼ qðH RÞ; ð1 qÞ D W D
(3)
the equilibrium price at date 1 in state L is determined by RD ¼ P¼ ðW DÞL
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi q2 ðH RÞ2 þ 4ð1 qÞ2 RL qðH RÞ 2ð1 qÞL
:
(4)
Furthermore, equilibrium price indeed satisfies the condition δ < P < 1.
PROOF. See Appendix.
The fact that δ < P < 1 implies that the allocation of the equilibrium is inferior to the second-best allocation. In fact, the second-best allocation requires a minimum amount of liquidity provision and putting money into risky projects as much as possible. By equation (1), the price is increasing with liquidity provision. Therefore, optimal allocation asks for a minimum price at which the firm is willing to sell; that is, P ¼ δ. However, this price is attractive to investors and will encourage them to invest more in deposits at date 0 to exploit this chance. This money hoarding behavior reduces allocation efficiency because, ex ante, liquidity that exceeds the necessary amount to prevent the moral hazard problem is less efficient than project investment. We are interested in the comparative statics of the model. First, the increase in cash flows at different states have asymmetric impacts on the equilibrium. When the gross return H increases, it directly increases the demand for risky assets resulting in a lower amount of liquidity D. However, the increase in gross return L, while also increasing the expected return, will increase the amount of liquidity. This is because the revenue of selling assets in the liquidation market is constrained by the total amount of liquidity. Thus, the increase in L has no direct impact on the demand for risky assets. However, the increase in L will lower the liquidation price P, which increases the demand for hoarding. Therefore, the equilibrium amount of liquidity will increase. Second, the impact on the liquidity provision in response to the increase in R is ambiguous. On the one hand, the increase in the short-term cash flow will increase the demand for deposits. On the other hand, however, it will increase the total amount of liquidity available in the liquidation market, which pulls the liquidation price up and also increases the demand for risky assets. Nonetheless, we can show that the provision for liquidity will increase R as long as the economy is more likely to be in the H state. We summarize all the results in the following corollary. Corollary 1.
The amount of social liquidity provision D is
(i) increasing with L and decreasing with H; (ii) increasing with R if q 12. PROOF. See Appendix. In later sections, we assume that q > 12 to make sure that the liquidity provision is increasing with R. Assumption 4. q > 12. That is, the economy is more likely to be in a good state. Based on the change in liquidity provision, we can also study the change in liquidation price in response to changes in the parameters. In our model, the price is less than the face value in the bad state. In other words, there is a fire sale problem due to the lack of liquidity. The following corollary demonstrates how returns affect the fire sale price. Corollary 2.
The liquidation price P is
(i) decreasing with L and H. (ii) increasing with R if q 12.
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PROOF. See Appendix. Corollary 2 shows that the increase in risky cash flows will lower the fire sale price. However, just as Corollary 1 shows, while the increase in cash flows in state L will enlarge the discount and worsen the fire sale problem, the increase in cash flows in state H actually reduces the liquidity provision. The corollary also shows that the increase in return on deposits will lower the discount and mitigate the fire sale problem. 3. Capital requirements Recall that the second-best allocation requires the minimum amount of liquidity provision as long as it is still beneficial to sell all the assets in the market. We have shown that liquidity provision decreases if R decreases. If the bank only finances through issuing safe securities, then R ¼ Rf , which is determined by the real factors in the economy. However, based on the scarcity assumption, only banks have access to the safe asset technology. Therefore, it is possible that the gross return on safe security R is lower than Rf , and the provision of social liquidity will decrease and social welfare will be improved. One way to reach this goal is to set a capital requirement because raising capital is expensive for banks compared to issuing deposits and may reduce the return of deposits if they are forced to raise equity capital. In this section, we assume policy makers can announce a regulation at date 0 that the proportion of equity must be no less than C for every bank. For simplicity, we assume the cost of capital for issuing equity is γ > Rf and is exogenously given. In this framework, the capital requirement is a useful policy instrument as it effectively reduces the deposit rate R offered by the bank. To see this, notice that since the bank only has access to the risk-free Project, and banks are perfectly competitive, for any bank, a zero-profit condition implies that Rf ¼ ð1 CÞR þ Cγ;
