Description
The author assembles three hypothetical regulatory regimes and deploys computer
simulations to contrast different banking systems based on conventional strategies for appointing
risk-based capital minimum thresholds. The paper aims to discuss these issues
Journal of Financial Economic Policy
The search for an optimal RBC regulatory system
Dror Parnes
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Dror Parnes , (2014),"The search for an optimal RBC regulatory system", J ournal of Financial Economic
Policy, Vol. 6 Iss 1 pp. 78 - 92
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The search for an optimal
RBC regulatory system
Dror Parnes
Finance Department, College of Business,
University of South Florida, Tampa, Florida, USA
Abstract
Purpose – The author assembles three hypothetical regulatory regimes and deploys computer
simulations to contrast different banking systems based on conventional strategies for appointing
risk-based capital minimum thresholds. The paper aims to discuss these issues.
Design/methodology/approach – The author instigates cascading failure models within
numerous directed graphs and measures the in?icted costs, the accumulated bank failures, and the
general robustness of the networks following various economic shocks.
Findings – The author ?nds that a homogeneous regulatory regime is an inferior approach.
However, a selected too-big-to-fail scheme portrays the best defensive banking model with the lowest
number of total bank failures and the fewest banks’ costs and social costs.
Research limitations/implications – The author can only theoretically examine this topic.
Originality/value – The author overcomes some obstacles in prior studies including the use of a
large and complex network and the proportional allocation of funds upon a bank failure.
Keywords Network, Bank failure, Risk-based capital, Directed graph, Contagion channel,
Regulatory system
Paper type Research paper
1. Introduction
One of the most noticeable responses to the recent ?nancial crisis is the ongoing
dialogue among regulators about the general necessity for banks and depository
institutions to hold more capital as a buffer that can absorb probable losses. To date,
policy makers are still split over the speci?c capital standards for these ?nancial ?rms.
International regulators mostly agree that key ?nancial institutions that pose a major
risk to the system should maintain thicker capital cushions than other banks. Yet,
supervisors are largely divided over just how much capital is really necessary in the
present circumstances. Some regulators have proposed a more consistent risk-based
capital (RBC) regulatory threshold across all institutions in the banking system, while
others have demanded less uniform increments in banks’ capital.
In this study, we present an analytical framework for these alternative attitudes
through computer simulations that examine some pertinent economic variables and
their direct impact on the failure rates, the various costs they in?ict, and the overall
stability of the banking industry. Our motivation to search for an optimal RBC
regulatory structure is meant to direct policy makers to form more stable banking
systems that pose lower systemic risk and simultaneously exhibit lower social costs.
To explore the alternative approaches for allocating an optimal RBC regulatory
threshold among banks and depository institutions, we analyze the potential contagion
The current issue and full text archive of this journal is available at
www.emeraldinsight.com/1757-6385.htm
JEL classi?cation – G01, G17, G21, G28
Journal of Financial Economic Policy
Vol. 6 No. 1, 2014
pp. 78-92
qEmerald Group Publishing Limited
1757-6385
DOI 10.1108/JFEP-05-2013-0021
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within three substitute architectures. The ?rst one considers a homogeneous
regulatory regime, which requires the same capital increments from all ?nancial
institutions within. The second model contemplates a selected too-big-to-fail (TBTF)
regime, which obligates only the larger and the most connected banks to uniformly
increase their capital ratios. The third model studies a heterogeneous regime, which
attaches to all banks different capital requirements based on their relative connectivity
and in?uence within the entire ?nancial system.
Since real data on the business links among US banks is unavailable to us, our study
remains a theoretical exercise[1]. The main results of our notional study reveal that while
the homogeneous regime is an inferior approach, the selected TBTF scheme exhibits
the most defensive banking system against a widespread contagion with the lowest
volume of accumulated bank failures. Moreover, the selected TBTF methodology
reaches the least overall costs and it is the most protective system against both
instantaneous and continuous economic shocks. Nevertheless, we ?nd that the exact
de?nition of “TBTF” is not critical, as long as it clearly distinguishes those larger and
more connected ?nancial institutions. Furthermore, when early withdrawal of funds is
expected, it is legitimate to command higher RBC requirements from TBTF institutions.
To prevent the next banking crisis, regulators must pre-classify and obligate higher
capital requirements from those highly in?uential banks.
As recently surveyed by Upper (2011) and Battiston et al. (2012), the literature has
discussed three key channels of contagion in the ?nancial system. The ?rst contagion
channel considers “bank runs,” which occur when a large volume of customers
simultaneously attempt to withdraw their deposits from a single ?nancial institution
due to a recent failure of a related bank and widespread rumors about further liquidity
complications. The dissemination of liquidity constraints among retail and central
banks are explored, among others, by Bryant (1980), Diamond and Dybvig (1983),
Jacklin and Bhattacharya (1988), Donaldson (1992), Temzelides (1997), Allen and Gale
(2000), Freixas et al. (2000), Diamond and Rajan (2005), Leitner (2005), Brusco and
Castiglionesi (2007) and Brunnermeier and Pedersen (2009).
The second contagion channel accounts for direct interbank business connections,
such as lending, payments, credit exposures, and various security, foreign exchange,
and derivative settlements. Within this path, the coupled claims among ?nancial
institutions further link their respective balance sheets. The toxicity of this channel is
examined by Angelini et al. (1996), Rochet and Tirole (1996) and Bech and Garratt
(2006). Other studies that concentrate on the risk of contagion through the federal
funds market include Fur?ne (1999, 2003) and Bech and Atalay (2008).
The third contagion channel refers to the indirect realm of reduced asset prices
triggered by prior bank failures. Thus, far, the literature has given somewhat less
attention to this knock-on conduit, perhaps because of its reduced abundance in
practice. Nevertheless, Fecht (2004), Cifuentes et al. (2005) and Shin (2008) provide some
insight into this notion. Gai and Kapadia (2010) further present a theoretical model that
contemplates both the second and the third contagion channels.
These prior studies largely accentuate the economic foundations for contagion in
?nancial systems, how systemic risk arises endogenously, the role of the lender of last
resort (in most nations the central bank) upon multiple bank failures, the propagation
of ?nancial crises among different regions, the optimal size and con?guration (i.e. the
level of concentration and the number of business ties across institutions) of the
Optimal RBC
regulatory
system
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banking industry, the degree to which the failure of one bank would cause subsequent
collapse of other banks (largely based on various centrality measurements), or
the limitations of various ?nancial safety nets (like institutional guarantees and
cooperative banks). In contrast, we do not examine these contagion channels per se, but
utilize them as driving forces that trigger a ?nancial crisis. We emphasize hereafter the
preferable architecture of a large and complex banking system within a resolution of
RBC regulatory minimum thresholds that is subject to these three contagion channels.
We are not the ?rst to deploy computer simulations when portraying a banking
network. Earlier studies including Nier et al. (2007) and Gai and Kapadia (2010) have
already encountered this approach. However, while these prior readings utilize
small-network limited analyses with merely few ?nancial institutions and short-run
simulations, we draw our inferences from a large-scale network having thousands of
banks and long-run iterations. It is not only that our endeavor allows us to better depict
the US banking sector, but we are also able to capture the real complexity of an
extended avalanche within. Furthermore, our models hereafter relax a few problematic
assumptions in some of these prior studies. For example, Nier et al. (2007) consider
identical probabilities to be connected to other banks within the entire network and Gai
and Kapadia (2010) assume that asset position of every bank is evenly distributed over
each of its incoming links[2]. Conversely, we realistically simulate various proportions
for these matters.
Our contribution therefore resides across multiple dimensions. We accentuate the
tolerance of different regimes based on their RBC regulatory thresholds within, we
simultaneously deploy all three contagion channels, we use a large-scale network with
extended cascading failure models, and we properly account for losses on interbank
assets as shared unequally across lenders.
The research proceeds as follows. In Section 2 we describe the building blocks of the
main simulations, their underlying assumptions, and the relevant parameters involved.
In Section 3 we explain the notional ?ndings along four main avenues: we examine the
results of the singular models, we contrast the outcomes across the three regulatory
regimes, and we further investigate the various trends and the end-compositions of
these synthetic banking systems. In Section 4 we deploy several robustness tests. In
Section 5 we conclude.
2. The simulations
To better design the speci?cations of the three alternative regulatory regimes, we must
clarify ?rst what usually happens before and after bank failures. Banks and other
depository institutions that are unable to service their outstanding debt or incapable of
sustaining the RBC adequacy minimum ratios are typically classi?ed as “failed banks.”
However, in most developed countries the bankruptcy codes do not allow insolvent
?nancial institutions to ?le for bankruptcy. Instead, domestic chartering authorities
order failed banks into receivership, while the Federal Deposit Insurance Corporation
(FDIC) is the appointed receiver in the USA.
Normally, US banks are not subject to actual closure by their chartering authority
until their leverage ratios fall below explicit thresholds. The FDIC routinely monitors
the capital adequacy of banks by examining a large set of risk factors. The FDIC
aggregates these risk components and computes for each inspected bank three
common capital ratios as follows:
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(1) Tier 1 capital adequacy ratio as Tier 1 capital divided by risk-adjusted assets;
(2) total capital ratio as Tiers 1 and 2 combined capitals divided by risk-adjusted
assets; and
(3) leverage ratio as Tier 1 capital divided by the average total consolidated assets.
Banks constantly report these capital ratios on the Call Report or the Thrift Financial
Report.
Following the principal architecture of the three Basel Capital Accords, the Board of
Governors of the Federal Reserve System dictates the RBC standards as the lower
thresholds for the RBC adequacy ratios. The minimum requirements can vary from
time to time, but the Tier 1 capital ratio normally ranges from 4 to 6 percent, the total
capital ratio usually varies from 8 to 10 percent, and the leverage ratio commonly
stretches from 4 to 5 percent[3]. Whenever a bank breaches these minimum required
RBC adequacy ratios, the FDIC assumes control over the bank’s receivership assets
and liabilities and acts as the insurer of all insured deposits for banks that are
chartered by the federal government, as well as for most state chartered banks.
A failed institution is typically closed on Friday evening, and reopens on the
following Monday either as a new branch of an acquiring institution or as a newly
chartered federal bank with the FDIC acting as a temporary conservator. The FDIC
makes attempt to distribute the failed bank’s capital and risky assets to other ?nancial
institutions that operate in the same geographical region or are relatively close to the
failed bank in terms of their operational segments or present customers, and to
institutions that already maintain business connections with the failed bank.
