Risk-shifting incentives of depository institutions: A new perspective on federal deposit insurance reform

Journal

of Banking

and Finance

15 (1991) 895-915. North-Nolland

Kose John* and Teresa A. John* Stern School of Business, New York University. New York, NY

looO3. USA

Lemma W. Senbet* College of Business and Management. University of Maryland, College Park, MD 20742, VSA

Received January

1991, final version received March 1991

We characterize the risk-shifting incentives of a depository institution as arising fundamentally from the existence of limited liability and the associated convex payoff to equity-holders. This risk incentive feature is unchanged by deposits being insured, and hence excessive risk-taking by depository institutions is not solely attributable to the flat rate insurance premium. Consequently, the incentive problem cannot be resolved through a risk-based insurance premium, contrary to the prevailing view. We propose a solution that eliminates risk-shifting through an optimal tax structure and specify a corresponding insurance premium that is revenue neutral from the social planner’s (regulator’s) standpoint. The solution is derived in the context of a social objective function that trades off the benefits of liquidity services by banks and the unique informational role of bank loans with the costs of investment distortions engendered by risk-shifting.

1. Intduction

Thrift and bank failures are now at record levels. The depository insurance agencies are either completely insolvent or under a threat of insolvency. Before its demise, the ESLIC faceld liabilities which far exceeded its assets,

*We acknowledge helpful comments and suggestions from Mitcheil Berlin, Andrew Chen, Jan Cyr, George Kanatas, Ed Kane, Darius Palia, James Seward, Gregory Udell, Hal& IJnal, and especially Anthony Saunders. Kose John received financial support from the Yamaichi Faculty Fellowship, Teresa John from a New York University Summer Research Grant, and Lemma Senbet from the William E. Mayer professorship. 037&4266/91/$03.50

6:) 1991-Elsevier

Science Publishers

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K. Johtl er al., Risk-shifting incentioes of depository institutions

and the well-known savings and loan (S&L) debacle is expected to engender exorbitant costs to the taxpayers. 1 The Financial Institutions Reform, Recovery and Enforcement Act (FIRREA of 1989) addressed the thrift crisis and transferred :he responsibilizies of the FSLIC to the FDIC. It is now widzly believed tha.t the deregulation of the banking system that took place in the 1980s gave rise to relaxation of restrictions on bank investment behavior. Previously the regulatory restrictions were intended to prevent excessive risk-taking, while attempting to induce uniform risk-taking in accordance with the flat rate deposit insurance system. Under the post1980 regulatory environment, thrifts and banks had increased incentives to engage in excessively high risk lending, hoping for big payoffs when conditions we.re favorable but transferring losses to the insurance agencies under adverse conditions. These incentives were exaggerated by a laxity in monitoring, surveillance and bank closure (i.e., regulatory forebearance). The apparent incentive problems associated with deposit insurance came into sharper focus immediately after deregulation. A large number cd authors have sought to address the impact of fixed-rate, risk-insensitive deposit insurance on bank risk-taking [see, for instance, Buser et al. (1981), Ronn and Verma (i986), Pennachi (1987), Bierwag and Kaufman (1983), Marcus and Shaked (1984), Kane (1986,1989), Flannery (1989,1990), Keeley (1990), White (1991) and Acharya (1991)]. The prevailing view is that a flat rate insurance system is not incentive compatible, suggesting that incentives exist for banks to undertake higher asset risk levels when deposit insurance premiums are independent of the underlying risk of the bank’s portfolio. It seems to be generally accepted in the literature that asset risk-incentive problems would be alieviated through a risk-based insurance premium. For instance, Ronn and Vermz (1986) express the prevailing sentiment when they argue, ‘In the absence of deposit insurance, riskier banks will be able to attract deposits only at higher rates, and these higher costs of funding serve as builtin market-regulated incentives to limit excessive risk-taking by banks’ (p. 871). By analogy they suggest a risk-adjusted insurance premium system as a mechanism to reintroduce incentives for limiting excessive risk-taking. We take a view in this paper that the fundamental aspect of the asset riskiccentive problem is not inherent in the incentive system underlying a flat premium rate deposit insurance, nor even in the deposit insurance itself. Consequently, an actuarially fair price of deposit insurance has no impact on the risk incentive behavior of a depository institution. Specifically, the problem is fundamentally attributable to the convexity of the levered equity payoff resulting from limited liability, that exists in full force in a deposit

‘A study by the C’ongressional Budget (Mice (1990) mentions to the taxpayers of %90-150 billion.

an estimated present value cost

K. John et al., Risk-shifting incentives of depository institutions

897

market even without deposit insurance. a This is familiar from the financial agency literature where there is a conflict between debtholders and equityholders. We propose a mechanism which alters the incentives of the firm (bank) by altering the payoff structure to the residual claimants. One way to think of our proposed solution is that it is a properly designed system of taxation with convexity in the bank profits such that a higher tax rate is imposed on high levels of profits compared to the tax rate on low levels of profits. Such a tax scheme can be implemented in a manner very close to the existing scheme of corporate taxation with the following features: (1) tax deductibility of payments to depositors, (2) a specified amount of additional deductions (nondebt tax shields, such as depreciation), and (3) normal taxation of unshielded profits. The amount of additional deductions allowed in (2) will be endogenously determined as a function of the level of deposits and the menu of investment opportunities available to depository institutions. The overall idea here is that the after-tax payoffs to the bank equity-holders now have a concave region in addition to the convex region arising from deposit financing and limited liability. We show that, with a properly designed tax structure, the risk-shifting incentives of banks can be eliminated and that the asset risk choices made by banks conform to the Pareto optimal ones. Indeed, we show that there there is a tax structure that solves the risk incentive problem completely and a corm pondicg deposit insurance premium that is revenue neutral. Moreover, the features of the tax scheme can be suitably set such that the premium charged is a ‘fair price’ of the net transfers that the guarantor makes to the depository ;- rtitution appropriate for the investment incentives of institution’s insiders. in other words, even in the presence of moral hazard, a fairly priced deposit insurance scheme can be implemented under our proposed scheme if it is a desired priority of the regulator. A second way to view our solution is that the regulator (the guarantor) collects the insurance premium in the form of an upfront fee plus a specified number of warrants. The number of warrants required and their exercise price can again be endogenously determined as a function of the level of deposit and the menu of investment opportunities. As before, the payoffs to equity-holders now have a convex region followed by a concave region such that the risk-shifting incentives are eliminated. Although we do not pursue the details of this interpretation of our proposed solution, its isomorphism to the tax structure interpretation is complete and the corresponding qf the premium charged by the government insurance agency is not fairly priced in the sense that it does not represent the value of the guarantee provided, there would be a wealth transfer between the regulator (the insurance ag;acy) and the owners of a depository institution, We do not dispute this. However, our claim is that as long as the regulator cannot write and enforce contracts on asset risk choices by depository institutions, the risk-shifting incentives of the institutions exist in full force whether or not the deposit insurance premium is fairly priced.