(5)
where the left-hand side is the cash flow from assets, and the right-hand side is the cash flow owed to outsiders. By equation (5) we can solve the gross return of investors. Lemma 3. For capital requirement C, the gross return on safe securities issued by banks is R¼
Rf γC : 1C
(6)
Furthermore, R < Rf and is decreasing with C. PROOF. See Appendix. The reduced deposit rate will increase the investor’s incentive to invest in the risky projects, as we have seen in Corollary 1. Thus, we immediately find that at least some capital requirement will improve the social welfare because it leads to less liquidity provision. Lemma 4. Total amount of liquidity D is decreasing with C. PROOF.See Appendix. Although a higher capital requirement reduces the amount of liquidity in the economy, it is also disruptive because the constrained liquidity provision will lower the liquidation price P, as shown in Corollary 2. If the price falls to δ, it is indifferent for the firm between selling assets in the market or adding risk. This further increase in capital requirements will not change the expected return on investing in risky projects. However, the expected return on investing in bank-issued security continues to decrease by Lemma 3. As a result, if capital requirement increases further, the unduly low return of holding liquidity will make investing in the bank strictly inferior to investing in the capital market. Moreover, since there is no liquidity offered in the market, there is no asset sold, and risk will be added. This trade-off implies that the optimal capital requirement is such that the price is just equal to δ. The following proposition examines the optimal capital requirement policy. Proposition 2.
C ¼
The optimal capital requirement is
8 R R f > > < γ R
if qH þ ð1 qÞδL >
δq þ 1 q δ
> > : Rf 1 γ1
if qH þ ð1 qÞδL
δq þ 1 q δ
;
(7)
where R is defined as R ¼
δ ðqH þ ð1 qÞδLÞ: δq þ 1 q
PROOF. See Appendix. If the welfare loss of risk-adding behavior is mild, then capital requirements can attain the optimal allocation. On the other hand, if the moral hazard problem is too severe, then optimal allocation would require a negative return on deposits, which is infeasible. In this 6
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case, the optimal capital requirement is restricted by a zero interest rate on deposits. Proposition 2 gives us a new role for capital requirements in addition to regulating the conventional moral hazard problem. The new role is improving social welfare by reducing the unnecessary hoarding activities at date 0 in order to buy discounted assets when the economy is in a bad state. In the next section, we examine the possibility that a shadow banking system arises as regulatory arbitrage. 4. Shadow banking Since capital requirements constrain banks’ activities, banks may try to find some channels to circumvent the regulation. In this section, we consider the possibility that a bank can establish a shadow bank that can bypass the capital requirements. To focus on the role of regulatory arbitrage only, we assume that even if the shadow bank is not subject to capital requirements, it cannot invest in the capital market. This assumption captures the fact that shadow banking institutions, such as money market mutual funds and wealth management products, usually invest through money markets such as repos and offer similar products as traditional banks. To differentiate shadow banks from commercial banks without capital requirements, we make the following assumption. Assumption 5. The assets in the shadow banking system cannot be used as a medium of exchange in the liquidation market. This assumption describes the disadvantages of investing in shadow banking assets. By Assumption 4, the return on investing in shadow banking assets is just Rf . In reality, the assets created by the shadow banking system are often less liquid than deposits, particularly when the economy is in a bad state. Moreover, when making investments, investors need to first convert shadow bank securities to cash or deposits and then purchase other assets. We also assume that before the emergence of shadow banks, the social welfare is second best. Assumption 6. qH þ ð1 qÞδL > δqþ1q . δ , then the liquidity provision is minimized given that all assets are sold in the liquidation By Proposition 2, if qH þ ð1 qÞδL > δqþ1q δ market. The following result shows that the emergence of shadow banks will indeed be detrimental to social welfare. Proposition 3.
The allocation with the optimal capital requirement cannot be sustained if there is a shadow banking system.