Habitually, the majority of the failing bank’s assets remain intact by reallocating
them to other institutions, while the FDIC’s ultimate goal is minimizing costs to its
deposit insurance funds. In light of several regulations, the failed bank’s shareholders
and creditors may also shoulder the losses, but the precise ratio of their “haircut” is
undetermined in advance and can vary from one bank failure to another. Thus, in our
computer simulations, we allow stockholders, debt-holders, and the FDIC to absorb
some of the losses associated with periodic bank failures.
To evaluate alternative approaches for allocating an optimal RBC regulatory
threshold among banks and ?nancial institutions alike, we construct and contrast three
types of computer-generated ?nancial systems:
(1) a homogeneous regime, which requires the same capital increments from all
?nancial institutions within;
(2) a selected TBTF regime, which obligates only the larger and the most
connected banks to enhance their capital; and
(3) a heterogeneous regime, which attaches to banks different capital requirements
based on their relative connectivity and proportional weight within the ?nancial
system.
In the models described hereafter we simulate these three hypothetical types of
banking systems to examine network robustness to cascading failures under realistic
cost-bene?t tradeoffs.
We ?rst form a network of n ¼ 2,000 banks, where we assign to each bank up to
12 potential acquirers upon future failure[4]. We randomly pick the number of potential
Optimal RBC
regulatory
system
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acquirers d
i
from a uniform discrete distribution over the closed interval ½1; 12? and
then randomly designate the respective acquirers from the same network of 2,000
banks. These likely acquiring banks represent different ?nancial institutions within the
network having pre-identi?able (by the FDIC) business or geographical connections
to the reference bank, thus are rationally chosen to be suitable candidates for partial
acquisition of the corresponding capital and risky assets upon future failure.
This network effectively establishes a directed graph with 2,000 vertices (banks)
and 12,901 directed edges (business or geographical links that also label potential
acquirers), while the average out-degree per vertex d
i
is about 6.45. Due to our random
selection process, all 2,000 banks have potential acquiring banks upon failure (with
out-degrees $ 1). We then assume that the out-degree of each vertex d
i
further implies
the bank’s relative size. In essence, we realistically consider that the number of
business connections to other ?nancial institutions is proportional to the total capacity
of one’s risky assets R
i
. Therefore, we assign the banks’ initial risky assets as their
particular out-degrees multiplied by $1 million, hence R
i;0
¼ d
i;0
£ $1M. Following this
line, we also presume that upon the failure of a bank, each acquiring institution
absorbs the respective proportion of capital C
f
and risky assets R
f
of the failed bank f
based on the ratio of its distinct out-degree divided by the sum of out-degrees of all
potential acquirers. More formally, we measure changes in banks’ capital C
i
and risky
assets R
i
as a result of multiple direct predecessors’ failures as:
DR
i
¼
f
X
d
i
P
j
d
j
£ R
f
and DC
i
¼
f
X
d
i
P
j
d
j
£ C
f
8
<
:
9
=
;
; ð1Þ
where i denotes a speci?c direct successor bank, j represents any direct successor
acquiring ?nancial institution of a speci?c direct predecessor bank, and f signi?es any
direct predecessor acquired failed bank in the previous time step.
This notion asserts that larger ?nancial institutions can absorb more capital and
risky assets from failed banks, and vice versa. Thus, we attach to all direct successors
(acquiring banks) pre-identi?able weights v
i;j
¼ ðd
i
=
P
j
d
j
Þ associated with their direct
predecessors (acquired failed banks), which represent the relative acquisition powers
of the acquiring ?nancial institutions for each failed bank[5]. These weights, however,
remain constant throughout the simulations to allow shareholders, creditors, and the
FDIC to absorb some of the costs upon bank failures.
Since requiring banks to retain safety cushions is costly, we consider routine
“banks’ costs” as the excess capital they customarily hold beyond the RBC regulatory
minimum threshold. These funds have no real use and may re?ect banks’ alternative
costs. In our main setting, we assume that these banks’ costs are uniformly distributed
over a pre-de?ned interval as long as the banks remain operational. Conversely, we
de?ne “other costs” as the reallocation of monetary funds (both assets and liabilities)
associated with the failure of banks whenever a direct successor has failed before a
direct predecessor. In this case, shareholders, debt-holders, and the FDIC must absorb
the missing successor’s applicable proportion of the predecessor failed bank’s capital
and risky assets. We have decided on this collective criterion for redistribution of
assets and liabilities of failed banks because to date, there is no universal rule for the
precise liability of failed banks’ stakeholders and creditors, as well as the degree of
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regulators’ interference. We further illustrate this matter in Figure 1. This
redistribution of assets and liabilities of failed banks represents in our simulations
the second contagion channel of direct interbank business links. Moreover, we de?ne
“social costs” as the sum of “banks’ costs” and “other costs.” This inclusive term
accumulates the total costs to all parties involved.
According to the recent Basel agreement, which requires ?nancial institutions to
gradually adjust their capital cushions to 7 percent by 2019, we denote the current RBC
regulatory minimum threshold l
*
to be 0.07. We allow each bank to have a random
Figure 1.
Illustration of “other costs”
with sequential bank
failures
Notes: This hypothetical scenario demonstrates what happens when banks fail, and how
shareholders, creditors, and the FDIC may absorb “other costs”; bank 1, which has an
out-degree of two and an in-degree of one, fails and distributes its capital and risky
assets between banks 3 and 4; as a result, bank 1 vanishes and all of its directed edges
disappear; in the next time step, bank 2 fails; consequently, it allocates 50 percent of its
remaining capital and risky assets to bank 6, which has an out-degree of 5 (out of total
out-degrees of 10 among all original direct successors of bank 2), and 30 percent of its
outstanding capital and risky assets to bank 5, which has an out-degree of 3, but the
lingering 20 percent that was supposed to be sent to bank 1 must now be divided
between bank 2’s stakeholders, debt-holders, and the FDIC as “other costs” of failure;
these agents absorb an uncontrolled proportion of the failed bank’s capital and risky
assets, depending on the sequence of failures; if both bank 1 and bank 5 fail before
bank 2, the agents would absorb 50 percent of bank 2’s remaining capital and risky
assets at this point; if both banks 1 and 6 fail before bank 2, these agents would absorb
70 percent of bank 2’s enduring capital and risky assets, etc.; this dynamic allocation of
liability assists in preventing an unstoppable avalanche of bank failures within the
different simulations and realistically holds shareholders and creditors accountable for
bank failures, while allowing the FDIC to further assist in this process of redistribution
of assets and liabilities
Optimal RBC
regulatory
system
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distance a
i
[ 0; 0:01
à from the minimum threshold[6]. We further designate b $ 0 as a
?xed coef?cient added to the minimum threshold, depending on the regulatory approach
undertaken. We therefore test various homogeneous approaches by assigning b ¼
{0; 0:005; 0:01; 0:02} to all ?nancial institutions within the network. Whenever we test
the diverse selected TBTF banking systems, we assign b ¼ {0:005; 0:01; 0:02} to all
pre-identi?ed TBTF institutions within the network. These classi?cations of “TBTF”
evolve from the respective size and magnitude of business connections, thus we
arbitrarily de?ne vertices as TBTF ¼ {10; 11; 12} of out-degrees.
When we test the different heterogeneous regimes, we assign b ¼ {0:005; 0:01; 0:02}
to all ?nancial institutions within the network, but then adjust this ?xed coef?cient
with respect to the ratio between the idiosyncratic out-degree of a node d
i
raised to
the power of a tunable parameter g [ 0; 1
à and the average modi?ed out-degree
d
g
def
¼ð1=NÞ
P
N
i¼1
d
g
i
among all vertices in the earliest network. The weight d
g
i
=d
g
À Á
fundamentally controls the level of heterogeneity for allocation of banks’ capital and
risky assets. The case of g ¼ 0 enforces the original homogeneous regulatory regime,
while g q0 represents an extremely diverse network with signi?cantly higher
regulatory standards among the most connected banks.
Next, we compute for each bank its ?rst tangible RBC ratio l
i
as the sum of ?xed and
stochastic coef?cients. More formally, the homogeneous regulatory regime allocates:
l
i;0
¼ l
*
þb þa
i;0
;il
*
¼ 0:07; b $ 0; a
i;0
, U 0; 0:01
à ; ð2Þ
the selected TBTF regulatory regime commands:
l
i;0
¼ l
*
þb þa
i;0
;i [ {TBTF}b . 0 and ;j – ib ¼ 0; ð3Þ
while the heterogeneous regulatory regime dictates:
l
i;0
¼ l
*
þ
bd
g
i;0
d
g
þa
i;0
;ib . 0; 0 , g # 1; d , U½1; 12? ð4Þ
and since the ad hoc RBC ratio is set as:
l
i
def
¼
Bank
0
s Capital
Bank
0
s Risk Adjusted Assets
def
¼
C
i
R
i
; ð5Þ
we can now derive the initial banks’ capitals as C
i;0
; l
i;0
R
i;0
.
In these settings, we de?ne a periodic “bank cost” as ðl
i;t
2l
*
Þ £ R
i;t
, for every
operational bank i at time t, but zero whenever a bank has already failed. We also classify
immediate “other costs” as the loss of relative ðR
i;t
2C
i;t
Þ not covered by existing
acquiring banks due to a prior failure of other successor institutions only in the ?rst time
unit after a new bank failure, and “social costs” as the sum of these two ingredients.
Throughout the main simulations we de?ne a bank failure as an instant event
that occurs whenever the ad hoc RBC ratio l
i
falls below the universal regulatory
requirement l
*
þ b. These failure incidents arise due to continuous redistribution of
assets and liabilities from failed banks to other pre-identi?ed ?nancial institutions
within the network. As a result, subsequent cascading failures may follow until the
landslide eventually decays. Whenever a bank fails, we delete its vertex and remove all
of its direct edges from the directed graph.
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To start the cascading processes of bank failures under the three alternative
regulatory regimes we instigate a strong economic shock as follows. We drive
20 randomly selected banks to fail by arti?cially reducing their initial capital C
i,0
below
the minimum required by law. For the same 20 banks within all of the simulations
we de?ne different initial shock factors S:F [ {2; 5; 10} as common dividers for the
respective starting capitals, i.e. when launching each simulation we impose
C
l;0
¼ ðl
l;0
R
l;0
=S:FÞ ;l [ {20 randomly selected banks}. These initial shock
factors represent the third contagion channel of indirect impact due to reduced asset
values among failed banks.
Throughout the simulations we also permit several levels of conservation of funds
among banks that are destined to fail. Occasionally, depositors sense that their banks
are doomed, thus they withdraw some of their accounts at the ?nal stages just before a
failure occurs. We simulate various conservation factors C:F [ {1; 0:95; 0:90}, which
determine how much of a failed bank’s capital is conserved during the ?nal failure
process. A conservation factor of 1 denotes that the failed bank is able to preserve
100 percent of its pre-failure capital. A conservation factor of 0.95 suggests that 5 percent
of the pre-failure capital is lost through early withdrawals, etc. These conservation
factors represent the ?rst contagion channel of bank runs. We deploy these conservation
factors among all failed banks, thus we expect these continuous economic shocks to
convey signi?cant impact on the cascading processes of bank failures.
