The Forced Safety Effect: How Higher Capital Requirements Can Increase Bank Lending

• Author: FREDERIC MALHERBE,SALEEM BAHAJ
• DOI: http://doi.org/10.1111/jofi.12958
• Date: 01 December 2020
• Published date: 01 December 2020

THE JOURNAL OF FINANCE •VOL. LXXV, NO. 6 •DECEMBER 2020

The Forced Safety Effect: How Higher Capital

Requirements Can Increase Bank Lending

SALEEM BAHAJ and FREDERIC MALHERBE∗

ABSTRACT

Government guarantees generate an implicit subsidy for banks. A capital require-

ment reduces this subsidy, through a simple liability composition effect. However,

the guarantees also make a bank undervalue loans that generates surplus in states

of the world in which it defaults. Raising the capital requirement makes the bank

safer, which alleviates this problem. We refer to this mechanism, which we argue is

empirically relevant, as the forced safety effect.

SINCE THE GLOBAL FINANCIAL CRISIS, bank capital requirements have been

substantially tightened.1The merits of these reforms have been fiercely de-

bated. Critics argue that higher capital requirements raise banks’ cost of

funds, thereby reducing credit provision and dampening economic activity.2

Others, however, argue that increases in banks’ private cost of funds are not

necessarily relevant from a normative perspective (see, for example, Hanson,

Kashyap, and Stein (2011) and Admati et al. (2013)). Nonetheless, the idea

∗Saleem Bahaj is at the Bank of England (BoE). Frederic Malherbe is at the University College

London. We are indebted to the Editor Philip Bond, the Associate Editors, and two anonymous

referees. A previous version was circulated under the title: “APositive Analysis of Bank Behaviour

under Capital Requirements.” This paper drew extensively on the BoE Staff Working Paper (Ba-

haj et al. (2016)) that we wrote with Jonathan Bridges and Cian O’Neill. We thank them for their

contribution and for allowing us to build off this previous work. We are particularly grateful to

Jason Donaldson, and to Kartik Anand, Heski Bar-Isaak, Max Bruche, Matthieu Chavaz, Filippo

de Marco, Stijn Ferarri, Peter Feldhutter, Pablo Alberto Aguilar Garcia, Tirupam Goel, Sebastian

Hohmann, David Martinez-Miera, Caterina Mendicino, Tom Norman, Marcus Opp, Daniel Par-

avisini, Jose-Luis Peydro, Helene Rey, Oleg Rubanov, Carmelo Salleo, Javier Suarez, and Emily

Williams for their discussions and comments. We also thank numerous seminar and conference

participants for their feedback. The views expressed here are those of the authors and do not nec-

essarily reflect those of the BoE or its policy committees. We have read The Journal of Finance

disclosure policy and have no conflicts of interest to disclose.

Correspondence: Saleem Bahaj, Bank of England (BoE). e-mail: saleembahaj@gmail.com

1Specifically, minimum tier-one capital requirements were raised from 4% to 6% of risk-

weighted assets, but additional “buffers” were created to account, inter alia, for the systemic

importance of the institution, for the economic cycle, and to prevent accidental breaches of the

minimum. Effective requirements for large global banks are now in the double digits as a percent-

age of risk-weighted assets.

2See, for instance, p. 10 of Institute of International Finance (2011).

DOI: 10.1111/jofi.12958

© 2020 Bank of England. The Journal of Finance published by Wiley Periodicals LLC on behalf of

the American Finance Association

3013

3014 The Journal of Finance®

that such increases result in a reduction in lending has seeped into conven-

tional wisdom.

In this paper, we challenge such conventional wisdom. We develop a model

in which capital is costly from a bank’s perspective due to an implicit subsidy

from a government guarantee. At a given level of lending, a higher capital re-

quirement reduces the value of the subsidy and hence it increases the bank’s

weighted average cost of funds. But it also makes the bank safer, which can

actually make the marginal loan more appealing and therefore induce an in-

crease in lending.

How can the marginal loan become more appealing under a higher capital

requirement? To build intuition, it is useful to consider why the marginal loan

may not have been financed in the first place. Despite implying a subsidy, a gov-

ernment guarantee can generate a mechanism analogous to the debt overhang

problem in Myers (1977): the bank undervalues a loan (and potentially passes

on it) if a portion of its surplus, in effect, accrues to the taxpayer, who is backing

the guarantee. We refer to this problem as the guarantee overhang problem.

