macroeconomic shocks and banking regulation

8/10/2019 Macroeconomic Shocks and Banking Regulation

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Macroeconomic Shocks and Banking Regulation∗

Mathias Dewatripont† Jean Tirole ‡

September 7, 202

Abstract

The recent crisis has brought to the !ore the c"clical properties o! banking regu#

lation$ %ounterc"clical bu&ers and enhanced capital re'uirements meant to stabili(e

banks) balance sheets across the c"cle are not costless, and a delicate balance needs

to be reached between pro*iding incenti*es to generate *alue and discouraging e+#

cessi*e risk#taking$

The paper de*elops a model in which, in contrast with Modigliani#Miller, out#

side e'uit" and capital re'uirements matter$ t anal"ses banking regulation in

the presence o! macroeconomic shocks and studies the desirabilit" o! sel!#insurance

mechanisms such as counterc"clical capital bu&ers or d"namic pro*isioning, as wellas -macro#hedges. such as %o%os and capital insurance$

Keywords: Banking regulation, macroeconomic shocks, counterc"clical capital

re'uirements$

JEL numbers: /2, 12, 12$

∗This paper is an e+panded *ersion o! a presentation made b" Mathias Dewatripont at the JM%B#3B#4niBern 20 con!erence at the Stud" %enter 1er(ensee$ The authors are grate!ul to 5ans 1ersbach, the

editor and an anon"mous re!eree !or help!ul comments$ The research leading to these results has recei*ed!unding !rom the /uropean Research %ouncil under the /uropean %ommunit")s Se*enth Framework6rogramme F6782007#209 1rant :greement no$ 2;<;2<$

†Ban'ue 3ationale de Belgi'ue$ 4ni*ersit= >ibre de Bru+elles /%:R/S and Sol*a" Brussels School9$mathias$dewatripont?nbb$be @ mdewat?ulb$ac$be

‡Toulouse School o! /conomics$ Aean$tirole?tse#!r$eu$



1 Introduction and motivation

t is commonl" agreed that microprudential banking regulations, Basel and e*en more

so9 Basel , ampli!" the impact o! the economic c"cle on balance sheets and make banks

more *ulnerable to downturns$ To reduce this proc"clicalit" and to strengthen banking

stabilit", Basel re'uires more capital and introduces counterc"clical capital bu&ers$

More generall", banking recapitali(ation has been high on polic"makers) agenda despite

concerns about dele*eraging and a potential credit crunch$ Moreo*er, man" scholars, most

notabl" :dmati et al$ 2009, ha*e called !or much higher capital ratios than re'uired

e*en under Basel , arguing that e'uit" is not reall" costl"$

:dmati et al)s theoretical point goes as !ollows e+isting models o! capital ade'uac"

in banking and corporate Cnance emphasi(e the need !or inside e'uit", i$e$ e'uit" broughtb" those, such as managers and large monitors *enture capitalists, block shareholders9,

who can destro" *alue and there!ore must be gi*en skin in the game$ But the legal and

regulator" concepts o! e'uit" include outside e'uit", i$e$, e'uit" held b" passi*e share#

holders who do not necessaril" impact the corporate strateg"$ :dmati et al)s reasoning

is that, while inside e'uit" is, as is widel" acknowledged, costl"8 scarce, outside e'uit"

is not$ The cushion created b" e'uit" could be rein!orced b" adding, sa", mone" market

!unds as an e+tra line o! de!ense to protect depositors$ 6ut di&erentl", while inside e'uit"

is rele*ant, outside e'uit" and debt obe" the assumptions o! Modigliani#Miller <9

and so the social cost o! outside e'uit" e'uals that o! debt$ mplications o! this line

o! reasoning !or capital ade'uac" re'uirements are then unclear@ indeed, e+isting capi#

tal ade'uac" re'uirements and current attempts at rein!orcing bank capital cannot be

rationali(ed without addressing the *er" rele*ance o! outside e'uit"$

Ehile its theoretical, uncalibrated nature precludes an" Audgment about the desirabil#

it" o! Basel re!orms, this paper argues against the *iew that the social cost o! substan#

tiall" heightened capital re'uirements are negligible$ t e+tends Dewatripont#Tirole <<;

a, b9)s theor" o! outside capital structure to allow !or the presence o! macroeconomic

shocks$ t in*estigates the conse'uences o! such shocks !or e+isting regulation and re!ormproposals$

The theor" is based on the idea that managerial incenti*es depend on how broader

corporate choices are a&ected b" per!ormance$ 6olicies that *alidate managerial choices

!ollowing good per!ormance, and constrain8downsi(e8li'uidate a!ter a bad one ser*e as

a power!ul incenti*e !or managerial compliance$ Ehile !orward#looking proCt ma+imi(a#

tion implies that b"gones are b"gones and poor good9 per!ormance remains unpunished

unrewarded9, shareholder control in good times and a shi!t in control !rom shareholders