We run the simulations over 12 consecutive quarters (since the vast majority of
cascading failures completely decay at or before this phase) and document the rate
of new bank failures, the total accumulated bank failures, the quarterly banks’ costs,
other costs, and social costs, as well as the aggregated amounts. We further quantify
the proportion of remaining network at each point in time as an intuitive proxy for
network robustness. More formally we de?ne:
9
t
def
¼
Number of Survived Banks
Total Number of Banks at Origin
def
¼
N
0
t
N
; ð6Þ
while the integrity of the network is maintained as long as 9
t
ø 1, and a major
?nancial crisis evolves whenever 9
t
!0 or at any other given point within the interval
[0,1] as de?ned by the regulators.
The homogeneous regulatory regime contains four values for the ?xed coef?cient
b [ {0; 0:005; 0:01; 0:02}, three magnitudes for the initial shock factor S:F [ {2; 5; 10},
and three quantities for the conservation factor C:F [ {1; 0:95; 0:90}, thus overall 36
simulated tests. The selected TBTF regime comprises three values for the ?xed
coef?cient b [ {0:005; 0:01; 0:02}, three degrees for the preliminary shock factor
S:F [ {2; 5; 10}, three measures for the conservation factor C:F [ {1; 0:05; 0:90}, and
three de?nitions of TBTF as TBTF ¼ {10; 11; 12} of out-degrees, thus a total of 81
experiments. The heterogeneous regime includes three values for the ?xed coef?cient
b [ {0:005; 0:01; 0:02}, three levels for the initial shock factor S:F [ {2; 5; 10}, three
appraisals for the conservation factor C:F [ {1; 0:05; 0:90}, and three degrees of
heterogeneity g [ ð0:1; 0:2; 0:3?, thus 81 additional analyses.
Altogether, these 198 trials allow us to explore how each parameter affects the
unique structure of the networks, as well as to compare the gradual developments and
the ultimate stability of the different banking systems. To further mitigate inevitable
Optimal RBC
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variability within the random simulations, we run each of the 198 tests ?ve times and
pick a representative path with a median number of accumulated bank failures.
We obtain 198 tables that provide us vital information on banks’ costs, other costs,
social costs, incremental and accumulated number of bank failures, as well as the
proportions of networkleft at eachquarter throughout the three years under investigation.
Due to the immense volume of simulated output, we discuss hereafter some selected
?ndings but thoroughly examine the results along four principal dimensions:
(1) intra-regime analyses of the ?nal outcomes;
(2) cross-regime analyses of the ultimate banking systems;
(3) trend analyses during the 12 examined quarters post-initial economic shocks;
and
(4) ?nal compositions of the hypothetical banking systems.
3. Findings
We now turn to summarize the key results of our simulations. We ?rst present the
intra-regime ?ndings, then the cross-regime results, next the trend discoveries, and
?nally the end-compositions of the theoretical banking systems.
3.1 Intra-homogeneous regime analyses
The ?ndings within the intra-homogeneous regime analyses provide strong evidence
for a positive correlation between the conservation factor and banks’ costs, since a
higher C.F suggests that more unused capital is preserved and transferred to surviving
banks. In contrast, we observe a robust negative association between the C.F and other
costs, social costs, and accumulated bank failures. These inverse relations exhibit
increasing marginal impacts. A level of 100 percent conservation factor continuously
retains a large proportion of the network unharmed. Conversely, a level of 90 percent
conservation of funds among failed banks is suf?cient for causing severe unfavorable
effects to this banking system, with exceptionally low proportions of network left[7].
Furthermore, we spot negative correlations between the initial S.F and banks’ costs,
mainly because with a higher shock factor there is less reallocated capital to begin with.
However, we detect positive relationships between these shock factors and other costs,
social costs, and total bank failures. Nevertheless, these associations are not as
signi?cant as with the conservation factors, since shock factors are merely initial
economic shocks but conservation factors are continuous tremors to the banking system.
We further notice that a higher b regularly corresponds with higher banks’ costs,
other costs, social costs, and accumulated bank failures. These ?ndings indicate that
when we homogeneously increase the RBC regulatory thresholds for all banks at once,
we effectively hurt all critical aspects within the banking industry. When we uniformly
increase the capital requirements, we achieve undesired results, since we in?ate the
safety cushions for banks, but at the same time we also tighten the regulatory
constraints, thus we trigger more bank failures and instigate greater overall costs.
3.2 Intra-selected TBTF regime analyses
The simulated results within the intra-selected TBTF regime analyses show that
both the C.F and the S.F reveal similar in?uences as in the homogeneous regime,
respectively. Moreover, the precise de?nition of TBTF is not that signi?cant in the
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overall banks’ costs, other costs, social costs, and accumulated bank failures. None of
these measures expose distinctive patterns when we alter the minimum level of
out-degrees that classify TBTF ?nancial institutions.
Yet, within the selected TBTF regulatory regime, the ?xed RBC increment b exhibits
a unique behavior that depends on the conservation factor. For C:F [ {1; 0:95}, b is
positively correlated with banks’ costs, other costs, social costs, and total bank failures.
However, for C:F ¼ 0:90, b is inversely related to other costs, social costs, and
accumulated bank failures. These unusual results suggest that with a higher expected
withdrawal of funds among failed banks, it is a valid argument to command higher RBC
requirements from TBTF institutions. These higher b increments could save substantial
other costs and social costs, although banks’ costs could rise. This consequence follows
the spirit of the present law, since the FDIC’s decisive objective is minimizing costs to its
deposit insurance funds thus reducing taxpayers’ exposure.
3.3 Intra-heterogeneous regime analyses
Within the intra-heterogeneous regime simulations, both the C.F and the S.F disclose
comparable consequences to those within the homogeneous and the selected TBTF
regimes, respectively. Moreover, similar to the homogeneous regime analyses, the ?xed
RBC coef?cient b is positively related to banks’ costs, social costs, and accumulated
bank failures. We cannot, however, detect an obvious association between the ?xed
RBC increment b and other costs.
Interestingly, the heterogeneity parameter g does not express a clear association
with banks’ costs and social costs. However, when the C.F is relatively high, i.e. when
the C.F ¼ 1, g is positively correlated with total bank failures, hence it is inversely
related to the proportion of network left. Yet, when the C.F decays, for example when
the C.F ¼ 0.90, g uncovers the opposite impacts on these two measures of network
robustness. We thus conclude that with few or no early withdrawals from failed banks,
it would be better to preserve a more homogeneous banking system. Nevertheless, with
higher foreseeable withdrawal of funds, hence lower conservation ratios among failed
banks, a more heterogeneous banking system is likely to be more sustainable.
3.4 Cross-regime analyses
Throughout the cross-regime examinations, the selected TBTF banking system
achieves the best results. The selected TBTF arrangement obtains the lowest banks’
costs and social costs in all 27 simulated comparisons. Furthermore, throughout 25 out
of the 27 appraisals the selected TBTF regime exhibits the minimum number of
accumulated bank failures and the highest proportions of network left. Surprisingly,
the heterogeneous regime portrays the lowest other costs throughout 14 of the
27 comparisons. The selected TBTF regime attains the minimum other costs only
within 11 of the 27 assessments. Nonetheless, this minor impediment cannot conceal
the vigorous improvements within the selected TBTF banking system.
3.5 Trend analyses
The trend analyses provide inside view at the pace at which banks’ costs, other costs,
social costs, and total bank failures progress during the 12 quarters under
investigation. These ?ndings illustrate a coherent view of which banks’ costs and
social costs grow at reasonably the same pace within the homogeneous and the
Optimal RBC
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heterogeneous regimes, but more slowly within the selected TBTF system. We observe
no clear pattern concerning the growth rates of other costs, yet accumulated bank
failures typically progress more slowly within the selected TBTF regime than within
the other two banking systems. Altogether, these discoveries corroborate the
dominance of the selected TBTF structure.
3.6 Composition analyses
We also plot the original network and the ?nal results into schematic directed graphs
in Figure 2. From 2,000 banks and 12,901 business links in the initial network, we
follow three different scenarios, depending on the speci?c approach examined. After 12
consecutive quarters from the initial economic shocks, the homogeneous regime has
741 bank failures, thus 1,259 vertices with 5,051 edges left. After these three years, the
heterogeneous banking system has 520 bank failures, thus 1,480 vertices and 7,783
edges left. Yet, the healthier selected TBTF regime contains 1,597 banks with 8,324
business links left.
We use Figure 2 to delve into the ?nal compositions of the three regulatory regimes
by examining the number of directed edges and the average out-degree per vertex in
each simulation. From 12,901 edges and an estimated average of 6.45 business links
per bank in the original network, after three years the homogeneous banking system
reaches 5,051 edges with an approximated mean of 4.03 links per bank, the selected
TBTF model attains 8,324 edges and an average of approximately 5.21 business
connections per bank, and the heterogeneous scheme exhibits 7,783 directed edges with
an average out-degree per vertex of about 5.26. While the homogeneous approach
eliminates the highest number of business links, the selected TBTF technique
preserves many more of these ?nancial relationships and in particular those business
links connecting the more dominant institutions. We thus con?rm that the selected
TBTF regulatory regime is the most protective model, not only to the entire banking
system, but also to the largest and the most viable ?nancial institutions within.
4. Robustness tests
The simulations presented thus far describe an ordinary pathway for bank failures.
However, we wish to explore other variants that may lead to alternative avalanches.
We ?rst relax some of the underlying assumptions or adjust them to other probable
scenarios. For example, we transform the criterion for a bank failure to become less
uniform. In particular, instead of de?ning a universal regulatory threshold for a bank
failure as l
i
, l
*
þ b, we consider the diverse bargaining power among ?nancial
institutions while resolving differences with the chartering authority. This negotiating
strength is likely to depend upon the individual bank’s relative size and systemic
in?uence. Therefore, we rede?ne the criterion for a bank failure as
l
i
, l
*
þb 2ðððd
i
21ÞbÞ=11Þ. In this case, since d
i
, U½1; 12?, smaller banks
(vertices) with out-degrees of one would maintain the same failure threshold as before,
but larger institutions with out-degrees of 12 would have a lower closure point reset
at l
i
, l
*
.
