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Financial Distress And Banks'communication Policy In Crisis Times

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This paper analyzes banks’ communication policies in crisis times and the role of imperfect information in enhancing banks' financial distress. If banks differ in their exposure to dubious assets, fragile banks may claim to be sound only in order to manipulate investors' expectations. Then sound banks must pay a larger interest rate than in a perfect information set-up. A stronger sanction for false information would improve the situation of the low-risk banks but would deteriorate the situation of the high-risk banks. The total effect on the economy-wide frequency of default of credit institutions is ambiguous. It can be shown that, in some cases, the optimal sanction is lower than the sanction that rules out any manipulatory behavior.
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Romanian Journal of Economic Forecasting – 1/2010 5
FINANCIAL DISTRESS AND BANKS'
COMMUNICATION POLICY IN CRISIS
TIMES
Damien BESANCENOT
Radu VRÂNCEANU
Abstract
This paper analyzes banks’ communication policies in crisis times and the role of
imperfect information in enhancing banks' financial distress. If banks differ in their
exposure to dubious assets, fragile banks may claim to be sound only in order to
manipulate investors' expectations. Then sound banks must pay a larger interest rate
than in a perfect information set-up. A stronger sanction for false information would
improve the situation of the low-risk banks but would deteriorate the situation of the
high-risk banks. The total effect on the economy-wide frequency of default of credit
institutions is ambiguous. It can be shown that, in some cases, the optimal sanction is
lower than the sanction that rules out any manipulatory behavior.
Keywords: financial distress, financial crisis, banks, disclosure, transparency
JEL Classification: E44, G21, D82
1. Introduction
One major factor of uncertainty during the 2007-2009 financial crisis was the exposure
of banks' balance sheets to hard-to-value assets such as Mortgage Backed Securities
(MBSs) or Collateral Debt Obligations (CDOs) originated by US mortgage and
financial institutions heavily involved in subprime lending.1 Although these "toxic
securities" were in general made in USA, many European banks appeared to have
massively invested in such assets.
In general, banks and financial institutions perpetrate a tradition of opacity (Morgan,
2002). In particular, during the last crisis, they were extremely reluctant to disclose
their true exposure to these hard-to-value assets such as the CDOs. For instance, in
November 2007 the French bank Société Générale declared to have little exposure to
CEPN and University of Paris 13. Paris, France. email: besancenot.damien@u-paris13.fr.

ESSEC Business School, PB 50105, 95021 Cergy, France. email: vranceanu@essec.fr.
1 January 2007 marked the sharp increase in delinquency rates on sub-prime loans (Borio,
2008).
1.
Institute of Economic Forecasting
Romanian Journal of Economic Forecasting – 1/2010
6
high-risk US MBSs and CDOs; yet in January 2008 they wrote down as much as 1.2
billion euros related to such investment (WSJ, 22.01.08), and another 2.6 billions
euros in May 2008 (WSJ, 14.05.08). At Bearn Sterns, the CEO declared two weeks
before the bank's collapse that "we don't see any pressure on our liquidity, let alone a
liquidity crisis" (WSJ, 19.03.07). On September 10, 2008, one day after the executive
of Lehman Brothers calculated that the firm needs at least 3 billion US dollars in fresh
capital, they assured investors on a conference call that the bank needed no capital at
all (WSJ, 07.10.08). Such a lack of transparency brought about a generalized
shortage of trust that can be measured, for instance, by the wedge between interest
rates in the unsecured interbank credit market and the secured central bank short-
term lending. This indicator reached a peak of two percentage points in the aftermath
of Lehman Brothers' collapse (September 2008), to slide down in early 2009.
Quite recently (April 2009), policymakers all around the world tried to figure out what
regulation could help avoiding the next financial crisis. Many reform proposals build on
the widely held belief according to which "honesty is the best policy"; in particular,
many policymakers argue that more transparency could only improve the functioning
of the financial sector and its resilience to shocks. For instance, Jean-Claude Trichet,
the ECB President, declared in October 2007:
"In any case, we need more transparency. The illustration that what we
have in front of our eyes as regards the functioning of commercial
papers, asset-backed commercial papers in particular, is clearly that we
presently pay a high price for the lack of transparency. And the same in
the interbank money market, as I said".2
When leaders of developed or big emerging economies met in London on April 2,
2009 for a G-20 Summit aiming at reforming the financial system such as to avoid
further similar crises, enhancing transparency turned out as a key recommendation.3
During the 2007-2009 crisis, policymakers also brought direct support to commercial
banks by pushing down the cost of their short-term borrowing form the central bank. In
the US, the Fed slashed the target rate from 5.25% to almost zero between August
2007 and January 2008; it also agreed on lending money against a wider range of
collateral, including investment-grade MBS. The ECB begun to cut down the main
interest rate in October 15, 2008, in a coordinated move with the other major central
banks, bringing it down from 4.25% to 1.5 % in March 2009.