2



to debtholders a!ter poor per!ormance b" contrast rewards penali(es9 managers !or their

good poor9 per!ormance$ Thus the paradigm belongs to the !amil" o! models that *iew

debt as a disciplining de*ice Townsend <7<, 1ale#5ellwig <, :ghion#Bolton <<2,5art#Moore <<;9@ like in this literature, debt can operate through downsi(ing or li'uida#

tion a!ter low proCts$ The implications o! debt control are broader including all actions

that are not aligned with managerial pre!erences9$ :nd especiall", the model predicts a

role !or outside e'uit", unlike the rest o! the literature$

The desirabilit" o! toughening corporate policies a!ter poor per!ormance howe*er ap#

plies onl" to that part o! the per!ormance that is under managerial control$ From 5olm#

strm <7<9)s insulation principle, the !ate o! economic agents should a priori not be

conditioned on e*ents, such as macroeconomic shocks, that lie outside their control$ n#

*estigating the conse'uences o! this basic principle leads to the !ollowing conclusions

• The Basel and polic" o! ignoring macroeconomic shocks in the determination o!

capital ade'uac" re'uirements leads to too much inter*ention in recessions and too

much lenienc" in booms the regulation rewards the Gluck" dollarG9$

• Forbearance, a commonl" adopted super*isor" polic" o! de !acto lowering capital

ade'uac" re'uirements during a recession in conHict with Basel rules9, does a bet#

ter Aob at insulating managers !rom macroeconomic shocks@ but it creates si(able

incenti*es !or gambling b" then#undercapitali(ed banks$

• Iptimal regulation re'uires that macroeconomic shocks be automaticall" neutral#

i(ed, so as to keep the incenti*es o! the in*estor in control unchanged$ This neutral#

i(ation can take the !orm o! d"namic pro*isioning or a Basel 9 counterc"clical

capital bu&er pro*ided sel!#insurance is !easible@ i! it is not, macro#hedging such as

capital insurance or %o%os can achie*e this goal$

• 1eneral e'uilibrium properties o! these alternati*e instruments are an important

topic !or research$

The paper is organi(ed as !ollows Section 2 sets up the basic model$ Section

introduces macroeconomic shocks$ Section ; brieH" discusses general e'uilibrium aspects

and section concludes$

Finall", the e+isting literature on macroprudential regulation has a rather di&erent

!ocus$ Iur paper !ocuses on how prudential regulation should deal with macro shocks,

not on other reasons that ha*e been in*oked as Ge+ternalit"#basedG rationales !or macro#

prudential regulation, such as interconnectedness e$g$, :llen#1ale 2000, %aballero#Simsek



200, Rochet#Tirole <<9, Cre sales e$g$, >oren(oni 2009, sur*eillance o! asset bubbles,

or widespread maturit" mismatches e$g$, Farhi#Tirole 2029$

2 A simple setting

n the spirit o! the branch o! the securit" design literature initiated b" :ghion and Bolton

<<29, who argued that securities are characteri(ed not onl" b" income rights but also

b" control rights, we anal"(ed in Dewatripont and Tirole <<;a9 a managerial moral

ha(ard problem in which it is optimal to discipline the manager at least in part through

per!ormance#contingent corporate choices$

Ee argued that, i! the corporate actions meant to discipline the manager are not con#

tractible, and i!, as is generall" the case, optimal corporate choices are time#inconsistent,

in*estors in control o! corporate choices must !ace an incenti*e that di&ers !rom Crm#*alue

ma+imi(ation, in order to be induced to take the e+#ante optimal action$ This -double

moral ha(ard problem. in turn calls !or the presence o! at least a second group o! outside

in*estors who recei*e the remainder o! the re*enue o! the Crm$ This second group o!

in*estors is similar to the Gbudget breakerG introduced b" 5olmstrm <29 to address

moral ha(ard in teams$

Suppose that the action the manager pre!ers call it C !or GcontinuationG9 is riskier

than the action she likes less call it L !or Gli'uidationG9@ the eKcient pro*ision o! man#agerial incenti*es calls !or allocating control to in*estors with a conca*e, i$e$, Gdebt#likeG,

return a!ter bad per!ormance, and a con*e+, i$e$, Ge'uit"#likeG, return a!ter good per!or#

mance$ This suggests that the second#best optimum can be implemented with standard

debt and outside9 e'uit", with contingent control e'uit" control a!ter good per!ormance,

and debt control a!ter bad per!ormance$ The model thus predicts securities which consist

o! realistic bundles o! control and income rights$

This section describes the obAecti*e !unctions, the timing, the second#best optimal

per!ormance#contingent action choice, and Cnall" the latter)s implementation through an

appropriate debt#e'uit" ratio$

2.1 Timing

:s discussed abo*e, the model in*ol*es both managerial and corporate choices$ : banking

manager8entrepreneur has no Cnancial resources to co*er an in*estment cost, and turns

to in*estors !or Cnancing$ The capital structure# that is, the allocation among in*estors o!

contingent cash#How and control rights# is designed at this Cnancing stage$ The manager

;



then e+erts either a high or low e&ort$ This e&ort results in a good or bad short#term

per!ormance$ This short#term proCt is *eriCable, and so conditions the allocation o!

