Journal of Economics and Finance �9 Volume 19, Number 1 = Spring 1995 �9 Pages 63-74

Deposit Insurance Subsidies, Moral Hazard, and Bank Regulation Chandrasekhar Mishra and Jorge L. Urrutia

ABSTRACT

The model developed in the paper separates deposit insurance subsidies into two components: a premium-linked subsidy which arises from an ex-antc mispricing of the deposit insurance premium, and an asset-linked subsidy which arises from a lack of ex-post monitoring of the bank's actions. The identification of these two subsidies provides important insight into the relation between deposit-insurance subsidies and bank risk. The asset-linked subsidy is higher for banks of average risk and lower for very-high and very-low risk banks. The premium- linked subsidy behaves differently under risk-adjusted and fixed-rate premiums. The model also indicates that the implementation of a risk- adjusted insurance-rate schedule alone would not be sufficient to eliminate the bank's excessive risk-taking behavior. Thus, some combination of risk-sensitive deposit-insurance pricing and regulatory control is necessary to reduce the moral hazard problem.

Introduction

The flat-rate insurance premium charged by the Federal Deposit Insurance Corporation (FDIC) has been criticized for encouraging risk-taking behavior by financial institutions [Kane (1985)]. An alternative to the flat-premium is a risk- adjusted insurance premium or a requirement for increased capital levels for insured institutions. A problem with these approaches is that bank managers know morn about the riskiness of their loan portfolio than do the regulators. Another problem with a risk-adjusted deposit insurance system is the change in investment incentives that accompany its implementation. This paper analyzes both the information

Clum~raa~ Mishra is As.6~larg Professor. Loyola University of Chicago 60611 Jorge L. Urt~ia is Associ~e Profe~or of Fu~nce. Loy~a University of ChicaSo 60611

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JOURNAL OF ECONOMICS AND FINANCE Volume 19 Number 1 Sprin 8 1995

asymmetry problem arising when the regulator is less informed than the bank about the inherent risk of the bank's assets, and the moral hazard problem arising when the regulator is unable to monitor the extent to which bank resources are being directed away from normal operations toward activities that lower asset quality. Bhattacharya (1982) suggests that regulation of interest-rates and entry controls should be part of an optimal deposit-insurance contract in the presence of moral hazard. Buser, Chen and Kane (1981) argue that the FDIC systematically undercharges banks for deposit insurance. They suggest that an unregulated bank's optimal capital structure is influenced by taxes, bankruptcy costs, and a FDIC-typ* deposit-insurance contract. While bankruptcy costs provide incentives to hold more equity (less leverage), tax shields and a fixed-rate insurance contract create incentives to hold less equity (more leverage). The magnitude of these opposite effects is such that the optimal choice of an unregulated bank is different from the socially optimal choice. As a result, the bank has a lower capital ratio and the FDIC has a higher net liability.

Dothan and Williams (1980) examine the bank-portfolio problem under three alternative deposit-insurance regimes: (1) a fixed-rate regime; (2) an actuarially fair regime; and (3) variable and subsidized regime. These authors conclude that the three types of deposit insurance induce banks to select portfolios of risky loans. They also indicate that, under any type of subsidized deposit insurance, the bank's optimal portfolio is radically altered to exploit fully the deposit insurance subsidies. Thus, direct public supervision of loan portfolios of banks is necessary with any subsidized- type of deposit insurance regime. Kareken and Wallace (1978) reach similar conclusions and find that in a FDIC-type of deposit insurance, a minimum capital requirement by itself does not prevent a bank's insolvency. Chan, Greenbaum, and Thakor (1992) show that, in a competitive, deregulated financial services industry, it is impossible to implement risk-adjusted, incentive- compatible deposit-insurance prices without deposit-linked subsidies. The authors show that fairly priced deposit insurance and incentive compatibility may not be consistent. Thus, when incentives are taken into account, the optimal regime may involve the intentional mispricing of deposit insurance. Giammarino, Lewis and Sappington (1993) extend the focus of Chan, Crreenbaum and Thakor (1992) on incentive compatibility requirements by analyzing the regulator's concern for social welfare.