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K. John rt al., Risk-shiftingincentivesof depositoryinstituticns

solutions can be constructed easily. 3 In both of the above interpretations, our approach provides a confluence of the corporate finance and financial intermedi? tion paradigms. ----r~tp risk choices has been The effect of taxes and warrants on ~l,,~.,._. sufficiently recognized in corporate finance, but not so in financiai intermediation [see, for example, Green (1984), Green and Talmor (1985), Barnea, Haugen and Senbet (1985) and John and Senbet (1990)]. We capitalize on this role in designing and implementing an optimal tax structure and an associated revenue-neutral deposit insurance scheme. Such an optimal design is in the context of a sociai objective function which trades off the social value of depository financing (say, liquidity services, and special informational role of bank debt) with the loss in value due to risk-shifting incentives of

debt. At the core of the asset or lending risk incentive problem is imperfect observability by outsiders (depositors and regulators) of the asset or lending quality choices made by corporate insiders (bank managers). The solution we propose is incentive-compatible and does not call for observability of private action. We think the debate on excessive risk taking can be resolved easily if the risk quality choices by depository institutions are completely observab!e, because forcing contracts (or regulatory devices) can be structured to achieve the first-best, efficient solution. If the only aspect of bank debt under limited liability were the risk-shifting incentives and the associated investment distortions, then the solution is simple: a bank would optimally choose no leverage (deposits). However, an unlevered firm (with no depository financing) can hardly be considered a ‘bank’. Here the social planner would provide inducements for banking if the activity serves some special or unique purpose. It has been argued that depository financing and banks play a special role which has social value and that federal deposit insurance enhances that value. It is uniformly suggested that deposit insurance is a means of preventing bank runs on distressed institutions and contagion effects on even healthier institutions. The positive externality of prevention of widespread failures of depository . . . mstltutrons and of ad.,. 3_ consequences on the aggregate economic activity .rmrc* calls for subsidization of the institutions. The subsidies may come in the form of valuable bank charters or an insurance premium priced on a less than actuarially fair basis. 31t is apprcpriate here to mention two actual cases which could be viewed as implementatiocs of a similar idea. Warrants were held by Ihe government as part of its loan guarantee arrangement for the Chrysler Corporation. Similarly, warrants were held by the FDIC whe.1 Continental Illinois Bank was ‘nationalized’in April 1984. Such arrangements are ignored in the context of the deposit insurance literature and policies presumably because the premium can be collected in advance when the institutions are not financially distressed. In the two cases mentioned above, the warrants were used because the premium or the value of the loan guarantee was not collectible in advance.

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899

A less commonly discussed special function of a bank comes from its asset or lending decision and its unique function as an informed insider in the financial market. It is argued that the role of bank finance in mitigating the effects of informational asymmet ies among contracting parties in the capital market allows for a larger scale of debt finance than in the absence of banks [see Fama (1985), Bernanke ( 1983), James ( I987)]. Any discussion of deposit insurance reform and proper pricing of the insurance premia has to be done in a framework of a social objective function which takes into account the social value of this special role of bank lending on the asset side. Thus, in this paper we take account of the social value of (a) liquidity services by banks on the liability sii-ie of the balance sheet and (b) the special role of bank lending on the asset side. An important aspect of our analysis is a specification af the social objective function underlying the deposit insurance reform. Although it is customary to model the objective as that of minimizing the regulator’s costs of maintaining a system of federally insured depository financing [see, e.g., Buser, Chen and Kane (1981) or Acharya ( 1991)], we have specified it in more general terms Our specification of the objective function consists of two components; the first represents the costs to the society arising from distortions on the asset side of the bank’s balance sheet due to leverage (deposit financing) and deposit insurance in a world of limited liability, and the second component represents the offsetting social value arising from liquidity services that banks provide as well as the special role of bank lending. We focus our analysis on the incentive effects of depository financing on the risk characteristics of assets (loans) chosen by banks and on how a properly designed deposit insurance contract can mitigate the distortionary effects of deposits. The speciai nature of bank loans and its unique role in a world of imperfect information has been emphasized before [see, e.g., Bernanke (1983), Fama (1985) and Merrick and Saunders (1985)J. The argument could be made that a well-designed FDIC scheme should increase the benefits of the unique role played by bank lending while minimizing its distortionary costs. We focus our analysis on such a tax-revenue scheme which eliminates ass&/lending distortions. Moreover, the scheme can be implemented in a revenue-neutral fashion. Section 2 characterizes a risk incentive agency problem of a depository . . instrtutlon through a simple model. In section 2.1 we examine the berichma~k case of the firm financed partially with deposits. The incentive impact of deposit insurance on asset quality choice is provided in section 2.2. Section 3 proposes a solution that is incentive compatible through an optimal tax structure and specifies a corresponding insurance premium that is revenue neutral from the standpoint of a social planner (regulator). Conclusions and policy implications are in section 4.

