# Rebalancing the three pillars of Basel II.

1. INTRODUCTION

The ongoing reform of the Basel Accord is supposed to rely on three "pillars": a new capital ratio, supervisory review, and market discipline. But even a cursory look at the proposals of the Basel Committee on Banking Supervision reveals a certain degree of imbalance between these three pillars. Indeed, the Basel Committee (BIS 2003) gives a lot of attention (132 pages) to the refinements of the risk weights in the new capital ratio, but it is much less precise about the other pillars (16 pages on Pillar 2 and 15 pages on Pillar 3). (1)

Even though the initial capital ratio (BIS 1988) has been severely criticized for being too crude and opening the door to regulatory arbitrage, (2) it seems strange to insist so much on the importance of supervisory review (3) and market discipline as necessary complements to capital requirements while remaining silent on the precise ways (4) this complementarity can work in practice. One possible reason for this imbalance is a gap in the theoretical literature. As far as I know, there is no tractable model that allows a simultaneous analysis of the impact of solvency regulations, supervisory action, and market discipline on the behavior of commercial banks.

This paper aims to fill that gap by providing a simple framework for analyzing the interactions between the three pillars of Basel II. We start by offering a critical assessment of the academic literature on the three pillars, (5) and argue that none of the existing models allows for a satisfactory integration of these pillars. We therefore develop in Section 3 a new formal model that tries to incorporate the most important criticisms of existing theoretical models of bank regulation. Section 4 shows that minimum capital ratios can be justified by a classical agency problem, a la Holmstrom (1979), between bankers and regulators, even in the absence of mispriced deposit insurance. We demonstrate in Section 5 that, under restrictive conditions> these capital requirements can be reduced if banks are mandated to issue subordinated debt on a regular basis (direct market discipline). Finally, Section 6 explores the interactions between market discipline and supervisory action and shows that they are complementary rather than substitutes.

2. THE THREE PILLARS IN THE ACADEMIC LITERATURE

Most of the academic literature on Basel I concentrates on the credit crunch of the early 1990s (6) and on the distortions of banks' asset allocation generated by the wedge between the market assessment of banks' asset risks and its regulatory counterpart in Basel I. Several theoretical articles (for example, Koehn and Santomero [1980], Kim and , Santomero [1988], Furlong and Keeley [1990], Rochet [1992], and Thakor [1996]) use static portfolio models to explain these distortions. In such models, appropriately designed capital requirements could be used to correct the incentives of bank shareholders to take excessive risks, due to the mispricing of deposit insurance or simply to the limited liability option. Using a different approach, Froot and Stein (1998) model the buffer role of bank capital in absorbing liquidity risks. They determine the capital structure that maximizes the bank's value when there are no audits or deposit insurance.

Yet, as pointed out by Hellwig (1998) and Blum (1999), static models fail to capture important effects of capital requirements. The empirical literature (for example, Hancock, Laing, and Wilcox [1995] and Furfine [2001]) has tried to calibrate dynamic models of bank behavior in order to study these intertemporal effects. However, none of these papers has studied the interactions of capital requirements with supervisory action (7) and market discipline.

The literature on continuous time models of bank behavior was initiated by Merton (1977). Assuming an exogenous closure date, he shows that the fair price of deposit insurance can be computed as a European put option. Merton (1978) extends this framework by considering random audits and endogenous closure dates. (8)

Merton's seminal contributions have been extended in several directions, in particular:

* Fries, Mella-Barral, and Perraudin (1997) introduce deposit withdrawal risk and study the impact of banks' closure policies on the fair pricing of deposit insurance;

* Bhattacharya et al. (2002) study closure rules that can be contingent on the level of risk taken by banks; and

* Levonian (2001) introduces subordinated debt in Merton's (1977) model and studies its impact on bankers' incentives for risk taking.

3. A FORMAL MODEL

Our model aims to take seriously most of the criticisms of previous models of bank regulation while remaining tractable. (9)

First, it is a dynamic model, because static models necessarily miss important consequences of bank solvency regulations. (10) The simplest dynamic models are in discrete time, like those of Calem and Rob (1996) or Buchinsky and Yosha (1997), but they typically do not yield closed-form solutions and entail the use of numerical simulations. For transparency, we instead use a continuous time model, a la Merton (1977, 1978), which requires using diffusion calculus but is ultimately revealed to be more tractable. Following Merton, we therefore assume that the (economic) value [A.sub.t] of a bank's assets at date t follows a diffusion process:

(1) dA/A = [mu]dt + [sigma]dW,

where dW is the increment of a Wiener process and [mu] and [sigma] are the drift and volatility of asset value. For simplicity, we assume that all investors are risk neutral (11) and discount the future at a constant rate r > [mu]. The bank's assets continuously generate an instantaneous cash flow [x.sub.t] = [beta][A.sub.t], where [beta] > 0 is the constant payout rate. (12)

We depart from the complete frictionless markets assumption made by Merton (1977, 1978) (13) and many of his followers, since this assumption implies that the social value of banks is independent of their liability structure, a hardly acceptable feature if one wants to study the consequences of solvency regulations for banks. Following Gennotte and Pyle (1991), we assume instead that banks create value by monitoring borrowers, and thus acquire private information about these borrowers. The counterpart to this private information is that the resale value of a bank's assets (typically, in case of liquidation) is only a fraction [lambda]A (with [lambda] < 1) of the economic value A of these assets. (14)

We also assume that the monitoring of borrowers has a fixed-cost component, (15) equivalent to a flow cost r[gamma] per unit of time (its present value is therefore [gamma]). From a social perspective, a bank should thus be closed when its asset value falls below some threshold [A.sub.L] (the liquidation threshold). The social value of the bank, denoted V(A), equals the expected present value of future cash flows [x.sub.t], = [beta][A.sub.t], net of monitoring costs r[gamma], until the stopping time [[tau].sub.L] (the first time t that the bank hits the liquidation threshold [A.sub.L]), when the bank is liquidated and its assets are resold at price [lambda][A.sub.L]. As shown in the appendix, this social value equals:

(2) V(A) = (A - [gamma]) + {[gamma] - (1 - [lambda])[A.sub.L]}[(A/[A.sub.L]).sup.-a],

where a is the positive root of the quadratic equation:

(3) [1/2][[sigma].sup.2]x(x + 1) - [mu]x = r.

Notice that this total value is composed of two terms:

* the value A of its assets, net of monitoring costs [gamma], and

* the option value associated with the (irreversible) closure decision.

As in the real options literature (see, for example, Dixit and Pindyck [1994]), the social value of the bank is maximized for a threshold [A.sub.L] that is below the break-even threshold [A.sub.0] = [gamma]/1 - [lambda]. More specifically, the level of [A.sub.L] that maximizes the social value of the bank (notice that this level is independent of A, and thus is time consistent) is what we call the first-best closure threshold:

(4) [A.sub.FB] = [a/(a + 1)][[gamma]/(1 - [lambda]).

Thus, our model captures an important feature of real-life banking systems: (16) even in the absence of moral hazard, government subsidies, and the like, the failure rate of banks cannot be zero. The socially optimal failure rate takes into account tile embedded real option: given that bank closures are irreversible (and entail a real cost, due to the imperfect resaleability of banks' assets), it is optimal to let banks operate (up to a certain point) below the break-even level, defined by the condition [A.sub.0] - [gamma] = [lambda][A.sub.0], in the hope that they recover. In more concrete terms, the fact that the resolution of bank failures costs money (ex post) m the Deposit Insurance Fund (DIF) does not necessarily imply some kind of inefficiency. This feature is illustrated in Exhibit 1. (17)

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So far, we have introduced only one of the two important features of banking: the opacity of banks' assets, (18) which implies that they have to be monitored and cannot be resold at full value. We now introduce the second feature: the bulk of a bank's liabilities consists of retail deposits D, fully insured by a DIF and paying interest rD. The DIF is financed by a premium P paid at discrete dates. We assume that this premium is fair (so we rule out systematic subsidies from the DIF to the banks) but cannot be revised by continuous readjustments. The academic literature has insisted a lot on the "moral hazard" problem created by the put-option feature of deposit insurance. It has been extensively argued that this feature, and more generally the limited liability of bank shareholders, gives these shareholders incentives to take excessive risks, especially when banks are insufficiently capitalized. We focus here on a different agency problem, also created by limited liability, but of a different nature: bankers (19) may not have enough incentives to monitor their assets when their value becomes too small. (20) We assume that when monitoring stops (we say that the banker "shirks"), the quality of bank assets deteriorates, (21) and the dynamics of asset value become:

(5) dA/A = ([mu] - [DELTA][mu])dt + [sigma]dW,

where [DELTA][mu] > 0. Equation 5 indicates that the shirking/ monitoring decision impacts only the expected profitability of the bank's assets and not the risk. Most of the academic literature has considered the polar case in which [mu] is unchanged but [sigma] increases by moral hazard (the asset-substitution problem). Which specification is more appropriate is an empirical question. (22) In Decamps, Rochet, and Roger (2004), we consider the general case in which both [mu] and [sigma] are altered by the banker's decision.

In the absence of shirking, the value of the bank's equity is given by a simple formula in the spirit of equation 2 (see the appendix for all mathematical derivations):

(6) E(A) = A - D - [gamma] + (D + [gamma] - [A.sub.L])[(A/[A.sub.L]).sup.-a].

As in Merton (1977, 1978), the value of the bank's equity is the sum of two terms:

* the value of assets A net of debt (deposits) D (and of the monitoring cost, which does not appear in Merton [1974]) and

* the value of the limited liability option.

However, as in Merton (1978) but in contrast to Merton (1977), the value of the limited liability option is not of the Black-Scholes type (it is actually simpler). This is because it can be exercised at any time, which corresponds to a down-and-out barrier option, instead of at a fixed date, which corresponds to a European option. In Merton (1978) the closure option can be exercised only after an audit by the supervisor. Here we assume that, thanks to the information revealed by the market (indirect market discipline), oh)sure can occur at any time.

[A.sub.L] is now chosen by shareholders so as to maximize equity value. The corresponding threshold is:

(7) [A.sub.E] = [a/a + 1](D + [gamma]).

At this threshold, the marginal value of equity is zero: E'([A.sub.E]) = 0 (smooth-pasting condition). Shirking is optimal for bankers whenever their expected instantaneous loss from shirking, AE'(A)[DELTA][mu], becomes less than the instantaneous monitoring cost [gamma]r. Since E'([A.sub.E]) = 0, this has to be true for some interval [[A.sub.E], [A.sub.S]].

Proposition 1: When the cost of monitoring [gamma]/D (per unit of deposits) is smaller than a + 1/[lambda]a - 1, there is a conflict of interest between shareholders and the DIF: insufficiently capitalized banks shirk.

Interestingly, there are parameter values for which the agency problem does not matter: when [gamma]/D is large (> a + 1/[lambda]a - 1), shareholders decide to close the bank before the shirking constraint becomes binding. However, when [gamma]/D is smaller than this threshold, there is a conflict of interest, even in the absence of mispriced deposit insurance. It is similar to the conflict of interest between bondholders and shareholders of undercapitalized firms.

Exhibit 2 represents the typical pattern of the value of the bank's equity E, as a function of the value A of its assets, in the case where deposits are fully insured (and therefore depositors have no incentives to withdraw), but the bank is left unregulated. The closure threshold [A.sub.E] (below which the bank declares bankruptcy) (23) and the shirking threshold [A.sub.S] (below which the bank shirks) are chosen by bankers so as to maximize the value of equity. The reason why shirking is sometimes preferred by shareholders (in the intermediate region [A.sub.E] [less than or equal to] A [less than or equal to] [A.sub.S]) even though it is socially inefficient is not the deposit insurance option (as is the case for asset-substitution problems, where typically [gamma] = [DELTA][mu] = 0, [DELTA][[sigma].sup.2] > 0), but rather the agency problem between the bank and the Deposit Insurance Fund. Indeed, the cost of monitoring is entirely borne by the bank, but the bank collects only a fraction of the benefits of monitoring. When these benefits are small, the banker prefers to shirk. As we describe in the next section, this can be prevented by imposing a minimum capital ratio.

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4. JUSTIFYING THE MINIMUM CAPITAL RATIO

In our model, the justification of a minimum capital ratio is not an asset-substitution problem (as in the vast majority of academic papers on the topic (24)), but an agency problem between the banker and the supervisors, who represent the interests of the DIF: insufficiently capitalized banks shirk, that is, they stop monitoring their assets. To avoid this problem, we assume now that when the value of the bank's assets hits some threshold [A.sub.R] chosen by the regulator, the bank is liquidated and the shareholders are expropriated. (25) This regulatory threshold [A.sub.R] is designed in such a way that bankers are never tempted to shirk.

Proposition 2:

1) Under the assumption of Proposition 1 (that is, [gamma]/D < a + 1/[lambda]a - 1), bank shirking can be eliminated if bank regulators impose liquidation whenever the bank's assets fall below the following threshold:

(8) [A.sup.O.sub.R] = a(D + [gamma]) + r[gamma]/[DELTA][mu]/a + 1.

2) When [gamma]/D is larger than [DELTA][mu]/r + a[DELTA][mu], this liquidation threshold can be implemented by imposing a minimum capital ratio:

(9) A - D/A [greater than or equal to] [[rho].sub.R] [equivalent to] [gamma](r + a[DELTA][mu]) - D[DELTA][mu]/[gamma](r + a[DELTA][mu]) + aD[DELTA][mu].

The condition [gamma]/D > [DELTA][mu]/r + a[DELTA][mu] ensures that the minimum capital ratio [[rho].sub.R] is positive. When it is not satisfied, banks can be allowed to continue for negative equity values. We focus here on the more interesting case of Proposition 2, where [[rho].sub.R] > 0.

Notice that when liquidation costs are large enough, the first-best liquidation threshold

[A.sub.FB] = [a/a + 1][[gamma]/1 - [lambda]]

is smaller than the regulatory threshold

[A.sup.O.sub.R] = a(D + [gamma]) + r[gamma]/[DELTA][mu]/a + 1.

This means that bank supervisors are confronted with time consistency problems: even if ex ante, agency considerations imply that a bank should be closed whenever A [less than or equal to] [A.sup.O.sub.R], ex post it is optimal to let it continue (and provide liquidity assistance). These forbearance problems are examined in Section 6.

We now examine the policy implications of our first results. We interpret bank solvency regulations as a closure rule intended to avoid shirking by insufficiently capitalized banks: every time the asset value of the bank falls below [A.sup.O.sub.R], the bank should be closed. However, we argue that bank assets are opaque and cannot be marked to market in continuous time. The traditional view of the role of supervisors was to evaluate these assets periodically through on-site examinations. In particular, most academic papers (26) assumed that [A.sub.t] was observable only through costly auditing that had to be performed more or less with uniform frequency across banks. We argue in favor of a more modern modeling strategy, whereby bank supervisors can rely on market information and adapt the intensity or frequency of their examinations to the market assessment of the bank's situation. This can be done by conditioning risk weights on market ratings of assets (Pillar 1) or using yield spreads of bank liabilities and private ratings to reassess the solvency of the bank (Pillars 2 and 3). In our model, it would mean inferring A,, the (unobservable) value of the bank's assets, from the market price of equity (if the bank is publicly listed), that is, inverting the function A [right arrow] E{A). This is how our model captures the notion of "indirect market discipline": using as much publicly available information as possible to allocate scarce regulatory resources in priority to the banks m distress. In our model, it leads to a simple policy recommendation of organizing a regulatory framework with two regimes:

* A light regime for "healthy" banks (those for which asset value A is way above the closure threshold [A.sup.O.sub.R], where A is inferred from accounting data and market information), only imposing accurate reporting and transparency.