This paper aims at analyzing the impact of imperfect information on the risk of bank
default in crisis times, as well as banks' communication strategy during a financial
crisis. In the model, there are two types of banks that differ in their exposure to
dubious assets. Private investors, called to lend to short-term funds to banks during
the crisis, are assumed to have only imperfect information about the true exposure of
a given bank. Bank managers can send either honest or misleading signals. In
particular, the manager of a fragile bank (i.e., with high exposure to risky assets) may
2 Jean-Claude Trichet, "ECB Introductory statement swith Q&A", 10.09.2007, http://www.ecb.int/
press/ pressconf/ 2007 / html/ is070906.en.html.
3 See www.g20.org for main working documents and the final declaration.
Financial Distress and Banks' Communication Policy in Crisis Times
Romanian Journal of Economic Forecasting – 1/2010 7
want to claim that their exposure is small, in order to benefit of better financing terms
until "the storm is over". If generalized, this strategy is harmful for solid banks that
have no means to signal themselves and must borrow at a higher interest rate than in
a perfect information set-up. The model builds on our early analysis of communication
policy as pertaining to the corporate sector (Besancenot and Vranceanu, 2009), yet
the banking sector model features additional complexity due to non-linear
relationships.
An increase in the sanction for dishonest communication comes with two antagonistic
effects: on the one hand, since there are fewer liars in the economy, the interest rate
required by investors to finance low risk institutions should decline and their frequency
of defaults should diminish. On the other hand, managers who honestly announce that
their bank has a high exposure to risky assets will have to pay a larger interest rate,
and their frequency of defaults should increase. The theoretical analysis points out
that the two effects tend to offset each other. We perform several numerical
simulations in order to find out which is the dominant one. It turns out that in some
cases the sanction that drives to zero the number of dishonest managers can be
socially inefficient: a lower sanction would bring about a smaller number of bank
defaults. In a related paper, Cordella and Yeyati (1996) have shown that if banks have
no complete control over their risk exposure, the presence of uniformed investors may
reduce the risk of bank failures. The model can also show the impact on defaults of a
reduction in the interest rate on borrowed funds from the central bank.
A substantial literature on corporate financial distress has emphasized that the image
clients and suppliers have about a company plays an important role in determining its
actual financial stance. More precisely, if creditors start having doubts about the
financial position of a company, they may ask for a higher risk premium, which
represents an indirect cost for the firm (e.g., Altman, 1984; Wruck, 1990; Andrade and
Kaplan, 1998). To avoid this additional strain, in difficult times the manager may well
communicate on better than actual performances only to get more favorable
contracting terms and push down these indirect costs. Our analysis can also be
connected to traditional studies in the financial market micro-structure where
accounting information is shown to have a bearing on a firm valuation (e.g., Diamond
and Verrecchia, 1991; Baiman and Verrecchia, 1996; Bushman et al., 1996). The
specific nature of information asymmetries and regulation of the banking sector were
analyzed by Aghion, Bolton and Fries (1998), or Freixas and Jorgé (2007).
Inter alia, the going financial crisis has put an end to the myth of risk-sharing through
widespread recourse to securitization. It turned out that securitization actually
increased the risk of contagion and shock propagation between interconnected
players, which, in turn, brought about a dramatic risk of systemic failure of the financial
system (Brunnermeier, 2009). It is beyond the scope of this paper to address this
extremely important question; for sure, in presence of mechanisms of transmitting
shocks from one bank to another, additional strain on every individual bank – such as
described in our paper – would amplify the systemic risk.4
4 See for instance the classical paper by Rochet and Tirole (1996) on bank systemic risk
originated in interbank lending.