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K. John et al., Risk-shifting incentives of depository institutions

2. The model

The model here is designed to capture the focal issues in a simple framework. For simplicity, consider a representative depository institution (bank) and representative risk a.ssets (loans). The risky choices made by the bank (as embodied in the loans extended) are modeled as ‘private action’. That is, there is less-than-perfect external monitoring of the risk choices by outsiders (including regulators), and consequently there is ‘incomplete contracting’ vis-&vis those choices. Imperfect observability of private action is at the heart of the agency tradition, and it is crucial for our analysis. Ours is a three date two-period model. At t=O, the bank collects deposits and engages in residual financing through equity subject to existing regulatory constraints. The deposits are insured by a government agency (say by the FDIC) and the bank pays the relevant insurance premium 4. All the associated optimal contracts are written and ‘priced’ at t=O, given the information available at t =0 and admissible contracting opportunities.4 The price of the financing claims (interest rates on deposits and the price of equity) are determined in a ratic’nal-expectations manner. At t = 1, investment opportunities appear, This represents the possible loans (asset choices) that thr; bank can make. For simplicity we assume that these investment opportunities are of :Y-J types; (1) safs investments which are basically opportunities with zero risk and zt;ic net present value (NPV) (e.g., U.S. Treasury bills), and (2) one from a men’u of possiblle risky investments (loans) which are indexed by a parameter p. These projects underlying the loans require an investment I to be made at t= 1, and for simplicity we assume a zero risk free rate of interest. The returns from the loan-backed projects are high or low (h dollars or 1 dollars, respectively), with h > I > 1, 1>O, where p is the probability of the high outcome, h, and (1 -p) the probability of the low outcome, 1. The bank insiders observe the parameter p at t = 1 before they choose between the riskless loan and the risky loan. The value of the parameter p is not observed iy either depositors or regulators (government). This precludes any contracting contingent on the value of the parameter (p). Uowever, all the relevant parties know that p is distributed uniformly over the interval [0,11. The modeling device captures the intuition that, given the level of monitoring undertaken by regulators and outside investors in a cost-effective manner, the bank has additional information about the prospects of the loan (captured in p). Therefore, the bank continues to have discretion in its choice of investment risk. I-PI. 111eamoW ILr Y J%:~a hm” to be raised by the bank at t =O. At this time bank Wders contribute capital of amount Q, raise additional funds by selling 4Although at this time we restrict our menu of financing claims to debt and equity,we will show that a richer set of claims are isomorphic to the solution that is proposed in this paper.

K. John et al., Risk-shifting

incentives of depository

institutions

901

equity to outside investors, and issue deposits with promised payments to depositors. The depositors invest an amount d, at t =O, where do represents the rational expectations price of the promised payment (6) at t=2. Similarly, the equity-holders contribute an amount at t =0 which is the fair price for the cash flow they expect to receive at t =2. In our framework, # can also be determined in a rational expectations basis as the fair value of the deposit insurance provided. However, the regulator may choose to charge an insurance premium that is less than actuarially fair value (i.e., fixed) as a means of inducing the bank to undertake deposits. This may serve the regulator’s social objectives better, in conjunction with a system of bank taxes and subsidies which will be considered later. At t= 2, the loans mature and proceeds are collected. Let p denote this terminal cashflow which is equal to I if the riskless investment was chosen at t = 1, or equal to h or 1 depending on the outcome from the risky investment if that choice was made at t = 1. The deposit insurance agency (say FDIC) honors its guarantee by paying the depositors max(O,d -p). The depositors are thus paid off fully if their deposits are fully insured. We assume that all deposits are insured, although we will have d commentary on the role of uninsured deposits in our concluding section. The residual amount max {p-d, 0} may be taxable according to the tax structure in place. In our proposed solution to the incentive problems, the tax structure is an important component The after-tax residual amount is distributed to equity-holders. The insiders of the bank (including management) act to maximize the wealth of the current shareholders subject to the tax and regulatory structure in place. We abstract. from discounting in all time periods by assuming that riskless interest rate is zero. In our frictionless capital market with no transactions costs, the firm’s securities (deposits, equity and deposit insurance) can be valued using a risk-neutral valuation approach by taking the relevant conditional expectation of cashflows (say, with respect to the equivalent martingale measure). Now we turn to the underlying social goals and the social planner’s (regulator’s) objective function. This objective function is based on two goals: (1) to minimize the risk incentive agency costs or the loss of vatuc resulting from distortions in investment policy, and (2) to maximize the social value of banking arising from (a) the liquidity services that banks provide and (b) the social value of the ‘special’ nature of bank lending in a world with imperfect information. In our framework we will show that the large comwnent of financing provided by deposits lies at the heart of a bank’s investment distortions. That is, the bank may choose to overinvest in risky projects relative to net present value maximization. Such ‘risk-shifting’ incentives of’ the firm associated with the issuance of risky debt have been studied in t eckling (1976), corporate finance literature [see, for example, Jensen and

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K. John et al., Risk-shijting incentives of depository imtitutions