* A heavy regime for "problem" banks (those for which A gets close to [A.sup.O.sub.R]), imposing restrictions on what the bank can do and closely examining its books.

This two regime regulatory framework (a simplified version of the prompt corrective action provisions of the Federal Deposit Insurance Corporation Improvement Act, or FDICIA) (27) is examined formally in Section 6. For the moment, we discuss direct market discipline and, more specifically, how the subdebt proposal can, under certain conditions, reduce capital requirements.

5. MARKET DISCIPLINE AND SUBORDINATED DEBT

We now consider that the bank is mandated to issue a certain volume B of bonds, each paying a continuous coupon c per unit of time. (28) These bonds are subordinated to deposits: if the bank is liquidated (when asset value hits threshold [A.sub.L]), the DIF receives [lambda][A.sub.L] but bondholders receive nothing. Anticipating this possibility, bondholders require a coupon rate c above the riskless rate r. To maintain the convenience of the stationarity of the bank's financial structure, we assume that bonds have an infinite maturity (unless of course the bank is liquidated) but are randomly renewed according to a Poisson process of intensity m. (29) In more intuitive terms, a fraction mdt of outstanding bonds is repaid at each instant at its face value B and the same volume mdt is reissued, (30) but at its market value B(A). This is where market discipline comes in: (31) if the bank's asset value A deteriorates (for example, if bankers stop monitoring their assets), the finance cost of the bank increases immediately, since at each instant a fraction m of the bonds has to be repaid at face value B and reissued at market value B(A) < B (notice also that B' > 0). In the appendix, we show that the value of equity becomes:

(10) E(A, B) = A - [gamma] - D - B[c + m/r + m] + (D + [gamma] + [A.sub.L])[(A/[A.sub.L]).sup.-a] + [c + m/r + m]B[(A/[A.sub.L]).sup.-a(m)],

where a(m) is the positive root of the quadratic equation

[1/2][[rho].sup.2]x(x + 1) - [mu]x = r + m.

The new regulatory threshold [A.sup.SD.sub.R] is the smallest value of [A.sub.L] that guarantees that bankers will not shirk. It is defined implicitly by:

[A.sup.SD.sub.R][[differential]E/[differential]A]([A.sup.SD.sub.R], B) = [gamma]r/[DELTA][mu],

where [A.sub.L] is taken to equal [A.sup.SD.sub.R]. After easy computations, we obtain:

(11) [A.sup.SD.sub.R] = [A.sup.O.sub.R] + [a(m)/a + 1](c + m/r + m)B.

Not surprisingly, this threshold is higher than [A.sup.O.sub.R] (all else being fixed), since the bank is now more indebted. However, the capital ratio becomes:

(12) [[rho].sup.SD.sub.R] = 1 - D + B/[A.sup.SD.sub.R].

It is smaller than [[rho].sub.R] = 1 - D/[A.sup.O.sub.R], whenever [A.sup.SD.sub.R]/D + B < [A.sup.O.sub.R]/D, which is equivalent to:

(13) a(m)[c + m/r + m] < a + [[gamma]/D](a + r/[DELTA][mu]).

Since a(m) increases with m (which a(0) = a and a (+ [infinity]) = + [infinity]), we see that this condition can be satisfied, but m (the frequency of renewal of bonds, which is inversely proportional in our model to their average maturity) and c - r/r (the relative spread on subordinated debt) have to be small enough. Thus, we obtain:

Proposition 3: If banks are mandated to issue subordinated bonds on a regular basis, regulators can reduce capital requirements (Tier 1) if two conditions are satisfied: the average maturity must not be too small (32) (m small) and the coupon paid on the bonds must not be too large (c/r close to 1). However, the total requirement, capital + subdebt (Tier 1 + Tier 2), is always increased.

Proposition 3 shows the limits of the mandatory subdebt proposal. Only when properly designed (that is, with a maturity that is not too small or a frequency of renewal that is not too large) and when markets are sufficiently liquid and bank assets not too risky (so that the relative spread c - r/r is not too large) can mandatory subdebt allow regulators to decrease capital requirements.

6. MARKET DISCIPLINE AND SUPERVISORY ACTION

We now come to what we consider the most convincing rationale for market discipline: preventing regulatory forbearance by forcing regulators to intervene before it is too late. As is well documented in the literature on banking crises, banking authorities are very often subject to political pressure for bailing out the creditors of banks in distress. To capture this in our model, we consider what would happen if subdebt holders where de facto insured in the case where the bank is liquidated (that is, whenever the value of its assets hits the regulatory threshold). This bailout obviously does not affect the social value of the bank but only leads to a redistribution of wealth between the DIF and bondholders. Bonds become riskless (33) and perfect substitutes for deposits in the view of equityholders. The frequency of renewal of bonds ceases to play any disciplining role.

Proposition 4: If subdebt holders are insured by the DIF, subdebt ceases to play any disciplining role: Direct market discipline can work only in the absence of regulatory forbearance.

Proposition 4 shows the existence of some form of complementarity between market discipline and supervisory action: direct market discipline can work only if supervisors can credibly commit not to bail out bondholders.

We now examine a second form of complementarity between market discipline and supervisory action: if financial markets are suitably efficient and liquid, and if banks issue publicly traded securities (equity or bonds), the market prices (or yields) of these securities will provide objective signals about the situation of these banks. We do not address the difficult statistical question of which security (equity or subordinated bonds) gives the most useful information to bank supervisors. (34) Our model has only one state variable, A, and both the equity price E(A) and the subdebt price B(A) are monotonic functions of A and thus sufficient statistics for A. In our simple model, by observing market prices of either equity or bonds, regulatory authorities can perfectly infer the true value of A.

Our model is obviously not appropriate for analyzing such statistical considerations. It is, however, well adapted to study another, equally important question: namely, how market discipline can limit forbearance. Market information is then viewed as providing objective signals that oblige supervisors to intervene. Indirect market discipline is thus useful in two ways: it allows supervisors to save on audit costs for the banks that are well capitalized, and simultaneously it forces supervisors to intervene early enough when a bank is in trouble. This is captured in our model in the following way.

We consider that bank supervisors are required to inspect banks whenever the value of their assets hits an inspection threshold [A.sub.I] (with [A.sub.I] > [A.sub.R]). Inspection allows them to detect shirking and close the banks that do shirk. The value of equity is still given by equation 6 (for simplicity, we return to the case with no subordinated debt):

E(A) = A - [gamma] - D + (D + [gamma] - [A.sub.R]) [(A/[A.sub.R]).sup.-a].

But now the condition for no shirking becomes

(14) [for all] A [greater than or equal to] [A.sub.I], AE' (A) [greater than or equal to] [gamma]r/[DELTA][mu],

which is equivalent to:

(15) [A.sub.I] - a(D + [gamma] - [A.sub.R]) [([A.sub.I]/[A.sub.R]).sup.-a] [greater than or equal to] [gamma]r/[DELTA][mu].

This formula shows that for any closure threshold [A.sub.R], there is a minimum inspection threshold At that prevents shirking: it is given by equality in equation 15. The corresponding curve in the ([A.sub.R], [A.sub.I]) plane is represented in Exhibit 3. Notice that the previous case (no inspection, closure at [A.sup.O.sub.R]) corresponds to the intersection of this curve with the first diagonal ([A.sub.R] = [A.sub.I] = [A.sup.O.sub.R]).

In Exhibit 3, we represent the optimal combination of inspection and closure thresholds by ([A.sup.*.sub.R], [A.sup.*.sub.I]). It is obtained by maximizing the social value of the bank:

V(A, [A.sub.R]) = A - [gamma] + [[gamma] - (1 - [lambda]) [A.sub.R]] [(A/[A.sub.R]).sup.-a),

net of the expected present value of auditing costs:

(16) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]

where the auditing cost [xi] is incurred only when the asset value of the bank lies in the interval [[A.sub.R], [A.sub.I], [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] is the indicator function that takes a value of 1 when [A.sub.t] [less than or equal to] [A.sub.I] (and zero otherwise). Here, [[tau].sub.R] denotes the first time that [A.sub.t] = [A.sub.R] (closure time). It can be shown that the expected present value of auditing costs C is proportional to [A.sup.-a]:

(17) C(A, [A.sub.R], [A.sub.I]) = [A.sup.-a] [phi] ([A.sub.R], [A.sub.I]).

Thus, after simplification by [A.sup.-a], we obtain:

Proposition 5: The optimal value of the closure threshold [A.sup.*.sub.R] and the inspection threshold [A.sup.*.sub.I] can be obtained by maximizing

(18) W(A.sub.R, [A.sub.I) [equivalent to] ([gamma] - (1 - [lambda]) [A.sub.R]) [A.sup.a.sub.R] - [phi] ([A.sub.R, [A.sub.I]),

under the incentive compatibility constraint (equation 15).

We have that [A.sup.*.sub.R] < [A.sup.O.sub.R], which indicates that prompt corrective action allows the reduction of capital requirements. When auditing costs are small, [A.sup.*.sub.R] becomes close to the first-best closure threshold [A.sub.FB], which means that prompt corrective action also reduces the severity of the time consistency problem of bank supervisors.

Proposition 5 illustrates the substitulability between Pillar 2 (supervisory action) and Pillar 1 (capital requirements). This was already a feature of Merton's (1978) model, in which the frequency of bank examinations could be substituted for more stringent capital requirements. However, here the introduction of Pillar 3 (market discipline) changes the picture: the intensity of regulation can be modulated according to market information (in the spirit of the prompt corrective action provisions of FDICIA), and symmetrically, supervisors can be forced to intervene when market signals reveal the distress of a bank (so that forbearance becomes more costly to supervisors or politicians). Notice also that market discipline decreases the (ex-post) benefits of forbearance by reducing the bank closure threshold (capital requirements), another illustration of the complex interactions between the three pillars of Basel II.

7. CONCLUSION

This paper develops a formal model of banking regulation that permits analysis of the interactions between the three pillars of Basel II. It differs from previous models in several important ways:

* it is a dynamic model, in which solvency regulation are interpreted as closure thresholds, rather than complex tools intended to correct the mispricing of deposit insurance;

* the justification of regulation is not (primarily) to prevent asset substitution by banks (deposits are not subsidized in our model), but rather to prevent shirking by the managers of undercapilalized banks;

* bank supervisors can rise market information as a complement to the information provided by bank examinations; thus, they can save on scarce supervisory resources and allocate them in priority to the banks in distress; and

* the returns on banks' assets are endogenous, since they depend on the monitoring decisions of bankers.

Although very simple, this model allows a formal analysis of the interactions between the three pillars of Basel II. In particular, we show in Proposition 3 that mandatory subdebt (direct market discipline) may, under some restrictions, allow regulators to decrease capital requirements. More important, we show that market discipline and supervisory action are complementary rather than substitutes (Propositions 4 and 5): one cannot work well without the other.

In terms of policy implications, our theory, points to a serious rebalancing of the three pillars of Basel II. The initial motivation of Basel I was to guarantee a level playing field for international banking, given that the large banks of some countries could take enormous risks without having much capital, benefiting from implicit guarantees by their governments. So the fundamental idea behind the Cooke ratio was harmonization, that is, to set a uniform standard for internationally active banks. It turns out that the Cooke ratio (or more generally, the risk-based capital methodology), although imperfect, was revealed to be extremely useful as an instrument for measuring bank risk. That is probably why it was applied rapidly (with minor changes) by the regulatory authorities of many countries within their jurisdictions (although it was initially designed for large, internationally active banks).

Probably in response to the harsh critiques of the crudeness of the Cooke ratio, the Basel Committee began a process of complexification, alternating new proposals and consultation periods with the banking industry (BIS 1999, 2001, 2003). The outcome of this long process is an extremely complex instrument (the McDonough ratio) that results from intense bargainings with large banks, and will probably never be implemented as such.

In this analysis, we argue that banking authorities should instead keep arm's-length relationships with bankers and that scarce supervisory resources should be used, according to priority, to control the behavior of banks in distress, rather than to implement an extremely complex regulation that will ultimately be bypassed in some way or another by the largest or most sophisticated banks. By contrast, there is an urgent need (once again) to guarantee a level playing field in international banking. The development of large and complex banking organizations with multinational activities implies that supervisory authorities of different countries urgently need to harmonize their institutional practices. Market discipline can provide a very useful tool for defining a harmonized and clear mandate for banking authorities across the world, in an attempt to eliminate political pressure and regulatory forbearance. This should be the top priority of the Basel Committee.

MATHEMATICAL APPENDIX

Here we derive the mathematical formulas used in our analysis.

FIRST-BEST VALUE OF THE BANK

The value of the bank (when assets are monitored) equals the expected present value of future cash flows [beta][A.sub.t], net of the monitoring cost r[gamma], until the stopping time [[tau].sub.L] (the first time t that [A.sub.t] hits the liquidation threshold [A.sub.L]) when the bank is liquidated. The formula is:

(A1) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]

Using classical formulas (see, for example, Dixit [1993] or Karlin and Taylor [1981]), we obtain:

(A2) V = A - [gamma] + {[gamma] - (1 - [lambda])[A.sub.L]} [(A/A.sub.L]).sup.-a],

where A is the current value of [A.sub.t], and a is the positive root of the quadratic equation:

(A3) 1/2 [[sigma].sup.2] x (x + 1) - [mu] x = r.

VALUE OF THE BANK'S EQUITY

In the absence of regulation, equityholders choose the liquidation threshold that maximizes the value of their equity. Using the same classical formulas as we use to establish equation A2, we obtain:

(A4) E(A) = (A - [gamma] - D) + (D + [gamma] - [A.sub.L]) [(A/[A.sub.L]).sup.-a].

As for the total value of the bank (equation A2), the second term is an option value that is maximized when

(A5) [A.sub.L] = [A.sub.E] [equivalent to] a/z + 1 (d + [gamma]).

At this threshold, the value of the bank's equity has a horizontal tangent (as represented in Exhibit 2 in the text):

(A6) E'([A.sub.E]) = 0.

If equityholders decide to stop monitoring, the dynamics of asset value become

dA/A = ([mu] - [DELTA][mu])dt + [sigma]dW,

but they save the monitoring cost r[gamma]. Shirking becomes optimal for equityholders whenever the instantaneous loss of equity value E'(A)A [DELTA][mu] is less than this monitoring cost. Because E'([A.sub.E]) = 0 (see equation A5), this condition is always satisfied in the neighborhood of the liquidation point. However, we have to check that this incentive constraint binds after the bank becomes insolvent. This is true whenever

[lambda][A.sub.E] [less than or equal to] D

or

[lambda]a(D + [gamma]) [less than or equal to] (a + 1)D,

which is equivalent to the condition of Proposition 1, namely:

[gamma]/D [less than or equal to] a + 1/[lambda]a - 1.

This ends the proof of Proposition 1.

MINIMUM CAPITAL RATIO

Suppose bank regulators impose a closure threshold [A.sub.R] [less than or equal to] D/[gamma]: if the bank's asset value hits [A.sub.R], the bank is liquidated and shareholders receive nothing. By an immediate adaptation of equation A4, shareholders' value becomes:

(A7) E(A) = A - [gamma] - D + (D + [gamma] - [A.sub.R]) (A/[A.sub.R]).sup.-a].