PROOF. See Appendix. Proposition 3 shows that the shadow banking system will arise endogenously in the economy if the capital requirement regulation on commercial banks is optimal without shadow banks. The intuition is as follows. According to the previous section, we know that the interest rate on commercial bank deposits, R, is less than Rf when the economy attains the second-best allocation. This motivates investors to use shadow banks to bypass capital requirement regulation because they can offer a higher expected return (Rf ) than other investment channels. As a result, investors move money from commercial banks to shadow banks, and the total market liquidity decreases. Lower liquidity reduces the fire sale price of risky assets leading to a reduction in capital market investment returns. Therefore, investors choose to invest less in the ex ante more efficient capital market investments, and social welfare decreases. This result is consistent with the regulatory arbitrage view of the shadow banking system. (For instance (Acharya et al., 2013; Harris et al., 2014; Plantin, 2014),). The result also implies that the regulator is restricted in the sense that they cannot set the capital requirement as high as they would like, which is demonstrated in the next proposition. Proposition 4.
b < C defined by There is a threshold value for capital requirements C
b b ¼ Rf R ; C b γR
(8)
where b¼ R
Rf L q þ ð1 qÞ2 Rf qH
;
such that: b then there is no shadow banking system, and the allocation is the same as in Proposition 1 but with R ¼ Rf γC. (i) If C C, 1C b then all wealth is invested in the shadow banking system. (ii) If C > C, PROOF. See Appendix. Proposition 4 shows that introducing shadow banks in an environment with strict capital requirements will exhaust the liquidity provision offered by commercial banks, lower the expected return on risky projects, and exacerbate the fire sale problem. As a result, there will be less resources allocated to more efficient risky projects, and social welfare will decrease. On the other hand, if capital requirements are moderate, without shadow banks, the total return earned by the investors is higher than the return from shadow bank securities (risk-free rate). Thus, investors will not deviate to invest in shadow banks. Consequently, the optimal capital requirement is one whereby shadow banks are just about to emerge, which is lower than the capital requirement in the case with no shadow banks.
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Corollary 3.
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b The optimal capital requirement with shadow banking system is C.
PROOF. Omitted. In summary, the emergence of shadow banks undermines the effect of capital requirements. After introducing shadow banks, a large capital requirement may induce shadow banks, which reduces social welfare instead of improving it. The capital requirement regulation should be more discreet in the presence of shadow banks as the shadow banking system might exhaust the liquidity in the liquidation market, and the maximal social welfare that can be achieved through capital requirement decreases. 5. Conclusion Commercial banks are subject to many regulations among which capital requirements are the most prominent. We extend the model in (Gorton & Huang, 2004) to consider the role of capital requirements. Liquidity is necessary as it can promote transactions and prevent the detrimental moral hazard problem by transferring projects from distressed agents to normal agents. However, liquidity is also costly as it reduces the amount of investment in more efficient risky projects. Capital requirements reduce the cost of liquidity and improve social welfare. However, excessively high capital requirements are also not desirable as liquidity becomes so expensive that no investors are willing to hold, which leads to a drying up of liquidity. The optimal capital requirement is achieved when the price of risky projects makes the project holders indifferent between selling them and adding risk when the negative shock occurs. Shadow banks perform a similar function to commercial banks by issuing money-like securities to finance loans. The emergence of shadow banks undermines the effect of capital requirements. Before introducing shadow banks, a large capital requirement is desirable while, after introducing shadow banks, a large capital requirement may induce shadow banks, which reduces social welfare instead of increasing it. Therefore, the capital requirement regulation should be more discreet in the presence of shadow banks, and the maximal social welfare that can be achieved through capital requirement decreases. Our model has several empirical implications. First, the scale of shadow banks increases with an increase in capital requirements. Second, deposit returns decrease with an increase in capital requirements. Third, the holding of cash and deposits in the economy decreases with an increase in capital requirements. These issues can be further explored in future research. Acknowledgements This research was supported by the Fundamental Research Funds for the Central Universities and the Research Funds of Renmin University of China (Grant No. 19XNF001). We thank seminar participants of the Fifth Chinese Economy Symposium and an anonymous referee for helpful comments. Appendix A. Proofs Proof of Lemma 1.