control$ :!ter obser*ing a signal about !uture prospects, the group o! in*estors put incontrol b" the reali(ation o! the short#term proCt then chooses a corporate action or

strateg"@ it can li'uidate or more generall" take a conser*ati*e polic" action L9, continue

action C9, or gamble !or resurrection action G9$ Finall", the *eriCable long#term proCt

is reali(ed$

Figure 1: Timing

More precisel", the timing, depicted in Figure , goes as !ollows

$ Financing $ The manager8entrepreneur raises an amount I !or in*estment !rom out#

side in*estors$ The capital structure concomitantl" designed speciCes the incenti*e

scheme o! the in*estor in control at stage ; below$

2$ Moral hazard $ Manager chooses unobser*able e&ort a ∈ {a, a}$ The high e&ort costs

her Ψ, the low e&ort costs her nothing$ Ee assume the bank has a positi*e 36L

onl" i! a is chosen$

$ hort!term "ro#t realization $ The *eriCable short#term proCt π ∈ {π, π } is reali(ed$

: high e&ort increases the probabilit" o! a high short#term proCt 6r (π |a) = p > 6r

(π |a ) = p$ Ee assume that π < 0 < π $ Ee interpret a negati*e proCt as a short!all



o! income to honor some liabilities to workers or suppliers, liabilities that are senior

to in*estor claims on the Crm@ such liabilities ha*e to be paid at stage ;, either out

o! li'uidation proceeds, or b" in*estors i! the" choose to a*oid li'uidation$

;$ E$ercise of cor"orate control $ :n un*eriCable signal s ∈ [s, s ] with s < 1/29,

independent o! π , is obser*ed$ :!ter obser*ing this signal, in*estors in control as

speciCed at stage 9 select un*eriCable9 action A ∈ {L,C,G}$ :ction L Gli'uida#

tionG9 generates ℓ !or sure$ The other two actions generate a random Glong#term

proCtG later on, at stage $

$ Long!term "ro#t realization% The long#term proCt is *eriCable and independent o!

pre*ious managerial e&ort$ ts probabilit" distribution thus depends onl" on the

choice o! corporate strateg" A

• :ction C GcontinuationG9 generates 1 with probabilit" s, α with probabilit" s

and 0 with probabilit" 1 − 2s$

• :ction G GgamblingG9 generates with probabilit" s+τ and 0 with probabilit"

1 − s − τ$

Ee assume that ℓ + π > 0, so that, i! at stage , π < 0 is reali(ed, the liabilities it

represents can be repaid at stage ; out o! ℓ i! action L is chosen$ In the other hand,an in*estor who wishes to choose another action has to Crst pa" up −π since the other

actions ma" not deli*er an" income$

For e+positional con*enience, all pla"ers are risk#neutral and do not discount the !u#

ture$ The problem is interesting onl" i! it is optimal to induce the high managerial e&ort,

which we will posit$ More importantl", we assume that monetar" incenti*es do not per#

!ectl" align managerial and in*estor incenti*es@ !or simplicit", we capture this through an

assumption o! e+treme risk a*ersion The manager does not respond at all to monetar"

incenti*es@ that is, she demands a gi*en wage, normali(ed to 0, and does not enAo" mone"

be"ond that le*el as shown in Dewatripont#Tirole <<;a, the results e+tend to the case in

which the manager responds to monetar" incenti*es, as long as the moral ha(ard problem

is inconsistent with the reali(ation o! the Crst best9$ B" contrast, the manager cares about

the corporate action choice She recei*es pri*ate beneCt B unless the li'uidation action L

is selected$ Ee assume that B > Ψ/( p − p)$

The manager)s utilit" !unction is there!ore

− Ψ1(a=a) + B1(A=L),



where 1(.) denotes the indicator !unction$

For conciseness, we also assume that action C is not onl" the action pre!erred b" the

manager, but also the e+#post eKcient one$ n particular, it "ields a higher e+pectedlong#term proCt than action L e*en a!ter the worst possible signal$ n turn, we assume

that action L generates in e+pectation more long#term proCt than action G, e*en !or the

most !a*orable signal$ These two assumptions can be concisel" e+pressed b" the !ollowing

condition

s + τ < ℓ < s(1 + α ). 9

The e+#post eKcienc" o! action C combined with the managerial pre!erence !or that

action implies that it is alwa"s optimal to continue a!ter a good short#term per!ormance$

%ontinuation then both increases in*estor return and boosts managerial incenti*es$:nticipating on our treatment, the rationale !or introducing action G is to create

scope !or asset substitution b" shareholders in control o! an undercapitali(ed bank$ :sset

substitution will be a concern under a negati*e macroeconomic shock, and the presence

o! action G will make !orbearance undesirable$

The *eriCabilit" o! proCts gi*es *alue to e'uit" as the Gresidual claimG b" contrast,

onl" GhardG claims ha*e *alue in models with un*eriCable proCts9$ The non#*eriCabilit"

o! the action choice introduces a second moral ha(ard problem to the model besides the

managerial e&ort choice, and there!ore creates a need !or endowing the in*estor in control

with an incenti*e scheme, so as to appropriatel" discipline the manager$ Finall", adding

a continuous un*eriCable signal s which is deCned so as to be higher, the higher the gain

o! choosing action C o*er action L9 will allow us to uni'uel" deCne the capital ratio which

implements the second#best managerial incenti*e scheme$

2.2 Managerial incentives

/+#post proCt ma+imi(ation is inconsistent with the manager choosing a, which is costl"

!or her@ !or, e+#post proCt ma+imi(ation leads to a continuation rule Galwa"s CG9 that

is independent o! past proCt and so to a managerial utilit" that does not respond to the

choice o! e&ort$

Ee alread" noted that regardless o! the *alue o! s, continuation is optimal a!ter the

high proCt π t ma+imi(es the e+#post proCt and it strengthens the incenti*e to choose

the high e&ort a$ B" contrast, inducing some li'uidation a!ter π is necessar" to induce

the high e&ort a$ The least#cost approach to inducing managerial e&ort is to li'uidate

when the short#term proCt is π and the e+pected long#term proCt is low$ 5ence ignoring

Strictl" speaking, and because o! our e+treme assumption on managerial pre!erences, the man#

7



implementation issues the topic o! subsection 2$9, there should be li'uidation a!ter π ,

i& s ≤ s∗ with s∗ deCned b"

[1 − (1 − p) 6r(s ≤ s∗)]B − ψ = [1 − (1 − p) 6r(s ≤ s∗)]B

or

( p − p) 6r(s ≤ s∗)B = ψ.