The condition for eliminating shirking is:

(A8) [for all]A [greater than or equal to] [A.sub.R], E'(A)A [DELTA] [mu] [greater than or equal to] [gamma]r.

Using equation A7, we see that this is equivalent to:

(A9) [for all]A [greater than or equal to] [A.sub.R], A - a(D + [gamma] - [A.sub.R]) [(A/[A.sub.R]).sup.-a] [greater than or equal to] [gamma]r/[DELTA][mu].

Provided that [A.sub.R] [less than or equal to] [gamma] + D (this will be checked ex post), the left-hand side of equation A9 is increasing in A, therefore equation A9 is equivalent to:

[A.sub.R](1 + a) - a(D + [gamma]) [greater than or equal to] [gamma]r/[DELTA][mu]

or

(A10) [A.sub.R] [greater than or equal to] [A.sup.O.sub.R] [equivalent to] a(d + [gamma] + [gamma]r/[DELTA][mu]/a + 1.

[A.sup.O.sub.R] represents the minimum asset value that preserves the incentives of the banker. The associated capital ratio is:

[[rho].sup.R] = [A.sup.O.sub.R] - D/[A.sup.O.sub.R] = [gamma](a + r/[DELTA][mu]) - D/ a(D + [gamma]) + [gamma]r/[DELTA][mu].

SUBORDINATED DEBT

Consider now that the bank issues a volume B of subordinated bonds, paying a coupon cB per unit of time, and randomly renewed with frequency m. The market value of these bonds B(A), as a function of the bank's asset value, satisfies the differential equation

(A11) rB(A) = cB + m(B - B(A)) + [mu]AB'(A) + 1/2 [[sigma].sup.2][A.sup.2]B"(A),

with the boundary conditions:

B([A.sub.L]) = 0 and B (+ [infinity]) = cB/r.

The solution of this equation is:

(A12) B(A) = B c + m/r + m [1 - [(A/[A.sub.L].sup.-a(m)]],

where a(m) is the positive root of the quadratic equation:

(A13) 1/2 [[sigma].sup.2] x (x + 1) - [mu]x = r + m.

In a comparison with equation A3, we see immediately that a(0) = a. Moreover, equation A13 shows that a(m) increases with m.

The value of equity becomes:

(A14) E(A,B) = A [gamma] - D - c + m/ r + m B + (D + [gamma] - [A.sub.L]) [(A/[A.sub.L]).sup.-a]

+ c + m/r + m B[(A/[A.sub.L]).sup.-a(m).

AUDITING COSTS

By definition, the expected present value of auditing costs is defined by

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]

where [[tau].sub.R] is the first time that [A.sub.t] hits the closure threshold [A.sub.R]. By the usual arguments (see Dixit [1993]), one can establish that C satisfies the following differential equation:

rC = [mu]AC'(A) + 1/2 [[sigma].sup.2] [A.sup.2] C"(A) A [greater than or equal to] [A.sub.t],

with the limit condition

c(+ [infinity]) = 0.

Therefore, C(A) = k[A.sup.-a], where a is (as before) the positive solution of the equation:

r = [mu]x + 1/2 [[sigma].sup.2]x(x + 1),

and k is a constant that depends on [A.sub.R] and [A.sub.I]:

k = [phi]([A.sub.R], [A.sub.I]).

ENDNOTES

(1.) This imbalance is also reflected in the comments on Basel II; see Saidenberg and Schuermann (2003) for an assessment.

(2.) See, for example, Santos (1996) and Jones (2000). The alleged role of risk-based capital ratios in the "credit crunch" of the early 1990s is discussed in Bernanke and Lown (1991), Berger and Udell (1994), Peek and Kosengren (1995), and Thakor (1996).

(3.) For example, the Basel Committee (BIS 2003) insists on the need to "enable early supervisory intervention if capital does not provide a sufficient buffer against risk."

(4.) In particular, despite the existence of very precise proposals by U.S. economists (Calomiris [1998]; Evanoff and Wall [2000]; see also the discussion in Bliss [2001]) for mandatory subordinated debt, these proposals are not discussed in the Basel II project.

(5.) Reviews of this literature can be found in Thakor (1996), Jackson et al. (1999), and Santos (2000).

(6.) Discussions of this issue can be found in Berger and Udell (1994), Thakor (1996), Jackson et al. (1999), and Santos (2000).

(7.) However, Peek and Rosengren (1995) provide empirical evidence of the impact of increased supervision on bank lending decisions.

(8.) Merton (1977, 1978) assumes that bank assets are traded on financial markets (in order to use the arbitrage pricing methodology), which implies that the social value of banks is independent of their liability structure.

(9.) The model is a variant of the one used by Decamps, Rochel, and Roger (2004), who also analyze the interactions between the three pillars of Basel II.

(10.) The main problem is that, in a static model, solvency regulations have an impact only when they are binding. However, the great majority of banks today have much more capital than the regulatory minimum (this was not the case in 1988). Hence, it is difficult to explain the impact of a capital ratio in today's world by using a static model. For other critiques, see Blum (1999).

(11.) Small depositors are risk averse but they are fully insured and do not play all active role in our model. In any case, risk neutrality is not crucial for our results, but it simplifies the analysis. We could assume alternatively that all investors use the same risk-adjusted measure for evaluating risky cash flows.

(12.) Because of risk neutrality, the expected net present value of these cash flows (conditional on the information available at date t) has to coincide with [A.sub.t], which is equivalent to the condition [beta] = r - [mu].

(13.) In Merton (1978), there are audit costs but no liquidation costs due to the resale of banks' assets, as we have here. As a result, social surplus is unaffected by liquidation decisions.

(14.) A similar assumption is made in the corporate finance literature (Leland 1994; Leland and Toft 1996; Fries, Mella-Barral, and Perraudin 1997), but (1 - [lambda]) is interpreted as a "physical" liquidation cost. Here, it is a cost due to the opacity of bank assets.

(15.) A proportional cost of monitoring, if any, can be subtracted with the drift in equation 1.

(16.) Of course, our desire to get closed form solutions limits our model to one state variable only. This means that we cannot address important questions such as the way banks allocate their assets among different classes of risks and the hoarding of liquid assets as another buffer against risk. The first topic is addressed by the vast literature on risk-weighted ratios (Koehn and Santomero 1980; Kim and Santomero 1988; Furlong and Keeley 1990; Rochet 1992; Thakor 1996). The second topic is addressed in Milne and Whalley (2001).

(17.) Notice that the first-best social value of the bank is a convex function of asset value. However, when agency problems are taken into account, and make the liquidation threshold become greater than [A.sub.0], the value function becomes concave, and thus exhibits risk aversion.

(18.) Morgan (2002) provides indirect empirical evidence on this opacity by comparing the frequency of disagreements among bond rating agencies over the values of firms across sectors of activity. He shows that these disagreements are much more frequent, all else being equal, for banks and insurance companies than for other sectors of the economy.

(19.) We assume that bank managers act in the best interest of shareholders. It would be interesting, but presumably difficult, also to introduce an agency problem between managers and shareholders.

(20.) Bliss (2001) argues that this agency problem may be fundamental: "Poor (apparently irrational) investments are as problematic as excessively risky projects (with positive risk-adjusted returns). Evidence suggests that poor investments are likely to be the major explanation for banks getting into trouble."

(21.) We assume that this deterioration--that is, [DELTA][mu] in equation 5--is so large that shirking is never optimal from a social viewpoint.

(22.) In the appendix to his paper, Bliss (2001) convincingly argues that the asset-substitution problem might have been overemphasized. He reviews several empirical articles that conclude that bank failures are often provoked by "bad investments" rather than "bad luck" (and excessive risk taking).

(23.) Following Leland (1994), we assume that shareholders are not cash constrained. In Decamps, Rochet, and Roger (2004), we examine the alternative case in which bankruptcy is precipitated by the bank's liquidity problems. Note that when there is shirking, the value of [A.sub.E] is no longer given by equation 7.

(24.) See Santos (2000) for a review.

(25.) This is similar to protected debt covenants, whereby bondholders (or banks) retain the option of restructuring a firm before it is technically bankrupt. See Black and Cox (1976) for a formal analysis.

(26.) The seminal paper on this topic is Merton (1978). More recent references are Fries, Mella-Barral, and Perraudin (1997) and Bhattacharya et al. (2002).

(27.) The consequences of FDICIA are assessed in Jones and King (1995) and Mishkin (1996).

(28.) The mandatory subdebt proposal has been discussed extensively: see, for example, Calomiris (1998), Estrella (2000), and Evanoff and Wall (2000, 2001). The only formal analysis I am aware of is Levonian (2001). However, Levonian uses a Black-Scholes type of model in which the bank's returns on assets are exogenous. For empirical assessments of the feasibility of the subdebt proposal, see Hancock and Kwast (2001) and Sironi (2001).

(29.) This approach is borrowed from Leland and Toft (1996) and Ericsson (2000).

(30.) The average maturity of bonds is thus [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.].

(31.) The disciplining role of periodical repricing of debt has been shown by Levonian (2001). It is close in spirit to the disciplining role of demandable deposits (Calomiris and Kahn 1991; Carletti 1999).

(32.) Recall that in our model, bonds theoretically have an infinite maturity but are randomly repaid with frequency m. The average (effective) maturity is 1/m.

(33.) Arbitrage considerations then imply that the coupon rate c must equal r.

(34.) On this topic, see, for example, Bliss (2001), Evanoff and Wall (2002), Gropp, Vesala, and Vulpes (2002), and the references therein.

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COMMENTARY

I would like to start by focusing on the method and model used in the paper by Jean-Charles Rochet. In particular, I will consider some of the paper's assumptions. This discussion will bring me to some specific remarks on Basel II, after which I will circle back and comment on Rochet's policy conclusions.

I found the Rochet paper to be interesting, and I liked it very much. Speaking as a bank supervisor, I believe there is a clear need for more research in this vein, which as I see it is an effort to make the theoretical models of banking and bank supervision more realistic in various ways, thus in part to make their conclusions more influential. Most of the value I can add with regard to the model therefore is to focus on the assumptions that still seem somewhat at odds with what the world looks like from a bank supervisor's perspective.

Foremost is probably the fact that the true economic value of a bank's assets is not known with certainty. I believe the uncertainty associated with this economic value is qualitatively different than assuming that the assets' liquidation value would be less than their economic value. This is part of the uncertainty, but not all of it. Obviously, there are some who believe that this problem should be addressed in practice by requiring mark-to-market accounting for banks. For those who follow accounting developments, moves in this direction by the International Accounting Standards Board--in particular, International Accounting Standard 39--have been receiving a great deal of attention. My only comment on this topic is to suggest that developing a fair-value accounting approach for the entirety of a bank's balance sheet in the absence of liquid market prices for many of its assets is a challenge of the same--or possibly even greater--order of magnitude as the problem of the first pillar of the Basel II framework.

A second and closely related issue is the fact that the volatility parameter, [sigma], that governs the underlying stochastic process for the bank's asset value is itself unlikely to be known with certainty. Importantly, this uncertainty is not limited to outsiders. In considering models that are meant to apply to the largest global banks--which clearly has been a primary focus of Basel II--an important issue that must be grappled with is the sheer size and scope of the banks' activities. For example, Citigroup has about 250,000 employees throughout the world. A critical risk management challenge for such a firm is simply to make sure that the head office receives accurate information on the activities of all its operations and that it has a plausible mechanism lot seeking to actually influence the risk level of these disparate units.

In other words, I would argue that it takes considerable effort and discipline just to ensure that the level of a bank's risk is transparent and controllable by insiders, much less outsiders. These points also lead me to conclude that the agency problems within large financial firms are absolutely critical to a complete understanding of how they should be managed and supervised. Moreover, if one looks at the list of financial scandals in recent years it is clear that internal agency problems leading to excessive risk taking by the overall firm in a manner that was not transparent to its own top management has played a key role in a number of these scandals.

Thus, I would propose an alternative interpretation of "shirking" to the one presented by Rochet: a bank is shirking when it fails to invest sufficiently in risk management and control systems and thus is unable to identify or control its overall level of risk properly. This leads it to make "bad" investments in the sense that such investments would not have presented an attractive risk-return trade-off had the bank accurately assessed the risk involved. It is not clear to me whether this change in interpretation would lead to a change in the model's results, but it would be interesting to see.

I now turn to a discussion of Basel II, of which I have been a major participant and am therefore likely to be guilty of bias. Perhaps I have a unique view of Basel II and of capital requirements in general. To me, the essence of the project is the development of a largely comparable and comprehensive measure of risk, particularly credit risk. I believe that the approach to credit risk management is changing fundamentally, as demonstrated by the rapid growth of credit risk transfer markets involving participants other than banks. I do not think that we are likely to see a return to the days when global banks measured their credit risk by rules of thumb.

I believe that the need for a measure of credit risk that achieves greater comparability and greater comprehensiveness than the Basel I measure is of importance to supervisors and to the marketplace generally. Regardless of the outcome of the Basel II effort, I am convinced that something along these lines is both necessary and inevitable. In my view, common tools and a common vocabulary for expressing risk will be significant aids to the development of more liquid markets for the trading of credit risk. In this sense, it is reasonable to think of the supervisory development of the first pillar of Basel II as an effort to solve a marketwide collective action problem related to the development of a common measure of risk.

In addition, the prospect of Basel II is spurring significant investment in risk management by global banks. Many banks have obviously developed sophisticated risk management tools and approaches, but the level of rigor that has surrounded these calculations and the degree to which data have been retained to check and improve the accuracy of these systems are not where they need to be, given the scale and importance of these institutions.

There are two fundamental trade-offs at the heart of Basel II. The first trade-off is between flexibility and comparability. The second is between risk sensitivity and complexity. There is no easy answer to either of these trade-offs; veering too far in either direction has its costs, and there is no doubt that the resulting proposal lacks the formal elegance of the best economic models. But we are not designing an economic model. Rather, we are working to improve steadily the risk management capabilities of those financial firms in which significant weakness would no doubt be quite costly, and we are seeking to establish a considerably better overall measure of the risks taken by such firms. In undertaking such a project, I think there is no better alternative than a highly transparent and consultative process. The balances achieved on the aforementioned trade-offs reflect the outcome of this somewhat messy, time-consuming process.

The result will be far from perfect, but I believe quite strongly that it will be better than what we have today. In particular, one way in which it will be better is by providing a shared signal to supervisors, the market, and bank management that credit quality is deteriorating. The current framework essentially embodies no such signal and puts the onus on the reserving/charge-off decision instead. A risk measure that responds dynamically to changes in credit quality has the potential to alert bank management, supervisors, and others to emerging problems much more quickly than before. Like Rochet, I believe that a key focus of supervisory policy should be on designing frameworks that discourage forbearance and create incentives for addressing problems promptly.

As to the topic of Pillar 3 and market discipline, I must take issue with Rochet's assessment based purely on "page count." Indeed, I believe that at the heart of Basel II is the development of a risk measure. Step one of Pillar 3 is therefore disclosure of this risk measure, on which basis it would not be unreasonable to assign to Pillar 3 all of the pages devoted to Pillar I. But this is a quibble. The key fact is that Pillar 3 of the Basel II proposal does not stop there. It requests disclosure of a number of other items that focus on credit concentrations, the components of bank capital, and other more detailed breakdowns of risk by portfolio. This is intended to provide greater and better information--more frequently--to market participants. Importantly, the current version of Pillar 3 reflects significant consultations and interactions with market analysts over what information they would like to have that banks are reluctant to provide willingly.