John, John, and Senbet (1991) also characterize risk-shifting incentives of a depository institution as arising from the existence of limited liability and the associated convex payoff to equity holders. They show that the incentive problem cannot be resolved through a risk-based insurance premium and propose a solution that eliminates risk-shifting through an optimal tax structure such that the corresponding insurance premium is revenue neutral from the regulator's standpoint. Their approach calls for a self-enforcing, self-regulating device rather than regulation of bank assets through forcing contracts. Duan, Moreau and Sealey (1992) also test the risk-shifting hypothesis on a sample of US banks, using an option-based

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Deposit Insurance Subsidies, Moral Hazard, and Bank Regulation

methodology to price each bank's actuarial liability to the FDIC. Their results, however, suggest that risk-shlfting is not widespread.

Grossman (1992) compares risk-taking of thrifts operating under strict and less- strict regulatory regimes during the 1930s. He finds that insured institutions operating under permissive regulatory regimes were more prone to undertake risky lending activities than their more tightly regulated counterparts, indicating that effective regulation and supervision will play a key role in maintaining thrift stability in the 1990s.

Bhattacharya and Thakor (1993) examine the need for bank regulation. Merton (1977) shows that deposit insurance is a put option encouraging risk-taking, which then necessitates a regulatory response. Merton and Bodie (1992) note that this response may include monitoring, risk-based premiums, cash-asset reserves and capital requirements, portfolio restrictions and limits on discount window borrowing. Sharpe (1990) and Besanko and Thakor (1993) examine interbank competition which also creates excessive risk taking incentives, magnifying those due to deposit insurance. In a multi-period interaction between banks and borrowers, the incumbent bank has an advantage because of its knowledge of the borrower's quality. This could lead to ex-post rents that create potential distortions. The results appear to support the hypothesis that regulatory restrictions on entry into banking may be necessary to sustain the rents needed to deter banks from excessive risk.

A contribution of this paper is the separation of deposit insurance subsidies into two components: a premium-linked subsidy and an asset-linked subsidy. The premium-linked subsidy is an ex-ante mispricing of the deposit insurance premium which arises from the current practice of the FDIC to calculate the insurance premium ex-ante based on historical information about the bank. The asset-linked subsidy arises from the failure of the FDIC to monitor the bank's ex-post actions (i.e., to control the bank's investment decisions after the FDIC has priced the insurance premium). This lack of monitoring creates a moral hazard problem since banks can increase the risk exposure of their asset portfolios after their insurance premium has been priced.

The identification of these two subsidies provides important insight into the relation between deposit insurance subsidies and bank risk. In effect, our model shows that the asset-linked subsidy is higher for banks of average risk and lower for very-high and very-low risk banks. On the other hand, the premium-linked subsidy, behaves differently for a risk-adjusted insurance premium scheme than for a fixed rate scheme. Our model also indicates that deposit insurance schemes do not eliminate the subsidies arising from the moral haTard problem. Thus, assessing either an ex-ante risk-adjusted premium alone or imposing a minimum capital standard by itself cannot solve the problems of information asymmetries. Some combination of a risk-sensitive insurance premium and regulatory incentives is needed to reduce the moral hazard problem.

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JOURNAL OF ECONOMICS AND FINANCE Volume 19 Number 1 Sprin~ 1995.

The Model Without Deposit Insurance

This section develops a simple model without deposit insurance. There are two agents: a borrower and a lender. To focus only on incentive issues, and not on risk sharing issues, both agents are assumed to be risk-neutral. The model has two periods. In the first period, the borrower decides whether or not to undertake a positive net present value project which needs I dollars of investment. I The borrower contributes M dollars of equity and borrows the rest, (1-c0I dollars, from the lender. The lender has imperfect information about the project's quality and cannot monitor perfectly the states of the borrower, who has the power and, presumably, the incentive to change the unobservable stat~ in response to the loan contract. In the second period, the project is terminated and, if the project is successful, that is, if the proceeds from the project S exceed the contractual repayment, the loan is paid off.

The probability of success of the project is p. In the case of success, the borrower must pay (1-et)Ir, dollars in the final period,'- where r, is the gross rate of return on the loan. If the project fails, the borrower defaults and pays nothing. A rational borrower would invest his equity in the risky project only if the proceeds from the project exceed those from some risk-free investment. The expected payoff to the borrower from the project is p(S - (1-~)Ir,) dollars. The payoff from the riskless investment is Mrf dollars, where rt is the risk-free gross rate of return. Therefore, the borrower will undertake the project only if he finds a sufficiently favorable p, such that p > I~,, where~

Pb = ( s - f 1 -

(D

The critical value of p increases as the borrower's equity, increases: The greater his equity participation, the more cautious the borrower is in undertaking the project [Leland and Pyle (1977)]. On the other hand, the greater the project return, the more risk the borrower is willing to take.