Green (I%!), Barnea, Haugen and Senbet (1985) and John (1987)]. Here the social costs of risk-shifting incentives will be measured by the difference in the value between that under a distorted investment policy in as world of moral hazard and limited liability and that under the full-information Pareto-optimal one. The second aspect of the social planner’s objective is the social value of bank lending. This has two components: (a) the first component is the social value of liquidity services supplied by banks on the liability side of the balance sheet, and (b) the second component is the social value generated by banks on the asset side which represents the special lole of bank lending in a world of imperfect information. Diamond and Dybvig (1983) make a case for government deposit insurance in a model where depository intermediaries provide important liquidity services by offering insurance against privately observed shocks. Any study of deposit insurance reform has to consider the social objectives associated with the liquidity services provided by banks. However, this aspect of the social objective is not explicitly modelled in this paper. Endogenizing this component of the objective in a model of bank runs -with demand deposits would be interesting [see Berlin and John (1991) for such an attempt]. However, we abstract from these details and focus on the asset side of the bank’s balance sheet resulting from deposit financing and limited liability. Thus, our modelling strategy assumes that deposit insurance fully eliminates the incentive for depositors to engage in bank runs for any level of depository financing d (such that depository financing can be modelled isomorphic to a ‘time deposit’ maturing at t =2) and that the society obtains value equal to g,(d) in the form of liquidity services from the existence of such deposits. Further assume that gb(d) represents the social value of bank asset/lending policy in (b) above. Let g(q=gJdj+g,(d). We assume g(*) is a unimodal concave function and the units of value are commensurate with the value derived from investments. Since the two values in the social welfare function are additive by assumption, the social planner’s objective is to maximize the value of liquidity services and ‘uniqueness’ of bank lending, g(d), minus the loss in social value due to suboptimal investments by banks, It will be clear that the following analysis is valid for any level of deposits d in the economy, and consequently the specification of g(a) is very general. Since the proposed deposit insurance scheme eliminates bank investment distortions, and is revenue-neutral for any specified level of depository

financing d in the economy, the only role played by g( .) is to pick a level of d (say n*) which is optimal from the perspective of the social planner based on the optimal level of liquidity and lending services to be provided by the banking system.

2. I. Deposit financir~g md risk-s ijhng incentiws

As was described in the introduction of the paper, an extensive literature on deposit insurance has attributed excessive risk-taking by banks to the existence of risk-insensitive insurance premia. Accordingly, a frequent suggestion for the reform system is an introduction of risk-based actuarily fair deposit insurance premium. However, if we assume that risk choices made by banks are not perfectly monitored, so that forcing contracts regarding such choices would be ineffective, then at least in the first analysis, debt fmancing (by deposits) and not a mispricing of deposit insurance can be shown to be responsible for excessive risk taking by banks. In this section we derive the investment incentives of an ‘all-equity financed’ bank as a benchmark for such comparisons, then derive the investment policy of a bank financed partially with deposits. ’ We also show that the risk-shifting incentives of a levered capital structure are not affected by the nature of pricing (fair or not) of deposit insurance, nor by the existence of deposit insurance itself. It is important to recognize this from : policy perspective so that any proposed reform can be directed to the real cause of the problem. (1) An all-equity case. First let us consider a bank which is financed entirely by equity. Here the bank insiders contribute Q and raise equity financing e such that Q + e= I + 4. The optimal investment policy choice (between riskless and risky loans) to be made at t = 1 is as follows. The bank insiders observe p and choose to invest in the risky project if ph+(l -p)lZ/. That is, they inve;t in :he risky project only if it yields a higher present value, otherwise invest in the riskless project (say government bonds) yielding zero net present value. Denote as p* the lowest (cut-off) value of p which satisfies (1) such that the risky investment dominates the riskless one. That is, p*=(z-c)/(!r--I).

(2)

The investment policy in (1) is equivalent to investing in the risky project for all values p2?p”. Definition I. An investment policy of investing in the risky asset for all pS~p* will be denoted as investment policy (p*). ‘WC recognize that an ‘a!!-equity’ bank ceases to be a bank in the usual sense. We use this as a theoretical benchmark. because it provides a sharper focus on our view of the real source of risk incentive problems.

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incentives of depository institutions

An investment policy {p*) produces the following terminal distribution (given that p is uniformly distributed on [0, I]):

it1 -P*Y \

It follows that the net present value of an investment policy {p*) is given by NPV(p*)=p*l+(1/2)[1

-~*]~l++[l

-p*2]h-f.

(3)

An ah-equity ‘bank’ firm implements an investment policy (p”), where p” is given in (2). The value achieved from this investment policy is ~~v(p~)=p~1+(1/2)[1

-p”)‘l+$[l

-p’*]h-I.

(4)

The expression in (4) characterizes the value which could have been achieved if p were perfectly observed by all parties (including investors and regulators) and if a complete set of enforceable contracts specifying any investment policy could have been written. In other words, NPV(p’) is the highest value achievable in a full-information scenario with complete contracting. Thus, the invesrmcr$ policy {p”j and the resulting value, NPV(p’), forms a useful benchmark to measure the distortions caused by the risk shifting incentives due to financing with deposits. (2) Financing with deposits. In this sub-section we will consider the incentive effects of a bank’s typical financial structure whereby it issues a substantial proportion of deposit claims to finance assets. Let us examine the effects on investment incentives from financing with deposit claims of promised payment d, where d is no-w exogenously specified. (The promised payment d can also be thought of as the maximizer oTg(s), the social value of depository intermediation as defined earlier.) Risky debt (d>l) issued by hmited liability banks induces them to invest in excessively risky loans relative to the case of complete contracting and observability. This incentive problem is present whether or not deposits are insured. Moreover, we tvill show that fair pricing of deposit insurance is inconsequential to the bank’s

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905

investment behavior and hence will not ameliorate the asset risk incentive problems. Proposition 2. (a) For a level of deposits @promised payment d, the implement an investment policy {p(d)} where p(d) is given by

P(d)=

(I-d)/(h-6)

when I
0

when d 2 1.

(b) For any ualue of deposits such that d>

I

(i.e., in some states the bank

cannot honor the promise to depositors from the cashflows of its investments), the implemented investment policy {p(d)) is riskier than the Pareto optimal one {PO). (c) For values of d such that I
ProoJ (a) With a promised payment d outstanding to depositors, the bank insiders will invest for values of p, p zp(d), where the residual payoffs to equity-holders are higher, i.e., pmax{0,h-d)+(1-p)max{0,I-d}~max(0,I-d). Now the cut-off probability p(d) is the lowest value of and which satisfies (6) as an equality. (b) For d > 1,

(6) p

which satisfies (5)

p(d)=(I-d)/(h-d)<(I-l)/(h--I)=p’.

