The Concerted Run on the DSB Bank:
An Exploratory System Dynamics Approach
Erik Pruyt and Caner Hamarat
Faculty of Technology, Policy and Management; Delft University of Technology
P.O. Box 5015, 2600 GA Delft, The Netherlands — E-mail: e.pruyt@tudelft.nl
March 18, 2010*
Abstract
In this paper, an Exploratory System Dynamics model of a concerted run is first of all
presented. The immediate cause for modelling a concerted bank run was the mediatised call
for a run on the DSB bank. This Exploratory System Dynamics model was developed the
morning of the call for the bank run, before the start of the ensuing bank crisis, in order to
quickly foster understanding of possible dynamic behaviours of ‘con
perform rough-cut policy/strategy analyses. The model is subsequently used to illustrate the
combination of Exploratory System Dynamics modelling and Exploratory Modelling and Anal-
ysis, or Exploratory System Dynamics Modelling and Anal
The paper starts with a short overview of the DSB Bank crisis, the description of the ex-
ploratory System Dynamics model and some quick exploratory analyses. The model is then
bank runs and to
used as a scenario generator for Exploratory System Dynamics Modelling and Analysis in
order to analyse and deal with deep uncertainties surrounding the issue and its modelling
(parameters and functions). The paper ends with some applied conclusions and policy recom-
mendations, methodological conclusions, and venues for future work.
Keywords: Bank Run, DSB Bank, SD, EMA, ESDMA, Exploratory System Dynam-
ics Modelling and Analysis
1 Introduction
1.1 The Issue: The Abbreviated Story of a Concerted Bank Run
The immediate cause for the development of the model presented/used in this paper, was the call
on the morning of 1 October 2009, broadcasted on Dutch television, for a run on the DSB bank”,
The DSB Bank -the Dirk Scheringa Beheer Bank~ was a very special case in the Dutch finan-
cial landscape: the relatively small DSB bank was founded and owned by Dirk Scheringa, a former
policy agent and self-made banker, who held the limelight as main sponsor of the Dutch so
club AZ, the DSB speed skating team, and a museum of realist art. Being a popular figure head
and claiming that his bank was untouched by the 2008-2009 economic crisis, he even suggested
becoming crisis minister to steer the Netherlands out of the economic crisis.
*Published as: Pruyt, E. and Hamarat, C. 2010. The Concerted Run on the DSB Bank: An Exploratory
System Dynamics Approach. Proceedings of the 18th International Conference of the System Dynamics Society,
July 25-29, Seoul, Korea. (Available online at jwww.systemdynamics .org])
1 For a detailed reconstruction of the ‘DSB story’, see the official report of the Scheltema Commission
(Graafsma, Koedijk, du Perron, et al. 2010) available on www. commissiedsbbank.nl) The ‘Scheltema Report’ and
many of the details revealed in it were not available at the time of modelling and writing.
E. Pruyt and C. Hamarat, 2010. The Concerted Run on the DSB Bank 2
insurance policies! (in Dutch: ‘woekerkoopsompolissen’) with low starting interest rates for luring
customers, but with exorbitant commissions (51% according to DSB but 80-90% according to
other sources) that were added to the principal, resulting in mortgages far above execution values
(on average 146%) and —once the luring interest rates were raised— far above debtors’ abilities
to pay the interests, not to mention their abilities to repay the principal. Many debtors were
-soon after borrowing~ unable to (re)pay their loans and many of them could not refinance their
disproportionably high mortgages nor sell their homes without ending up with large residual debts.
The DSB Bank and its umbrella holding were under surveillance by the financial authorities
for insufficient disclosure of information, conditional sale (which is actually forbidden), exceeding
intransparent financing between subsidiaries, etc.
on overdraft facilities.
In the months preceding the concerted bank run, angry debtors and organisations representing
them were able to get media attention regarding their grievances, damaging the Bank’s reputation.
Additionally, many Dutch savers experienced hindrance from other bank failures and —although
most of them got all their money back~ the hindrance these bank failures caused also received
media coverage, raising Dutch awareness of bank failure risks beyond the deposit guaranted#,
Then on the morning of 1 October 2009, Pieter Lakeman, a lawyer claiming to represent a
group of angry clients who were in financial problems because of buying financial products from
DSB, called all depositors -on Dutch public television- to join for a run on the bank. Thousands
of depositors followed Lakeman’s call, and emptied their liquid deposits. On 1 and 2 October, the
average outflow amounted to €90 million, followed by more than €120 million on 3 October, and
an average of €50 million on each of the following 5 days. Although by 11 October the outflow
had practically stopped, the bank was severely affected by a cumulative outflow of €664 million
in less than 2 weeks.