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8
The paper is organized as following. The next section introduces the main
assumptions. The section 3 presents the equilibrium of the model. We work out
several numerical simulations in section 4. The last section presents the conclusion.
2. The main assumptions
We recall that the model is developed to analyze banks' disclosure decisions once
that the crisis is unwinding. The composition of the assets portfolio is given, the
banker cannot "get rid" of the high risk securities. The proportion of central bank
funding is also determined by the central bank (CB). The model is cast as a game
between investors – who must lend money to a financial institution, and the manager
of the latter, who decides on the communication policy with the aim at maximizing the
survival chances of his company. There are two types of financial institutions. The H-
type institution has a high exposure to risky assets; the L-type has a low exposure. Let
q be the frequency of L-type, low-risk banks in total population of banks.
Investors know the distribution of types, but do not know the type of each institution.
The manager knows the true exposure of his institution and must issue a signal before
he raises funds.
More in detail, the balance sheet of a typical financial institution has the simplified
form:
Table 1
Simplified balance sheet of a commercial bank
Assets Liabilities
,
j
D1 Risk-free assets, bearing
interest
R
b
,E1 Central Bank funds, bearing
interest k
,
j
D Risky assets, bearing interest
U
,
E
Private funds, bearing interest
i
a
The total market value of the bank is normalized to one. Then j
D can be interpreted
as the proportion of risky assets in total assets, j
D1 being the proportion of risk-
free assets. Banks of H-type have a proportion of risky assets ,
H
D banks of L-type
have a proportion ,
L
D with .
LH D!D Let b
R be the interest rate on the risk-free
assets of the bank, and let U be the interest rate on risky assets.
On the liabilities side, E1 is the proportion of funds borrowed from the central bank
at a pre-determined interest rate k and E is the proportion of funds that the institution
must raise in the private market at a market-determined interest rate .i a Private debt
is subordinated to central bank debt.
The interest rate on private funds depends on the investors beliefs about the type of
the bank, and these beliefs depend on the manager's announcement a. More
precisely, the manager can state that the bank has a high exposure to risk, so the
announcement is a=h or a low exposure, that is a=l.
Financial Distress and Banks' Communication Policy in Crisis Times
Romanian Journal of Economic Forecasting – 1/2010 9
At the end of the game, a proportion W of the risky assets will default (completely,
their residual value is zero). The proportion
W
is a random variable on the support
];,[ 10 the p.d.f. is denoted by )(f W and the c.d.f. will be denoted by )(F W .
The sequence of decisions is the following:
x At time t=1, Nature chooses the type of bank },{ HLj with j
D
the share of
risky assets in total assets.
x At time t=2, the bank's manager announces the type of the bank, }.,{ hla He
is honest if ,ja and dishonest if .ja z
x At time t=3, given ,a investors ask an interest rate a
i
to lend money to the
bank (short term).
x At time t=4, the shock
W
is realized, and, depending on its true exposure j
D
and its liabilities, the bank defaults or not. In the case of default, the liar must pay
a fine T . The game is over.
The default condition
A bank of type j defaults when the shock
W
is realized if, given the announcement
a (and thus ),
a
i its liabilities exceed its assets. This can happen if the proportion of
default on risky assets exceeds a critical threshold ja
W
ˆ . More precisely, we can write
that default occurs if:
)k)(()i())(()R)(( aj
b
jEEUWDD1111111
.
)(
k)(iR)R(
ˆj
a
bb
j
ja
UD
EEUD
{W!W1
1 (1)
We notice that default can happen only if 1
ˆ
ja
W
, which is tantamount to
)R(k)(iR b
ja
bDEE11 .
)R(
k)(iR
b
a
b
j
EE
!D1
1
A negative term )R(
k)(iR
b
a
b
EE
1
1 is not a realistic assumption. Indeed, in such a
case, “very sound” banks that have no exposure to risky assets (DL=0) would be in a
situation of default just because the interest rate they have to pay to private investors
(il) is too big. In equilibrium, only high-risk banks would participate to the market
(adverse selection), and the problem would become trivial.
Therefore in the following we focus on situations where the term )R(
k)(iR
b
a
b
EE
1
1 is
strictly positive,
^`
h,la . This requires that ia should be relatively small (in turn, this
is possible if the interest rate on risk-free assets available to private investors is
relatively small).