The result follows from the general observation that the investment policy generates a terminal cashflow distribution riskier in the sense of Rothschild and Stiglitz (1970,197l). (c) Again, from eq. (5), d >d’ implies p(d)
(p’), with p’
2.2. Deposit insurance and investment incentives

The risk-shifting incentives described in proposition 1 are fami the agency literature in corporate finance. In the banking literature, it is a widely held view that the existence of deposit insurance and the riskinsensitive (flat) premia lead to increased risk-taking incentives. T ment runs as follows. Since deposit insurance represents a put bank has purchased from the government, it pays the bank to i

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K. John et al., Risk-shi/ting

incentives of depository institutions

RESIDUAI PAY-OFF

X=Y c

0

d

BANK’S CASH FLOW

Fig. 1. Equity pay-om a convex function of bank’s cash flow.

riskiness of its investment choices in order to increase the value of that put. As argue1 by Ronn and Verma (1986), in the absence of deposit insurance, riskier banks are able to attract deposits only at higher interest rates and this higher cost serves as a ‘built-in’ market disciplining device. Under this view, the flat rate deposit insurance system needs to *: reformed into a risk-based system, where the premium varies with the riskiness of banks. However, in the scenario described above without any deposit insurance, the bank has purchased the same put from the depositors in the form of limited liability protection to default. Again, the incentives of the bank would be to increase the riskiness of its asset investment policy to maximize the value of the put. Another way of seeing the result is that the risk-shifting incentives arise fundamentally from the convex pay-off structure of equity-holders. In fig. 1, OXZ is the pay-c:, to equity-holders with or without deposit insurance. This convexity in the pay-off structure induces risk-shifting incentives which arise irrespective of the existence of deposit insurance and the fair (unfair) premium charged for insurance. Thus, the premium 4 paid for deposit insurance by the bank does not influence the investment incentives. Rather, it is the residual pay-off structure which determines the bank’s investment policy (p(~!)>.This can be summarized in Proposition 2.

K. John et al.,

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907

Proposition 2. Given a level of deposits of promised payment d, the firm implements an investment 0 Aicy p(d) whether or not the deposits are insured and whether or not 4 is the fair price for the deposit insurance.

In our framework, a deposit level of d>l induces an investment policy {p(d)>, and the fair pries SC@!)of the deposit insurance can be easily determined. Let pd= p(d) as given in eq. (5). Then $‘(d)=pd(d-I)+

+(f/2)(1 -p’)2(d-r)+,

(7)

where a quantity q+ denotes max (0,q). Now if the bank with a level of deposits d can obtain deposit insurance at a price 4 <4’(d), it clearly gains from it and there is a wealth transfer of 4’(d)- 4 from the regulator to the equity holders of the bank. What we art emphasizing here is that the first order effect of a fair pricing of deposit insurance does not affect investment incentives directly due to limited liability and the attendant risk shifting incentives. It should be pointed out that the objective we have specified for the social planner is more general than minimizing the costs of providing FDIC insurance, since it takes into account the minimization of the costs of investment (or lending) distortions by the banking sector net of the benefits of bank lending and provision of liquidity services in the economy. If the objective of the regulator is to achieve efficient risk choice by the bank, the issue of fair pricing of deposit insurarce is not a central issue. From the bank’s standpoint, the residual equity pay-off and the associated risk incentives remain intact irrespective of deposit insurance. By charging a deposit insurance premium of 4~4’ and undertaking to insure the deposits, the insuring agency is taking on a contingent liability at t =2 whose value at t-0 is 4’. In other words, the insuring agency loses an amount, +‘-@, at t =O. Although this loss can be eliminated by charging the fair premium $‘, the loss in social value due to inefficient investment persists even though the fair pisemium 4’ is implemented. Using eq. (3), the net present value of implementing an investment policy (p”} (pd=p(d) as in Proposition 1) can be easily computed. The loss in value A I’(d) = NPV(pO) - NPV(pd),

(8)

represents the cost due to distorted investment incentives when a deposit level d is used for financing. Recall that we formulated the social objective (the objective of the social planner) to be s(d)=&%-AI’(d),

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incentives

of depository

institutions

where g(d) represents the value of liquidity services provided by a deposit financing at level d. As g(m)is increasing in d up to Id, and AV(d) is increasing in d up to bi=I, the trade-off will determine an optimal level of deposit financing desired in the economy.6 In the following section we will explore mechanisms that can be used by the social planner or the regulator to reduce AV(d) by realigning the investment incentives of the firm with those of the social planner even at high levels of d. We will propo!:e a scheme of taxation wh5ch provides sufficient incentives for the bank to implement their Pareto optimal asset investment policy (p”}. It should also be mentioned that the ‘bank’, if given a free choice of its own capital structure, will choose an all-equity financing mode. The reason is that by choosing any level of deposits d> 1, it incurs an agency cost associated with the distorted invsstment incentives {p”> and the resulting loss in value Al’(d). In other words, the bazk has to be eithsr mandate{1 to take on deposit financing at an appropria’e level d or given some incentives to ;dke on debt in its capital >tructure. This point is familiar in the agency literature of debt financing. The schen:e proposed below will provde such incentives to the banking firm by giving ia tax advantage to debt.’ 3. A proposed solutia