Behind the screens, De Nederlandsche Bank (DNB), the Dutch central bank, contacted all ma-
jor Dutch banks in an attempt to set up a rescue operation. On 11 October, the negotiations with
the major Dutch banks to rescue DSB via a take-over by these banks failed after they requested
an unlimited guarantee (possibly amounting up to €5 billion) from the Ministry of Finance, which
the Ministry refused. Other plans failed too. That Sunday evening, DNB asked the court for
an ‘emergency measure’ (‘noodmaatregel’) in order to place the DSB Bank under legal restraint.
That evening, the DSB Bank was still judged sufficiently solvent and liquid. But that same night,
leaks/rumours about the failed rescue operation caused an early-morning panick and second run
on the bank (of about €30 million between 5.30am and 11.30am), because of which DNB asked
the court once more for an emergency measure. This time, DSB Bank was placed under legal
restraint. Being made a ward of court, Schcringa tried to save his bank but failed. On 19 October
2009 an adjudication order was issued: the bank went bankrupt, unseating Scheringa’s imperium.
Although it is estimated that —after deducting the costs of the compulsory liquidation~ 96%
~or €4.07 billion of the €4.24 billion- of all outstanding claims will be refunded, and the savings
guarantee reduces much of the damage for most depositors, the concerted bank run made a lot
1400 employees immediately lost their jobs, about 4500 clients with subordinated
its will most likely lose all deposits, about 4000 clients with deposits e: ings
guarantee may lose that part of their deposits, the other deposit banks are forced to finance the
uncovered part of guaranteed deposits, and Dirk Scheringa lost his bank and holdings, museum
and art collection, as well as his soc
club and skate team. And Lakeman’s clients... will most
likely be among the lo
5 too.
2It should be noted though that the DSB Bank was not the only financial institution in the Netherlands to sell
such financial products.
3A single premium insurance policy is an insurance policy that is sold in combination with a consumptive credit
or a mortgage, and for which the full insurance premium needs to be paid upfront and is financed by inclusion in
the consumptive credit or mortgage itself.
4Up to €100000 of deposits per person per bank are covered by the deposit guarantee system.
E. Pruyt and C. Hamarat, 2010. The Concerted Run on the DSB Bank 3
1.2 Exploratory System Dynamics, Exploratory Modelling and Analy-
sis, and Exploratory System Dynamics Modelling and Analysis
System Dynamics (SD) (Forrester 1968) (Meadows and Robinson 1985) (Sterman 2000) is tradi-
i used for modelling and simulating dynami i ing their result-
ing non-linear behaviours over time in order to develop and test effectiveness and robustness of
structural policies (see appendix [Alon page [22|for an introduction to SD).
The traditional SD approach may have to be turned into an exploratory approach for deeply
uncertain issues. Deep uncertainty is defined by{Lempert, Popper, and Bankes (2003)]as situations
‘where analysts do not know, or the parties to a decision cannot agree on: (i) the
appropriate conceptual models that describe the relationships among the key driving
forces that will shape the long-term future [e.g. different drivers and underlying struc-
tures than today], (ii) the probability distributions used to represent uncertainty about
key variables and parameters in the mathematical representations of these conceptual
models, and/or (iii) how to value the desirability of alternative outcomes.’
Improving models by increasing the level of detail or their size does not seem to help much for
such issues. Instead of trying to develop ever more detailed models validated on past conditions,
it may be more useful to focus on
¢ quickly exploring plausible behaviours with a relatively simple model —or relatively simple
models~ without aiming to uncover the structures underlying the real issue and forecasting
the behaviour or exact probabilities of precise behaviours or the real iss
ie;
¢ exploring and analysing the entire space of plausible behaviours that can be generated by
large uncertainty ranges for all uncertain parameters and structurally uncertain model for-
mulations; and
¢ exploring and analysing the (relative) effectiven given all sorts
in other word:
of parametric and structural uncertaintie
in the face of deep uncertainty.
More exploratory SD modelling, use and interpretation may be very useful for the first bullet,
and Exploratory System Dynamics Modelling and Analysis a combination of Exploratory System
Dynamics and Exploratory Modelling and Analysis~ may be very useful for the second and third
bullet.