In this regard, it is worth emphasizing the point that determining what sort of information is most useful to disclose is not a trivial problem, particularly if the concern is to gauge in a forward-looking manner the risk to which a complex firm is exposed. Many of the analysts that I have spoken with have expressed some frustration with finding suitable ways to assess this risk on the basis of current financial statements. Personally, I wonder if this frustration has in some way been responsible for what appears to have been an overemphasis on the stability of reported earnings by some market analysts.

In any case, I believe that trying to make publicly available better measures of firm risk is a critical part of trying to make market discipline more effective. I also believe that this is a potentially fruitful avenue for empirical research on, for example, the types of risk disclosures that would be the most useful indicators of true underlying risk.

I now turn to two of the policy conclusions of the Rochet paper. First is the conclusion that market information can be a useful tool in allocating scarce supervisory resources. This is not seriously disputed by anyone I am aware of. In the United States, bank supervisors are extensive users of information such as stock prices, debt spreads, KMV, and market costs of credit protection. This information helps inform the allocation of our supervisory resources. Although I should add that here at the New York Fed, we have long sought to have extensive direct market contacts in an effort to ensure that we are not behind those markets in terms of their views of key participants.

More broadly--and with several recent cases in mind--I believe that there has been a marked increase in the intensity of supervision that has occurred simultaneously for those firms that have seen their market spreads widen significantly. But from the perspective of academic research, I know that the question is, Why has there not been a greater effort or willingness to develop approaches that "hard-wire" supervisory reactions to market signals, in particular, the subordinated debt proposals that have been made?

In the United States, there has been extensive discussion and research on this subject, such as the Treasury/Fed study mandated by the Gramm-Leach-Bliley Act. In many other countries, I honestly think there has been somewhat less enthusiasm. I believe this reflects concerns about giving up control as well as concerns about whether the underlying market signals are fully reliable--that is, that market prices may reflect excess volatility. But the concept has not been ignored, and I believe the supervisory community wants to see more research. In this regard, I commend to you a recent working paper by the Basel Committee's research task torte that discusses the existing markets for subordinated debt in the G-10 countries. The paper is available on the Bank for International Settlements' website.

Specifically with regard to subordinated debt, my own concerns have always centered on the idea that the proposal is premised on the creation of a liquid market in a product that does not seem to be desired today in the quantity and frequency that some of the models imply are necessary. In addition, there is the observation that the subdebt holders have become the "de facto regulators" of the bank in various ways. But if that is truly the case, then again, as some recent scandals suggest, we need to worry significantly about the potential conflicts of interest between the de facto regulators and the regulated. We need to ensure that banks are not simply buying and holding each other's subdebt in quid pro quo arrangements. We need to be able to police potential conflicts of interest between asset managers and the banks that provide custodial services for those asset managers. I do not believe that this would end tip being so simple in practice.

However, the future may be brighter for credit derivatives. A downside is that these derivatives are typically written on senior debt. But the upside is that a relatively liquid market with standardized terms is emerging in which contracts on the largest global banks are among the most active products, in particular, to help these firms manage their counterparty risks with each other. Moreover, in the past six months, we have seen credit derivative index products grow significantly, potentially enabling the marketwide signal to be disentangled from the firm-specific signal. Again, I would suggest this as a fruitful area for empirical research that explores the possibilities of linking supervisory intensity or even specific supervisory actions to these market signals.

The second major policy conclusion I will discuss is the need for a greater focus on the harmonization of supervisory practices around the world. Again, this idea has a lot of appeal. In the United States, I think it is fair to say that the supervisory community generally believes that it does a reasonably good job on Pillars 2 and 3. In regard to Pillar 2, the view of U.S. supervisors is that the primary responsibility is lot bank managers to determine what their desired level of capital is and how they want to allocate that capital, but that supervisory interaction--which benefits from having a window into the practices era number of the major banks--with banks on those decisions is advantageous.

Frankly, a major part of the original U.S. impetus for Basel II was to help export our preferred supervisory concepts and approaches more broadly around the world. For example, we believe that a mix of supervision and regulation works better than a purely regulatory approach with little on-site presence. I believe that, in large part driven by the realities of their responsibilities under a Basel II regime, many other supervisors have been moving toward us in approach, in particular, in the view that quality supervision requires substantial investment in skilled staff with the ability to understand modern risk management methods.

Changing embedded institutional arrangements and eliminating political pressures will not happen overnight. Realistically, efforts to harmonize supervisory approaches should not be seen as a substitute lot Basel II. From a practical perspective, a successful resolution to the Basel II negotiations will enhance the Basel Committee's pursuit of further efforts to increase supervisory cooperation and converge supervisory methods.

In conclusion, I agree very much with Rochet's view that focusing more attention on supervisory practices and on market discipline would be extremely worthwhile. Further efforts to harmonize and improve supervisory practices globally are desirable. However, I do not share the author's opinion that the Pillar t project is sufficiently unimportant that it could or should simply be abandoned. As I have said, the development of better risk measures is both necessary and inevitable. It is indeed largely inconceivable to me that the global capital markets could continue to develop over the next ten or twenty years in a way that avoids the need for such comprehensive and comparable measures of risk.

COMMENTARY

In his very interesting paper, Jean-Charles Rochet argues that instead of spending so much time on refining Pillar 1 (risk-based capital), the Basel Committee should seriously think about Pillars 2 (supervisory action) and 3 (market discipline). I certainly agree with the broad theme of Rochet's paper, which I would interpret as saying that one can get too lost in the details of implementing risk-based capital standards and that it is useful to step back and ask, what fundamental economic problem are we trying to solve, and how can we best deploy all the tools at our disposal together? These tools include not only capital requirements, but also market-based information as well as supervision and early intervention.

Rather than going through the details of Rochet's model, I will try to illustrate some of his ideas using an alternative-and much homelier--model. My model is also designed to highlight one critical variable not emphasized in Rochet's analysis, namely, the cost to banks of holding equity capital. I want to demonstrate that the cost of bank equity has an important impact on how one thinks about the optimality of using other policy tools, such as risk-based (as opposed to flat) capital requirements. I also want to suggest that, in addition to focusing on the three pillars, policymakers might want to devote more attention to thinking about ways to reduce the cost of equity for banks.

The model proceeds as follows. Imagine that bank i can invest in a loan of type i at time 0. With a probability 1/2, the loan yields a gross return of (1 + [v.sub.i]) + 2 [R.sub.i] at time 2, and with a probability 1/2, the loan yields (1 - [v.sub.i]) at time 2. Thus, the loan has an expected return of [R.sub.i], and a "volatility" of [v.sub.i]. Let [R.sub.i] = b[v.sub.i], so that riskier loans have higher expected returns to the bank that makes them.

As an alternative to bank lending, the loan can also be made in the bond market, where the market discount rate is zero. However, in this case, the time-2 payoff on the loan is only (1 + [v.sub.i]) in good state, instead of (1 + [v.sub.i]) - 2 [R.sub.i]. In other words, bond market borrowing is always zero net present value, while the bank can create an expected surplus of [R.sub.i] by virtue of its monitoring efforts. Note that since [R.sub.i] = b[v.sub.i], the relative appeal of bank lending compared with bond market lending is greater for riskier borrowers--one can think of these borrowers as firms for whom monitoring is most valuable.

To create a role for capital regulation, I assume that there are externalities associated with banks getting into trouble. A simple way to do so is to assume that bank managers do not attach any private costs to bank defaults, but that each bank default has a social cost of X. Finally, I assume that banks have two ways of raising funds. They can borrow, in which case they have to offer their investors an expected return of zero. Alternatively, they can finance themselves with equity, but equity has a cost of k. For the time being, this added cost represents an unspecified deviation from the Modigliani-Miller capital structure irrelevance benchmark; I will discuss its possible origins shortly. And as will become clear momentarily, it is precisely this cost of bank equity that makes the regulatory problem a nontrivial one.

Let us first ask what happens in a world with no regulation of any sort. Absent regulation, every bank holds zero equity capital--that is, debt finance is strictly preferred because it is viewed as cheaper--and makes all loans. The good news in this scenario is that all gains from intermediation are realized. The bad news is that society bears an expected default cost of X/2 per loan.

Now consider some possible regulatory approaches. First, one might try a regime of "flat," or non-risk-based, capital requirements. This corresponds to forcing banks to hold some fixed amount of equity v against all loans, irrespective of their risk. The benefit of this approach is that it eliminates the possibility of default for the less risky loans, those for which [v.sub.i] < v. The downside, however, is that the bank's cost of capital for all loans is now vk. This results in disintermediation--loans leaving the banking sector for the bond market--and hence a loss of the monitoring-related surplus if [R.sub.i] = b[v.sub.i] < vk. In other words, flat capital requirements distort cross-sectional pricing and discourage banks from making safe loans where they might otherwise create value.

These types of problems make clear the appeal of risk-based capital requirements. In this context, risk-based requirements amount to forcing a bank to hold [v.sub.i] against loan type i. The obvious advantage is that this eliminates all defaults, and can do so with less distortion of pricing and hence less disintermediation because the capital charge for low-risk loans can be reduced. At the same time, going from flat to risk-based capital requirements is not without its costs. As Rochet emphasizes, these costs arise from the real-world complexities associated with implementing a risk-based system, along with its potential vulnerabilities to lobbying and political pressure.

Taking these political-economy considerations into account, which regime--flat or risk-based--is better? Observe that the answer will depend crucially on the cost of bank equity k. For high values of k, the distortions in loan pricing associated with a flat-capital regime are severe, so it is better to go with risk-based capital despite the political-economy costs. In contrast, for low values of k, it makes sense to stick with the simpler and less politically vulnerable flat-capital requirement. (1)

Said a bit differently, the complex risk-based capital approach envisioned in the Basel II proposals can make sense only if one believes that k is relatively high--that is, that there is a significant violation of the Modigliani-Miller conditions that makes bank equity costly. This observation leads to two questions. First, what are the primitive frictions that make bank equity so expensive? And second, are there any steps that policymakers can take to help reduce the cost of bank equity, thereby mitigating the distortions associated with capital regulation?

With respect to the first question, it is easy enough to enumerate the usual suspects that are thought to make equity finance more expensive than debt finance: 1) tax disadvantages; 2) free-cash-flow-type agency problems, whereby investors discount the value of a bank when management has too much slack and might be tempted to make bad investments; 3) asymmetric information, which can make raising new equity difficult; and 4) market inefficiencies, which can lead to (real or perceived) transient undervaluations, and again discourage new equity issues.

Of course, it is harder to get a good handle on the relative importance of each of these frictions for banks. But this may he a very useful area for further study because if we had a better understanding of exactly why bank equity is thought to be so costly, we might be able to take steps to bring the cost down. And again, with a lower cost of bank equity, capital regulation can be made more efficient, and potentially simpler.

Let me offer a couple of examples. First, and most directly, if it is the case that taxes play an important role in pushing up the cost of bank equity, it follows that one might want to increase scope for tax-favored instruments to count toward capital requirements. I will not try to get into the specifics of how this could be implemented, but it is worth noting that the tax angle provides an alternative motivation--distinct from market discipline--for the types of subordinated debt proposals that Rochet discusses.

My second example is motivated by the free-cash-flow agency problem. If the primitive friction is that investors do not like a bank having a lot of capital just sitting around on the balance sheet, why not employ some sort of conditional capital arrangement that only channels the equity to the bank in those states where it is needed to avert default? Specifically, suppose a bank has 100 in loans today; these loans will be worth either 90 or 110 next period, with a probability 1/2 of either outcome. One way for the bank to avoid default would be to finance itself with 90 of debt and 10 of equity. But this approach leaves the bank with 20 of free cash in the good state. If investors worry that this excess slack in good times will lead to waste, they will discount the bank's stock.

An alternative--in the spirit of a recent proposal by Mark Flannery--would be for the bank to raise 90 in debt, 5 in equity, and 5 with a "reverse convertible debenture." The reverse convertible would be structured as follows. It would have a face value of 10, and in the good state, it would remain as a 10 debt claim, so the bank's total debt obligation would be 100. In the bad state, it would convert into a prespecified number of shares, so the bank's total debt obligation would remain at 90. (Note that in this extremely simple example, any shares would turn out to be worthless in the bad state.)

From a regulator's perspective, the bank should be viewed as just as well capitalized as before, since it is still guaranteed not to default in either state. Thus, the reverse convertible should "count" as regulatory capital. At the same time, the free-cash-flow problem is attenuated, because after paying off its debt, the bank now has less slack in the good state (10, rather than 20). (2) This is just a specific example of a general corporate risk management principle: capital structure and derivatives should be used to match net inflows with investment opportunities on a state-by-state basis, so that to the extent possible, firms never have too little or too much cash on hand at any point in time (see Froot, Scharfstein, and Stein [1993]).

Of course, this reverse convertible idea raises a host off practical questions concerning, for example, the specifics of security design, which are beyond the scope of this brief comment. (3) However, my goal is not to make the case for a particular new financial instrument, but simply to suggest that further creative thinking along these lines is likely to be valuable.

ENDNOTES

(1.) As Rochet points out, for any given value of k, one can improve the terms of the trade-off by relying on market-based signals and prompt corrective action. In the context of the model, suppose that at some interim time 1, one can observe a market signal that suggests that the bad state is coming. Moreover, if the bank is liquidated promptly, instead of waiting until time 2, one can recover (1 - h[v.sub.i]), where h < 1. This has the benefit that capital charges can be lowered in either the flat or risk-based regime.

(2.) If accounting concerns, such as a desire to have a high return on equity, also drive bank managers' reluctance to carry too much equity on the balance sheet, the reverse convertible may also be helpful on that dimension, to the extent that return on equity is now calculated based on balance-sheet equity of 5, rather than 10.

(3.) See Flannery (2002) for a detailed discussion of many of these issues.

REFERENCES

Flannery, M. J. 2002. "No Pain, No Gain? Effecting Market Discipline via Reverse Convertible Debentures." Unpublished paper, University of Florida.

Froot, K. A., D. S. Scharfstein, and J. C. Stein. 1993. "Risk Management: Coordinating Corporate Investment and Financing Policies." JOURNAL OF FINANCE 48, no. 5 (December): 1629-58.

The author thanks Jean-Paul Decamps and Benoit Roger for allowing him to use material from their joint paper. He also thanks Mark Flannery, Diana Hancock, and his two discussants, Darryll Hendricks and Jeremy Stein, for comments. All errors are the author's. The views expressed are those of the author and do not necessarily reflect the position of the Federal Reserve Bank of New York or the Federal Reserve System.

The views, expressed are those of the author and do not necessarily reflect the position of the Federal Reserve Bank of New York or the Federal Reserve System.

Jean-Charles Rochet is a professor of mathematics and economics at Toulouse University and research director of the Institut d'Economic Industrielle. <rochet@cict.fr>

Darryll Hendricks is a senior vice president at the Federal Reserve Bank of New York.

Jeremy C. Stein is a professor of economics at Harvard University and a research associate at the National Bureau of Economic Research.