The obAecti*e to induce the high e&ort in the least#cost !ashion thus uni'uel" deCnes the

threshold s∗$

&esult ': (he o"timal way to induce the manager to e$ert the high e)ort is to choose

action L after bad short!term "erformance whene*er the un*eri#able signal is lower than s∗.

The higher the cost o! e&ort ψ, or the lower the pri*ate beneCt B, the higher the

threshold s∗, and thus the higher the probabilit" 6r(s ≤ s∗) o! li'uidation a!ter a low

short#term proCt$

2.3 Allocation of control

Ee now show that standard securities, debt and e'uit", can be chosen so as to implement

the contingent polic" described in subsection 2$2$ Ee let D denote the !ace *alue o! debt$

Debt is here a claim on the bank)s long#term proCt@ it is senior to the shareholders) claim$

:s we will show below, we can implement the second best with a moderate debt le*el, i$e$

D < α $

Ee Crst determine under which conditions shareholders choose action C when in con#

trol$ First, note that the" ne*er pick action L !or an" nonnegati*e9 le*el o! debt, since

this sa!est action is not e+#post eKcient and !urthermore debtholders are senior claimants

relati*e to shareholders$ 3either do shareholders choose action G !or an arbitrar" signal

s, pro*ided the le*el o! debt is not too high, that is, pro*ided that D satisCes

(s + τ)(1 − D) ≤ s(1 − D) + s(α − D),

ager8entrepreneur onl" aims at minimi(ing li'uidation subAect to obtaining Cnancing !rom outsidein*estors$ This least#cost i$e$ constrained#eKcient9 solution is onl" weakl" optimal !or the man#ager8entrepreneur in general$ 5owe*er, with more general pre!erences monetar" responsi*eness !ore+ample9, or with *ariable proAect si(e and si(e#dependent pri*ate beneCts B(I)9, it would be strictly optimal$



or

τ(1 − D) ≤ s(α − D).

%all D+(s) the ma+imum le*el o! debt such that this condition is satisCed

D+(s) = sα − τ

s − τ . 29

3ote that the le*el D+(s) is positi*e !rom 99, rises with s and is strictl" less than

α and there!ore less than 9@ it approaches α as τ goes to 0$

3ow that we ha*e determined shareholders) action choice conditional on proCt, let us

consider the !ollowing capital#ade'uac"#re'uirement implementation mechanism Share#

holders are in control pro*ided the" keep debt less than or e'ual to some D∗ to be deCned

below@ posit !or now that D∗ is lower than D+(s∗) and bigger than the net proceeds !rom

li'uidation ℓ + π

ℓ + π < D∗ < D+(s∗). 9

Itherwise, control shi!ts to debtholders who, we assume !or now, choose action L$

:ssume !urther that the bank has a le*el o! long#term9 debt e'ual to D∗ at the initial

stage we shall discuss this later9$

! π = π > 0, at stage , shareholders ha*e control and can distribute up to π as

di*idend without increasing le*erage, and the" Cnd it in their interest to distribute this

ma+imal amount$ ndeed, shareholders do pre!er to recei*e di*idends whene*er this does

ha*e an" impact on control allocation 3ot ma+imall" distributing di*idends Aust raises

the *alue o! the debt, without an" impact on total surplus$

! instead π = π < 0, shareholders lose control unless the" re#in*est the absolute *alue

o! π into the bank$ The" are willing to recapitali(e pro*ided that

π + s(1 + α − 2D∗) ≥ 0. ;9

ndeed, shareholders obtain nothing when control shi!ts to debtholders, pro*ided the" go

!or li'uidation$ :lternati*el", shareholders can recapitali(e the bank at the cost o! the

absolute *alue o! π 9 and implement action C, which gi*es them an e+pected re*enue o!

s(1 − D∗) + s(α − D∗)$2

%learl", recapitali(ation is more attracti*e, the higher the signal s$ Ine can deCne D∗

2This reasoning assumes that α ≥ D∗, because shareholders are meant to recei*e ma+ {0, α − D∗}$ Butwe ha*e alread" assumed that D∗ ≤ D+(s∗) an assumption we discuss later on9, which implies D∗ < α $

<



such that

π + s∗(1 + α − 2D∗) = 0,

or

D∗ = s∗(1 + α ) + π

2s∗ , 9

and this implies that shareholders keep control i! and onl" i! s ≥ s∗$

To ensure that our capital#ade'uac"#re'uirement mechanism implements the desired

actions, we Cnall" ha*e to check that debtholders Cnd it pre!erable to li'uidate instead

o! pa"ing −π to workers and suppliers and go !or continuation whene*er s ≤ s∗$; This

re'uires

ℓ ≥ 2s∗D∗ = s∗(1 + α ) + π, 9

an assumption which will be satisCed pro*ided π is low enough$

Remark 1$ Iur *arious conditions re'uire some assumptions on the possible *alues o! π $