It was r+ointed out L- section 2.1.1th’dt risk-shifting incentives are induced by convex:ty in the residiyal pay-off !‘unct& (to equity-holders) in the banrc’s cashflows ?v\len a debt level, d, is o\;tstanding. Fair or below-fair pricing of deposit ins30 rice may not ci:3nge thti pry-off structure of equity claims. On the I?ther hand, any scheme which c:ltcrs t”e pay-off stricture to equityhol&rs ca:i cl?aiage the investment En,entives in our mcdyl. Conseqi.ently, any ,ncen’ ve compatible solution to i’le investment problem could come fnm a fam..i;r of such schemes. The scheme proposed here allows for an cptimal sharing ruls for claimants, where if is now recognized that the deposit insurance agency or the regulator as j,.$s ar>other claimant. ihe scheme takes a form of bank 6A social ob, ective, whit,. is similx itI spirit, guia 2s thi: analysis of Goodman and Santomero (1986). They a; gue that switc !ng to a variable-rate Jeposit insurance, while decreasing the costs of financial firnl iailure, may i, ‘.retise the social costs connected with real sector bankruptcy and that an approp.iate deposit inst. .ance oricing must ueigh the tctsl socia) COO arising from both sectors. ‘While we argued earlier that :..E oricing of depcsit insurance is inconsequential tao the investment disacxrtionassociated with a given level of deposits, it may serve as an inducement for taking on addi:ional debt (deposits: if it is priced less than actuarially fair. However, ouproposed solution is applicable even L-r high levels of debt. Also the vaiue associated with a bank charter can be an additional indu. lent for taking on depobits, although in recent years its value might .&lavediminished as a resth of deregulaticn and ir.crea.sed competition in the banking and financial system [see, for instar ce, Keeley (1990)].

K. John et al., Risk-shgting

L’

X 0

incentives ojdepositor~: institutions

909

45”

d

Fig. 2. After-tax equity pay-off: a convex-concave

c!+d

BANK’S CASH FLOW

function of bank’s cash flow.

taxation and the solution calis for an optimal desic 1 of taxation in a vein s&lar to the public finance literature or to the design of i;lcentivecompatible contracts in the financial agency literatlcre. One possible implementation of the tax scheme can be specified as follows. First, make the bank’s payments to debtholders (of the amount d at t = 2j tax deductible. An additiona! amount, 6, to be specified as a policy parameter, is tax deductible. Impose a base tax rate z on all residual cashflow distributions to equity holders beyond the amount, 6 (i.e., the tax rate 7 is impose3 on cashflows above d+6). Note that this proposed implementation is very close to the current tax regime if 6 is consic’zred as a non-debt tax shield available to the bank. The tax shield, 6, ha.2 to be determined as specified below, as a function of the tax rate 7 in place and the investment opportunities available to the bank. It can be seen hm dig. 2 that for b >C and z >O the pay-o% to cquityholders has a convex region (OXY) and a concave region (XYW). controlling the relative importance of the convex region and the concave region through parameters S and t the investment incentives can be realisned with that of Pareto optimal levels for any given level of deposit ~~a~~i~~ The fo!!owing proposition specifies the value of S which restores Pareto optimal investments for any level of d and a given tax rate in place, 0 5 r < I..

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et a!.. Risk-sh#ing incentives of deyosiiory institurrons

Proposition 3. Assume 7 is the marginal tax rate in place and d is the level of deposit fi;lancing used. Ex deductibility of payments to debtholders and an additional tax deductible amount

,j-(l -- -‘)(&I) , 7 induces a bank asset investment policy (pt> vvhere p:=p’. That is, the Pareto optimal investment policy {p”> in eq. (2) will be implemented. Proof.

Under the specified tax system equity-holders till invest in the risky project for all p 1 of, where pf is given by p;[(h-d)-r(h-d-6)]=[(I-d)--r(l-d-6)],

(12) For the investment policy {pf) to be identical to the Pareto optimal investment policy (p”>, set the right-han,d side of (12) equal to the right-hand side of (2). Simplifying yields 6 as in (IO). 0 For any level of deposit financing for the tax rate 7 already in place (possibly in accord with other social agendas), and the specified technology, we have characterized the additional tan deductible amount 6 which precisely induces Pareto optimal investments such that {p:} ={p”). What is more important is the general principle involved here. By imposing an incremental tax on the high cash flows of the bank (i.e., by imposing a convex tax structure on the bank’s cash flows), the residual pay-off to the bank*s owners now has a c’jncave region. The risk-shifting incentives of depository tinaqcing can be ameliorated by adjusting the importance of the concave region suita.bly. This basic principle is very general and goes beyond the specifics of the technology modelled here.* An important aspect of our approach is that by implementing the tax scheme (7,d) characterized in Proposition 3, the regulator can accomplish the right incentives for asset risk choices by banks independently of the nature (fixed or variable) and the level (fairly priced or underpriced) of the insurance premium +. charged to the banks upfront. One possibility is that the social %nder the proposed scheme the equity-holders are their returns above d+S with an outside claimant, the agenfjf costs of outside equity [as studied in Jensen and promon of effort or excessive perk consumption1. We and abstracted from other incentive problems.

precommitted to taxing authority. Meckling (19X)] have focused on

share a fraction T of This may give rise to leading to suboptimal

risk-shifting

incentives

K. John et al.. Risk-shifting incentives of depository institutions

911

planner would like to implement a self-financing scheme such that the deposit insurance premium #0 collected at t=O plus the present value of taxes collected at t =2 equals the present value of the pay-offs made to depositors under the guarantee. The details of such a revenue-neutral scheme is specified in Proposition 4. On the other hand, the regulator may choose to set the premium below the fair price of the guarantee so as to induce additional deposit financing by banks. In this case, the underpricing of deposit insurance provides a subsidy from the regulator to the bank owners similar in spirit to that provided by the tax deductibility of debt payments. Whethsr the deposit insurance premium & is underpriced or fixed does not induce asset choice distortions by banks so long as the tax scheme (t,S) in Proposition 3 is in place. Proposition 4. Suppose the social planner (or regulator) has chosen to implement a deposit level d>i. Then a tax structure (z,&), where 6 is as in Proposition (3) and a deposit insurance premium &, paid at t = 0, as specified in eq. (13) achieves revenue neutrality and Parer0 opttmal investment incentives. #,,=p’(d-I)+

++(l -p’)*(d-l)+

+(l

-p’*)(h-d-6).