The ongoing reform of the Basel Accord is supposed to rely on three "pillars": a new capital ratio, supervisory review, and market discipline. But even a cursory look at the proposals of the Basel Committee on Banking Supervision reveals a certain degree of imbalance between these three pillars. Indeed, the Basel Committee (BIS 2003) gives a lot of attention (132 pages) to the refinements of the risk weights in the new capital ratio, but it is much less precise about the other pillars (16 pages on Pillar 2 and 15 pages on Pillar 3). (1)

Even though the initial capital ratio (BIS 1988) has been severely criticized for being too crude and opening the door to regulatory arbitrage, (2) it seems strange to insist so much on the importance of supervisory review (3) and market discipline as necessary complements to capital requirements while remaining silent on the precise ways (4) this complementarity can work in practice. One possible reason for this imbalance is a gap in the theoretical literature. As far as I know, there is no tractable model that allows a simultaneous analysis of the impact of solvency regulations, supervisory action, and market discipline on the behavior of commercial banks.

This paper aims to fill that gap by providing a simple framework for analyzing the interactions between the three pillars of Basel II. We start by offering a critical assessment of the academic literature on the three pillars, (5) and argue that none of the existing models allows for a satisfactory integration of these pillars. We therefore develop in Section 3 a new formal model that tries to incorporate the most important criticisms of existing theoretical models of bank regulation. Section 4 shows that minimum capital ratios can be justified by a classical agency problem, a la Holmstrom (1979), between bankers and regulators, even in the absence of mispriced deposit insurance. We demonstrate in Section 5 that, under restrictive conditions> these capital requirements can be reduced if banks are mandated to issue subordinated debt on a regular basis (direct market discipline). Finally, Section 6 explores the interactions between market discipline and supervisory action and shows that they are complementary rather than substitutes.

2. THE THREE PILLARS IN THE ACADEMIC LITERATURE

Most of the academic literature on Basel I concentrates on the credit crunch of the early 1990s (6) and on the distortions of banks' asset allocation generated by the wedge between the market assessment of banks' asset risks and its regulatory counterpart in Basel I. Several theoretical articles (for example, Koehn and Santomero [1980], Kim and , Santomero [1988], Furlong and Keeley [1990], Rochet [1992], and Thakor [1996]) use static portfolio models to explain these distortions. In such models, appropriately designed capital requirements could be used to correct the incentives of bank shareholders to take excessive risks, due to the mispricing of deposit insurance or simply to the limited liability option. Using a different approach, Froot and Stein (1998) model the buffer role of bank capital in absorbing liquidity risks. They determine the capital structure that maximizes the bank's value when there are no audits or deposit insurance.

Yet, as pointed out by Hellwig (1998) and Blum (1999), static models fail to capture important effects of capital requirements. The empirical literature (for example, Hancock, Laing, and Wilcox [1995] and Furfine [2001]) has tried to calibrate dynamic models of bank behavior in order to study these intertemporal effects. However, none of these papers has studied the interactions of capital requirements with supervisory action (7) and market discipline.

The literature on continuous time models of bank behavior was initiated by Merton (1977). Assuming an exogenous closure date, he shows that the fair price of deposit insurance can be computed as a European put option. Merton (1978) extends this framework by considering random audits and endogenous closure dates. (8)

Merton's seminal contributions have been extended in several directions, in particular:

* Fries, Mella-Barral, and Perraudin (1997) introduce deposit withdrawal risk and study the impact of banks' closure policies on the fair pricing of deposit insurance;

* Bhattacharya et al. (2002) study closure rules that can be contingent on the level of risk taken by banks; and

* Levonian (2001) introduces subordinated debt in Merton's (1977) model and studies its impact on bankers' incentives for risk taking.

3. A FORMAL MODEL

Our model aims to take seriously most of the criticisms of previous models of bank regulation while remaining tractable. (9)

First, it is a dynamic model, because static models necessarily miss important consequences of bank solvency regulations. (10) The simplest dynamic models are in discrete time, like those of Calem and Rob (1996) or Buchinsky and Yosha (1997), but they typically do not yield closed-form solutions and entail the use of numerical simulations. For transparency, we instead use a continuous time model, a la Merton (1977, 1978), which requires using diffusion calculus but is ultimately revealed to be more tractable. Following Merton, we therefore assume that the (economic) value [A.sub.t] of a bank's assets at date t follows a diffusion process:

(1) dA/A = [mu]dt + [sigma]dW,

where dW is the increment of a Wiener process and [mu] and [sigma] are the drift and volatility of asset value. For simplicity, we assume that all investors are risk neutral (11) and discount the future at a constant rate r > [mu]. The bank's assets continuously generate an instantaneous cash flow [x.sub.t] = [beta][A.sub.t], where [beta] > 0 is the constant payout rate. (12)

We depart from the complete frictionless markets assumption made by Merton (1977, 1978) (13) and many of his followers, since this assumption implies that the social value of banks is independent of their liability structure, a hardly acceptable feature if one wants to study the consequences of solvency regulations for banks. Following Gennotte and Pyle (1991), we assume instead that banks create value by monitoring borrowers, and thus acquire private information about these borrowers. The counterpart to this private information is that the resale value of a bank's assets (typically, in case of liquidation) is only a fraction [lambda]A (with [lambda] < 1) of the economic value A of these assets. (14)

We also assume that the monitoring of borrowers has a fixed-cost component, (15) equivalent to a flow cost r[gamma] per unit of time (its present value is therefore [gamma]). From a social perspective, a bank should thus be closed when its asset value falls below some threshold [A.sub.L] (the liquidation threshold). The social value of the bank, denoted V(A), equals the expected present value of future cash flows [x.sub.t], = [beta][A.sub.t], net of monitoring costs r[gamma], until the stopping time [[tau].sub.L] (the first time t that the bank hits the liquidation threshold [A.sub.L]), when the bank is liquidated and its assets are resold at price [lambda][A.sub.L]. As shown in the appendix, this social value equals:

(2) V(A) = (A - [gamma]) + {[gamma] - (1 - [lambda])[A.sub.L]}[(A/[A.sub.L]).sup.-a],

where a is the positive root of the quadratic equation:

(3) [1/2][[sigma].sup.2]x(x + 1) - [mu]x = r.

Notice that this total value is composed of two terms:

* the value A of its assets, net of monitoring costs [gamma], and

* the option value associated with the (irreversible) closure decision.

As in the real options literature (see, for example, Dixit and Pindyck [1994]), the social value of the bank is maximized for a threshold [A.sub.L] that is below the break-even threshold [A.sub.0] = [gamma]/1 - [lambda]. More specifically, the level of [A.sub.L] that maximizes the social value of the bank (notice that this level is independent of A, and thus is time consistent) is what we call the first-best closure threshold:

(4) [A.sub.FB] = [a/(a + 1)][[gamma]/(1 - [lambda]).

Thus, our model captures an important feature of real-life banking systems: (16) even in the absence of moral hazard, government subsidies, and the like, the failure rate of banks cannot be zero. The socially optimal failure rate takes into account tile embedded real option: given that bank closures are irreversible (and entail a real cost, due to the imperfect resaleability of banks' assets), it is optimal to let banks operate (up to a certain point) below the break-even level, defined by the condition [A.sub.0] - [gamma] = [lambda][A.sub.0], in the hope that they recover. In more concrete terms, the fact that the resolution of bank failures costs money (ex post) m the Deposit Insurance Fund (DIF) does not necessarily imply some kind of inefficiency. This feature is illustrated in Exhibit 1. (17)

[GRAPHIC OMITTED]

So far, we have introduced only one of the two important features of banking: the opacity of banks' assets, (18) which implies that they have to be monitored and cannot be resold at full value. We now introduce the second feature: the bulk of a bank's liabilities consists of retail deposits D, fully insured by a DIF and paying interest rD. The DIF is financed by a premium P paid at discrete dates. We assume that this premium is fair (so we rule out systematic subsidies from the DIF to the banks) but cannot be revised by continuous readjustments. The academic literature has insisted a lot on the "moral hazard" problem created by the put-option feature of deposit insurance. It has been extensively argued that this feature, and more generally the limited liability of bank shareholders, gives these shareholders incentives to take excessive risks, especially when banks are insufficiently capitalized. We focus here on a different agency problem, also created by limited liability, but of a different nature: bankers (19) may not have enough incentives to monitor their assets when their value becomes too small. (20) We assume that when monitoring stops (we say that the banker "shirks"), the quality of bank assets deteriorates, (21) and the dynamics of asset value become:

(5) dA/A = ([mu] - [DELTA][mu])dt + [sigma]dW,

where [DELTA][mu] > 0. Equation 5 indicates that the shirking/ monitoring decision impacts only the expected profitability of the bank's assets and not the risk. Most of the academic literature has considered the polar case in which [mu] is unchanged but [sigma] increases by moral hazard (the asset-substitution problem). Which specification is more appropriate is an empirical question. (22) In Decamps, Rochet, and Roger (2004), we consider the general case in which both [mu] and [sigma] are altered by the banker's decision.

In the absence of shirking, the value of the bank's equity is given by a simple formula in the spirit of equation 2 (see the appendix for all mathematical derivations):

(6) E(A) = A - D - [gamma] + (D + [gamma] - [A.sub.L])[(A/[A.sub.L]).sup.-a].

As in Merton (1977, 1978), the value of the bank's equity is the sum of two terms:

* the value of assets A net of debt (deposits) D (and of the monitoring cost, which does not appear in Merton [1974]) and

* the value of the limited liability option.

However, as in Merton (1978) but in contrast to Merton (1977), the value of the limited liability option is not of the Black-Scholes type (it is actually simpler). This is because it can be exercised at any time, which corresponds to a down-and-out barrier option, instead of at a fixed date, which corresponds to a European option. In Merton (1978) the closure option can be exercised only after an audit by the supervisor. Here we assume that, thanks to the information revealed by the market (indirect market discipline), oh)sure can occur at any time.

[A.sub.L] is now chosen by shareholders so as to maximize equity value. The corresponding threshold is:

(7) [A.sub.E] = [a/a + 1](D + [gamma]).

At this threshold, the marginal value of equity is zero: E'([A.sub.E]) = 0 (smooth-pasting condition). Shirking is optimal for bankers whenever their expected instantaneous loss from shirking, AE'(A)[DELTA][mu], becomes less than the instantaneous monitoring cost [gamma]r. Since E'([A.sub.E]) = 0, this has to be true for some interval [[A.sub.E], [A.sub.S]].

Proposition 1: When the cost of monitoring [gamma]/D (per unit of deposits) is smaller than a + 1/[lambda]a - 1, there is a conflict of interest between shareholders and the DIF: insufficiently capitalized banks shirk.

Interestingly, there are parameter values for which the agency problem does not matter: when [gamma]/D is large (> a + 1/[lambda]a - 1), shareholders decide to close the bank before the shirking constraint becomes binding. However, when [gamma]/D is smaller than this threshold, there is a conflict of interest, even in the absence of mispriced deposit insurance. It is similar to the conflict of interest between bondholders and shareholders of undercapitalized firms.

Exhibit 2 represents the typical pattern of the value of the bank's equity E, as a function of the value A of its assets, in the case where deposits are fully insured (and therefore depositors have no incentives to withdraw), but the bank is left unregulated. The closure threshold [A.sub.E] (below which the bank declares bankruptcy) (23) and the shirking threshold [A.sub.S] (below which the bank shirks) are chosen by bankers so as to maximize the value of equity. The reason why shirking is sometimes preferred by shareholders (in the intermediate region [A.sub.E] [less than or equal to] A [less than or equal to] [A.sub.S]) even though it is socially inefficient is not the deposit insurance option (as is the case for asset-substitution problems, where typically [gamma] = [DELTA][mu] = 0, [DELTA][[sigma].sup.2] > 0), but rather the agency problem between the bank and the Deposit Insurance Fund. Indeed, the cost of monitoring is entirely borne by the bank, but the bank collects only a fraction of the benefits of monitoring. When these benefits are small, the banker prefers to shirk. As we describe in the next section, this can be prevented by imposing a minimum capital ratio.

[GRAPHIC OMITTED]

4. JUSTIFYING THE MINIMUM CAPITAL RATIO

In our model, the justification of a minimum capital ratio is not an asset-substitution problem (as in the vast majority of academic papers on the topic (24)), but an agency problem between the banker and the supervisors, who represent the interests of the DIF: insufficiently capitalized banks shirk, that is, they stop monitoring their assets. To avoid this problem, we assume now that when the value of the bank's assets hits some threshold [A.sub.R] chosen by the regulator, the bank is liquidated and the shareholders are expropriated. (25) This regulatory threshold [A.sub.R] is designed in such a way that bankers are never tempted to shirk.

Proposition 2:

1) Under the assumption of Proposition 1 (that is, [gamma]/D < a + 1/[lambda]a - 1), bank shirking can be eliminated if bank regulators impose liquidation whenever the bank's assets fall below the following threshold:

(8) [A.sup.O.sub.R] = a(D + [gamma]) + r[gamma]/[DELTA][mu]/a + 1.

2) When [gamma]/D is larger than [DELTA][mu]/r + a[DELTA][mu], this liquidation threshold can be implemented by imposing a minimum capital ratio:

(9) A - D/A [greater than or equal to] [[rho].sub.R] [equivalent to] [gamma](r + a[DELTA][mu]) - D[DELTA][mu]/[gamma](r + a[DELTA][mu]) + aD[DELTA][mu].

The condition [gamma]/D > [DELTA][mu]/r + a[DELTA][mu] ensures that the minimum capital ratio [[rho].sub.R] is positive. When it is not satisfied, banks can be allowed to continue for negative equity values. We focus here on the more interesting case of Proposition 2, where [[rho].sub.R] > 0.

Notice that when liquidation costs are large enough, the first-best liquidation threshold

[A.sub.FB] = [a/a + 1][[gamma]/1 - [lambda]]

is smaller than the regulatory threshold

[A.sup.O.sub.R] = a(D + [gamma]) + r[gamma]/[DELTA][mu]/a + 1.

This means that bank supervisors are confronted with time consistency problems: even if ex ante, agency considerations imply that a bank should be closed whenever A [less than or equal to] [A.sup.O.sub.R], ex post it is optimal to let it continue (and provide liquidity assistance). These forbearance problems are examined in Section 6.

We now examine the policy implications of our first results. We interpret bank solvency regulations as a closure rule intended to avoid shirking by insufficiently capitalized banks: every time the asset value of the bank falls below [A.sup.O.sub.R], the bank should be closed. However, we argue that bank assets are opaque and cannot be marked to market in continuous time. The traditional view of the role of supervisors was to evaluate these assets periodically through on-site examinations. In particular, most academic papers (26) assumed that [A.sub.t] was observable only through costly auditing that had to be performed more or less with uniform frequency across banks. We argue in favor of a more modern modeling strategy, whereby bank supervisors can rely on market information and adapt the intensity or frequency of their examinations to the market assessment of the bank's situation. This can be done by conditioning risk weights on market ratings of assets (Pillar 1) or using yield spreads of bank liabilities and private ratings to reassess the solvency of the bank (Pillars 2 and 3). In our model, it would mean inferring A,, the (unobservable) value of the bank's assets, from the market price of equity (if the bank is publicly listed), that is, inverting the function A [right arrow] E{A). This is how our model captures the notion of "indirect market discipline": using as much publicly available information as possible to allocate scarce regulatory resources in priority to the banks m distress. In our model, it leads to a simple policy recommendation of organizing a regulatory framework with two regimes:

* A light regime for "healthy" banks (those for which asset value A is way above the closure threshold [A.sup.O.sub.R], where A is inferred from accounting data and market information), only imposing accurate reporting and transparency.

* A heavy regime for "problem" banks (those for which A gets close to [A.sup.O.sub.R]), imposing restrictions on what the bank can do and closely examining its books.