First, there is condition 9$ Second, the abo*e condition deCning D∗ implies, together

with 9, that π should not be too low, or more precisel" that

ℓ + π < s∗(1 + α ) + π

2s∗ . 79

The third rele*ant technical condition rele*ant is that the prescribed debt le*el D∗ does not

induce shareholders to pick action G when the" are in control$ This means D+(s) > D∗

!or all s ≥ s∗$ Since dD+/ds > 0, this re'uires D+(s∗) > D∗, or

s∗α − τ

s∗ − τ >

s∗(1 + α ) + π

2s∗ . 9

Ince again, this will be satisCed pro*ided π is low enough$

Taken together, conditions 9 to 9 re'uire that π must satis!"

ℓ + π <

s∗(1 + α ) + π

2s∗ < min ℓ

2s∗ ,

s∗α − τ

s∗ − τ

. <9

Since s < 0.5, these conditions are not incompatible$ Ee thus ha*e the !ollowing result

3ote that, !or s = s∗, shareholders are indi&erent between lea*ing control to debtholders and pa"ing−π in order to choose action C$ Since we ha*e assumed that D∗ < D+(s∗), this means that, when s = s∗,the" strictl" pre!er lea*ing control to debtholders to choosing action G$ Since the pa"o& associated withG is increasing in s, this also means shareholders will not be tempted to pa" −π in order to choose actionG !or an" s < s∗$

;Ee do not need to consider action G, as debtholders alwa"s pre!er C to G !rom (s + τ)D∗ < 2sD∗

!or all s and conditions 29 and 99$

0



&esult +: ssuming conditions -'. and -/., one can im"lement the "erformance!

contingent cor"orate action choice described in &esult ' through a ca" on le*erage de!

#ned by D∗

% (his ca" can alternati*ely be reinter"reted as a minimum ca"ital re0uirement (I − D∗)/I$ 1re*enting shareholders from choosing the gambling action G re0uires that

D∗ < D+(s∗)%

Recapitali(ation is less attracti*e, the higher D∗ is, which is a !orm o! Gdebt o*erhangG$

Moreo*er, when π is lower, so must D∗ be otherwise, one will ha*e e+cessi*e li'uidation,

because shareholders will too o!ten be unwilling to recapitali(e the bank$

Remark 2 $ Ehile contingent control and non#contingent securities can implement the

second#best optimum, so can non#contingent control and contingent securities$ The model

onl" predicts i9 the per!ormance sensiti*it" o! the compensation o! the in*estors in con#

trol, and ii9 the need !or a second group o! outside in*estors to Gbalance the booksG$

But, !or the sake o! realism, it makes sense to implement the second#best with standard

securities$

2.4 Discussion

Renegotiation$ Eould renegotiation among in*estors make the capital structure irrele*ant

and thus bring us back to a Modigliani#Miller world Ehile properl" allocated control

b" an in*estor who does not ma+imi(e e+#post proCt boosts managerial e&ort, once e&ort

has been chosen, it is in the communit" o! in*estors) interest to renegotiate awa" the

e+#post ineKcienc"$ :s discussed in Dewatripont and Tirole <<;a9, !or the Modigliani#

Miller irrele*ance#o!#Cnancial#structure theorem not to appl", one needs either imper!ect

renegotiation or the inabilit" !or the manager to a*oid concessions and to !ull" !ree#ride

on the renegotiation process$ For e+ample, when !aced with the prospect o! li'uidation,

the manager might be !orced in the renegotiation process to gi*e up some o! her Cnancial

compensation in the more general *ersion o! this model, in which the manager responds to

monetar" incenti*es9 or to disclose some wa" o! increasing proCtabilit" under continuationat the detriment o! her pri*ate beneCts$

Rationale for regulation$ :s !or the rationale !or regulating banks, our book Dewatripont

and Tirole, <<;b9 argued that banks and !or similar reasons insurance companies, pen#

sion !unds $$$9 di&er !rom regular Crms in that their debtholders, i$e$ depositors, are

:llowing π to be distributed, and re'uiring π to be )neutrali(ed), maintains the capital ratio un#changed, at least when we take a historical#cost#accounting approach$ Such an approach makes sensebecause the true *alue o! the bank onl" *aries as a !unction o! the un*eri#able signal s, !or which thereis thus no market#based measurement$



not able to e+ert control rights appropriatel" and need to be GrepresentedG$ Disciplin#

ing managers appropriatel" then calls !or a depositors) representati*e$ The e+ercise o!

regulator" control is !or e+ample ke" to pre*enting banks in trouble !rom Ggambling !orresurrectionG b" raising interest rates on deposits and attracting !unds !rom depositors

who GcountG on implicit or e+plicit support !rom the authorities deposit insurance !und9

or !rom ta+pa"ers$

Deposit insurance in this respect has a !urther beneCt be"ond its primar" goal, the

pre*ention o! bank runs Diamond#D"b*ig <9$ ! coupled in bad times with control

rights allocated to either the deposit insurance !und or to the regulator entrusted with the

de!ence o! depositors, deposit insurance pro*ides the representati*e o! passi*e depositors

with an incenti*e scheme$ 4nder this *iew, the depositor representati*e)s mission is

to minimi(e losses borne b" the insurance !und, or e'ui*alentl" ma+imi(e the *alue o!