Exploratory System Dynamics (ESD) refers to the use of fast-to-build, relatively-small, highly-
simplified, data-poor, easy-to-use SD models to quickly/easily explore possible behaviours and
plausible scenarios, and develop a rough idea about the effectiv
(Pruyt 2010d). The focus of ESD lies on testing whether behaviours of interest (e.g. plav
trajectories that require attention) can be generated (at all), and exploration of plausible types of
behaviours. Scenario analyses, risk analyses and what-if analyses are used in ESD, but in a slightly
, with a very different interpretation, and for a very different goal than traditionally,
because the issues for which ESD is useful are just too uncertain and the ESD models developed
too wrong® (but also more useful for the purpose of exploration). In ESD, it does not make
ense to derive firm conclusions about specific values or sets of conditions that may lead to this
or that behaviour, or to interpret outcomes in a probabilistic sense. Hence, ESD may be good as
an introduction to dealing with complex and uncertain issues, it is not useful for detailed analysis
in view of detailed implementation or to totally reduce uncertainties, and more importantly, ESD
on its own may not be sufficiently systematic for well-founded decision support for issues charac-
terised by deep uncertainty.
different
se:
Exploratory Modelling and Analysis (EMA) (Agusdinata 2008) (Lempert, Popper, and Banke
(2003) allows generating insights and understanding about the functioning of s and the ef
fectiveness and robustness of policies, while taking complexities and uncertainties seriously into
SAll models are wrong, but some are just more useful (Sterman 2002).
E. Pruyt and C. Hamarat, 2010. The Concerted Run on the DSB Bank 4
account. It consists of using exploratory models for generating an ensemble of future worlds (tens
of thousands of scenarios) in order to test the effectiveness and robustness of policy options across
the ensemble of future worlds. The question for EMA is not ‘when to measure more’ nor ‘when to
model better’, but ‘how to explore and analyse under deep uncertainty in order to design policies
that effectively and robustly improve the system/behaviour given the deep uncertainty’.
Since EMA requires handy models to generate thousands of plausible scenarios (future states),
and ESD requires methods to systematically explore deep uncertainty, they are actually natu-
ral complementary allies and can be combined into Exploratory System Dynamics
Modelling and Analysis (ESDMA). ESDMA consists of (i) developing (one or) several ESD models
regarding an uncer sue, (ii) simulating them with extended ranges of parametric uncertainty
and different structures/formulations, (iii) analysing the resulting dynamic behaviours and bifur-
cations given the structural and parametric uncertainties, and (iv) testing the effectiveness and
robustness of policy options given these and other uncertainties. In other words, the Exploratory
SD models are thus used as scenario generators for the Exploratory Modelling and An
order to explore deeply uncertain issues and support decision-making under deep uncertainty.
Practical tools to ease the combination of ESD and EMA are currently under development at
Delft University of Technology. A simple example of ESDMA is provided in section{d] and typical
outputs are attached in appendix C. Other examples are discussed in (Pruyt 2010d),
Hamarat 2010), and (Pruyt 2010c).
1.3. Goal and Organisation
1.3.1 Goals
The three main goals of this paper are to:
e explain the use of ESD for its own sake, in other words, without combining it with EMA;
e explain the use of ESDMA — the combination of ESD and EMA;
illustrate the application of ESD and ESDMA on a relatively simple example, namely the
concerted run on the DSB Bank, and hence, shed light on the dynamic complexity of poten-
tially concerted bank runs.
1.3.2 Organisation
The exploratory System Dynamics model is presented in section Qj and its behaviour is analysed
(in an exploratory sense) in section 3) The ESD is subsequently used for ESDMA in section [2
Concluding remarks and recommendations are formulated in section
SD and SD diagrammatic conventions are briefly explained in appendix [A] A ‘hot testing &
teaching case’ corresponding to the base model is provided in appendix{B] (the sim of the hot case
and base model is available at {nttp://forio.com/simulate/simulation/e.pruyt/dsb). And
appendix C contains the ESDMA outputs referred to in section 4)
2 An Exploratory System Dynamics Simulation Model of a
Concerted Bank Crisis
An exploratory System Dynamics simulation model is presented in this section. It may be wise
for readers without SD foreknowledge to get acquainted to traditional SD and SD diagrammatic
conventions before reading the remainder of this paper. These readers are advised to start with
appendix section [A] on page [22| first.