Institute of Economic Forecasting
Romanian Journal of Economic Forecasting – 1/2010
10
In this case, if we write
,
)(
k)(iR
)(
)R(
)(
ˆj
a
bb
jja
UD
EE
U
U
DW 1
1
1 this is a decreasing
function in ,
j
D

0
1
1
2
UD
EE
Dw
DWw
)(
k)(iR
)(
ˆ
j
a
b
j
jja
. We also notice that 1
1
U
U
)(
)R( b.
The default probability of a bank can be written as:
).
ˆ
(F]
ˆ
[Pr jaja W W!W 1 (2)
This probability of default increases with .
ˆ
)
ˆ
(f
d
]
ˆ
Pr[d
:j
ja
ja
j
ja
j0!
¸
¸
¹
·
¨
¨
©
§
Dw
Ww
W
D
W!W
D
In case of the bank's default, investors, who have invested the amount ,E get the
residual value ).k)(())(()R)(( j
b
jEUWDD111111 If the bank does not
default, investors get )i( a
E 1.
If the bank defaults ( ja
WW
ˆ
!), the profit is zero; if the bank does not default ( ja
WW
ˆ
d),
it makes a profit that depends on the actual W:
@
.)k)(()i())(()R)(()a,j|( aj
b
jEEUWDD W3 1111111
Hence the bank's expected profit is thus ).(dF)a,j|(
ja
ˆWW3
³W
0
The managers' payoff. Managers are assumed to be risk-neutral. To keep the model
as simple as possible, we will assume that the manager aims at maximizing chances
that his company survives during a temporary crisis; more specifically, the payoff of a
manager of a j-type bank who announces a is proportional to the survival probability
].
ˆ
Pr[ ja
WW
5 In addition, if the company defaults and the manger has issued a false
signal, he will bear a fine .
T
We thus write the manager's payoff as:
.]
ˆ
[Pr]
ˆ
[Pr)j|a(Z ja
aj
ja TW!WWW z
1 (3)
where the factor aj z
1 takes the value 0 if aj and 1 if .aj z
3. Equilibrium of the game
A Nash equilibrium of this game is a situation where managers chose the optimal
communication policy given investors' beliefs, and investors beliefs are correct given
managers' optimal policies.
3.1 The bank manager’s strategy and investors' beliefs
A bank manager’s strategy is defined as the optimal announcement conditional upon
5 Many senior executives, in general at the head of the fixed-income branches, loose their jobs
during the 2007-2009 crisis. After Citigroup reported a huge loss in the third quarter of 2008,
its CEO had to resign and so did the CEO of Merrill Lynch.
Financial Distress and Banks' Communication Policy in Crisis Times
Romanian Journal of Economic Forecasting – 1/2010 11
his type. Formally, it can be represented by a function a=a(j), with
^`
HLj ,.In this
particular game, the manager’s strategy is written as:
.
Hj],,[,h)(l
Lj,l
)j(a ¯
®
PPP
for10 with1
for
(4)
where
P
is the probability that a liar is running a H-type bank (he thus announces
)l
.
Notice that a manager at the head of a low-risk bank has no incentive to claim that the
bank has a high exposure to risky assets, if else he must pay a bigger interest rate to
private investors and chances that his firm defaults increase. They will always tell the
truth )( la . To the contrary, managers at the head of H-type banks might claim that
their bank is of the L-type )( la in order to manipulate investors' expectations and
benefit from a lower interest rate. Thus, they can push down the risk of default, but
have to bear a larger expected fine if caught. There can also be managers running H-
type banks that honestly announce their type, )( ha .
Given the managerial strategy, investors' beliefs can be represented by the probability
of the manager announcing l contingent upon the type of the bank:
,
]L|lPr[
],[,]H|lPr[
¯
®
PP
4 1
10 where
(5)
It can be shown that this game presents a separating equilibrium where each type of
bank has a specific communication policy, more precisely lLa )( and hHa )( ,
apooling equilibrium where all banks adopt the same communication policy, more
precisely jlja ,)( and a hybrid equilibrium where a fraction
P
of the managers
at the head of H-type banks announce l (lie) and the rest of them announce h (are
honest); managers of the L-type banks always announce l. In the following, we will
focus on this hybrid equilibrium ( [1,0]
P
), given that the pooling and the separating
situations appear to be special cases that correspond to 1
P
and respectively
.0
P
3.2. Interest rates
Private investors are risk neutral. They have access to risk-free assets bearing an
interest
R
. We assume that in a world with trade frictions banks have better risk-free
opportunities than private agents, so b
RR
.