deposits$

Lower leverage? >et us now return to the assumption that the manager8entrepreneur

chooses to start at stage with debt le*el D∗, and not with a lower le*el, that is, le*erage

is the ma+imum le*el compatible with the capital ade'uac" re'uirement$ :ctual regula#

tion indeed onl" sets a cap on le*erage, and not a prescribed le*el$ But in !act, setting D

below D∗ would compromise Cnancing as this would reduce the probabilit" o! li'uidation

a!ter low short#term proCt and there!ore *iolate the manager)s incenti*e constraint in

this sense, debt no longer acts as a managerial disciplining de*ice9$ So, here, the man#ager8entrepreneur is induced to choose a debt le*el no lower than D∗, e*en though we

ha*e not introduced an" ta+ ad*antage o! debt or Gbailout premiumG$

Risk weights and the Basel regulation regime $ The abo*e setting is an o*ersimpliCed

*ersion o! the Basel regulator" regime$ n particular, it lacks risk weights whether e+#

ogenousl" chosen N as in Basel N or ratings# or internal#model#based N as in Basel

and 9$ 5owe*er, a simple reinterpretation o! the model demonstrates the beneCts o!

risk weights$ ntroduce a stage# choice o! in*estment that increases its riskiness, in that

π decreases and π increases this is a mean#preser*ing spread i! p π + (1 − p)π remainsconstant9$ From 9, D∗ must decrease$ That is, an increase in risk must result in a lower

allowed le*erage ratio, which is e+actl" what risk weights on assets, as used since Basel ,

achie*e$

n sum, our setting indicates that the GBasel philosoph"G, namel" a risk#based9 cap

on le*erage, is not incompatible with optimalit"$ This assertion should howe*er be ac#

companied b" two ca*eats$ First, it is o! course onl" 'ualitati*e, since our setting does

not allow us to discuss the calibration o! the Basel capital ade'uac" ratio$ Second, our

2



macroprudential approach be!ore the 2007# Cnancial crisis, see Borio, 2009$ 3ote how#

e*er that the idea is o!ten cast more in terms o! the dangers o! Gproc"clicalit"G, that is,

in terms o! its impact on third parties N ampli!"ing impact o! dele*eraging through Cresales, domino e&ects, $$$ N than in terms o! the incenti*es it implies !or bank managers

and in*estors$

3.2 Forbearance is not optimal either

Ehile an e+plicit macroprudential approach is a new concept in regulator" rules, macro#

economic shocks ha*e not alwa"s been GignoredG in regulator" practice$ n !act, G!orbear#

anceG is a !re'uent response to banking crises caused b" negati*e macroeconomic shocks$

For e+ample, as has been widel" documented see Dewatripont and Tirole <<;b9 !or asummar"9, in the 4S <0)s Sa*ings and >oans crisis, a reduction o! the capital ratio as

well as regulator" accounting changes reduced the recapitali(ation re'uirements o! SO>)s

i$e$ allowed a rise in le*erage9 when these institutions were hurt b" a sharp rise in in#

terest rates and then b" a recession$ n terms o! our setting, this amounts to allowing

shareholders to put onl" the absolute *alue o! π back into the bank to keep control, rather

than the higher absolute *alue o! π + ε, namel" to GignoreG the negati*e ε$7

Such !orbearance is also suboptimal Ehile it partiall" protects the bank manager

against e+cessi*e li'uidation it does not do it !ull", since the rise in le*erage reduces

their incenti*e to recapitali(e9, it does alter shareholder incenti*es b" allowing le*erage to

increase in a recession$ ! debt goes be"ond D+(s), shareholders choose action G, namel"

gambling !or resurrection$ n !act, this practice was widespread in the SO> crisis$

The point to stress here is that neither Basel 8 nor !orbearance Gremo*e noiseG !rom

both the shareholders2 and managers2 incenti*e schemes$ The ne+t subsections in*estigate

*arious schemes that neutrali(e the impact o! macroeconomic shocks on shareholders and

thereb" maintain appropriate discipline on managers$

7This was also done to some e+tent in 200, and one o! the man" purposes o! Basel is to eliminate

that b" G!ocusing onl" on high#'ualit" capitalG$ nterestingl", there seems to be a pattern where e+istingregulation is GtwistedG a!ter big recessions, which leads to a need !or a new regulation$1ambling occurs whene*er

1 + α − 2D+(s)

1 + α − 2D∗ >

π + ε

π .