This two regime regulatory framework (a simplified version of the prompt corrective action provisions of the Federal Deposit Insurance Corporation Improvement Act, or FDICIA) (27) is examined formally in Section 6. For the moment, we discuss direct market discipline and, more specifically, how the subdebt proposal can, under certain conditions, reduce capital requirements.

5. MARKET DISCIPLINE AND SUBORDINATED DEBT

We now consider that the bank is mandated to issue a certain volume B of bonds, each paying a continuous coupon c per unit of time. (28) These bonds are subordinated to deposits: if the bank is liquidated (when asset value hits threshold [A.sub.L]), the DIF receives [lambda][A.sub.L] but bondholders receive nothing. Anticipating this possibility, bondholders require a coupon rate c above the riskless rate r. To maintain the convenience of the stationarity of the bank's financial structure, we assume that bonds have an infinite maturity (unless of course the bank is liquidated) but are randomly renewed according to a Poisson process of intensity m. (29) In more intuitive terms, a fraction mdt of outstanding bonds is repaid at each instant at its face value B and the same volume mdt is reissued, (30) but at its market value B(A). This is where market discipline comes in: (31) if the bank's asset value A deteriorates (for example, if bankers stop monitoring their assets), the finance cost of the bank increases immediately, since at each instant a fraction m of the bonds has to be repaid at face value B and reissued at market value B(A) < B (notice also that B' > 0). In the appendix, we show that the value of equity becomes:

(10) E(A, B) = A - [gamma] - D - B[c + m/r + m] + (D + [gamma] + [A.sub.L])[(A/[A.sub.L]).sup.-a] + [c + m/r + m]B[(A/[A.sub.L]).sup.-a(m)],

where a(m) is the positive root of the quadratic equation

[1/2][[rho].sup.2]x(x + 1) - [mu]x = r + m.

The new regulatory threshold [A.sup.SD.sub.R] is the smallest value of [A.sub.L] that guarantees that bankers will not shirk. It is defined implicitly by:

[A.sup.SD.sub.R][[differential]E/[differential]A]([A.sup.SD.sub.R], B) = [gamma]r/[DELTA][mu],

where [A.sub.L] is taken to equal [A.sup.SD.sub.R]. After easy computations, we obtain:

(11) [A.sup.SD.sub.R] = [A.sup.O.sub.R] + [a(m)/a + 1](c + m/r + m)B.

Not surprisingly, this threshold is higher than [A.sup.O.sub.R] (all else being fixed), since the bank is now more indebted. However, the capital ratio becomes:

(12) [[rho].sup.SD.sub.R] = 1 - D + B/[A.sup.SD.sub.R].

It is smaller than [[rho].sub.R] = 1 - D/[A.sup.O.sub.R], whenever [A.sup.SD.sub.R]/D + B < [A.sup.O.sub.R]/D, which is equivalent to:

(13) a(m)[c + m/r + m] < a + [[gamma]/D](a + r/[DELTA][mu]).

Since a(m) increases with m (which a(0) = a and a (+ [infinity]) = + [infinity]), we see that this condition can be satisfied, but m (the frequency of renewal of bonds, which is inversely proportional in our model to their average maturity) and c - r/r (the relative spread on subordinated debt) have to be small enough. Thus, we obtain:

Proposition 3: If banks are mandated to issue subordinated bonds on a regular basis, regulators can reduce capital requirements (Tier 1) if two conditions are satisfied: the average maturity must not be too small (32) (m small) and the coupon paid on the bonds must not be too large (c/r close to 1). However, the total requirement, capital + subdebt (Tier 1 + Tier 2), is always increased.

Proposition 3 shows the limits of the mandatory subdebt proposal. Only when properly designed (that is, with a maturity that is not too small or a frequency of renewal that is not too large) and when markets are sufficiently liquid and bank assets not too risky (so that the relative spread c - r/r is not too large) can mandatory subdebt allow regulators to decrease capital requirements.

6. MARKET DISCIPLINE AND SUPERVISORY ACTION

We now come to what we consider the most convincing rationale for market discipline: preventing regulatory forbearance by forcing regulators to intervene before it is too late. As is well documented in the literature on banking crises, banking authorities are very often subject to political pressure for bailing out the creditors of banks in distress. To capture this in our model, we consider what would happen if subdebt holders where de facto insured in the case where the bank is liquidated (that is, whenever the value of its assets hits the regulatory threshold). This bailout obviously does not affect the social value of the bank but only leads to a redistribution of wealth between the DIF and bondholders. Bonds become riskless (33) and perfect substitutes for deposits in the view of equityholders. The frequency of renewal of bonds ceases to play any disciplining role.

Proposition 4: If subdebt holders are insured by the DIF, subdebt ceases to play any disciplining role: Direct market discipline can work only in the absence of regulatory forbearance.

Proposition 4 shows the existence of some form of complementarity between market discipline and supervisory action: direct market discipline can work only if supervisors can credibly commit not to bail out bondholders.

We now examine a second form of complementarity between market discipline and supervisory action: if financial markets are suitably efficient and liquid, and if banks issue publicly traded securities (equity or bonds), the market prices (or yields) of these securities will provide objective signals about the situation of these banks. We do not address the difficult statistical question of which security (equity or subordinated bonds) gives the most useful information to bank supervisors. (34) Our model has only one state variable, A, and both the equity price E(A) and the subdebt price B(A) are monotonic functions of A and thus sufficient statistics for A. In our simple model, by observing market prices of either equity or bonds, regulatory authorities can perfectly infer the true value of A.

Our model is obviously not appropriate for analyzing such statistical considerations. It is, however, well adapted to study another, equally important question: namely, how market discipline can limit forbearance. Market information is then viewed as providing objective signals that oblige supervisors to intervene. Indirect market discipline is thus useful in two ways: it allows supervisors to save on audit costs for the banks that are well capitalized, and simultaneously it forces supervisors to intervene early enough when a bank is in trouble. This is captured in our model in the following way.

We consider that bank supervisors are required to inspect banks whenever the value of their assets hits an inspection threshold [A.sub.I] (with [A.sub.I] > [A.sub.R]). Inspection allows them to detect shirking and close the banks that do shirk. The value of equity is still given by equation 6 (for simplicity, we return to the case with no subordinated debt):

E(A) = A - [gamma] - D + (D + [gamma] - [A.sub.R]) [(A/[A.sub.R]).sup.-a].

But now the condition for no shirking becomes

(14) [for all] A [greater than or equal to] [A.sub.I], AE' (A) [greater than or equal to] [gamma]r/[DELTA][mu],

which is equivalent to:

(15) [A.sub.I] - a(D + [gamma] - [A.sub.R]) [([A.sub.I]/[A.sub.R]).sup.-a] [greater than or equal to] [gamma]r/[DELTA][mu].

This formula shows that for any closure threshold [A.sub.R], there is a minimum inspection threshold At that prevents shirking: it is given by equality in equation 15. The corresponding curve in the ([A.sub.R], [A.sub.I]) plane is represented in Exhibit 3. Notice that the previous case (no inspection, closure at [A.sup.O.sub.R]) corresponds to the intersection of this curve with the first diagonal ([A.sub.R] = [A.sub.I] = [A.sup.O.sub.R]).

In Exhibit 3, we represent the optimal combination of inspection and closure thresholds by ([A.sup.*.sub.R], [A.sup.*.sub.I]). It is obtained by maximizing the social value of the bank:

V(A, [A.sub.R]) = A - [gamma] + [[gamma] - (1 - [lambda]) [A.sub.R]] [(A/[A.sub.R]).sup.-a),

net of the expected present value of auditing costs:

(16) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]

where the auditing cost [xi] is incurred only when the asset value of the bank lies in the interval [[A.sub.R], [A.sub.I], [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] is the indicator function that takes a value of 1 when [A.sub.t] [less than or equal to] [A.sub.I] (and zero otherwise). Here, [[tau].sub.R] denotes the first time that [A.sub.t] = [A.sub.R] (closure time). It can be shown that the expected present value of auditing costs C is proportional to [A.sup.-a]:

(17) C(A, [A.sub.R], [A.sub.I]) = [A.sup.-a] [phi] ([A.sub.R], [A.sub.I]).

Thus, after simplification by [A.sup.-a], we obtain:

Proposition 5: The optimal value of the closure threshold [A.sup.*.sub.R] and the inspection threshold [A.sup.*.sub.I] can be obtained by maximizing

(18) W(A.sub.R, [A.sub.I) [equivalent to] ([gamma] - (1 - [lambda]) [A.sub.R]) [A.sup.a.sub.R] - [phi] ([A.sub.R, [A.sub.I]),

under the incentive compatibility constraint (equation 15).

We have that [A.sup.*.sub.R] < [A.sup.O.sub.R], which indicates that prompt corrective action allows the reduction of capital requirements. When auditing costs are small, [A.sup.*.sub.R] becomes close to the first-best closure threshold [A.sub.FB], which means that prompt corrective action also reduces the severity of the time consistency problem of bank supervisors.

Proposition 5 illustrates the substitulability between Pillar 2 (supervisory action) and Pillar 1 (capital requirements). This was already a feature of Merton's (1978) model, in which the frequency of bank examinations could be substituted for more stringent capital requirements. However, here the introduction of Pillar 3 (market discipline) changes the picture: the intensity of regulation can be modulated according to market information (in the spirit of the prompt corrective action provisions of FDICIA), and symmetrically, supervisors can be forced to intervene when market signals reveal the distress of a bank (so that forbearance becomes more costly to supervisors or politicians). Notice also that market discipline decreases the (ex-post) benefits of forbearance by reducing the bank closure threshold (capital requirements), another illustration of the complex interactions between the three pillars of Basel II.

7. CONCLUSION

This paper develops a formal model of banking regulation that permits analysis of the interactions between the three pillars of Basel II. It differs from previous models in several important ways:

* it is a dynamic model, in which solvency regulation are interpreted as closure thresholds, rather than complex tools intended to correct the mispricing of deposit insurance;

* the justification of regulation is not (primarily) to prevent asset substitution by banks (deposits are not subsidized in our model), but rather to prevent shirking by the managers of undercapilalized banks;

* bank supervisors can rise market information as a complement to the information provided by bank examinations; thus, they can save on scarce supervisory resources and allocate them in priority to the banks in distress; and

* the returns on banks' assets are endogenous, since they depend on the monitoring decisions of bankers.

Although very simple, this model allows a formal analysis of the interactions between the three pillars of Basel II. In particular, we show in Proposition 3 that mandatory subdebt (direct market discipline) may, under some restrictions, allow regulators to decrease capital requirements. More important, we show that market discipline and supervisory action are complementary rather than substitutes (Propositions 4 and 5): one cannot work well without the other.

In terms of policy implications, our theory, points to a serious rebalancing of the three pillars of Basel II. The initial motivation of Basel I was to guarantee a level playing field for international banking, given that the large banks of some countries could take enormous risks without having much capital, benefiting from implicit guarantees by their governments. So the fundamental idea behind the Cooke ratio was harmonization, that is, to set a uniform standard for internationally active banks. It turns out that the Cooke ratio (or more generally, the risk-based capital methodology), although imperfect, was revealed to be extremely useful as an instrument for measuring bank risk. That is probably why it was applied rapidly (with minor changes) by the regulatory authorities of many countries within their jurisdictions (although it was initially designed for large, internationally active banks).

Probably in response to the harsh critiques of the crudeness of the Cooke ratio, the Basel Committee began a process of complexification, alternating new proposals and consultation periods with the banking industry (BIS 1999, 2001, 2003). The outcome of this long process is an extremely complex instrument (the McDonough ratio) that results from intense bargainings with large banks, and will probably never be implemented as such.

In this analysis, we argue that banking authorities should instead keep arm's-length relationships with bankers and that scarce supervisory resources should be used, according to priority, to control the behavior of banks in distress, rather than to implement an extremely complex regulation that will ultimately be bypassed in some way or another by the largest or most sophisticated banks. By contrast, there is an urgent need (once again) to guarantee a level playing field in international banking. The development of large and complex banking organizations with multinational activities implies that supervisory authorities of different countries urgently need to harmonize their institutional practices. Market discipline can provide a very useful tool for defining a harmonized and clear mandate for banking authorities across the world, in an attempt to eliminate political pressure and regulatory forbearance. This should be the top priority of the Basel Committee.

MATHEMATICAL APPENDIX

Here we derive the mathematical formulas used in our analysis.

FIRST-BEST VALUE OF THE BANK

The value of the bank (when assets are monitored) equals the expected present value of future cash flows [beta][A.sub.t], net of the monitoring cost r[gamma], until the stopping time [[tau].sub.L] (the first time t that [A.sub.t] hits the liquidation threshold [A.sub.L]) when the bank is liquidated. The formula is:

(A1) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]

Using classical formulas (see, for example, Dixit [1993] or Karlin and Taylor [1981]), we obtain:

(A2) V = A - [gamma] + {[gamma] - (1 - [lambda])[A.sub.L]} [(A/A.sub.L]).sup.-a],

where A is the current value of [A.sub.t], and a is the positive root of the quadratic equation:

(A3) 1/2 [[sigma].sup.2] x (x + 1) - [mu] x = r.

VALUE OF THE BANK'S EQUITY

In the absence of regulation, equityholders choose the liquidation threshold that maximizes the value of their equity. Using the same classical formulas as we use to establish equation A2, we obtain:

(A4) E(A) = (A - [gamma] - D) + (D + [gamma] - [A.sub.L]) [(A/[A.sub.L]).sup.-a].

As for the total value of the bank (equation A2), the second term is an option value that is maximized when

(A5) [A.sub.L] = [A.sub.E] [equivalent to] a/z + 1 (d + [gamma]).

At this threshold, the value of the bank's equity has a horizontal tangent (as represented in Exhibit 2 in the text):

(A6) E'([A.sub.E]) = 0.

If equityholders decide to stop monitoring, the dynamics of asset value become

dA/A = ([mu] - [DELTA][mu])dt + [sigma]dW,

but they save the monitoring cost r[gamma]. Shirking becomes optimal for equityholders whenever the instantaneous loss of equity value E'(A)A [DELTA][mu] is less than this monitoring cost. Because E'([A.sub.E]) = 0 (see equation A5), this condition is always satisfied in the neighborhood of the liquidation point. However, we have to check that this incentive constraint binds after the bank becomes insolvent. This is true whenever

[lambda][A.sub.E] [less than or equal to] D

or

[lambda]a(D + [gamma]) [less than or equal to] (a + 1)D,

which is equivalent to the condition of Proposition 1, namely:

[gamma]/D [less than or equal to] a + 1/[lambda]a - 1.

This ends the proof of Proposition 1.

MINIMUM CAPITAL RATIO

Suppose bank regulators impose a closure threshold [A.sub.R] [less than or equal to] D/[gamma]: if the bank's asset value hits [A.sub.R], the bank is liquidated and shareholders receive nothing. By an immediate adaptation of equation A4, shareholders' value becomes:

(A7) E(A) = A - [gamma] - D + (D + [gamma] - [A.sub.R]) (A/[A.sub.R]).sup.-a].

The condition for eliminating shirking is:

(A8) [for all]A [greater than or equal to] [A.sub.R], E'(A)A [DELTA] [mu] [greater than or equal to] [gamma]r.

Using equation A7, we see that this is equivalent to:

(A9) [for all]A [greater than or equal to] [A.sub.R], A - a(D + [gamma] - [A.sub.R]) [(A/[A.sub.R]).sup.-a] [greater than or equal to] [gamma]r/[DELTA][mu].