a)If the manager announces ,ha then the bank must be
H
. With risk neutral
investors, the interest rate h
i is implicitly defined by the zero trade-off condition:
°
¯
°
®
W!WEUWDD
WdWE
E HhH
b
H
Hhh
ˆ
),k)(())(()R)((
ˆ
),i(
)R( if111111
if1
1 (6)
which is equivalent to:
Institute of Economic Forecasting
Romanian Journal of Economic Forecasting – 1/2010
12
),(dF)()(
)(dF
)k)((
)R)((
)(dF)i(R
Hh
Hh
Hh
ˆ
H
ˆ
b
H
ˆ
h
WWUDE
W
»
»
¼
º
«
«
¬
ª
E
D
EW
³
³³
W
W
W
11
11
11
11
1
1
1
1
0 (7)
where, according to equation (1),
.
)(
k)(iR)R(
ˆH
h
bb
H
Hh
UD
EEUD
W 1
1 (8)
We notice that for a given c.d.f. (),F Eq.(7) can be solved for .
i
h The latter is
independent of T ; it depends on .k
b) If the manager announces ,la the bank can be either
H
with ]l|HPr[ or L
with ].l|HPr[]l|LPr[ 1 The interest rate l
i
is implicitly defined by the zero
trade-off condition:
.
ˆ
),k)(())(()R)((
ˆ
),i(
]l|LPr[
ˆ
),k)(())(()R)((
ˆ
),i(
]l|HPr[
)R(
LlL
b
L
Lll
HlH
b
H
Hll
9
if111111
if1
with
if111111
if1
with
1
°
°
¯
°
°
®
°
¯
°
®
W!WEUWDD
WdWE
°
¯
°
®
W!WEUWDD
WdWE
E
which, with additional notation
)k)(()R)((S b
HH ED 1111 and
,)k)(()R)((S b
LL ED 1111 is equivalent to:
,)(dF)()()(dFS)(dF)i(]l|L[Pr
)(dF)()()(dFS)(dF)i(]l|H[PrR
LlLl
Ll
HlHl
Hl
ˆ
L
ˆ
L
ˆ
l
ˆ
H
ˆ
H
ˆ
l
¿
¾
½
¯
®
WWUDEWEW
¿
¾
½
¯
®
WWUDEWEW
³³³
³³³
W
W
W
W
W
W
111
1111
1
1
1
1
0
1
1
1
1
0(10)
with:
,
)(
k)(iR)R(
ˆH
l
bb
H
Hl
UD
EEUD
W 1
1 (11)
and
.
)(
k)(iR)R(
ˆL
l
bb
L
Ll
UD
EEUD
W 1
1 (12)
We notice that for a given c.d.f. ()F , the former equation becomes a relationship
between the interest rate l
i
and ],l|HPr[ that is: .C])l|HPr[,i( l )
3.3. The indifference condition
As already mentioned, we assume that the managers' payoff is proportional to
chances that the bank survives, and there is a sanction
T
for liars when their bank
Financial Distress and Banks' Communication Policy in Crisis Times
Romanian Journal of Economic Forecasting – 1/2010 13
defaults. So, for an honest manager, we have:
]
ˆ
[Pr)H|h(Z hH
WW (13)
and for a liar:
].
ˆ
[Pr]
ˆ
[Pr)H|l(Z lHlH W!WTWW (14)
The indifference condition )H|l(Z)H|h(Z allows us to determine the interest
rate l
i
for which the manager is indifferent between policies h or .l
>@
)
ˆ
(F)
ˆ
(F)
ˆ
(F
]
ˆ
[Pr]
ˆ
[Pr]
ˆ
[Pr
)H|l(Z)H|h(Z
HlHlHh
HlHlHh
WTW W
W!WTWW WW
1
)
ˆ
(F)
ˆ
(F)
ˆ
(F HlHhHl WT WW 1 (15)
As )i(
ˆˆ lHlHl W W and ),i(
ˆˆ hHhHh W W the last equation determines l
i
with respect
to .
h
i
It can be shown that .
hl ii For so doing, we assume that .
i
i
hl ! Then
,
ˆˆ HhHl WW and ).