The lender has access to deposits (D) and equity (E) markets so she can borrow (1 - ~)I dollars. The lender, acting in the best interest of her shareholders, would lend if the expected contractual repayments on the loan exceed the promised payoff to depositors plus a reservation level of payoff demanded by the shareholders, both at the risk-free ra te : If E(p) is the risk-neutral lender's expectation of the true p, conditioned on p > I~, then the following inequality holds:

E(p)(1-~)/r~ > (l-~)Ir: (2)

Where (1 - ct)I = D + E, it follows that E(p) > rf/r,. That is, the lender will lend only if she has expectations of a sufficiently favorable outcome of the project

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Deposit Insurance Subsidies, Moral Hazard, and Bank Regulation

the loan rate increases, it follows that the higher the loan rate, the greater the incentive for the lender to lend. Bhatmcharya (1982) points out that these relationships justify the imposition of interest rate controls on bank loans as a way to discourage moral hazard problems. ~

The Model With Deposit Insurance

Let us now introduce a deposit-insurance regime where the bank pays to the deposit insurer (i.e., the FDIC) an insurance premium per dollar of deposit, P. Let us further assume that the insurance premium is paid from deposit receipts before the bank makes the loan choice, and that the loan matures before the deposit insurer can reprice the premium. This mismatch of the premium and the riskiness of the assets of the bank creates incentives for the lender to increase her risk exposure. 6 Since the insurer cannot observe the bank's loan choice, E(p) is not known to the FI)IC at the time the deposit insurance premium is computed, and a subsidy is attached to the premium. Thus, P = [1 - E(p)] - s, corresponds to the ex-ante or up-front insurance premium charged by the FDIC. The subsidy is realized by the bank in the second period, provided the bank is solvent. 7' z

The loan of (1 - a)I dollars is funded by insured deposits net of the insurance premium, (D - PD), and equity, (E). I f the gross rate of return on the loan is r., the borrower is required to repay (1 - c0Ir, dollars. In the second period, if the project is successful, the proceeds from it are used to repay the Ioan and the depositors are paid off. However, if the project fails, the borrower defaults and pays nothing, and the deposit insurer must repay the depositors. Also, in the second period, if the bank is solvent, the deposit insurance contract is renewed for another two periods.

Let rr be the risk-free gross rate of return (oppommity cost) of the loan to the bank or lender. A rational bank would lend (1 - c~)I dollars if the expected repayment from the loan exceeds the opportunity cost of the loan plus the cost of deposit i~urance. Thus, the bank's individual rationality constraint requires that:

E(p)[( I -E(p)-P)D+ (1-~)Ir~] + [ 1 - E ( p ) I D ( I - P ) > ( I -~)Ir / (3)

where E(p) is the bank's expectation of the true p, conditional on p ~1%. That is, the bank expects to be solvent with probability E(p), in which case it earns the insurance subsidy plus the return on the loan: (1 - E(p) - P)D + (1 - c0Ir .. The bank expects to be insolvent with probability (1 - E(p)), in which case it gets a transfer of (1 - P)D to repay its depositors. The above expression can be rewritten as: The

[z@)C1-E(p)) + (1 -Z(p ) -e ) ]D + E(p)O-,,)Zro ~ (1-=)Zr/ (4)

expression [E(p) (1 - E(p) + (1 - E(p) - P)] = k, corresponds to the ex-post or effective deposit insurance subsidies per dollar of deposit after the bank has made

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JOURNAL OF ECONOMICS AND FINANCE Volume 19 Number I Sprin~ 1995

the loan choice?. )o Deposit insurance subsidies arise partly from the mispricing of the insurance premium, since the FDIC has incomplete information about the bank. Further subsidies arise from the bank's subsequent choice of loan risk, since the premium is computed before the bank makes its loan choice. The ~ea ter the variance of the loan asset, the greater the moral hazard, and the greater the subsidies to the bank. The excessive loan risk pursued by the bank after the deposit insurance is purchased, characterizes the moral hazard problem. Expression (4) indicates that

0.4

FIll

DEPOSIT I~SI.IRM~I~ S~'R~IDIF.3

0 . |

0 . ~

G.I

j "