The result is obvious from the market clearing condition
PL LðW DÞ ¼ R0 D:
Proof of Lemma 2. Investing one dollar in deposits will pay R0 R1 in state H and R0 =PL ¼ R0 R1 =P in state L. Investing in one dollar in risky projects will pay H in state H and PL R1 L ¼ PL in state L. Taking the expectation gives the result immediately. Proof of Proposition 1. Combine equation (1) with (2) and we obtain the result. Note that the left-hand side of (3) is decreasing with D, and it is þ∞ when D ¼ 0 and ∞ when D ¼ W. Therefore, the solution always exists and is unique since the right-hand side is a constant. To prove the last argument, note that if P 1, then the left-hand side of (2) is always larger than the right-hand side by Assumption 1. On the other hand, if P δ, then the left-hand side is always smaller than the right-hand side by Assumption 3. Thus, we conclude that δ < P < 1. Proof of Corollary 1. Define f ðDÞ WD D and gðDÞ 1=f ðDÞ, and take differentials on both sides with respect to D and L: ð1 qÞ½f ðDÞdL þ Lf ’ðDÞdD Rg’ðDÞdD ¼ 0; since f ’ðDÞ < 0 and g’ðDÞ > 0, we can conclude that dD Rg’ðDÞ Lf ’ðDÞ ¼ > 0: dL f ðDÞ with a similar approach, we can prove that dD ð1 qÞðLf ’ðDÞ Rg’ðDÞÞ ¼ < 0; dH q 8
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and dD ð1 qÞðLf ’ðDÞ Rg’ðDÞÞ : ¼ ð1 qÞgðDÞ q dR we now prove that gðDÞ 1. If gðDÞ > 1; then f ðDÞ < 1, the left-hand side of equation (3) will be negative since L < R ¼ Rf . Then, as long as q > 12, then 1 q < q, which implies that ð1 qÞgðDÞ < q, and we can conclude that dD dR > 0. Proof of Corollary 2. By equation (2), if L increases, then P has to decrease because, otherwise, the left-hand side will be larger than the right-hand side. Similarly, if R increases, then the price has to be higher because, otherwise, the left-hand side will be smaller than dD dP the right-hand side. According to the fact that dH < 0, we can infer that dH < 0 by equation (1). Proof of Lemma 3. The first part is derived from equation (5). The second part is obvious by noting that R Rf ¼ decreasing with C by (6). Proof of Lemma 4.
CðRf γÞ 1C
< 0, and R is
Combining Corollary 1 with Lemma 3, we can immediately get the result.
Proof of Proposition 2. At the optimal capital requirement, the liquidation price is just δ. By equation (2), we immediately solve the R . However, if qH þ ð1 qÞδL δqþ1q , then R 1, in which case investors will choose not to invest in deposits and will store the δ goods that are not invested in risky assets instead. In this case, the optimal capital requirement is such that R ¼ 1. Proof of Proposition 3. We prove the proposition by showing that at the optimal capital requirement, the expected return on investing in bank or capital markets is lower than the expected return on investing in shadow banks. To see this, note that the expected return when the capital requirement is C is actually qH þ ð1 qÞδL. By Assumption 3, this is lower than Rf , which is the expected return on investing in shadow banks. Thus, if the capital requirement is set at C , then investors will spend all their money purchasing shadow bank assets, implying that the original allocation cannot be an outcome of an equilibrium in the presence of the shadow banking system. Proof of Proposition 4. When C ¼ 0, the allocation is the same as in Proposition 1, with an equilibrium expected return larger than Rf . This implies that there are no shadow banks at all. As C increases, the expected return on investing in the capital market decreases because of the decrease in price by Corollary 2 (see the left-hand side of equation (2)). Due to Proposition 3, there must exist a threshold b At the threshold, the price is at which the expected return on investing in the capital market is equal to Rf . We denote the threshold by C. determined by the following equation: R qH þ ð1 qÞPL ¼ qR þ ð1 qÞ ¼ Rf : P b based on equation (5): b by the equation above. Therefore, we can calculate C Moreover, R ¼ R b b ¼ Rf R : C b γR b then the gross return R determined by equation (6) is lower than R. b However, this means the expected return on investing in If C > C, commercial banks is lower than investing in shadow banks. Thus, there will be no liquidity in the market, which implies that risk will be added to all risky assets making the expected return on investing in risky assets lower than Rf also. As a result, no one will invest in risky assets nor commercial bank deposits. Investors only invest in shadow banking assets. b < C since R is decreasing with b is apparently larger than R since the liquidation price is larger than δ. As a consequence, C Finally, R C.
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