(13)

Proof:

A tax structure (t,S) implements the investment policy {p”} as in Proposition (3) and specification of 4. will not alter that. Now to achieve revenue neutrality, we simply set $. plus the value of tax collected [ = $. + fr( 1 - po2)(h - d - S)] equal to the fair value of the deposit insurance under investment policy {p’}. Substituting p” in eq. (7) and rearranging yields (13). 0

’

For any level of deposit financing which is optimal for t1.e economy [say in terms of the social value of liquidity services characterized by g(d)] and for any tax rate r which may be in place due to some social agenda, Propositions 3 and 4 provide 6 a,nd &o which achieve value-balancing for the social planner and induce the right investment incentives. Two things should be noted here. The social planner still retains the flexibility of setting the deposit level d, or more generally, the size of the banking sector, and the marginal tax rate r to satisfy othe social agendas. For example, suppose do, the maximizer of g(s), is chosen. Note that under the proposed scheme the value of loss AV(do) has been eliminated. Consequently, implemen.;ng do along with the corresponding tax structure (z,6) in Proposition 3 and (b. in Proposition 4 will achieve the maximal value for the social objective in (9). The deposit level in the economy do can be set by a number of policy variables available to the social planner, including capital requirements, reserve requirements, corporate (bank) tax rate T, and, more importantly, barriers to sntry into the banking system (e.g., non-tax barriers, such as

912

K. John et al., Risk-shifting incentioes of depository institutions

difficulty of attaining charters). We have proposed a revenue-neutral deposit insurance scheme which achieves the maximum value for the social objective. In arriving at the solution proposed in Proposition 4, we satisfy an objective for the social planner which is very general. In making it revenueneutral, the FDIC scheme is self-financing and therefore minimizes the cost of the net FDIC scheme to zero if that happens to be a priority of the social planner. Minimizing the cost of providing deposit insurance has been used commonly as an objective for the regulator. Similarly ‘fair pricing’ of the deposit insurance is also accomplished by our scheme, if that happens to be a priority of the social planner. The scheme proposed here can also satisfy larger goals of minimizing distortions on the asset side of the banking sector or that of maintaining an optimal level of liquidity services in the economy. 4. Conclusions We have taken a view that excessive risk-taking incentives of depository institutions are endemic to the existence of limited liability and the associated convex pay-off to equity-holders. The moral hazard problem arises from imperfect observability of private investment incentives controlled by bank insiders or decision-makers. It is important to recognize that the risk incentive feature of limited liability and incomplete contracting issues are unchanged by deposits being insured, and hence excessive risk-taking incentives are not solely embedded in the flat rate insurance system. The policy prescription which calls for a reform of deposit insurance system through a risk-adjusted premium structure may be misguided in addressing the depository institution’s risk-shifting incentives. Our proposed solution calls for an optimal design of a sharing rule for depositors and equity-holders through a well-designed tax structure. We show that the scheme is incentive compatible in the sense of serving as a selfenforci .rg device to induce socially optimal risk choices by bank managers working on behalf of existing equity-holders. These risk choices need not be observed by the regulator. If they were to be observed, the regulator can trivially achieve the desired risk choices through forcing contracts. Tht solution we propose is consistent with the agency tradition of corporate finance, because our view combines ideas from this tradition with issues in financial institutions. From our standpoint, a depository institution is a levered firm allowed to issue guaranteed loans. It is interesting that the warrants held by the government in the early 1980s in conjunction with the Chrysler ioan guarantees and Continental Illinois warrants of 1984 held by the FDIC are in the same vein of our proposed tax scheme. The loan guarantee is isomorphic to deposit insurance, but the government had to rely on an ex post sharing rule via warrants in lieu of an insurance premium because of Chrysler’s cash flow crisis. However, this warrant scheme had,

K. Johr

et al.,

Risk-shijbg incentivesof depositoryinsrimions

913

intended or not, an incentive compatibility feature in the sense of potentially controlling undue risk choices.’ While the primary goal of our proposed scheme is to achieve incentive compatibility of risk choices, we also show that it can be modified to include a fixed component insurance premium if the regulator desires that the scheme be revenue neutral beyond controlling adverse investment incentives. In addition, the scheme, through its tax subsidy feature, provides an appropriate incentive for issuing deposits in accordance with the socially desirable level of banking activities. Thus, the proposed solution has three desirable features, namely (a) incentive compatibility, (b) revenue neutrality, and (c) subsidy. Our approach calls for a self-enforcing device as an alternative to regulating investment behavior through forcing contracts. The flat rate insurance premium might have worked efficiently in the regulated financial environment when the portfolio choices of depository choices were readily observable. If regulation had achieved observable uniform risk-taking by all institutions, it might have been justified to charge a uniformly flat premium. However, with the deregulated environment of the 198Os, institutions had wide latitudes in investment choices with increased problems associated with observability of private investment behavior. Forcing uniform risk-taking would require frequent and costly monitoring and may even lead to inefficient investment (albeit with low risk). Indeed, it is well known in the agency tradition that forcing contracts can achieve first best efficient choices only if private actions are perfectly observable.” Of course, our proposed scheme is not intended to be unique. There may be other mechanisms which serve similar purposes.’ ’ One fruitful area of research in this regard is the potential role of uninsured deposits in serving as a private mechanism. In John and Senbet (1990), it is shown that risky debt can align socially and privately optimal investment levels when there is ‘An alternative scheme for reducing the risk incentive problem may include imposing double liability for ba;lk shareholders as done by many states in pre-1913 (see Merrick and Saunders (1985) on this;. This scheme has a desirable feature of forcing shareholders to share in the downside (losses), but its role is limited so long as shareholders zc-ptinue to face limited liability (albeit less limited). “‘T’here is another negative side effct ?f regulation when there is conflict between the management of the regulatory agency and the society (the taxpayers). Examples include press reports on those individuals who left the regulatory agencies to generate large sums of money for their private law practices in the advisement of restructuring of failed thrifts. Some of these individuals were known to be among architects of financial deregulation that precipitated risk incentive problems. “A recent wng%ssional study [CBO study (1990)] provides a synopsis of selected reform proposals submitted by organizations and individuals to the Treasury Department. The prevalent suggestions are risk-based premia and regulatory or mandatory enforcements and constraints. The latter are in the same vein of forcing contracts which are eficient only if private actions are readily observable. By contrast, our paper advances a mechanism to deal with risk incentive problems arising from imperfect observability of private investment risk choices.