We also create various links between the bank’s capital and its distinct risk-taking
behavior[8]. In this setting we remove the random selection process for the
idiosyncratic distances to default a
i
, Uð0; 0:01? and impose a
i
to be a function of d
i
in equations (2)-(4), respectively. More speci?cally, we test several functions including
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a
i
¼ ðd
i
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i
¼ ð0:01=d
i
Þ, which generate monotonic increasing or decreasing
bonds between any bank’s size and its endogenous risk-tolerance. Through these
functions we map the feasible domain of d
i
[ ½1; 12? into an equitable interval
a
i
[ ð0; 0:01?.
In addition, we distinguish between low- and high-capital ?nancial institutions[9].
These additional tests de?ne {a
i
¼ 0:005 ;d
i
$ 7; a
i
¼ 0:01 ;d
i
# 6} as
well as the complement classi?cations. Nonetheless, the simulated results in all of
those robustness tests are not materially different from the ones in the main setting.
Figure 2.
The various networks as
directed graphs
Homogeneous Regime
• 1,259 banks (vertices)
• 5,051 business links (edges)
• b = 0.02; CF = 0.95; SF = 5
• Average out-degree per
vertex 4.03
After three
years…
Selected Too-Big-To-Fail Regime
• 1,597 banks (vertices)
• 8,324 business links (edges)
• b = 0.02; CF = 0.95; SF = 5;
TBTF ? 11
• Average out-degree per vertex 5.21
Initial network
• 2,000 banks (vertices)
• 12,901 business links (edges)
• Average out-degree per
vertex 6.45
Heterogeneous Regime
• 1,480 banks (vertices)
• 7,783 business links (edges)
• b = 0.02; CF = 0.95; SF = 5;
? = 0.2
• Average out-degree per
vertex 5.26
After three
years…
Optimal RBC
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Hence, we con?rm, once again, our main conclusions supporting the exclusive
advantages of the selected TBTF banking system over other network con?gurations.
5. Summary and conclusions
In this research we utilize computer simulations to test various approaches towards
building a more sustainable banking system. We deploy three different theoretical
regulatory regimes as directed graphs that represent:
(1) a homogeneous RBC regulatory threshold with ?xed capital increments to all
?nancial institutions within;
(2) a heterogeneous regime, which assigns diverse capital requirements to its
banks, depending on their relative size and amount of business connections to
other institutions in the system; and
(3) a selected TBTF regime that allocates higher capital constraints only to some
designated larger banks.
The results of our theoretical study repeatedly show that while the homogeneous regime
is an inferior approach, the selected TBTF scheme displays the most defensive banking
system with the lowest number of accumulated bank failures. The selected TBTF
methodology attains the lowest banks’ costs and social costs. Furthermore, the selected
TBTF strategy is the best protective policy against instantaneous catastrophic events,
in the form of sudden depleted capital at several institutions, or continuous anxiety
among depositors, which could lead to reduced conservation of funds across failed
banks, making it the superior ?nancial con?guration. Nevertheless, the exact de?nition
of “TBTF” is not crucial, as long as it differentiates some ?nancial institutions from the
smaller and the less connected banks.
We also ?nd that with a higher expected withdrawal of funds from failed banks,
regulators should mandate higher RBC requirements from TBTF institutions.
However, when no early depositors’ withdrawals are anticipated, the selected TBTF
policy recommends only minor capital increments, though differences among the paths
are virtually negligible. We therefore conclude that to prevent the next banking crisis,
regulators must pre-identify and demand higher capital requirements from the highly
in?uential banks, while the precise capital increments should be designed with respect
to the ad hoc predictions for the level of conservation of funds within the banking
system during a ?nancial calamity.
Additionally, we provide strong conjectural evidence to support the common practice
by the FDIC of closing failed banks on Friday evening, while taking all necessary
measures to prevent public hysterics that could cause higher early withdrawals from
failed institutions hence lower conservation of funds in the banking system and much
intensi?ed ?nancial crisis.
Notes
1. Fur?ne (2003) elaborates on the limitations of only incorporating federal funds transactions
among banks.
2. Upper (2011) criticizes these over-simpli?ed perceptions.
3. In our simulations we consider total common equity requirements as the chief inception for
bank failures.
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4. Bech and Atalay (2008) report that in 2006, 470 banks were participating, on average, each
day in the federal funds market with an average of 1,543 interbank relationships per day
hence a rough average of 3.28 trade links per bank per day.
5. These weights can also designate the respective probabilities of acquisition, as interpreted
by the FDIC, thus equation (1) effectively presents the expected changes in banks’ capital
and risky assets.
6. The individual distance from default a
i
is uniformly distributed over the semi-open interval
and is capped at 1 percent to represent a genuine situation where banks aim to minimize
their unused capital.
7. These ?ndings support the logic underlying the conduct that failed banks are typically
closed on Friday evening following undisclosed measures by regulators.
8. Calem and Rob (1999) model a dynamic portfolio choice problem and enforce a relationship
between a bank’s capital and its risk-taking conduct.
9. Beatty and Gron (2001) ?nd signi?cant differences between the impacts of regulatory
variables on these two groups.
References
Allen, F. and Gale, D. (2000), “Financial contagion”, The Journal of Political Economy, Vol. 108
No. 1, pp. 1-33.
Angelini, P., Mariesca, G. and Russo, D. (1996), “Systemic risk in the netting system”, Journal of
Banking and Finance, Vol. 20, pp. 853-868.
Battiston, S., Gatti, D.D., Gallegati, M., Greenwald, B. and Stiglitz, J.E. (2012), “Liaisons
dangereuses: increasing connectivity, risk sharing, and systemic risk”, Journal of
Economic Dynamics and Control, Vol. 36, pp. 1121-1141.
Beatty, A.L. and Gron, A. (2001), “Capital, portfolio, and growth: bank behavior under risk-based
capital guidelines”, Journal of Financial Services Research, Vol. 20 No. 1, pp. 5-31.
Bech, M.L. and Atalay, E. (2008), “The topology of the federal funds market”, Working Paper
Series No. 986, European Central Bank.
Bech, M.L. and Garratt, R. (2006), Illiquidity in the Interbank Payment System Following
Wide-Scale Disruptions, Staff Report No. 239, Federal Reserve Bank of New York.
Brunnermeier, M.K. and Pedersen, L.H. (2009), “Market liquidity and funding liquidity”, Review
of Financial Studies, Vol. 22 No. 6, pp. 2201-2238.
Brusco, S. and Castiglionesi, F. (2007), “Liquidity coinsurance, moral hazard, and ?nancial
contagion”, The Journal of Finance, Vol. 62 No. 5, pp. 2275-2302.
Bryant, J. (1980), “A model of reserves, bank runs, and deposit insurance”, Journal of Banking
and Finance, Vol. 4, pp. 335-344.
Calem, P. and Rob, R. (1999), “The impact of capital-based regulation on bank risk-taking”,
Journal of Financial Intermediation, Vol. 8, pp. 317-352.
Cifuentes, R., Ferrucci, G. and Shin, H.S. (2005), “Liquidity risk and contagion”, Journal of the
European Economic Association, Vol. 3 Nos 2/3, pp. 556-566.
Diamond, D.W. and Dybvig, P.H. (1983), “Bank runs, deposit insurance, and liquidity”, Journal of
Political Economy, Vol. 91, pp. 401-419.
Diamond, D.W. and Rajan, R.G. (2005), “Liquidity shortages and banking crises”, The Journal of
Finance, Vol. 60 No. 2, pp. 615-647.
Optimal RBC
regulatory
system
91
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1
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4
8
2
4
J
a
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u
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r
y
2
0
1
6
(
P
T
)
Donaldson, R.G. (1992), “Costly liquidation, interbank trade, bank runs and panics”, Journal of
Financial Intermediation, Vol. 2, pp. 59-82.
Fecht, F. (2004), “On the stability of different ?nancial systems”, Journal of the European
Economic Association, Vol. 2 No. 6, pp. 969-1014.
Freixas, X., Parigi, B.M. and Rochet, J.C. (2000), “Systemic risk, interbank relations, and liquidity
provision by the central bank”, Journal of Money, Credit and Banking, Vol. 32 No. 3,
pp. 611-638.
Fur?ne, C.H. (1999), “The microstructure of the federal funds market”, Financial Markets,
Institutions and Instruments, Vol. 8 No. 5, pp. 24-44.
Fur?ne, C.H. (2003), “Interbank exposures: quantifying the risk of contagion”, Journal of Money,
Credit and Banking, Vol. 35 No. 1, pp. 111-128.
Gai, P. and Kapadia, S. (2010), “Contagion in ?nancial networks”, Proceedings of the Royal Society
A, Vol. 466, pp. 2401-2423.
Jacklin, C.J. and Bhattacharya, S. (1988), “Distinguishing panics and information-based bank
runs: welfare and policy implications”, Journal of Political Economy, Vol. 96, pp. 568-592.
Leitner, Y. (2005), “Financial networks: contagion, commitment, and private sector bailouts”,
The Journal of Finance, Vol. 60 No. 6, pp. 2925-2953.
Nier, E., Yang, J., Yorulmazer, T. and Alentorn, A. (2007), “Network models and ?nancial
stability”, Journal of Economic Dynamics and Control, Vol. 31, pp. 2033-2060.
Rochet, J.C. and Tirole, J. (1996), “Interbank lending and systemic risk”, Journal of Money, Credit
and Banking, Vol. 28, pp. 733-762.
Shin, H.S. (2008), “Risk and liquidity in a system context”, Journal of Financial Intermediation,
Vol. 17, pp. 315-329.
Temzelides, T. (1997), “Evolution, coordination and bank panics”, Journal of Monetary
Economics, Vol. 40, pp. 163-183.
Upper, C. (2011), “Simulation methods to assess the danger of contagion in interbank markets”,
Journal of Financial Stability, Vol. 7, pp. 111-125.
About the author
Dror Parnes is an Assistant Professor of ?nance at the University of South Florida. His research
focus is theoretical models and empirical analyses of various credit risk, operational risk,
systemic risk, and bank failure risk issues. Parnes holds multiple publications in many refereed
journals including, among others, the Journal of Fixed Income, Journal of Credit Risk, Journal of
Operational Risk, Quantitative Finance, The Financial Review, Journal of Behavioral Finance,
Managerial Finance, Applied Financial Economics, and The Banking and Finance Review. Parnes
has also presented his working papers at numerous academic conferences and has been
acknowledged for assisting authors writing several textbooks. Parnes completed his PhD studies
at Baruch College, the senior business college of the City University of New York. He also holds a
Master’s degree in ?nance from Baruch College, and a BSc in statistics, operations research, and
computer science from Tel Aviv University, Israel. Parnes’ professional experience includes
work as a Software Engineer, Research Analyst, and Portfolio Manager. Dror Parnes can be
contacted at: [email protected]
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doc_397757128.pdf
The author assembles three hypothetical regulatory regimes and deploys computer
simulations to contrast different banking systems based on conventional strategies for appointing
risk-based capital minimum thresholds. The paper aims to discuss these issues
Journal of Financial Economic Policy
The search for an optimal RBC regulatory system
Dror Parnes
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To cite this document:
Dror Parnes , (2014),"The search for an optimal RBC regulatory system", J ournal of Financial Economic
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The search for an optimal
RBC regulatory system
Dror Parnes
Finance Department, College of Business,
University of South Florida, Tampa, Florida, USA
Abstract
Purpose – The author assembles three hypothetical regulatory regimes and deploys computer
simulations to contrast different banking systems based on conventional strategies for appointing
risk-based capital minimum thresholds. The paper aims to discuss these issues.