The exploratory System Dynamics model presented in this section was developed on the morn-
ing of Pieter Lakeman’s call, without any information about the further course of events. It was
E. Pruyt and C. Hamarat, 2010. The Concerted Run on the DSB Bank 5
made and simulated in order to foster understanding about the possible mechanisms and dynam-
ics of concerted bank runs, and to test some high-level policies to prevent concerted bank runs
from succeeding. The model is small, simple, high-level, exploratory, data-poor (no specific struc
tures nor detailed data about DSB beyond some crude guestimates were added), and history-poor
(previous and subsequent events were not included). The model was really used in an ex-ante
exploratory way: developments were not awaited for, and the model has not been calibrated at
a later moment in time to the actual course of events. The model has neverthe!
an simple example of ESD and ESDMA.
value as an
introduction to concerted bank runs and as
The applied goal of this paper is to present and use an exploratory SD model of a concerted
bank run in order to generate general insights into the potential dynamics of such financial cris
not to present a detailed ‘going concern’ model validated upon past conditions that represents the
inner functioning of banks for all situations. Generative mechanisms for going concern banking
are more complex than the generative mechanisms dominant during acute bank crises. The model
presented in this paper only focu: is provoked by a (concerted) bank run: the
model therefore does not focus on expli through the bank —and the
underlying bank’s net worth~ as in ( 1993), nor on detailed operations
and decisions of a commercial bank a
In that sense, the model presented here is models like the Fortis Bank model
and the Northern Rock model than to traditional bank models.
Since the model is a short-term crisis model, it is assumed that (i) there is no change in assets
due to profits, (ii) fived and guaranteed deposits and loans do not come at terms, (iii) there are no
net shifts from liquid to fixed assets, and (iii) there are no net shifts from liquid to fixed deposits
and loans.
eS,
on a bank
The basic model structure of the exploratory SD model is visualised in Figure [I] by means of
a Stock-Flow diagram. Data/numbers used in this section are fictitious or just guestimates, and
are used for illustrative purposes only. Most of the numbers and some of the functions described
in this section will be varied and their influence explored— in the following sections.
sits that are emptied are —in this model and from the point of view of the bank~ liquid
s and loans lost. These liquid deposits and loans lost drain the liquid deposits and loans,
which are assumed to amount initially to €4,500,000,000.
Liquid lost are equal to the liquid deposits and loans lost because of the double account-
ing system. Liquid assets lost decrease the stock of liquid assets, which initially amounted to
€1,150,000,000. It is assumed here that there is a liquid asset liquid liability target of 20%, which
means that fixed assets, which initially amounted to €4,600,000,000, need to be liquidated and
turned into liquid assets if less than 20% of liquid deposits and loans are covered by liquid assets.
Assuming that the liquidation time is only 1 day, which means that there are enough interested
ies to almost instantly sell assets to, there is a liquidation premium of 10% on these emergenc
In other words, only 90% of the fixed asset value is turned into liquid in these emer-
gency sales, and 10% of the fixed asset value is lost as liquidation losses. It is supposed that DSB
also administered fixed deposits and loans worth €1,000,000,000 which remained constant during
the crisis because fixed deposits and loans cannot be emptied by depositors or lenders before their
due date.
In a normal bank run, the amount of liquid deposits and loans lost equals the liquid fraction
running away times the liquid deposits and loans divided by the withdrawal time. However, two
amplified the running away effect in the case of DSB c ents were angry because
acceptable sales practices and the mediatised unwillingness of the bank to compensate the
victims of these practices, and people understood the hindrance of a bank failurc®l after having
6Even without losing money (in case of depositor guarantees), depositors have to wait for months to get their
money back.
E. Pruyt and C. Hamarat, 2010. The Concerted Run on the DSB Bank 6
bank faore potccived Ekcthood
declaration by DNB dank failure risk —-
liguid faction
perceived likethood | creibiiry denials monning
solvency filure \
. anger
a ai erp disp seed
Tiriciy " faction ruming hindrance bank
faihares
total assct total
— fred || quid
deposis | deposis | Gags aepacte and
liquid asset liquid
loans lost
liability ratio bw
‘withdrawal time
liquid assets fixed assets
liquid asscts lost
Figure 1: Stock-Flow Diagram of the basic DSB model
witnessed several bank failures in the months preceding the run on the DSB Bank. The previous
right hand side of the equation is therefore multiply by two factors: (1+hindrance of bank failures)
and (1+anger). In the base simulation, it is assumed that the anger and hindrance of bank failures
amount to 0.5.