J i

~ - ~ ~

deposit-insurance subsidies have two components: An asset-linked subsidy E(p)(1 - E(p)) and a premium-linked subsidy (1 - E(p) - P). These two components are illustrated in Figure I, which has been drawn assuming a risk-sensitive deposit insurance pricing scheme with the premium set equal to 80% of the fair premium based on the true loan-asset risks (1 - E(p)). zl Notice that the asset-linked subsidy, which increases in the loan asset variance, is higher when the loan asset risk (1 - E(p)) is near average (i.e., the probability of failure is 0.5). The asset-linked subsidy arises from the deposit insurer's failure to monitor the bank's ex-post actions. Figure 1 suggests that the monitoring or moral hazard problem becomes more important for near average banks (i.e., banks near 50% probability of failure). This result agrees with Diamond (1991), who determines the conditions under which a borrower's loan contract will be monitored by lenders in circumstance~ in which reputation effects are important. He finds that borrowers with credit ratings toward the middle of the spectrum rely on bank loans. High-rated borrowers and very-low rated borrowers provide less uncertainty and thus they do not need monitoring. Our explanation of Figure 1 is as follows: Since the FDIC calculates the insurance premiums ex-ante based on historical information about the banks, it knows the tendency of low risk and high risk banks to choose low risk or high risk loans, respectively. The FDIC has more information (less uncertainty) about these banks and, thus, the insurance

68

Deposit Insurance Sub,dies, Moral Hazard, and Bank Re~,ulation

mispricing is small and the subsequent moral hazard problem is less serious. However, for near average banks, it is harder for the FDIC to predict when they will significantly deviate from the average and undertake riskier loans, worsening the moral hazard problem. The asset-linked subsidy first increases and then decreases in the loan-asset risk, while the premium-linked subsidy is an inereasing function of the loan-asset risk. As a result, the total deposit-insurance subsidy first increases and then decreases with the loan-asset risk.

FIGURE 2

DEPOSIT INSUK~CE SUBSIDIES

NXI~ P ~ 0.5

0.45

0.4

0.35

~, ~ 0.15 ~ 0.1

0.05

o . -- . r ~q

03 0.2 03 0.,I 05 0.6 ~7 O.a &9

~ " ' d k - f i Tl

LOAN-ASSET RISK

Figure 2 presents the case of a fixed deposit insurance premium (where p =0.5). It can be seen from Figures 1 and 2 that the asset-linked subsidy is the same under fixed-premium and risk-sensitive premium schemes. However, the premium-linked subsidy follows a different pattern in Figure 2. In this case, the premium-linked subsidy equals Max (0, 1-E(p)-P). This is similar to the payoff on a call option written by the FDIC to the bank. As a call option, the premium-linked subsidy is an increasing function of: the riskiness of the loan assets, the distribution of the risky insured institutions and the repricing interval; and, a decreasing function of the deposit insurance premium.

Figures 1 and 2 also indicate that both pricing regimes do not eliminate the subsidies completely. Consequently, some combination of risk-adjusted insurance premiums and regulatory incentives is needed to monitor effectively the bank's moral hazard problem, e These findings are consistent with findings by Dothan and Williams (1980), Chart, Greenbaum and Thakor (1992), Grossman (1992), and Besanko and Thakor (1993), who indicate that some regulatory restrictions are necessary.

The moral hazard problem illustrated in this paper is similar to the well known agency problem of asset substitution between shareholders and bondholders of a

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more risky investments, which would increase the firm value and shareholder wealth. Bondholders protect themselves against these potential adverse actions of the firm by enforcing bond covenants on the firm's operations. In addition, our finding that subsidies are a direct function of the variance of the loan asset agrees with Merton's (1977) characterization of the value of deposit insurance as a put option sold to the bank by the FDIC. t~ The value of the put option increases as the variance of the loan-asset portfolio increases.

Deposit insurance subsidies can be reduced by increasing the capital requirement for hanks. Let w be the fraction of the loan financed by insured deposits. Bank regulators may have a minimum capital standard in fore~, which translates to bounds on w such that 0 < w < 1. In effect, substituting D -- w(1 - a)l , into Equation (4) leads to the result that the greater the bank capital, the lower the value of w and, therefore, the less the deposit insurance. The moral harnrd problem can be controlled by limiting the asset variance. Kahane (1977) suggests restricting lenders from undertaking excessively risky projects and speculative investments. Alternatively, Blair and Heggestad (1978) recommend that regulators specify an upper bound on the asset variance and let the lender work out the composition of the asset portfolio. 14