Design/methodology/approach – The author instigates cascading failure models within
numerous directed graphs and measures the in?icted costs, the accumulated bank failures, and the
general robustness of the networks following various economic shocks.
Findings – The author ?nds that a homogeneous regulatory regime is an inferior approach.
However, a selected too-big-to-fail scheme portrays the best defensive banking model with the lowest
number of total bank failures and the fewest banks’ costs and social costs.
Research limitations/implications – The author can only theoretically examine this topic.
Originality/value – The author overcomes some obstacles in prior studies including the use of a
large and complex network and the proportional allocation of funds upon a bank failure.
Keywords Network, Bank failure, Risk-based capital, Directed graph, Contagion channel,
Regulatory system
Paper type Research paper
1. Introduction
One of the most noticeable responses to the recent ?nancial crisis is the ongoing
dialogue among regulators about the general necessity for banks and depository
institutions to hold more capital as a buffer that can absorb probable losses. To date,
policy makers are still split over the speci?c capital standards for these ?nancial ?rms.
International regulators mostly agree that key ?nancial institutions that pose a major
risk to the system should maintain thicker capital cushions than other banks. Yet,
supervisors are largely divided over just how much capital is really necessary in the
present circumstances. Some regulators have proposed a more consistent risk-based
capital (RBC) regulatory threshold across all institutions in the banking system, while
others have demanded less uniform increments in banks’ capital.
In this study, we present an analytical framework for these alternative attitudes
through computer simulations that examine some pertinent economic variables and
their direct impact on the failure rates, the various costs they in?ict, and the overall
stability of the banking industry. Our motivation to search for an optimal RBC
regulatory structure is meant to direct policy makers to form more stable banking
systems that pose lower systemic risk and simultaneously exhibit lower social costs.
To explore the alternative approaches for allocating an optimal RBC regulatory
threshold among banks and depository institutions, we analyze the potential contagion
The current issue and full text archive of this journal is available at
www.emeraldinsight.com/1757-6385.htm
JEL classi?cation – G01, G17, G21, G28
Journal of Financial Economic Policy
Vol. 6 No. 1, 2014
pp. 78-92
qEmerald Group Publishing Limited
1757-6385
DOI 10.1108/JFEP-05-2013-0021
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within three substitute architectures. The ?rst one considers a homogeneous
regulatory regime, which requires the same capital increments from all ?nancial
institutions within. The second model contemplates a selected too-big-to-fail (TBTF)
regime, which obligates only the larger and the most connected banks to uniformly
increase their capital ratios. The third model studies a heterogeneous regime, which
attaches to all banks different capital requirements based on their relative connectivity
and in?uence within the entire ?nancial system.
Since real data on the business links among US banks is unavailable to us, our study
remains a theoretical exercise[1]. The main results of our notional study reveal that while
the homogeneous regime is an inferior approach, the selected TBTF scheme exhibits
the most defensive banking system against a widespread contagion with the lowest
volume of accumulated bank failures. Moreover, the selected TBTF methodology
reaches the least overall costs and it is the most protective system against both
instantaneous and continuous economic shocks. Nevertheless, we ?nd that the exact
de?nition of “TBTF” is not critical, as long as it clearly distinguishes those larger and
more connected ?nancial institutions. Furthermore, when early withdrawal of funds is
expected, it is legitimate to command higher RBC requirements from TBTF institutions.
To prevent the next banking crisis, regulators must pre-classify and obligate higher
capital requirements from those highly in?uential banks.
As recently surveyed by Upper (2011) and Battiston et al. (2012), the literature has
discussed three key channels of contagion in the ?nancial system. The ?rst contagion
channel considers “bank runs,” which occur when a large volume of customers
simultaneously attempt to withdraw their deposits from a single ?nancial institution
due to a recent failure of a related bank and widespread rumors about further liquidity
complications. The dissemination of liquidity constraints among retail and central
banks are explored, among others, by Bryant (1980), Diamond and Dybvig (1983),
Jacklin and Bhattacharya (1988), Donaldson (1992), Temzelides (1997), Allen and Gale
(2000), Freixas et al. (2000), Diamond and Rajan (2005), Leitner (2005), Brusco and
Castiglionesi (2007) and Brunnermeier and Pedersen (2009).
The second contagion channel accounts for direct interbank business connections,
such as lending, payments, credit exposures, and various security, foreign exchange,
and derivative settlements. Within this path, the coupled claims among ?nancial
institutions further link their respective balance sheets. The toxicity of this channel is
examined by Angelini et al. (1996), Rochet and Tirole (1996) and Bech and Garratt
(2006). Other studies that concentrate on the risk of contagion through the federal
funds market include Fur?ne (1999, 2003) and Bech and Atalay (2008).
The third contagion channel refers to the indirect realm of reduced asset prices
triggered by prior bank failures. Thus, far, the literature has given somewhat less
attention to this knock-on conduit, perhaps because of its reduced abundance in
practice. Nevertheless, Fecht (2004), Cifuentes et al. (2005) and Shin (2008) provide some
insight into this notion. Gai and Kapadia (2010) further present a theoretical model that
contemplates both the second and the third contagion channels.
These prior studies largely accentuate the economic foundations for contagion in
?nancial systems, how systemic risk arises endogenously, the role of the lender of last
resort (in most nations the central bank) upon multiple bank failures, the propagation
of ?nancial crises among different regions, the optimal size and con?guration (i.e. the
level of concentration and the number of business ties across institutions) of the
Optimal RBC
regulatory
system
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banking industry, the degree to which the failure of one bank would cause subsequent
collapse of other banks (largely based on various centrality measurements), or
the limitations of various ?nancial safety nets (like institutional guarantees and
cooperative banks). In contrast, we do not examine these contagion channels per se, but
utilize them as driving forces that trigger a ?nancial crisis. We emphasize hereafter the
preferable architecture of a large and complex banking system within a resolution of
RBC regulatory minimum thresholds that is subject to these three contagion channels.
We are not the ?rst to deploy computer simulations when portraying a banking
network. Earlier studies including Nier et al. (2007) and Gai and Kapadia (2010) have
already encountered this approach. However, while these prior readings utilize
small-network limited analyses with merely few ?nancial institutions and short-run
simulations, we draw our inferences from a large-scale network having thousands of
banks and long-run iterations. It is not only that our endeavor allows us to better depict
the US banking sector, but we are also able to capture the real complexity of an
extended avalanche within. Furthermore, our models hereafter relax a few problematic
assumptions in some of these prior studies. For example, Nier et al. (2007) consider
identical probabilities to be connected to other banks within the entire network and Gai
and Kapadia (2010) assume that asset position of every bank is evenly distributed over
each of its incoming links[2]. Conversely, we realistically simulate various proportions
for these matters.
Our contribution therefore resides across multiple dimensions. We accentuate the
tolerance of different regimes based on their RBC regulatory thresholds within, we
simultaneously deploy all three contagion channels, we use a large-scale network with
extended cascading failure models, and we properly account for losses on interbank
assets as shared unequally across lenders.
The research proceeds as follows. In Section 2 we describe the building blocks of the
main simulations, their underlying assumptions, and the relevant parameters involved.
In Section 3 we explain the notional ?ndings along four main avenues: we examine the
results of the singular models, we contrast the outcomes across the three regulatory
regimes, and we further investigate the various trends and the end-compositions of
these synthetic banking systems. In Section 4 we deploy several robustness tests. In
Section 5 we conclude.
2. The simulations
To better design the speci?cations of the three alternative regulatory regimes, we must
clarify ?rst what usually happens before and after bank failures. Banks and other
depository institutions that are unable to service their outstanding debt or incapable of
sustaining the RBC adequacy minimum ratios are typically classi?ed as “failed banks.”
However, in most developed countries the bankruptcy codes do not allow insolvent
?nancial institutions to ?le for bankruptcy. Instead, domestic chartering authorities
order failed banks into receivership, while the Federal Deposit Insurance Corporation
(FDIC) is the appointed receiver in the USA.
Normally, US banks are not subject to actual closure by their chartering authority
until their leverage ratios fall below explicit thresholds. The FDIC routinely monitors
the capital adequacy of banks by examining a large set of risk factors. The FDIC
aggregates these risk components and computes for each inspected bank three
common capital ratios as follows:
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(1) Tier 1 capital adequacy ratio as Tier 1 capital divided by risk-adjusted assets;
(2) total capital ratio as Tiers 1 and 2 combined capitals divided by risk-adjusted
assets; and
(3) leverage ratio as Tier 1 capital divided by the average total consolidated assets.
Banks constantly report these capital ratios on the Call Report or the Thrift Financial
Report.
Following the principal architecture of the three Basel Capital Accords, the Board of
Governors of the Federal Reserve System dictates the RBC standards as the lower
thresholds for the RBC adequacy ratios. The minimum requirements can vary from
time to time, but the Tier 1 capital ratio normally ranges from 4 to 6 percent, the total
capital ratio usually varies from 8 to 10 percent, and the leverage ratio commonly
stretches from 4 to 5 percent[3]. Whenever a bank breaches these minimum required
RBC adequacy ratios, the FDIC assumes control over the bank’s receivership assets
and liabilities and acts as the insurer of all insured deposits for banks that are
chartered by the federal government, as well as for most state chartered banks.
A failed institution is typically closed on Friday evening, and reopens on the
following Monday either as a new branch of an acquiring institution or as a newly
chartered federal bank with the FDIC acting as a temporary conservator. The FDIC
makes attempt to distribute the failed bank’s capital and risky assets to other ?nancial
institutions that operate in the same geographical region or are relatively close to the
failed bank in terms of their operational segments or present customers, and to
institutions that already maintain business connections with the failed bank.