;



3.3 Transient macroeconomic shoc: d#namic provisioning and

counterc#clical capital bu$ers

Suppose Crst that the econom" goes through a deterministic c"cle o! booms and reces#

sions@ in order to rule out potentiall" comple+ multi#period incenti*e schemes, we assume

that managers li*e !or onl" one period where each period is made up o! stages through

9@ the action L should here be *iewed not as a li'uidation, but as a conser*ati*e polic"

that "ields a sa!e pa"o& to the in*estors and no pri*ate beneCt !or the manager$ More#

o*er, a!ter ha*ing chosen action L, the debtholder representati*e will Cnd a new set o!

shareholders willing to in*est at the start o! the !ollowing period$ Finall", b" deCning π

and π ade'uatel", we can alwa"s assume that ε + ε = 0$

n this e+treme situation, the bank can self!insure and does not need to contract !ora macro hedge$ n the spirit o! the Spanish Gd"namic pro*isioningG polic" o! the last

decade or Basel )s counterc"clical capital bu&er, assume that when ε is reali(ed, it has

to be GhoardedG so as to be GreleasedG when ε is reali(ed one period later :ssuming that

the interest rate on the sa!e store o! *alue in the econom" is 0, we can then get back to a

D∗ deCned b"

π + s∗(1 + α − 2D∗) = 0.

This scheme !orces the bank to be better capitali(ed in booms and allows it to use

retained earnings accumulated during a boom to eliminate its need !or recapitali(ation ina recession$ D"namic pro*isioning and the counterc"clical capital bu&er howe*er share

the usual drawbacks o! sel!#insurance@ !or e+ample, it cannot address the possibilit" o!

i$i$d$ shocks there might be multiple negati*e shocks in a row9, let alone the case o!

permanent shocks$ The re'uirement !or a negati*e shock to be GtransientG in the sense

adopted here is there!ore strong@ we here mean a certitude o! a !uture o&set$

3.4 Macro hedges: capital insurance and %o%os

The simplest wa" o! keeping managerial and in*estor incenti*es unchanged in the presenceo! macroeconomic shocks is to keep capital ratios constant and arrange automatic cash

inHows and outHows$ That is, the bank ma" contract with a pro*ider o! insurance who

commits to bring cash in a recession and recei*e mone" !rom the bank in a boom$

This solution is straight!orward, and admits se*eral *ariants considered below$ But it

raises diKcult, general#e'uilibrium issues that we will onl" touch on in Section ;$ ndeed

risk#shi!ting onl" displaces the problem 1i*en that the shock is b" deCnition a macro

shock, who will bear it 5ow will the insurance pro*ider cope with its own dual incenti*e



problem %learl" some economic agents must bear the macroeconomic risk$

GMacro hedgingG is related to the possibilit" o! capital insurance, as suggested b"

Pash"ap et al$ 2009 Ehen a bad shock occurs, the bank automaticall" recei*es capitalas an insurance pa"ment, against a premium paid to a pri*ate or public insurance !und$<

The appeal o! capital insurance is that it complies with 5olmstrm)s precept o! G!ull"

neutrali(ingG shocks that are not controlled b" management$

%apital insurance can in a sense be interpreted as a Gpre!unded bailoutG$ Such a

GbailoutG is not a source o! moral ha(ard pro*ided that the insurance pa"ment o&set

solel" the macroeconomic shock$ To take an e+ample, let us keep the assumption that

ε + ε = 0 and assume that ε and ε are e'uiprobable$ %onsider now a contract where the

insurer makes a pa"ment ε to the bank when ε = ε, and recei*es ε !rom the bank when

ε = ε$ The bank will still be li'uidated whene*er π = π and s ≤ s∗, regardless o! whether

the macroeconomic shock is !a*orable or un!a*orable$

n our setting, the optimal polic" can alternati*el" be implemented through a capital

insurance line or the use o! contingent con*ertible bonds %o%os9$0 The trick !or the

capital insurance implementation is to deCne ma+imum le*erage D∗ as be!ore and to ha*e

the bank sign a capital insurance contract which )neutrali(es) the macro shock represented

b" ε and ε$ :lternati*el", one can introduce %o%os, such that a !raction is con*erted into

shares in a recession$ This con*ersion wipes out an amount ∆ o! debt D > D∗9 such

thatπ + ε + s∗

1 + α − 2 D

= 0

and

π + ε + s∗

1 + α − 2( D − ∆)

= 0.

Thus, capital insurance and %o%os look prett" similar in partial e'uilibrium$

3.& Macroeconomic shoc to prospects

Ee ha*e so !ar assumed that the macroeconomic shock a&ects the short#term proCt$:lternati*el", this shock could a&ect prospects$ Suppose that the distribution o! s is

conditioned b" the macro shock ε the cumulati*e distribution !unction, G(s |ε ), is a

!unction o! ε9$ /Kcienc" re'uires that the same cuto& s∗ be applied when short#term

<n Dewatripont and Tirole <<;b9, we had a similar idea when we ad*ocated proc"clical depositinsurance premia with the insurer being then the public sector9$

0 %o%os are con*ertible bonds !or which the con*ersion into shares is contingent on a speciCed, *eriCablee*ent$ Ee here take the contingenc" to be a macroeconomic e*ent, although more generall" %o%os ma"be contingent on all kinds o! *eriCable e*ents$ See !or e+ample Bolton and Samama 2029 !or a discussiono! *arious alternati*es$



proCt is π , regardless o! the reali(ation o! ε$ >etting 6r (s ≤ s∗) ≡ Eε [6r (s ≤ s∗ |ε )], the

manager)s incenti*e constraint is still

6r (s ≤ s∗)( p − p)B = Ψ.

The optimum can there!ore be implemented through a ma+imum le*erage D∗ gi*en

b" the !amiliar e+pression

π + s∗ (1 + α − 2D∗) = 0.