ˆ
(F)
ˆ
(F HhHl WW We have ,)
ˆ
(F)
ˆ
(F HhHl 0WW while
>
@
,)
ˆ
(F Hl 01 !WT which is false. The opposite is true: hl
i
i
and, also
).
ˆ
(F)
ˆ
(F HhHl W!W
The direct consequence is that the H-type bank has an incentive to claim that it is of L-
type in order to benefit of the more advantageous borrowing terms.
We can show now that, in the hybrid equilibrium, an increase in the sanction pushes
down the interest rate of the banks that announce l, that is .d/di l0T
For so doing, we recall that ih is independent on il, thus 0
w
Ww
l
Hh
i
ˆ. We also know that
;
)(
k)(iR)R(
ˆH
l
bb
H
Hl
UD
EEUD
W 1
1 hence, 0
1
UD
E
w
Ww
)(i
ˆ
Hl
Hl
.
The total differentiation of the indifference condition (Eq. 15) allows us to determine
the co-movements between the equilibrium il and the sanction T:
>@
>@

 
0
1
111
1
1
11
10
TE
UD
W
W
wWwTW
W
T
W
w
Ww
T WT
w
Ww
WTWT
w
Ww
W
)(
)
ˆ
(f
)
ˆ
(F
i/
ˆ
)
ˆ
(f
)
ˆ
(F
d
di
di)
ˆ
(f
i
ˆ
)
ˆ
(Fd
di
i
ˆ
)
ˆ
(
f)
ˆ
(Fddi
i
ˆ
)
ˆ
(f
H
Hl
Hl
lHlHl
Hll
lHl
l
Hl
Hl
l
l
Hl
HlHll
l
Hl
Hl
Institute of Economic Forecasting
Romanian Journal of Economic Forecasting – 1/2010
14
In turn, as ,0/
ˆ
ljl did
W
we get :0/
ˆ!
TW
dd jl when the sanction increases, the
probability of default decreases for all banks that announced .l
 
0
1
1
1
11
1!
WT
W
¸
¸
¹
·
¨
¨
©
§
D
D
»
»
¼
º
«
«
¬
ª
TE
UD
W
W
UD
E
T
w
Ww
T
W
)
ˆ
(f
)
ˆ
(F)(
)
ˆ
(f
)
ˆ
(F
)(
d
di
i
ˆ
d
ˆ
d
Hl
Hl
j
HH
Hl
Hl
j
l
l
jljl
For instance, with a uniform p.d.f. where ]1,0[
W
, the condition )|()|( HlZHhZ
implies:
>@
»
»
¼
º
«
«
¬
ª
UD
EEUD
T
UD
EEUD
UD
EEUD
)(
k)(iR)R(
)(
k)(iR)R(
)(
k)(iR)R(
H
l
bb
H
H
l
bb
H
H
h
bb
H
1
1
1
1
1
1
1
^
`
k)(iR)R(ii l
bb
Hhl EEDTE 11
1
with hl
i
i
and 0Td/di l:
>@
^`
.k)(iR)R(
d
di l
bb
H
l
011
1EEDE
T
(17)
3.4. Solution and policy implications
We have obtained a system of three equations (Eq. (7), Eq. (10), Eq. (15)) and three
unknowns: h
i
,l
i
and ].l|HPr[ To solve the model, we remark that the no trade-of
condition when the bank announces h (Eq. 7) allows us to determine h
i
and the
indifference condition (Eq.15) allows us to determine l
i as a function of the various
exogenous variables and ih. Then, for a given l
i
and h
i
, the no trade-off condition
Eq. (10) determines the probability ].l|HPr[
Once that we obtain ],l|HPr[ we can determine ,P the frequency of liars. Indeed,
according to Bayes rule we know that:
.
q)q(
)q(
]LPr[]L|lPr[]HPr[]H|lPr[
]HPr[]H|lPr[
]l|H[Pr P
P
1
1 (18)
So:
.
])l|HPr[)(q(
]l|HPr[q
P 11 (19)
In the corner situations 1 P ( )0 P , the pooling (respectively separating) equilibrium
prevails; if [,] 10P , managers running high risk banks play a mixed strategy, the
hybrid equilibrium prevails.