Habitually, the majority of the failing bank’s assets remain intact by reallocating
them to other institutions, while the FDIC’s ultimate goal is minimizing costs to its
deposit insurance funds. In light of several regulations, the failed bank’s shareholders
and creditors may also shoulder the losses, but the precise ratio of their “haircut” is
undetermined in advance and can vary from one bank failure to another. Thus, in our
computer simulations, we allow stockholders, debt-holders, and the FDIC to absorb
some of the losses associated with periodic bank failures.
To evaluate alternative approaches for allocating an optimal RBC regulatory
threshold among banks and ?nancial institutions alike, we construct and contrast three
types of computer-generated ?nancial systems:
(1) a homogeneous regime, which requires the same capital increments from all
?nancial institutions within;
(2) a selected TBTF regime, which obligates only the larger and the most
connected banks to enhance their capital; and
(3) a heterogeneous regime, which attaches to banks different capital requirements
based on their relative connectivity and proportional weight within the ?nancial
system.
In the models described hereafter we simulate these three hypothetical types of
banking systems to examine network robustness to cascading failures under realistic
cost-bene?t tradeoffs.
We ?rst form a network of n ¼ 2,000 banks, where we assign to each bank up to
12 potential acquirers upon future failure[4]. We randomly pick the number of potential
Optimal RBC
regulatory
system
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acquirers d
i
from a uniform discrete distribution over the closed interval ½1; 12? and
then randomly designate the respective acquirers from the same network of 2,000
banks. These likely acquiring banks represent different ?nancial institutions within the
network having pre-identi?able (by the FDIC) business or geographical connections
to the reference bank, thus are rationally chosen to be suitable candidates for partial
acquisition of the corresponding capital and risky assets upon future failure.
This network effectively establishes a directed graph with 2,000 vertices (banks)
and 12,901 directed edges (business or geographical links that also label potential
acquirers), while the average out-degree per vertex d
i
is about 6.45. Due to our random
selection process, all 2,000 banks have potential acquiring banks upon failure (with
out-degrees $ 1). We then assume that the out-degree of each vertex d
i
further implies
the bank’s relative size. In essence, we realistically consider that the number of
business connections to other ?nancial institutions is proportional to the total capacity
of one’s risky assets R
i
. Therefore, we assign the banks’ initial risky assets as their
particular out-degrees multiplied by $1 million, hence R
i;0
¼ d
i;0
£ $1M. Following this
line, we also presume that upon the failure of a bank, each acquiring institution
absorbs the respective proportion of capital C
f
and risky assets R
f
of the failed bank f
based on the ratio of its distinct out-degree divided by the sum of out-degrees of all
potential acquirers. More formally, we measure changes in banks’ capital C
i
and risky
assets R
i
as a result of multiple direct predecessors’ failures as:
DR
i
¼
f
X
d
i
P
j
d
j
£ R
f
and DC
i
¼
f
X
d
i
P
j
d
j
£ C
f
8
<
:
9
=
;
; ð1Þ
where i denotes a speci?c direct successor bank, j represents any direct successor
acquiring ?nancial institution of a speci?c direct predecessor bank, and f signi?es any
direct predecessor acquired failed bank in the previous time step.
This notion asserts that larger ?nancial institutions can absorb more capital and
risky assets from failed banks, and vice versa. Thus, we attach to all direct successors
(acquiring banks) pre-identi?able weights v
i;j
¼ ðd
i
=
P
j
d
j
Þ associated with their direct
predecessors (acquired failed banks), which represent the relative acquisition powers
of the acquiring ?nancial institutions for each failed bank[5]. These weights, however,
remain constant throughout the simulations to allow shareholders, creditors, and the
FDIC to absorb some of the costs upon bank failures.
Since requiring banks to retain safety cushions is costly, we consider routine
“banks’ costs” as the excess capital they customarily hold beyond the RBC regulatory
minimum threshold. These funds have no real use and may re?ect banks’ alternative
costs. In our main setting, we assume that these banks’ costs are uniformly distributed
over a pre-de?ned interval as long as the banks remain operational. Conversely, we
de?ne “other costs” as the reallocation of monetary funds (both assets and liabilities)
associated with the failure of banks whenever a direct successor has failed before a
direct predecessor. In this case, shareholders, debt-holders, and the FDIC must absorb
the missing successor’s applicable proportion of the predecessor failed bank’s capital
and risky assets. We have decided on this collective criterion for redistribution of
assets and liabilities of failed banks because to date, there is no universal rule for the
precise liability of failed banks’ stakeholders and creditors, as well as the degree of
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regulators’ interference. We further illustrate this matter in Figure 1. This
redistribution of assets and liabilities of failed banks represents in our simulations
the second contagion channel of direct interbank business links. Moreover, we de?ne
“social costs” as the sum of “banks’ costs” and “other costs.” This inclusive term
accumulates the total costs to all parties involved.
According to the recent Basel agreement, which requires ?nancial institutions to
gradually adjust their capital cushions to 7 percent by 2019, we denote the current RBC
regulatory minimum threshold l
*
to be 0.07. We allow each bank to have a random
Figure 1.
Illustration of “other costs”
with sequential bank
failures
Notes: This hypothetical scenario demonstrates what happens when banks fail, and how
shareholders, creditors, and the FDIC may absorb “other costs”; bank 1, which has an
out-degree of two and an in-degree of one, fails and distributes its capital and risky
assets between banks 3 and 4; as a result, bank 1 vanishes and all of its directed edges
disappear; in the next time step, bank 2 fails; consequently, it allocates 50 percent of its
remaining capital and risky assets to bank 6, which has an out-degree of 5 (out of total
out-degrees of 10 among all original direct successors of bank 2), and 30 percent of its
outstanding capital and risky assets to bank 5, which has an out-degree of 3, but the
lingering 20 percent that was supposed to be sent to bank 1 must now be divided
between bank 2’s stakeholders, debt-holders, and the FDIC as “other costs” of failure;
these agents absorb an uncontrolled proportion of the failed bank’s capital and risky
assets, depending on the sequence of failures; if both bank 1 and bank 5 fail before
bank 2, the agents would absorb 50 percent of bank 2’s remaining capital and risky
assets at this point; if both banks 1 and 6 fail before bank 2, these agents would absorb
70 percent of bank 2’s enduring capital and risky assets, etc.; this dynamic allocation of
liability assists in preventing an unstoppable avalanche of bank failures within the
different simulations and realistically holds shareholders and creditors accountable for
bank failures, while allowing the FDIC to further assist in this process of redistribution
of assets and liabilities
Optimal RBC
regulatory
system
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distance a
i
[ 0; 0:01
à from the minimum threshold[6]. We further designate b $ 0 as a
?xed coef?cient added to the minimum threshold, depending on the regulatory approach
undertaken. We therefore test various homogeneous approaches by assigning b ¼
{0; 0:005; 0:01; 0:02} to all ?nancial institutions within the network. Whenever we test
the diverse selected TBTF banking systems, we assign b ¼ {0:005; 0:01; 0:02} to all
pre-identi?ed TBTF institutions within the network. These classi?cations of “TBTF”
evolve from the respective size and magnitude of business connections, thus we
arbitrarily de?ne vertices as TBTF ¼ {10; 11; 12} of out-degrees.
When we test the different heterogeneous regimes, we assign b ¼ {0:005; 0:01; 0:02}
to all ?nancial institutions within the network, but then adjust this ?xed coef?cient
with respect to the ratio between the idiosyncratic out-degree of a node d
i
raised to
the power of a tunable parameter g [ 0; 1
à and the average modi?ed out-degree
d
g
def
¼ð1=NÞ
P
N
i¼1
d
g
i
among all vertices in the earliest network. The weight d
g
i
=d
g
À Á
fundamentally controls the level of heterogeneity for allocation of banks’ capital and
risky assets. The case of g ¼ 0 enforces the original homogeneous regulatory regime,
while g q0 represents an extremely diverse network with signi?cantly higher
regulatory standards among the most connected banks.
Next, we compute for each bank its ?rst tangible RBC ratio l
i
as the sum of ?xed and
stochastic coef?cients. More formally, the homogeneous regulatory regime allocates:
l
i;0
¼ l
*
þb þa
i;0
;il
*
¼ 0:07; b $ 0; a
i;0
, U 0; 0:01
à ; ð2Þ
the selected TBTF regulatory regime commands:
l
i;0
¼ l
*
þb þa
i;0
;i [ {TBTF}b . 0 and ;j – ib ¼ 0; ð3Þ
while the heterogeneous regulatory regime dictates:
l
i;0
¼ l
*
þ
bd
g
i;0
d
g
þa
i;0
;ib . 0; 0 , g # 1; d , U½1; 12? ð4Þ
and since the ad hoc RBC ratio is set as:
l
i
def
¼
Bank
0
s Capital
Bank
0
s Risk Adjusted Assets
def
¼
C
i
R
i
; ð5Þ
we can now derive the initial banks’ capitals as C
i;0
; l
i;0
R
i;0
.
In these settings, we de?ne a periodic “bank cost” as ðl
i;t
2l
*
Þ £ R
i;t
, for every
operational bank i at time t, but zero whenever a bank has already failed. We also classify
immediate “other costs” as the loss of relative ðR
i;t
2C
i;t
Þ not covered by existing
acquiring banks due to a prior failure of other successor institutions only in the ?rst time
unit after a new bank failure, and “social costs” as the sum of these two ingredients.
Throughout the main simulations we de?ne a bank failure as an instant event
that occurs whenever the ad hoc RBC ratio l
i
falls below the universal regulatory
requirement l
*
þ b. These failure incidents arise due to continuous redistribution of
assets and liabilities from failed banks to other pre-identi?ed ?nancial institutions
within the network. As a result, subsequent cascading failures may follow until the
landslide eventually decays. Whenever a bank fails, we delete its vertex and remove all
of its direct edges from the directed graph.
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To start the cascading processes of bank failures under the three alternative
regulatory regimes we instigate a strong economic shock as follows. We drive
20 randomly selected banks to fail by arti?cially reducing their initial capital C
i,0
below
the minimum required by law. For the same 20 banks within all of the simulations
we de?ne different initial shock factors S:F [ {2; 5; 10} as common dividers for the
respective starting capitals, i.e. when launching each simulation we impose
C
l;0
¼ ðl
l;0
R
l;0
=S:FÞ ;l [ {20 randomly selected banks}. These initial shock
factors represent the third contagion channel of indirect impact due to reduced asset
values among failed banks.
Throughout the simulations we also permit several levels of conservation of funds
among banks that are destined to fail. Occasionally, depositors sense that their banks
are doomed, thus they withdraw some of their accounts at the ?nal stages just before a
failure occurs. We simulate various conservation factors C:F [ {1; 0:95; 0:90}, which
determine how much of a failed bank’s capital is conserved during the ?nal failure
process. A conservation factor of 1 denotes that the failed bank is able to preserve
100 percent of its pre-failure capital. A conservation factor of 0.95 suggests that 5 percent
of the pre-failure capital is lost through early withdrawals, etc. These conservation
factors represent the ?rst contagion channel of bank runs. We deploy these conservation
factors among all failed banks, thus we expect these continuous economic shocks to
convey signi?cant impact on the cascading processes of bank failures.