Making the bank safer means that loan surplus accrues to the bank’s share-

holders in more states of the world. If, for the marginal loan, this surplus is pos-

itive in these specific states, forcing the bank to be safer makes the marginal

loan more appealing as doing so alleviates the guarantee overhang.

Our model has a single period in which a representative bank faces a capital

requirement and finances loans with a mix of liabilities that can be interpreted

as deposits and capital. The bank starts with existing loans and can make

new ones.

The bank maximizes the expected payoff of initial shareholders. Deposits

are insured by the government with no fee, and hence are implicitly subsi-

dized. This has two implications. First, the capital requirement is binding in

equilibrium: the bank chooses lending and adjusts capital to meet the require-

ment. Second, the objective function can be written as the sum of the economic

surplus from lending and a term that captures the value of the implicit subsidy

(as in Merton (1977)).

We first assume that the payoffs to new loans are perfectly correlated and

that new lending yields an increasing and strictly concave aggregate payoff.

This design allows us to study how the equilibrium level of lending responds to

marginal changes in the capital requirement using a first-order approach (we

refer to the response to an increase in the capital requirement as the lending

response). The derivative of the subsidy with respect to lending, the marginal

subsidy, is a wedge in the bank’s first-order condition. This wedge captures

the underlying moral hazard problem arising from the guarantee. Economic

surplus is independent of the capital requirement. Hence, if an increase in the

requirement increases the marginal subsidy, the bank increases lending.

Increasing the capital requirement has two effects on the marginal subsidy.

First, a smaller fraction of the marginal loan is financed by deposits. This gen-

erates a well-understood composition effect: the bank substitutes subsidized

deposits with capital, decreasing the marginal subsidy. This effect also exactly

The Forced Safety Effect 3015

captures how the capital requirement increases the bank’s weighted average

cost of funds.3

However, the change in the capital requirement also affects whether the

bank defaults in any given state. To go further, we note that the appropri-

ate measure of surplus from the marginal loan is its residual cash flow. This

variable, which we denote by Z, is the marginal loan’s realized payoff minus

the repayment on the deposits raised to finance it. In the states in which the

bank survives, Zcomes as an addition to the shareholder’s payoff. But if the

bank defaults, Zaccrues to the taxpayer.

We can now elaborate on the second effect, which we argue is overlooked by

conventional wisdom. Consider the default boundary, that is, the set of states

in which the bank can just repay depositors. Increasing the requirement in-

creases the buffer against losses and shifts this boundary. As a result, there

are more states in which Zaccrues to shareholders. In particular, increasing

the capital requirement makes shareholders internalize the expected value of

Zalong the default boundary.

This second effect reflects the fact that the requirement forces the bank to-

ward safety. Because the bank could have chosen to be safer and to internalize

these cash flows (by operating at a higher capital ratio than the requirement)

but preferred not to, we refer to the second effect the forced safety effect (FSE).

If, in expectation, the residual cash flows along the default boundary are

positive, the bank is internalizing cash flows that increase shareholders’ pay-

off. In this case, the FSE is positive and increases the value of the marginal

subsidy. If, in contrast, the residual cash flows are negative, the FSE makes

the bank internalize more losses, decreasing the value of the marginal subsidy

and reinforcing the composition effect.

Our main theoretical contribution is to show that (i) the FSE can be positive

and (ii) the FSE can dominate the composition effect, which is why lending can

increase with the capital requirement.

In equilibrium, the bank may optimally choose to finance negative net

present value (NPV) loans and/or not to finance positive NPV loans. Showing

that the guarantee overhang can lead to the latter is a third contribution of

this paper. Reasoning in terms of residual cash flows also helps clarify the link

between the guarantee and debt overhang. At the heart of both is that a portion

of the residual cash flows from investment accrue to another stakeholder.4In

Myers (1977), residual cash flows can only be positive.5In our context, residual

cash flows can be positive or negative. This is why government guarantees can

3The change in average funding costs is relevant in determining the impact on the bank’s profit.

See Kisin and Manela (2016) for a quantification.

4Papers that link bank underlending to the debt overhang problem include Hanson, Kashyap,

and Stein (2011), Admati et al. (2018), and Jakucionyte and van Wijnbergen (2018). Bank behav-

ior exhibiting symptoms of an overhang problem has been noted in different contexts in recent

literature. See, for instance, Gropp et al. (2019), who provide evidence from stress tests, or Duffie,

Andersen, and Song (2019), who show that funding-value adjustments correspond to the transfer

to existing debtholders associated with debt overhang.

5Investment is fully financed with equity,and hence the residual cash flow is the cash flow itself.