Provided that [A.sub.R] [less than or equal to] [gamma] + D (this will be checked ex post), the left-hand side of equation A9 is increasing in A, therefore equation A9 is equivalent to:

[A.sub.R](1 + a) - a(D + [gamma]) [greater than or equal to] [gamma]r/[DELTA][mu]

or

(A10) [A.sub.R] [greater than or equal to] [A.sup.O.sub.R] [equivalent to] a(d + [gamma] + [gamma]r/[DELTA][mu]/a + 1.

[A.sup.O.sub.R] represents the minimum asset value that preserves the incentives of the banker. The associated capital ratio is:

[[rho].sup.R] = [A.sup.O.sub.R] - D/[A.sup.O.sub.R] = [gamma](a + r/[DELTA][mu]) - D/ a(D + [gamma]) + [gamma]r/[DELTA][mu].

SUBORDINATED DEBT

Consider now that the bank issues a volume B of subordinated bonds, paying a coupon cB per unit of time, and randomly renewed with frequency m. The market value of these bonds B(A), as a function of the bank's asset value, satisfies the differential equation

(A11) rB(A) = cB + m(B - B(A)) + [mu]AB'(A) + 1/2 [[sigma].sup.2][A.sup.2]B"(A),

with the boundary conditions:

B([A.sub.L]) = 0 and B (+ [infinity]) = cB/r.

The solution of this equation is:

(A12) B(A) = B c + m/r + m [1 - [(A/[A.sub.L].sup.-a(m)]],

where a(m) is the positive root of the quadratic equation:

(A13) 1/2 [[sigma].sup.2] x (x + 1) - [mu]x = r + m.

In a comparison with equation A3, we see immediately that a(0) = a. Moreover, equation A13 shows that a(m) increases with m.

The value of equity becomes:

(A14) E(A,B) = A [gamma] - D - c + m/ r + m B + (D + [gamma] - [A.sub.L]) [(A/[A.sub.L]).sup.-a]

+ c + m/r + m B[(A/[A.sub.L]).sup.-a(m).

AUDITING COSTS

By definition, the expected present value of auditing costs is defined by

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]

where [[tau].sub.R] is the first time that [A.sub.t] hits the closure threshold [A.sub.R]. By the usual arguments (see Dixit [1993]), one can establish that C satisfies the following differential equation:

rC = [mu]AC'(A) + 1/2 [[sigma].sup.2] [A.sup.2] C"(A) A [greater than or equal to] [A.sub.t],

with the limit condition

c(+ [infinity]) = 0.

Therefore, C(A) = k[A.sup.-a], where a is (as before) the positive solution of the equation:

r = [mu]x + 1/2 [[sigma].sup.2]x(x + 1),

and k is a constant that depends on [A.sub.R] and [A.sub.I]:

k = [phi]([A.sub.R], [A.sub.I]).

ENDNOTES

(1.) This imbalance is also reflected in the comments on Basel II; see Saidenberg and Schuermann (2003) for an assessment.

(2.) See, for example, Santos (1996) and Jones (2000). The alleged role of risk-based capital ratios in the "credit crunch" of the early 1990s is discussed in Bernanke and Lown (1991), Berger and Udell (1994), Peek and Kosengren (1995), and Thakor (1996).

(3.) For example, the Basel Committee (BIS 2003) insists on the need to "enable early supervisory intervention if capital does not provide a sufficient buffer against risk."

(4.) In particular, despite the existence of very precise proposals by U.S. economists (Calomiris [1998]; Evanoff and Wall [2000]; see also the discussion in Bliss [2001]) for mandatory subordinated debt, these proposals are not discussed in the Basel II project.

(5.) Reviews of this literature can be found in Thakor (1996), Jackson et al. (1999), and Santos (2000).

(6.) Discussions of this issue can be found in Berger and Udell (1994), Thakor (1996), Jackson et al. (1999), and Santos (2000).

(7.) However, Peek and Rosengren (1995) provide empirical evidence of the impact of increased supervision on bank lending decisions.

(8.) Merton (1977, 1978) assumes that bank assets are traded on financial markets (in order to use the arbitrage pricing methodology), which implies that the social value of banks is independent of their liability structure.

(9.) The model is a variant of the one used by Decamps, Rochel, and Roger (2004), who also analyze the interactions between the three pillars of Basel II.

(10.) The main problem is that, in a static model, solvency regulations have an impact only when they are binding. However, the great majority of banks today have much more capital than the regulatory minimum (this was not the case in 1988). Hence, it is difficult to explain the impact of a capital ratio in today's world by using a static model. For other critiques, see Blum (1999).

(11.) Small depositors are risk averse but they are fully insured and do not play all active role in our model. In any case, risk neutrality is not crucial for our results, but it simplifies the analysis. We could assume alternatively that all investors use the same risk-adjusted measure for evaluating risky cash flows.

(12.) Because of risk neutrality, the expected net present value of these cash flows (conditional on the information available at date t) has to coincide with [A.sub.t], which is equivalent to the condition [beta] = r - [mu].

(13.) In Merton (1978), there are audit costs but no liquidation costs due to the resale of banks' assets, as we have here. As a result, social surplus is unaffected by liquidation decisions.

(14.) A similar assumption is made in the corporate finance literature (Leland 1994; Leland and Toft 1996; Fries, Mella-Barral, and Perraudin 1997), but (1 - [lambda]) is interpreted as a "physical" liquidation cost. Here, it is a cost due to the opacity of bank assets.

(15.) A proportional cost of monitoring, if any, can be subtracted with the drift in equation 1.

(16.) Of course, our desire to get closed form solutions limits our model to one state variable only. This means that we cannot address important questions such as the way banks allocate their assets among different classes of risks and the hoarding of liquid assets as another buffer against risk. The first topic is addressed by the vast literature on risk-weighted ratios (Koehn and Santomero 1980; Kim and Santomero 1988; Furlong and Keeley 1990; Rochet 1992; Thakor 1996). The second topic is addressed in Milne and Whalley (2001).

(17.) Notice that the first-best social value of the bank is a convex function of asset value. However, when agency problems are taken into account, and make the liquidation threshold become greater than [A.sub.0], the value function becomes concave, and thus exhibits risk aversion.

(18.) Morgan (2002) provides indirect empirical evidence on this opacity by comparing the frequency of disagreements among bond rating agencies over the values of firms across sectors of activity. He shows that these disagreements are much more frequent, all else being equal, for banks and insurance companies than for other sectors of the economy.

(19.) We assume that bank managers act in the best interest of shareholders. It would be interesting, but presumably difficult, also to introduce an agency problem between managers and shareholders.

(20.) Bliss (2001) argues that this agency problem may be fundamental: "Poor (apparently irrational) investments are as problematic as excessively risky projects (with positive risk-adjusted returns). Evidence suggests that poor investments are likely to be the major explanation for banks getting into trouble."

(21.) We assume that this deterioration--that is, [DELTA][mu] in equation 5--is so large that shirking is never optimal from a social viewpoint.

(22.) In the appendix to his paper, Bliss (2001) convincingly argues that the asset-substitution problem might have been overemphasized. He reviews several empirical articles that conclude that bank failures are often provoked by "bad investments" rather than "bad luck" (and excessive risk taking).

(23.) Following Leland (1994), we assume that shareholders are not cash constrained. In Decamps, Rochet, and Roger (2004), we examine the alternative case in which bankruptcy is precipitated by the bank's liquidity problems. Note that when there is shirking, the value of [A.sub.E] is no longer given by equation 7.

(24.) See Santos (2000) for a review.

(25.) This is similar to protected debt covenants, whereby bondholders (or banks) retain the option of restructuring a firm before it is technically bankrupt. See Black and Cox (1976) for a formal analysis.

(26.) The seminal paper on this topic is Merton (1978). More recent references are Fries, Mella-Barral, and Perraudin (1997) and Bhattacharya et al. (2002).

(27.) The consequences of FDICIA are assessed in Jones and King (1995) and Mishkin (1996).

(28.) The mandatory subdebt proposal has been discussed extensively: see, for example, Calomiris (1998), Estrella (2000), and Evanoff and Wall (2000, 2001). The only formal analysis I am aware of is Levonian (2001). However, Levonian uses a Black-Scholes type of model in which the bank's returns on assets are exogenous. For empirical assessments of the feasibility of the subdebt proposal, see Hancock and Kwast (2001) and Sironi (2001).

(29.) This approach is borrowed from Leland and Toft (1996) and Ericsson (2000).

(30.) The average maturity of bonds is thus [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.].

(31.) The disciplining role of periodical repricing of debt has been shown by Levonian (2001). It is close in spirit to the disciplining role of demandable deposits (Calomiris and Kahn 1991; Carletti 1999).

(32.) Recall that in our model, bonds theoretically have an infinite maturity but are randomly repaid with frequency m. The average (effective) maturity is 1/m.

(33.) Arbitrage considerations then imply that the coupon rate c must equal r.

(34.) On this topic, see, for example, Bliss (2001), Evanoff and Wall (2002), Gropp, Vesala, and Vulpes (2002), and the references therein.

REFERENCES

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--. 1999. "A New Capital Adequacy Framework." Basel Committee on Banking Supervision. June. Basel, Switzerland.

--. 2001. "The New Basel Capital Accord." Basel Committee on Banking Supervision, Second Consultative Paper. January. Basel, Switzerland.

--. 2003. "The New Basel Capital Accord." Basel Committee on Banking Supervision, Third Consultative Paper. April. Basel, Switzerland. Available at <http://www.bis.org/bcbs/bcbsp3.htm>.

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COMMENTARY

I would like to start by focusing on the method and model used in the paper by Jean-Charles Rochet. In particular, I will consider some of the paper's assumptions. This discussion will bring me to some specific remarks on Basel II, after which I will circle back and comment on Rochet's policy conclusions.

I found the Rochet paper to be interesting, and I liked it very much. Speaking as a bank supervisor, I believe there is a clear need for more research in this vein, which as I see it is an effort to make the theoretical models of banking and bank supervision more realistic in various ways, thus in part to make their conclusions more influential. Most of the value I can add with regard to the model therefore is to focus on the assumptions that still seem somewhat at odds with what the world looks like from a bank supervisor's perspective.

Foremost is probably the fact that the true economic value of a bank's assets is not known with certainty. I believe the uncertainty associated with this economic value is qualitatively different than assuming that the assets' liquidation value would be less than their economic value. This is part of the uncertainty, but not all of it. Obviously, there are some who believe that this problem should be addressed in practice by requiring mark-to-market accounting for banks. For those who follow accounting developments, moves in this direction by the International Accounting Standards Board--in particular, International Accounting Standard 39--have been receiving a great deal of attention. My only comment on this topic is to suggest that developing a fair-value accounting approach for the entirety of a bank's balance sheet in the absence of liquid market prices for many of its assets is a challenge of the same--or possibly even greater--order of magnitude as the problem of the first pillar of the Basel II framework.

A second and closely related issue is the fact that the volatility parameter, [sigma], that governs the underlying stochastic process for the bank's asset value is itself unlikely to be known with certainty. Importantly, this uncertainty is not limited to outsiders. In considering models that are meant to apply to the largest global banks--which clearly has been a primary focus of Basel II--an important issue that must be grappled with is the sheer size and scope of the banks' activities. For example, Citigroup has about 250,000 employees throughout the world. A critical risk management challenge for such a firm is simply to make sure that the head office receives accurate information on the activities of all its operations and that it has a plausible mechanism lot seeking to actually influence the risk level of these disparate units.

In other words, I would argue that it takes considerable effort and discipline just to ensure that the level of a bank's risk is transparent and controllable by insiders, much less outsiders. These points also lead me to conclude that the agency problems within large financial firms are absolutely critical to a complete understanding of how they should be managed and supervised. Moreover, if one looks at the list of financial scandals in recent years it is clear that internal agency problems leading to excessive risk taking by the overall firm in a manner that was not transparent to its own top management has played a key role in a number of these scandals.

Thus, I would propose an alternative interpretation of "shirking" to the one presented by Rochet: a bank is shirking when it fails to invest sufficiently in risk management and control systems and thus is unable to identify or control its overall level of risk properly. This leads it to make "bad" investments in the sense that such investments would not have presented an attractive risk-return trade-off had the bank accurately assessed the risk involved. It is not clear to me whether this change in interpretation would lead to a change in the model's results, but it would be interesting to see.

I now turn to a discussion of Basel II, of which I have been a major participant and am therefore likely to be guilty of bias. Perhaps I have a unique view of Basel II and of capital requirements in general. To me, the essence of the project is the development of a largely comparable and comprehensive measure of risk, particularly credit risk. I believe that the approach to credit risk management is changing fundamentally, as demonstrated by the rapid growth of credit risk transfer markets involving participants other than banks. I do not think that we are likely to see a return to the days when global banks measured their credit risk by rules of thumb.

I believe that the need for a measure of credit risk that achieves greater comparability and greater comprehensiveness than the Basel I measure is of importance to supervisors and to the marketplace generally. Regardless of the outcome of the Basel II effort, I am convinced that something along these lines is both necessary and inevitable. In my view, common tools and a common vocabulary for expressing risk will be significant aids to the development of more liquid markets for the trading of credit risk. In this sense, it is reasonable to think of the supervisory development of the first pillar of Basel II as an effort to solve a marketwide collective action problem related to the development of a common measure of risk.

In addition, the prospect of Basel II is spurring significant investment in risk management by global banks. Many banks have obviously developed sophisticated risk management tools and approaches, but the level of rigor that has surrounded these calculations and the degree to which data have been retained to check and improve the accuracy of these systems are not where they need to be, given the scale and importance of these institutions.

There are two fundamental trade-offs at the heart of Basel II. The first trade-off is between flexibility and comparability. The second is between risk sensitivity and complexity. There is no easy answer to either of these trade-offs; veering too far in either direction has its costs, and there is no doubt that the resulting proposal lacks the formal elegance of the best economic models. But we are not designing an economic model. Rather, we are working to improve steadily the risk management capabilities of those financial firms in which significant weakness would no doubt be quite costly, and we are seeking to establish a considerably better overall measure of the risks taken by such firms. In undertaking such a project, I think there is no better alternative than a highly transparent and consultative process. The balances achieved on the aforementioned trade-offs reflect the outcome of this somewhat messy, time-consuming process.

The result will be far from perfect, but I believe quite strongly that it will be better than what we have today. In particular, one way in which it will be better is by providing a shared signal to supervisors, the market, and bank management that credit quality is deteriorating. The current framework essentially embodies no such signal and puts the onus on the reserving/charge-off decision instead. A risk measure that responds dynamically to changes in credit quality has the potential to alert bank management, supervisors, and others to emerging problems much more quickly than before. Like Rochet, I believe that a key focus of supervisory policy should be on designing frameworks that discourage forbearance and create incentives for addressing problems promptly.

As to the topic of Pillar 3 and market discipline, I must take issue with Rochet's assessment based purely on "page count." Indeed, I believe that at the heart of Basel II is the development of a risk measure. Step one of Pillar 3 is therefore disclosure of this risk measure, on which basis it would not be unreasonable to assign to Pillar 3 all of the pages devoted to Pillar I. But this is a quibble. The key fact is that Pillar 3 of the Basel II proposal does not stop there. It requests disclosure of a number of other items that focus on credit concentrations, the components of bank capital, and other more detailed breakdowns of risk by portfolio. This is intended to provide greater and better information--more frequently--to market participants. Importantly, the current version of Pillar 3 reflects significant consultations and interactions with market analysts over what information they would like to have that banks are reluctant to provide willingly.