We run the simulations over 12 consecutive quarters (since the vast majority of
cascading failures completely decay at or before this phase) and document the rate
of new bank failures, the total accumulated bank failures, the quarterly banks’ costs,
other costs, and social costs, as well as the aggregated amounts. We further quantify
the proportion of remaining network at each point in time as an intuitive proxy for
network robustness. More formally we de?ne:
9
t
def
¼
Number of Survived Banks
Total Number of Banks at Origin
def
¼
N
0
t
N
; ð6Þ
while the integrity of the network is maintained as long as 9
t
ø 1, and a major
?nancial crisis evolves whenever 9
t
!0 or at any other given point within the interval
[0,1] as de?ned by the regulators.
The homogeneous regulatory regime contains four values for the ?xed coef?cient
b [ {0; 0:005; 0:01; 0:02}, three magnitudes for the initial shock factor S:F [ {2; 5; 10},
and three quantities for the conservation factor C:F [ {1; 0:95; 0:90}, thus overall 36
simulated tests. The selected TBTF regime comprises three values for the ?xed
coef?cient b [ {0:005; 0:01; 0:02}, three degrees for the preliminary shock factor
S:F [ {2; 5; 10}, three measures for the conservation factor C:F [ {1; 0:05; 0:90}, and
three de?nitions of TBTF as TBTF ¼ {10; 11; 12} of out-degrees, thus a total of 81
experiments. The heterogeneous regime includes three values for the ?xed coef?cient
b [ {0:005; 0:01; 0:02}, three levels for the initial shock factor S:F [ {2; 5; 10}, three
appraisals for the conservation factor C:F [ {1; 0:05; 0:90}, and three degrees of
heterogeneity g [ ð0:1; 0:2; 0:3?, thus 81 additional analyses.
Altogether, these 198 trials allow us to explore how each parameter affects the
unique structure of the networks, as well as to compare the gradual developments and
the ultimate stability of the different banking systems. To further mitigate inevitable
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variability within the random simulations, we run each of the 198 tests ?ve times and
pick a representative path with a median number of accumulated bank failures.
We obtain 198 tables that provide us vital information on banks’ costs, other costs,
social costs, incremental and accumulated number of bank failures, as well as the
proportions of networkleft at eachquarter throughout the three years under investigation.
Due to the immense volume of simulated output, we discuss hereafter some selected
?ndings but thoroughly examine the results along four principal dimensions:
(1) intra-regime analyses of the ?nal outcomes;
(2) cross-regime analyses of the ultimate banking systems;
(3) trend analyses during the 12 examined quarters post-initial economic shocks;
and
(4) ?nal compositions of the hypothetical banking systems.
3. Findings
We now turn to summarize the key results of our simulations. We ?rst present the
intra-regime ?ndings, then the cross-regime results, next the trend discoveries, and
?nally the end-compositions of the theoretical banking systems.
3.1 Intra-homogeneous regime analyses
The ?ndings within the intra-homogeneous regime analyses provide strong evidence
for a positive correlation between the conservation factor and banks’ costs, since a
higher C.F suggests that more unused capital is preserved and transferred to surviving
banks. In contrast, we observe a robust negative association between the C.F and other
costs, social costs, and accumulated bank failures. These inverse relations exhibit
increasing marginal impacts. A level of 100 percent conservation factor continuously
retains a large proportion of the network unharmed. Conversely, a level of 90 percent
conservation of funds among failed banks is suf?cient for causing severe unfavorable
effects to this banking system, with exceptionally low proportions of network left[7].
Furthermore, we spot negative correlations between the initial S.F and banks’ costs,
mainly because with a higher shock factor there is less reallocated capital to begin with.
However, we detect positive relationships between these shock factors and other costs,
social costs, and total bank failures. Nevertheless, these associations are not as
signi?cant as with the conservation factors, since shock factors are merely initial
economic shocks but conservation factors are continuous tremors to the banking system.
We further notice that a higher b regularly corresponds with higher banks’ costs,
other costs, social costs, and accumulated bank failures. These ?ndings indicate that
when we homogeneously increase the RBC regulatory thresholds for all banks at once,
we effectively hurt all critical aspects within the banking industry. When we uniformly
increase the capital requirements, we achieve undesired results, since we in?ate the
safety cushions for banks, but at the same time we also tighten the regulatory
constraints, thus we trigger more bank failures and instigate greater overall costs.
3.2 Intra-selected TBTF regime analyses
The simulated results within the intra-selected TBTF regime analyses show that
both the C.F and the S.F reveal similar in?uences as in the homogeneous regime,
respectively. Moreover, the precise de?nition of TBTF is not that signi?cant in the
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overall banks’ costs, other costs, social costs, and accumulated bank failures. None of
these measures expose distinctive patterns when we alter the minimum level of
out-degrees that classify TBTF ?nancial institutions.
Yet, within the selected TBTF regulatory regime, the ?xed RBC increment b exhibits
a unique behavior that depends on the conservation factor. For C:F [ {1; 0:95}, b is
positively correlated with banks’ costs, other costs, social costs, and total bank failures.
However, for C:F ¼ 0:90, b is inversely related to other costs, social costs, and
accumulated bank failures. These unusual results suggest that with a higher expected
withdrawal of funds among failed banks, it is a valid argument to command higher RBC
requirements from TBTF institutions. These higher b increments could save substantial
other costs and social costs, although banks’ costs could rise. This consequence follows
the spirit of the present law, since the FDIC’s decisive objective is minimizing costs to its
deposit insurance funds thus reducing taxpayers’ exposure.
3.3 Intra-heterogeneous regime analyses
Within the intra-heterogeneous regime simulations, both the C.F and the S.F disclose
comparable consequences to those within the homogeneous and the selected TBTF
regimes, respectively. Moreover, similar to the homogeneous regime analyses, the ?xed
RBC coef?cient b is positively related to banks’ costs, social costs, and accumulated
bank failures. We cannot, however, detect an obvious association between the ?xed
RBC increment b and other costs.
Interestingly, the heterogeneity parameter g does not express a clear association
with banks’ costs and social costs. However, when the C.F is relatively high, i.e. when
the C.F ¼ 1, g is positively correlated with total bank failures, hence it is inversely
related to the proportion of network left. Yet, when the C.F decays, for example when
the C.F ¼ 0.90, g uncovers the opposite impacts on these two measures of network
robustness. We thus conclude that with few or no early withdrawals from failed banks,
it would be better to preserve a more homogeneous banking system. Nevertheless, with
higher foreseeable withdrawal of funds, hence lower conservation ratios among failed
banks, a more heterogeneous banking system is likely to be more sustainable.
3.4 Cross-regime analyses
Throughout the cross-regime examinations, the selected TBTF banking system
achieves the best results. The selected TBTF arrangement obtains the lowest banks’
costs and social costs in all 27 simulated comparisons. Furthermore, throughout 25 out
of the 27 appraisals the selected TBTF regime exhibits the minimum number of
accumulated bank failures and the highest proportions of network left. Surprisingly,
the heterogeneous regime portrays the lowest other costs throughout 14 of the
27 comparisons. The selected TBTF regime attains the minimum other costs only
within 11 of the 27 assessments. Nonetheless, this minor impediment cannot conceal
the vigorous improvements within the selected TBTF banking system.
3.5 Trend analyses
The trend analyses provide inside view at the pace at which banks’ costs, other costs,
social costs, and total bank failures progress during the 12 quarters under
investigation. These ?ndings illustrate a coherent view of which banks’ costs and
social costs grow at reasonably the same pace within the homogeneous and the
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heterogeneous regimes, but more slowly within the selected TBTF system. We observe
no clear pattern concerning the growth rates of other costs, yet accumulated bank
failures typically progress more slowly within the selected TBTF regime than within
the other two banking systems. Altogether, these discoveries corroborate the
dominance of the selected TBTF structure.
3.6 Composition analyses
We also plot the original network and the ?nal results into schematic directed graphs
in Figure 2. From 2,000 banks and 12,901 business links in the initial network, we
follow three different scenarios, depending on the speci?c approach examined. After 12
consecutive quarters from the initial economic shocks, the homogeneous regime has
741 bank failures, thus 1,259 vertices with 5,051 edges left. After these three years, the
heterogeneous banking system has 520 bank failures, thus 1,480 vertices and 7,783
edges left. Yet, the healthier selected TBTF regime contains 1,597 banks with 8,324
business links left.
We use Figure 2 to delve into the ?nal compositions of the three regulatory regimes
by examining the number of directed edges and the average out-degree per vertex in
each simulation. From 12,901 edges and an estimated average of 6.45 business links
per bank in the original network, after three years the homogeneous banking system
reaches 5,051 edges with an approximated mean of 4.03 links per bank, the selected
TBTF model attains 8,324 edges and an average of approximately 5.21 business
connections per bank, and the heterogeneous scheme exhibits 7,783 directed edges with
an average out-degree per vertex of about 5.26. While the homogeneous approach
eliminates the highest number of business links, the selected TBTF technique
preserves many more of these ?nancial relationships and in particular those business
links connecting the more dominant institutions. We thus con?rm that the selected
TBTF regulatory regime is the most protective model, not only to the entire banking
system, but also to the largest and the most viable ?nancial institutions within.
4. Robustness tests
The simulations presented thus far describe an ordinary pathway for bank failures.
However, we wish to explore other variants that may lead to alternative avalanches.
We ?rst relax some of the underlying assumptions or adjust them to other probable
scenarios. For example, we transform the criterion for a bank failure to become less
uniform. In particular, instead of de?ning a universal regulatory threshold for a bank
failure as l
i
, l
*
þ b, we consider the diverse bargaining power among ?nancial
institutions while resolving differences with the chartering authority. This negotiating
strength is likely to depend upon the individual bank’s relative size and systemic
in?uence. Therefore, we rede?ne the criterion for a bank failure as
l
i
, l
*
þb 2ðððd
i
21ÞbÞ=11Þ. In this case, since d
i
, U½1; 12?, smaller banks
(vertices) with out-degrees of one would maintain the same failure threshold as before,
but larger institutions with out-degrees of 12 would have a lower closure point reset
at l
i
, l
*
.