3.' (umming up

The results o! this section can be summari(ed as !ollows

&esult 4: Ca"ital ade0uacy re0uirements can be rationalized as a way to achie*e o"timal

managerial disci"line, at least in the absence of macroeconomic shocks% 5eutralizing such

shocks in order to maintain o"timal managerial disci"line is at odds with Basel 6 or 66: a

macro"rudential a""roach is needed for o"timal managerial disci"line, and not solely to

a*oid macroeconomic "rocyclicality%

&esult 7: (he key to o"timality is to kee" the incenti*es of both managers and share!

holders una)ected by the macroeconomic shock% (his re0uires an automatic in8ection of

fresh ca"ital in a recession: like Basel 6966, forbearance is subo"timal%

&esult : ;hen "ositi*e and negati*e shocks alternate deterministically, re0uiring

banks to build u" ca"ital in booms and allowing them to release it in recessions, as with

dynamic "ro*isioning or with countercyclical ca"ital bu)ers, is an a""ro"riate solution%

&esult <: ;hen macroeconomic shocks are random, re0uiring banks to subscribe to a

ca"ital insurance scheme, or to issue CoCos, is an a""ro"riate solution% ;hile such a

scheme looks de facto like a "refunded bailout, it does not lead to moral hazard "ro*ided

that it is fully tied to e$ogenous macroeconomic shocks%

4 To)ards a general e*uilibrium setting

Ehile general e'uilibrium 'uestions are *er" interesting, the" lie be"ond the scope o! this

paper$ >et us there!ore content oursel*es with a couple o! remarks on this topic$

%o%os and capital insurance both Gdo the AobG !rom the point o! *iew o! an eKcient

bank go*ernance$ The" di&er, though, in the amount o! cash that is supplied to the

bank !rom outside$ Eith %o%os, a !raction o! long#term debt is de !acto written o&,

7



which restores shareholders) incenti*es without e+ternal inter*ention$ B" contrast, capital

insurance brings direct cash to the bank$

1i*en that the shock is macroeconomic, a natural 'uestion !or capital insurance isEho will suppl" the corresponding cash in case o! a negati*e shock The Crst possibilit"

is that the econom" has enough stores o! *alue that can be emplo"ed to this purpose$

5owe*er i! there is a shortage o! e+isting stores o! *alue to some e+tent, there must be,

otherwise hedging would be costless in our !ramework9, these stores o! *alue command a

premium, and insurance against macroeconomic shocks is limited$ :nd in !act, the same

'uestion arises concerning the use o! %o%os$ Ehile %o%os do not re'uire an inAection o!

e+ternal cash in a recession, the loss the" incur !rom con*ersion during a recession is nec#

essaril" priced out and there!ore must reHect the shortage o! cash in that macroeconomic

state$

: second wa" to address macro shocks is to ha*e the state bring li'uidit" in bad states

o! nature$ >i'uidit" pro*ision b" public authorities in the case o! macro shocks is then

use!ul !or two reasons 5olmstrm#Tirole <<, 209 i9 their ta+ing powers gi*e them

a uni'ue access to the !uture income o! consumers@ and ii9 the" can act e+ post a!ter

learning the state o! nature, while pri*ate e+#ante in*estments in li'uid assets are wasted

in the case o! positi*e macro shocks$ This argument, applied to the implementation o!

optimal managerial incenti*e schemes through capital regulation, points at some superi#

orit" o! state#pro*ided o*er pri*atel"#pro*ided capital insurance assuming awa" politicaleconom" problems9$

& %onclusion

Iur model departs !rom Modigliani#Miller in that the allocation o! control rights to out#

side in*estors ser*es to discipline managers, and income rights o! outside claims inHuence

in*estors) e+ercise o! their decision rights$ t predicts that debt and outside9 e'uit" can be

used to deli*er eKcient contingent control$ Together with the representation h"pothesis,

the model rationali(es t"pical capital#based banking regulation a!ter bad per!ormance,

control shi!ts !rom e'uit"holders to a debtholder representati*e unless e'uit"holders re#

capitali(e the bank$

Benchmarking actual regulation against the theoretical paradigm, we noted that Basel

8 regulation !ails to Gcontrol. !or macro shocks the regulations are too tough in reces#

sions and too lenient in booms$ Forbearance GignoringG the recession b" allowing lower

capital ratios9 is also inade'uate as it leads to gambling !or resurrection$ Ehat is needed

is Greal mone"G to control !or the macro shock$ n the case o! positi*e and negati*e shocks



that deterministicall" o&set each other o*er time, d"namic pro*isioning or the Basel

counterc"clical capital bu&er are appropriate wa"s to deal with these shocks$ n the case

o! random macro Huctuations, capital insurance or %o%os, both inde+ed on the macroshocks, are appropriate$

Ee conclude with two alle"s !or !uture research$ First, and as discussed in section ;,

a ke" issue with macroeconomic shocks is, in general e'uilibrium, that o! the suppl" o!

macro hedges$ Second, a number o! recent models ha*e posited substantial beneCts to

stores o! *alue that are sa!e or nearl" sa!e e$g$ Stein 202, 1ennaioli et al !orthcoming9@ it

would be interesting to anal"se implications o! such an h"pothesis !or the cost o! outside

e'uit" or that o! contingent instruments such as %o%os$

<



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2

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