In order to study the consequences of various policies we need an aggregate
objective for the government. One main policy objective of many governments during
the 2007-2009 financial turmoil was to prevent banks from massive default. Indeed,
several banks in the UK (Northern Rock), Germany (IKW,Hypo Real Estate), Belgium
Financial Distress and Banks' Communication Policy in Crisis Times
Romanian Journal of Economic Forecasting – 1/2010 15
(Dexia), or the United States (Citigroup) were actually saved from bankruptcy through
massive inflows of public money. It seems thus reasonable to consider that during this
crisis the frequency of defaulting banks is a good proxy for of the governments' payoff
function.
Our model allows to analyze how the overall frequency of defaults varies when
policymakers change either the sanction for liars (transparency)
T
or the cost of
borrowed resource k . Policies aiming at directly reducing the risk of home owner
default might also be analyzed as a leftward shift of the distribution )(f W.6
Let us denote by Vthe frequency of defaulting banks in the total population of banks
(since the number of bank has been normalized to one, the frequency and the number
of defaults is equivalent). The set of defaulting banks include defaults of
L
-banks and
defaults of
H
-banks, knowing that a proportion
P
of the latter have declared that
they are of the
L
-type. Formally, the expression of V is:
^
`
^`
)]
ˆ
(F)[()]
ˆ
(F[)q()]
ˆ
(F[q
]
ˆ
[Pr)(]
ˆ
[Pr)q(]
ˆ
[PrqV
HhHlLl
HhHlLl
WPWPW
W!WPW!WPW!W
11111
11 (20)
x Variations in k (the borrowing cost).
We can now study the impact on
V
of variations in k .
°
¿
°
¾
½
°
¯
°
®
W
WP
W
WPWW
P
W
W
°
¿
°
¾
½
°
¯
°
®
W
WPW
P
W
WPW
P
W
W
dk
ˆ
d
)
ˆ
(f)(
dk
ˆ
d
)
ˆ
(f)]
ˆ
(F)
ˆ
(F[
dk
d
)q(
dk
ˆ
d
)
ˆ
(qf
dk
ˆ
d
)
ˆ
(f)()]
ˆ
(F[
dk
d
dk
ˆ
d
)
ˆ
(f)]
ˆ
(F[
dk
d
)q(
dk
ˆ
d
)
ˆ
(qf
dk
dV
Hh
Hh
Hl
HlHlHh
Ll
Ll
Hh
HhHh
Hl
HlHl
Ll
Ll
11
1111 (21)
with .)
ˆ
(F)
ˆ
(F HlHh 0WW When the cost of borrowing from the central bank
increases, the interest rate l
i
increases too. We have therefore 0
W
dk
ˆ
dLl
and
0
W
dk
ˆ
dHl
, the risk of default increases for both banks. If ,
dk
d0!
P the outcome is
.
dk
dV 0!
x Variations in
T
(the sanction level).
If the sanction
T
goes up, more managers at the head of H-type banks honestly
state that their bank is ;h they are charged the large interest rate h
i and their
chances of default increase sharply. On the other hand, if there are less liars, the
value of the signal l improves, and the interest rate l
i goes down; managers who
announce l have better chances to survive (all the L banks and the remaining liars
H). Since the two effects tend to offset each others, the overall effect is ambiguous.
6 In December 2007 the Bush Administration worked out an emergency plan aiming to switch
subprime borrowers to more sustainable loans. Similar measures were adopted by the Obama
Administration in January 2009.
Institute of Economic Forecasting
Romanian Journal of Economic Forecasting – 1/2010
16
°
¿
°
¾
½
°
¯
°
®
T
W
WPWW
T
P
T
W
W
°
¿
°
¾
½
°
¯
°
®
W
T
P
T
W
WPW
T
P
T
W
W
T
d
ˆ
d
)
ˆ
(f)]
ˆ
(F)
ˆ
(F[
d
d
)q(
d
ˆ
d
)
ˆ
(qf
)]
ˆ
(F[
d
d
d
ˆ
d
)
ˆ
(f
)]
ˆ
(F[
d
d
)q(
d
ˆ
d
)
ˆ
(qf
d
dV
Hl
HlHlHh
Ll
Ll
Hh
Hl
HlHl
Ll
Ll
1
111
(22)
with ,)
ˆ
(F)
ˆ
(F HlHh 0WW 0!
T
W
d
ˆ
dLl
,0!