We also create various links between the bank’s capital and its distinct risk-taking
behavior[8]. In this setting we remove the random selection process for the
idiosyncratic distances to default a
i
, Uð0; 0:01? and impose a
i
to be a function of d
i
in equations (2)-(4), respectively. More speci?cally, we test several functions including
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a
i
¼ ðd
i
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i
¼ ð0:01=d
i
Þ, which generate monotonic increasing or decreasing
bonds between any bank’s size and its endogenous risk-tolerance. Through these
functions we map the feasible domain of d
i
[ ½1; 12? into an equitable interval
a
i
[ ð0; 0:01?.
In addition, we distinguish between low- and high-capital ?nancial institutions[9].
These additional tests de?ne {a
i
¼ 0:005 ;d
i
$ 7; a
i
¼ 0:01 ;d
i
# 6} as
well as the complement classi?cations. Nonetheless, the simulated results in all of
those robustness tests are not materially different from the ones in the main setting.
Figure 2.
The various networks as
directed graphs
Homogeneous Regime
• 1,259 banks (vertices)
• 5,051 business links (edges)
• b = 0.02; CF = 0.95; SF = 5
• Average out-degree per
vertex 4.03
After three
years…
Selected Too-Big-To-Fail Regime
• 1,597 banks (vertices)
• 8,324 business links (edges)
• b = 0.02; CF = 0.95; SF = 5;
TBTF ? 11
• Average out-degree per vertex 5.21
Initial network
• 2,000 banks (vertices)
• 12,901 business links (edges)
• Average out-degree per
vertex 6.45
Heterogeneous Regime
• 1,480 banks (vertices)
• 7,783 business links (edges)
• b = 0.02; CF = 0.95; SF = 5;
? = 0.2
• Average out-degree per
vertex 5.26
After three
years…
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Hence, we con?rm, once again, our main conclusions supporting the exclusive
advantages of the selected TBTF banking system over other network con?gurations.
5. Summary and conclusions
In this research we utilize computer simulations to test various approaches towards
building a more sustainable banking system. We deploy three different theoretical
regulatory regimes as directed graphs that represent:
(1) a homogeneous RBC regulatory threshold with ?xed capital increments to all
?nancial institutions within;
(2) a heterogeneous regime, which assigns diverse capital requirements to its
banks, depending on their relative size and amount of business connections to
other institutions in the system; and
(3) a selected TBTF regime that allocates higher capital constraints only to some
designated larger banks.
The results of our theoretical study repeatedly show that while the homogeneous regime
is an inferior approach, the selected TBTF scheme displays the most defensive banking
system with the lowest number of accumulated bank failures. The selected TBTF
methodology attains the lowest banks’ costs and social costs. Furthermore, the selected
TBTF strategy is the best protective policy against instantaneous catastrophic events,
in the form of sudden depleted capital at several institutions, or continuous anxiety
among depositors, which could lead to reduced conservation of funds across failed
banks, making it the superior ?nancial con?guration. Nevertheless, the exact de?nition
of “TBTF” is not crucial, as long as it differentiates some ?nancial institutions from the
smaller and the less connected banks.
We also ?nd that with a higher expected withdrawal of funds from failed banks,
regulators should mandate higher RBC requirements from TBTF institutions.
However, when no early depositors’ withdrawals are anticipated, the selected TBTF
policy recommends only minor capital increments, though differences among the paths
are virtually negligible. We therefore conclude that to prevent the next banking crisis,
regulators must pre-identify and demand higher capital requirements from the highly
in?uential banks, while the precise capital increments should be designed with respect
to the ad hoc predictions for the level of conservation of funds within the banking
system during a ?nancial calamity.
Additionally, we provide strong conjectural evidence to support the common practice
by the FDIC of closing failed banks on Friday evening, while taking all necessary
measures to prevent public hysterics that could cause higher early withdrawals from
failed institutions hence lower conservation of funds in the banking system and much
intensi?ed ?nancial crisis.
Notes
1. Fur?ne (2003) elaborates on the limitations of only incorporating federal funds transactions
among banks.
2. Upper (2011) criticizes these over-simpli?ed perceptions.
3. In our simulations we consider total common equity requirements as the chief inception for
bank failures.
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4. Bech and Atalay (2008) report that in 2006, 470 banks were participating, on average, each
day in the federal funds market with an average of 1,543 interbank relationships per day
hence a rough average of 3.28 trade links per bank per day.
5. These weights can also designate the respective probabilities of acquisition, as interpreted
by the FDIC, thus equation (1) effectively presents the expected changes in banks’ capital
and risky assets.
6. The individual distance from default a
i
is uniformly distributed over the semi-open interval
and is capped at 1 percent to represent a genuine situation where banks aim to minimize
their unused capital.
7. These ?ndings support the logic underlying the conduct that failed banks are typically
closed on Friday evening following undisclosed measures by regulators.
8. Calem and Rob (1999) model a dynamic portfolio choice problem and enforce a relationship
between a bank’s capital and its risk-taking conduct.
9. Beatty and Gron (2001) ?nd signi?cant differences between the impacts of regulatory
variables on these two groups.
References
Allen, F. and Gale, D. (2000), “Financial contagion”, The Journal of Political Economy, Vol. 108
No. 1, pp. 1-33.
Angelini, P., Mariesca, G. and Russo, D. (1996), “Systemic risk in the netting system”, Journal of
Banking and Finance, Vol. 20, pp. 853-868.
Battiston, S., Gatti, D.D., Gallegati, M., Greenwald, B. and Stiglitz, J.E. (2012), “Liaisons
dangereuses: increasing connectivity, risk sharing, and systemic risk”, Journal of
Economic Dynamics and Control, Vol. 36, pp. 1121-1141.
Beatty, A.L. and Gron, A. (2001), “Capital, portfolio, and growth: bank behavior under risk-based
capital guidelines”, Journal of Financial Services Research, Vol. 20 No. 1, pp. 5-31.
Bech, M.L. and Atalay, E. (2008), “The topology of the federal funds market”, Working Paper
Series No. 986, European Central Bank.
Bech, M.L. and Garratt, R. (2006), Illiquidity in the Interbank Payment System Following
Wide-Scale Disruptions, Staff Report No. 239, Federal Reserve Bank of New York.
Brunnermeier, M.K. and Pedersen, L.H. (2009), “Market liquidity and funding liquidity”, Review
of Financial Studies, Vol. 22 No. 6, pp. 2201-2238.
Brusco, S. and Castiglionesi, F. (2007), “Liquidity coinsurance, moral hazard, and ?nancial
contagion”, The Journal of Finance, Vol. 62 No. 5, pp. 2275-2302.
Bryant, J. (1980), “A model of reserves, bank runs, and deposit insurance”, Journal of Banking
and Finance, Vol. 4, pp. 335-344.
Calem, P. and Rob, R. (1999), “The impact of capital-based regulation on bank risk-taking”,
Journal of Financial Intermediation, Vol. 8, pp. 317-352.
Cifuentes, R., Ferrucci, G. and Shin, H.S. (2005), “Liquidity risk and contagion”, Journal of the
European Economic Association, Vol. 3 Nos 2/3, pp. 556-566.
Diamond, D.W. and Dybvig, P.H. (1983), “Bank runs, deposit insurance, and liquidity”, Journal of
Political Economy, Vol. 91, pp. 401-419.
Diamond, D.W. and Rajan, R.G. (2005), “Liquidity shortages and banking crises”, The Journal of
Finance, Vol. 60 No. 2, pp. 615-647.
Optimal RBC
regulatory
system
91
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Y
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V
E
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S
I
T
Y
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2
1
:
4
8
2
4
J
a
n
u
a
r
y
2
0
1
6
(
P
T
)
Donaldson, R.G. (1992), “Costly liquidation, interbank trade, bank runs and panics”, Journal of
Financial Intermediation, Vol. 2, pp. 59-82.
Fecht, F. (2004), “On the stability of different ?nancial systems”, Journal of the European
Economic Association, Vol. 2 No. 6, pp. 969-1014.
Freixas, X., Parigi, B.M. and Rochet, J.C. (2000), “Systemic risk, interbank relations, and liquidity
provision by the central bank”, Journal of Money, Credit and Banking, Vol. 32 No. 3,
pp. 611-638.
Fur?ne, C.H. (1999), “The microstructure of the federal funds market”, Financial Markets,
Institutions and Instruments, Vol. 8 No. 5, pp. 24-44.
Fur?ne, C.H. (2003), “Interbank exposures: quantifying the risk of contagion”, Journal of Money,
Credit and Banking, Vol. 35 No. 1, pp. 111-128.
Gai, P. and Kapadia, S. (2010), “Contagion in ?nancial networks”, Proceedings of the Royal Society
A, Vol. 466, pp. 2401-2423.
Jacklin, C.J. and Bhattacharya, S. (1988), “Distinguishing panics and information-based bank
runs: welfare and policy implications”, Journal of Political Economy, Vol. 96, pp. 568-592.
Leitner, Y. (2005), “Financial networks: contagion, commitment, and private sector bailouts”,
The Journal of Finance, Vol. 60 No. 6, pp. 2925-2953.
Nier, E., Yang, J., Yorulmazer, T. and Alentorn, A. (2007), “Network models and ?nancial
stability”, Journal of Economic Dynamics and Control, Vol. 31, pp. 2033-2060.
Rochet, J.C. and Tirole, J. (1996), “Interbank lending and systemic risk”, Journal of Money, Credit
and Banking, Vol. 28, pp. 733-762.
Shin, H.S. (2008), “Risk and liquidity in a system context”, Journal of Financial Intermediation,
Vol. 17, pp. 315-329.
Temzelides, T. (1997), “Evolution, coordination and bank panics”, Journal of Monetary
Economics, Vol. 40, pp. 163-183.
Upper, C. (2011), “Simulation methods to assess the danger of contagion in interbank markets”,
Journal of Financial Stability, Vol. 7, pp. 111-125.
About the author
Dror Parnes is an Assistant Professor of ?nance at the University of South Florida. His research
focus is theoretical models and empirical analyses of various credit risk, operational risk,
systemic risk, and bank failure risk issues. Parnes holds multiple publications in many refereed
journals including, among others, the Journal of Fixed Income, Journal of Credit Risk, Journal of
Operational Risk, Quantitative Finance, The Financial Review, Journal of Behavioral Finance,
Managerial Finance, Applied Financial Economics, and The Banking and Finance Review. Parnes
has also presented his working papers at numerous academic conferences and has been
acknowledged for assisting authors writing several textbooks. Parnes completed his PhD studies
at Baruch College, the senior business college of the City University of New York. He also holds a
Master’s degree in ?nance from Baruch College, and a BSc in statistics, operations research, and
computer science from Tel Aviv University, Israel. Parnes’ professional experience includes
work as a Software Engineer, Research Analyst, and Portfolio Manager. Dror Parnes can be
contacted at: [email protected]
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