In this regard, it is worth emphasizing the point that determining what sort of information is most useful to disclose is not a trivial problem, particularly if the concern is to gauge in a forward-looking manner the risk to which a complex firm is exposed. Many of the analysts that I have spoken with have expressed some frustration with finding suitable ways to assess this risk on the basis of current financial statements. Personally, I wonder if this frustration has in some way been responsible for what appears to have been an overemphasis on the stability of reported earnings by some market analysts.

In any case, I believe that trying to make publicly available better measures of firm risk is a critical part of trying to make market discipline more effective. I also believe that this is a potentially fruitful avenue for empirical research on, for example, the types of risk disclosures that would be the most useful indicators of true underlying risk.

I now turn to two of the policy conclusions of the Rochet paper. First is the conclusion that market information can be a useful tool in allocating scarce supervisory resources. This is not seriously disputed by anyone I am aware of. In the United States, bank supervisors are extensive users of information such as stock prices, debt spreads, KMV, and market costs of credit protection. This information helps inform the allocation of our supervisory resources. Although I should add that here at the New York Fed, we have long sought to have extensive direct market contacts in an effort to ensure that we are not behind those markets in terms of their views of key participants.

More broadly--and with several recent cases in mind--I believe that there has been a marked increase in the intensity of supervision that has occurred simultaneously for those firms that have seen their market spreads widen significantly. But from the perspective of academic research, I know that the question is, Why has there not been a greater effort or willingness to develop approaches that "hard-wire" supervisory reactions to market signals, in particular, the subordinated debt proposals that have been made?

In the United States, there has been extensive discussion and research on this subject, such as the Treasury/Fed study mandated by the Gramm-Leach-Bliley Act. In many other countries, I honestly think there has been somewhat less enthusiasm. I believe this reflects concerns about giving up control as well as concerns about whether the underlying market signals are fully reliable--that is, that market prices may reflect excess volatility. But the concept has not been ignored, and I believe the supervisory community wants to see more research. In this regard, I commend to you a recent working paper by the Basel Committee's research task torte that discusses the existing markets for subordinated debt in the G-10 countries. The paper is available on the Bank for International Settlements' website.

Specifically with regard to subordinated debt, my own concerns have always centered on the idea that the proposal is premised on the creation of a liquid market in a product that does not seem to be desired today in the quantity and frequency that some of the models imply are necessary. In addition, there is the observation that the subdebt holders have become the "de facto regulators" of the bank in various ways. But if that is truly the case, then again, as some recent scandals suggest, we need to worry significantly about the potential conflicts of interest between the de facto regulators and the regulated. We need to ensure that banks are not simply buying and holding each other's subdebt in quid pro quo arrangements. We need to be able to police potential conflicts of interest between asset managers and the banks that provide custodial services for those asset managers. I do not believe that this would end tip being so simple in practice.

However, the future may be brighter for credit derivatives. A downside is that these derivatives are typically written on senior debt. But the upside is that a relatively liquid market with standardized terms is emerging in which contracts on the largest global banks are among the most active products, in particular, to help these firms manage their counterparty risks with each other. Moreover, in the past six months, we have seen credit derivative index products grow significantly, potentially enabling the marketwide signal to be disentangled from the firm-specific signal. Again, I would suggest this as a fruitful area for empirical research that explores the possibilities of linking supervisory intensity or even specific supervisory actions to these market signals.

The second major policy conclusion I will discuss is the need for a greater focus on the harmonization of supervisory practices around the world. Again, this idea has a lot of appeal. In the United States, I think it is fair to say that the supervisory community generally believes that it does a reasonably good job on Pillars 2 and 3. In regard to Pillar 2, the view of U.S. supervisors is that the primary responsibility is lot bank managers to determine what their desired level of capital is and how they want to allocate that capital, but that supervisory interaction--which benefits from having a window into the practices era number of the major banks--with banks on those decisions is advantageous.

Frankly, a major part of the original U.S. impetus for Basel II was to help export our preferred supervisory concepts and approaches more broadly around the world. For example, we believe that a mix of supervision and regulation works better than a purely regulatory approach with little on-site presence. I believe that, in large part driven by the realities of their responsibilities under a Basel II regime, many other supervisors have been moving toward us in approach, in particular, in the view that quality supervision requires substantial investment in skilled staff with the ability to understand modern risk management methods.

Changing embedded institutional arrangements and eliminating political pressures will not happen overnight. Realistically, efforts to harmonize supervisory approaches should not be seen as a substitute lot Basel II. From a practical perspective, a successful resolution to the Basel II negotiations will enhance the Basel Committee's pursuit of further efforts to increase supervisory cooperation and converge supervisory methods.

In conclusion, I agree very much with Rochet's view that focusing more attention on supervisory practices and on market discipline would be extremely worthwhile. Further efforts to harmonize and improve supervisory practices globally are desirable. However, I do not share the author's opinion that the Pillar t project is sufficiently unimportant that it could or should simply be abandoned. As I have said, the development of better risk measures is both necessary and inevitable. It is indeed largely inconceivable to me that the global capital markets could continue to develop over the next ten or twenty years in a way that avoids the need for such comprehensive and comparable measures of risk.

COMMENTARY

In his very interesting paper, Jean-Charles Rochet argues that instead of spending so much time on refining Pillar 1 (risk-based capital), the Basel Committee should seriously think about Pillars 2 (supervisory action) and 3 (market discipline). I certainly agree with the broad theme of Rochet's paper, which I would interpret as saying that one can get too lost in the details of implementing risk-based capital standards and that it is useful to step back and ask, what fundamental economic problem are we trying to solve, and how can we best deploy all the tools at our disposal together? These tools include not only capital requirements, but also market-based information as well as supervision and early intervention.

Rather than going through the details of Rochet's model, I will try to illustrate some of his ideas using an alternative-and much homelier--model. My model is also designed to highlight one critical variable not emphasized in Rochet's analysis, namely, the cost to banks of holding equity capital. I want to demonstrate that the cost of bank equity has an important impact on how one thinks about the optimality of using other policy tools, such as risk-based (as opposed to flat) capital requirements. I also want to suggest that, in addition to focusing on the three pillars, policymakers might want to devote more attention to thinking about ways to reduce the cost of equity for banks.

The model proceeds as follows. Imagine that bank i can invest in a loan of type i at time 0. With a probability 1/2, the loan yields a gross return of (1 + [v.sub.i]) + 2 [R.sub.i] at time 2, and with a probability 1/2, the loan yields (1 - [v.sub.i]) at time 2. Thus, the loan has an expected return of [R.sub.i], and a "volatility" of [v.sub.i]. Let [R.sub.i] = b[v.sub.i], so that riskier loans have higher expected returns to the bank that makes them.

As an alternative to bank lending, the loan can also be made in the bond market, where the market discount rate is zero. However, in this case, the time-2 payoff on the loan is only (1 + [v.sub.i]) in good state, instead of (1 + [v.sub.i]) - 2 [R.sub.i]. In other words, bond market borrowing is always zero net present value, while the bank can create an expected surplus of [R.sub.i] by virtue of its monitoring efforts. Note that since [R.sub.i] = b[v.sub.i], the relative appeal of bank lending compared with bond market lending is greater for riskier borrowers--one can think of these borrowers as firms for whom monitoring is most valuable.

To create a role for capital regulation, I assume that there are externalities associated with banks getting into trouble. A simple way to do so is to assume that bank managers do not attach any private costs to bank defaults, but that each bank default has a social cost of X. Finally, I assume that banks have two ways of raising funds. They can borrow, in which case they have to offer their investors an expected return of zero. Alternatively, they can finance themselves with equity, but equity has a cost of k. For the time being, this added cost represents an unspecified deviation from the Modigliani-Miller capital structure irrelevance benchmark; I will discuss its possible origins shortly. And as will become clear momentarily, it is precisely this cost of bank equity that makes the regulatory problem a nontrivial one.

Let us first ask what happens in a world with no regulation of any sort. Absent regulation, every bank holds zero equity capital--that is, debt finance is strictly preferred because it is viewed as cheaper--and makes all loans. The good news in this scenario is that all gains from intermediation are realized. The bad news is that society bears an expected default cost of X/2 per loan.

Now consider some possible regulatory approaches. First, one might try a regime of "flat," or non-risk-based, capital requirements. This corresponds to forcing banks to hold some fixed amount of equity v against all loans, irrespective of their risk. The benefit of this approach is that it eliminates the possibility of default for the less risky loans, those for which [v.sub.i] < v. The downside, however, is that the bank's cost of capital for all loans is now vk. This results in disintermediation--loans leaving the banking sector for the bond market--and hence a loss of the monitoring-related surplus if [R.sub.i] = b[v.sub.i] < vk. In other words, flat capital requirements distort cross-sectional pricing and discourage banks from making safe loans where they might otherwise create value.

These types of problems make clear the appeal of risk-based capital requirements. In this context, risk-based requirements amount to forcing a bank to hold [v.sub.i] against loan type i. The obvious advantage is that this eliminates all defaults, and can do so with less distortion of pricing and hence less disintermediation because the capital charge for low-risk loans can be reduced. At the same time, going from flat to risk-based capital requirements is not without its costs. As Rochet emphasizes, these costs arise from the real-world complexities associated with implementing a risk-based system, along with its potential vulnerabilities to lobbying and political pressure.

Taking these political-economy considerations into account, which regime--flat or risk-based--is better? Observe that the answer will depend crucially on the cost of bank equity k. For high values of k, the distortions in loan pricing associated with a flat-capital regime are severe, so it is better to go with risk-based capital despite the political-economy costs. In contrast, for low values of k, it makes sense to stick with the simpler and less politically vulnerable flat-capital requirement. (1)

Said a bit differently, the complex risk-based capital approach envisioned in the Basel II proposals can make sense only if one believes that k is relatively high--that is, that there is a significant violation of the Modigliani-Miller conditions that makes bank equity costly. This observation leads to two questions. First, what are the primitive frictions that make bank equity so expensive? And second, are there any steps that policymakers can take to help reduce the cost of bank equity, thereby mitigating the distortions associated with capital regulation?

With respect to the first question, it is easy enough to enumerate the usual suspects that are thought to make equity finance more expensive than debt finance: 1) tax disadvantages; 2) free-cash-flow-type agency problems, whereby investors discount the value of a bank when management has too much slack and might be tempted to make bad investments; 3) asymmetric information, which can make raising new equity difficult; and 4) market inefficiencies, which can lead to (real or perceived) transient undervaluations, and again discourage new equity issues.

Of course, it is harder to get a good handle on the relative importance of each of these frictions for banks. But this may he a very useful area for further study because if we had a better understanding of exactly why bank equity is thought to be so costly, we might be able to take steps to bring the cost down. And again, with a lower cost of bank equity, capital regulation can be made more efficient, and potentially simpler.

Let me offer a couple of examples. First, and most directly, if it is the case that taxes play an important role in pushing up the cost of bank equity, it follows that one might want to increase scope for tax-favored instruments to count toward capital requirements. I will not try to get into the specifics of how this could be implemented, but it is worth noting that the tax angle provides an alternative motivation--distinct from market discipline--for the types of subordinated debt proposals that Rochet discusses.

My second example is motivated by the free-cash-flow agency problem. If the primitive friction is that investors do not like a bank having a lot of capital just sitting around on the balance sheet, why not employ some sort of conditional capital arrangement that only channels the equity to the bank in those states where it is needed to avert default? Specifically, suppose a bank has 100 in loans today; these loans will be worth either 90 or 110 next period, with a probability 1/2 of either outcome. One way for the bank to avoid default would be to finance itself with 90 of debt and 10 of equity. But this approach leaves the bank with 20 of free cash in the good state. If investors worry that this excess slack in good times will lead to waste, they will discount the bank's stock.

An alternative--in the spirit of a recent proposal by Mark Flannery--would be for the bank to raise 90 in debt, 5 in equity, and 5 with a "reverse convertible debenture." The reverse convertible would be structured as follows. It would have a face value of 10, and in the good state, it would remain as a 10 debt claim, so the bank's total debt obligation would be 100. In the bad state, it would convert into a prespecified number of shares, so the bank's total debt obligation would remain at 90. (Note that in this extremely simple example, any shares would turn out to be worthless in the bad state.)

From a regulator's perspective, the bank should be viewed as just as well capitalized as before, since it is still guaranteed not to default in either state. Thus, the reverse convertible should "count" as regulatory capital. At the same time, the free-cash-flow problem is attenuated, because after paying off its debt, the bank now has less slack in the good state (10, rather than 20). (2) This is just a specific example of a general corporate risk management principle: capital structure and derivatives should be used to match net inflows with investment opportunities on a state-by-state basis, so that to the extent possible, firms never have too little or too much cash on hand at any point in time (see Froot, Scharfstein, and Stein [1993]).

Of course, this reverse convertible idea raises a host off practical questions concerning, for example, the specifics of security design, which are beyond the scope of this brief comment. (3) However, my goal is not to make the case for a particular new financial instrument, but simply to suggest that further creative thinking along these lines is likely to be valuable.

ENDNOTES

(1.) As Rochet points out, for any given value of k, one can improve the terms of the trade-off by relying on market-based signals and prompt corrective action. In the context of the model, suppose that at some interim time 1, one can observe a market signal that suggests that the bad state is coming. Moreover, if the bank is liquidated promptly, instead of waiting until time 2, one can recover (1 - h[v.sub.i]), where h < 1. This has the benefit that capital charges can be lowered in either the flat or risk-based regime.

(2.) If accounting concerns, such as a desire to have a high return on equity, also drive bank managers' reluctance to carry too much equity on the balance sheet, the reverse convertible may also be helpful on that dimension, to the extent that return on equity is now calculated based on balance-sheet equity of 5, rather than 10.

(3.) See Flannery (2002) for a detailed discussion of many of these issues.

REFERENCES

Flannery, M. J. 2002. "No Pain, No Gain? Effecting Market Discipline via Reverse Convertible Debentures." Unpublished paper, University of Florida.

Froot, K. A., D. S. Scharfstein, and J. C. Stein. 1993. "Risk Management: Coordinating Corporate Investment and Financing Policies." JOURNAL OF FINANCE 48, no. 5 (December): 1629-58.

The author thanks Jean-Paul Decamps and Benoit Roger for allowing him to use material from their joint paper. He also thanks Mark Flannery, Diana Hancock, and his two discussants, Darryll Hendricks and Jeremy Stein, for comments. All errors are the author's. The views expressed are those of the author and do not necessarily reflect the position of the Federal Reserve Bank of New York or the Federal Reserve System.

The views, expressed are those of the author and do not necessarily reflect the position of the Federal Reserve Bank of New York or the Federal Reserve System.

Jean-Charles Rochet is a professor of mathematics and economics at Toulouse University and research director of the Institut d'Economic Industrielle. <rochet@cict.fr>

Darryll Hendricks is a senior vice president at the Federal Reserve Bank of New York.

Jeremy C. Stein is a professor of economics at Harvard University and a research associate at the National Bureau of Economic Research.

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Author: | Rochet, Jean-Charles; Hendricks, Daryll; Stein, Jeremy C. |
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Publication: | Federal Reserve Bank of New York Economic Policy Review |

Geographic Code: | 1USA |

Date: | Sep 1, 2004 |

Words: | 13684 |

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