T
W
d
ˆ
dHh
and .
d
d0
T
P
From a policy point a view, the former result is interesting insofar as is shows that,
depending on the strength of the two effects, transparency can bring about more or
less defaults. More intuition about this result can be provided by means of a numerical
simulation.
4. The numerical simulation
The model can be solved numerically for a specific p.d.f. )(f W . We choose a uniform
distribution on the interval ,0[ ]./ 31 With this upper bound, no more than 1/3 of the
risky assets of a bank can default. The other parameters are: interest rates ,.R 020
,.Rb050 ,.k 040 150. G ; the proportion of central bank funding,
0501 .)( E ; the proportions of risky assets, ,.
H250 D 100.
L D ; and the
frequency of highly exposed banks 3/1 q. We allow the sanction to vary between
].,.[ 04600350 T with a step of 0010..7
We obtain 040850.i h . As expected, when the sanction increases, the low interest
rate l
i
and the frequency of liars P both decline. Recall that for 0 P the
separating equilibrium is reached, there are no more liars.
7The Maple program used to solve this problem can be provided on request.
Financial Distress and Banks' Communication Policy in Crisis Times
Romanian Journal of Economic Forecasting – 1/2010 17
Figure 1
The low interest rate il with respect to the sanction T
Figure 2
The frequency of liars q with respect to the sanction T
Institute of Economic Forecasting
Romanian Journal of Economic Forecasting – 1/2010
18
Figure 3 shows the impact of a rising sanction on the overall frequency of defaults. In
a first step, a higher sanction brings about a reduction in the frequency of defaults.
The positive effect that comes with an improvement in the value of the l signal and
the lower l
i
offsets the increasing frequency of banks which declare to be of the
H
type (and are thus subject to a higher probability of default). However, in our
simulation, there is a critical sanction ( ).450 T above which the latter negative
effect takes over the positive effect. If the policymaker pushes the sanction up to the
point where the frequency of liars becomes zero, the overall frequency of default is
larger than if some lies were tolerated.
Figure 3
Frequency of defaults V with respect to the sanction T
for k=0.04
Figure 4 shows the consequences on the former relationship from reducing the
interest rate of central bank funds ( k) by 1/4 percentage point, from 0.04 to 0.0375.
As expected, the overall frequency of defaults V declines for all
T
; the optimal
sanction is also lower for a lower k .
Financial Distress and Banks' Communication Policy in Crisis Times
Romanian Journal of Economic Forecasting – 1/2010 19
Figure 4
Impact of a lower k on the frequency of defaults
As long as the actual sanction for fraudulent disclosure is lower than the optimal
sanction, increasing the sanction T or reducing the repo rate k brings about similar
effects in terms of reducing the frequency of defaults. Yet, if policymakers are
uncertain whether the actual sanction is to the left or to the right of the critical level,
policymakers who want to take no risk should reduce the repo rate.
5. Conclusions
The 2007-2009 financial crisis that developed on the foundations of the US subprime
turmoil recalled with strength the role of trust and honesty in the good functioning of
financial markets. This paper has analyzed from a theoretical perspective the banks'
communication strategy during such a financial crisis. It emphasizes the impact of a
manager's communication policy on the financial distress of his bank and showed that
a dose of uncertainty can contribute, in some cases, to improve social welfare.
It has been shown that when investors have only imperfect information about the
banks' true exposure to risky assets, some fragile bank may claim that they are strong
only to manipulate investors’ expectations. As the latter do figure out this strategy,
they ask for a larger interest rate that penalizes the genuine solid banks. A policy of
increasing the sanction on dishonest managers may help reducing the frequency of
Institute of Economic Forecasting
Romanian Journal of Economic Forecasting – 1/2010
20
defaults up to a point. If the sanction is too strong and the frequency of liars too small,
losses from further tightening the sanction can offset the benefits, since more fragile
banks are pushed to unveil their true situation and are subject to a larger risk of
default.
A reduction in the repo interest rate at which the central bank provides funding to all
banks appears to be a more efficient policy, at least in the short run. In a long run
perspective other considerations, such as moral hazard or inflation risks should be
brought into the picture.
Our results should not be interpreted as a plea against additional transparency in
financial markets. The analysis pertains to managing information during a crisis. We
argued that in such difficult times, full transparency might not be needed. But in
normal times, transparency is what we need the most to avoid further crises.
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