Conclusions

This paper explores the information asymmetry problem arising when the FDIC has less information than the bank about the risk of the bank's assets, and the moral hazard problem raised when the FDIC is unable to monitor riskier activities undertaken by the bank. Moral hazard problems arise when the bank pays the deposit-insurance premium up-front before the FDIC can observe the bank's loan choice. The greater the variance of the loan-assets selected by the bank, the greater the subsidies to the bank. A contribution of the model developed in this paper is the separation of the deposit-insurance subsidies into two components: an asset-linked subsidy and a premium-linked subsidy. The asset-linked subsidy arises from the deposit insurer's failure to monitor the bank's ex-post action. The premium-linked subsidy is an ex-ante mispricing of the deposit insurance premium. The identification of these two subsidies provides important insights into the relation between deposit insurance subsidies and bank risk. In effect, the model shows that the asset-linked subsidy is higher for bank.q of average risk and lower for very-high and very-low risk banks. On the other hand, the premium-linked subsidy follows different patterns for a risk-adjusted insurance premium regime than for a flat-rate regime.

The model also suggests that a risk-sensitive deposit insurance scheme does not eliminate deposit-insurance subsidies. Therefore, to reduce the moral hazard problem, some combination of a risk-sensitive deposit-insurance premium and regulatory control is needed.

Empirical support for our results is provided in Grossman (i992), who compares risk taking of thrifts operating under different regulatory regimes during the 1930s and finds that insured institutions operating under permissive regulatory regimes

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Deposit Insurance Subsidies, Moral Hazard, and Bank Re~lulation

were more l ikely to undertake risky lending activities, indicating that effect ive

regulation and supervis ion will play a key role in maintaining thrift stability in the 1990s.

NOTES

1. In this paper "he" refers to the borrower and "she" refers to the lender.

2. It is assumed that the credit market is competitive and that ro is exogenously and competitively determined.

3. Condition (1) guarantees only that expected profits to the risk-neutral borrower are non-negative. Thus, the model includes states in which the borrower may invest in projects with ex-ame negative NPV.

4. Notice that the deposit rate is assumed to be the same as ",he risk-free rate without any loss of generality.

5. The comparison of Pl and Ps indicates that moral hazard problems arise in bank lending because the borrower has the incentive to undertake projects in some states which are not favorable to the lender.

6. The argument that firms may increase the risk exposure of their assets after the price of their liabilities is not new (see Jensen and Meckling (1976) and Barnea, Haugen and Senbet (1980)). Wall, Pringle and McNulty (1990) justify bank's issuance of demandable debt as a mechanism for controlling banks' incentives to undertake investments in high risk assets. These authors note that if regulators rely on quarterly financial statements to evaluate interest rate risk, then banks can avoid the regulations by reducing their exposure immediately prior to issuing financial statements and subsequently increase their exposure.

7. The mispricing o f the deposit insurance premium arises because the bank's assets mature before the insurer reprices the insurance premium. Barnea, Haugen and Senbet (1980), suggest that the deposit insurance mispricing problem could be eliminated if all the bank's debt contracts (including deposit insurance premiums) were renegotiated before the bank's assets mature.

8. The model assumes that s is real and positive. However, s can, in principle, be negative since the insurer does not know E(p). Thus, a bank could be overcharged for the insurance it received even after the rebate is paid.

9. Notice that E(p)(1 - E(p)) is the variance of the loan asset per loan dollar since the loan asset is a random variable with two outcomes, the probability of success being E(p).

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JOURNAL OF ECONOMICS AND FINANCE Volume 19 Number 1 Sprin~, 1995

10. To verify that Equation (4) corresponds to the effective subsidies, compare Equations (2) and (4). ~ the absence of deposit insurance, the bank's individual rationality constraint requires the following inequality.

(5) E(p)(1-n)Ir, z (1-c~)Ir!

11. The true loan-asset risk is not observed nor can it be measured precisely by the deposit insurer.

12. Regulatory incentives can be effective regulation that restricts lenders from understanding excessively risky projects and speculative investments. Although we suggest that regulatory monitoring of bank portfolios would reduce the moral hazard problem, it may be that this type of monitoring has other incentive problems which are not addressed here.

13. Merton, however, does not address the moral hazard problem

14. Kim and Santomero (1988) derive risk-adjusted capital standards that can effectively bind the lender's insolvency risk by limiting the incremental value added to the shareholders' wealth. These weights, however, do not eliminate the probtem of moral hazard as they only suppress the original number of states in which the lender could have lent in the absence of deposit insurance.

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Deposit Insurance Subsich'es, Moral Hazard, and Bank Regulation

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Merton, Robert C., and Zvi Bodie. "On The Management of Financial Guarantees." Financial Management 21, no. 4 (Winter 1992): 87-109.

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