914

K. John et al., Risk-shifting

incentives of depository

institutions

between debt-holders and equity-holders. Private parties with conflicting interests may engage in contractual relationships and monitoring activities which may serve as positive externalities to the rest of the society. We think that some reliance of regulatory agencies on private agents is consistent with our basic approach of seeking a solution that is self-enforcing and self-regulating. The more rigorous analysis of the role of multiple classes of claimholders in mitigating risk-shifting incentives of depository institution’ is a research issue that we wish to pursue later.

conflict

eferences by Acharya, S.. 1991, Regulatory policies when banks control asset quality, unobserved requlators, Mimeo, Federal Reserve Board. Bamea, A., R.A. Haugen and W.L. Senbet, 1985, Agency problems and financial contracting (Prentice-Hall, Inc.). Berlin, M. and K. John, 1991, Bank runs, demand deposits, and the social objectives for deposit insurance, NYU Working Paper in progress. Bemanke, B.S., 1983, Nonmonetary effects of the financial crisis in the propagation of the great depression, American Economic Review. June, 257-276. Bierwag, GO., and G.G. Kaufman, !983. A proposal for federal deposit insurance with risk scnsitire premiums, Mimeo., March. Buser. S.A., A.H. Chen and E.J. Kane, 1981, Federal deposit insurance, regulatory policy and optimal bank capital, Journal of Finance, Sept., 51-60. Campbell, T.S. and W.A. Kracaw. 1980, Information production, market signalling and the theory of financial intermediation, Journal of Finance, Sept., 863-882. Chan, Yuk-Shee. S.I.. Greenbaum and A.V. Thakor, 1988. Is fairly priced deposit insurance possible?, Northwestern University Working Paper, Oct. Congressional Budget Office, 1990, Reforming federal deposit insurance, Sept. Diamond. D.. 1984, Financial intermediation and delegated monitoring, Review of Economic Studies, July, 393-414. Diamond, D. and P.H. Dybvig, 1983. Bank runs, deposit insurance and liquidity, Journal of Political Economy, June, 401-419. Fama, E.E.. 1985, What’s diRerent about banks?, Journal of Monetary Economics 15. 29-39. Flannery. M.J.. 1989. Capital regulation and insured banks’ choice of individual loan default risks, Journal of Monetary Economics 24, 235-258. Flannery, M.J.. 1990. Pricing deposit insurance when the insurer measures risk with error, Florida Working Paper, Feb. Goodman, L.S. and A. Santomero, 1986, Variable-rate deposit insurance, Journal of Banking and Finance IO. 203-218. Green, R.C., 1984, Investment incentives, debt and warrants, Journal of Financial Economics, March, 115-l 36. Green, R.C. and E. Talmor, 198i The structure and incentive effects of corporate tax liabilities, Journal of Finance 4, 1095-I 114. James, C., 1987, Some evidence on the uniqueness of bank loans, Journal of Financial Economics 19, 2 l7--236. Jensen, M. and W. Meekling, 1976, Theory of the firm: Managerial behavior, lgency costs and ownership structure, Journal of Financial Economics 3. 31X-360. John. K.. 1987. Risk-shifting incentives and signailing through corporate capital-structure, Journal of Finance. July, 6:!3-641. John, K. and L.W.Senbet. 1990, Limited liability, tax deductibility of debt and public policy, NYU and Marvland Working Pawr. Kane, E.J., 1986, ippearance aid riality in deposit insurance: The case fx reform, Journal of Banking and Finance 1C. ! 75-l 88.

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~~:‘l~~~~‘J (‘L’rban InstltutP Press. Kane, E.J., 1989, The S&L insurance mess: How did it Washington). Keeley, MC., 1990, Deposit insurance. risk and market power in ba .1 *. -‘.mc c ‘. J I: ~t.~_ Review, Dec., 1183- 1200. Marcus, A.J., and I. Shaked, 1984, The valuation of FDIC deposit insuramx using optionpricing estimates, Journal of Money, Credit. and Banking, No-:., ti6-460. Merrick, J.J. and .4. Saunders, 1985, Bank regulation and monetary polic:r, Journal of Mane;, Credit, and Banking, Nov., 691-726. Merton, R.C., 1977, An analytic derivation of the cost of deposit insurance and loan guarantees, Journal of Banking and Finance 1, 3-l 1. Pennachi, 6.. 1987, Alternative forms of deposit insurance: Pricing and bank incentive issues, Journal of Banking and Finance 11,291-312. Pyle, D., 1985, Capital regulation and deposit insurance, Journal of Banking and Finance 10. 189-201. Ronn, E.I. and A. Verma, 1986, Pricing risk-adjusted deposit insurance: An option-based model, Journal of Finance, Sept., 871-895. Rothschild, M. and J. Stiglitz, 1970, Increasing risk I: A definition, Journal of Economic Theory 2,225-243. Rothschild, M. and J. Stiglitz, 1971, Increasing risk 11: Its economic consequences, Journal of Economic Theory, 3,66-84. Seward, J.K., 1990, Corporate financial policy and the theory of tinancial intermediatIon, Journal of Finance 45, 351-378. Sharpe, W.F., 1978. Bank capital adequacy, deposit insurance and security values. journal of Financial and Quantitative Analysis, Nov., 701-718. White, L.J., 1991. The S&L debacle: Public policy lessons for bank and thrift regulation (Oxford University Press).