Since the DSB bank run was actually to some extent an organised bank run, an additional
term is taken into account for this concerted action: concerted liquid fraction running away times
liquid deposits and loans divided by withdrawal time of 1 day. The maximum amount of liquid de-
posits and loans lost equals the amount of liquid deposits and loans divided by the withdrawal time.
In the basic model, it is supposed that the liquid fraction running away amounts to 0% if the
perceived likelihood of a bank failure is 0%, that it amounts to 0% if the perceived likelihood of a
bank failure is 25%, that it amounts to 1% if the perceived likelihood of a bank failure is 50%, that
it amounts to 10% if the perceived likelihood of a bank failure 5%, and that it amounts to 50%
if the perceived likelihood of a bank failure is 100% (see Figure 2(a)).
The perceived likelihood of a bank failure is modelled as (100% - credibility of the denials) times
the maximum of either the perceived likelihood of a liquidity failure or the perceived likelihood of a
solvency failure.
In this base version of the model, it is assumed that the perceived likelihood of a liquidity failure
amounts to 100% if the liquid asset liquid liability ratio equals -1, that it amounts to 100% if the
liquid asset liquid liability ratio equals 0, that it amounts to 80% if the liquid asset liquid liability
ratio equals 0.1, that it amounts to 40% if the liquid asset liquid liability ratio equals 0.2, that it
amounts to 10% if the liquid asset liquid liability ratio equals 0.3, that it amounts to 1% if the
liquid asset liquid liability ratio equals 0.4, that it amounts to 0% if the liquid asset liquid liability
ratio equals 0.5, and that it amounts to 0% if the liquid asset liquid liability ratio equals 1 (see
E. Pruyt and C. Hamarat, 2010. The Concerted Run on the DSB Bank 7
Graph Lookup - liquid faction rmaing raph Lookup - perceived likelihood solvency feih iraph Lookup - perceived lkelhood liquidity falu
r i 1 :
1
0 Cy) 2 2 1
(a) liquid fraction running away (b) perceived likelihood of a liquid- (c) perceived likelihood of a sol-
lookup function ity failure lookup function vency failure lookup function
Figure 2: Quickly inserted lookup functions for three critical variables (the two perceived likelihood
functions are replaced by continuous parameterised ESDMA functions in the ESDMA ~ see Figure
(1)
Figure 2{b)).
It is also assumed that the perceived likelihood of a solvency failure amounts to 100% if the
total asset total liability ratio equals 0, that it amounts to 100% if the total asset total liability
ratio equals 0.8, that it amounts to 90% if the total asset total liability ratio equals 0.9, that it
amounts to 50% if the total asset total liability ratio equals 1, that it amounts to 10% if the total
asset total liability ratio equals 1.1, that it amounts to 0% if the total asset total liability ratio
equals 1.2, and that it amounts to 0% if the total asset total liability ratio equals 2 (sce Figure[2(c)).
The three lookup functions described above and displayed in Figure Qj are replaced in Figure
{IT by parameterised logistic functions in order to explore the influence of these functions on the
model behaviour.
The liquid asset liquid liability ratio equals the amount of liquid assets over the amount of
liquid deposits and loans. And the total asset total liability ratio equals the sum of the fixed assets
and the liquid assets over the sum of the liquid deposits and loans and the fixed deposits and loans.
It is assumed here that the central bank issues a bank failure declaration (forcing a bank into
bankruptcy) if the liquid asset liquid liability ratio falls below 0.05 or the total asset total liability
ratio falls below 0.9 {these values are fictitious and are used for illustrative purposes only].
The immediate reaction following on Pieter Lakeman’s call is introduced in the model by the
concerted liquid fraction running away jumping to 5% on day 2 and falling down to 0% on day 4,
and the credibility of the denials falling from 90% to 10% from day 2 on.
3 ESD: Fast and Intuitive Exploration of Uncertain Be-
haviours and Effectiveness of Policies
s of the main variables for four different scenarios.
All variables also the liquid deposits and loans lost and the perceived likelihood of a bank
failure~ remain constant if there is no anger nor perceived hindrance, if there is no loss of credibility
of denials, or if there is no call for a concerted bank run (see the DSBO scenario displayed in green
in Figures|3] and (4).
However, with Pieter Lakeman’s call, 50% anger, 50% expected hindrance of a bank failure, and
a liquidation premium of 15%, the initial concerted run is followed by a relatively long period of
liquid deposit and loan losses reducing the liquid deposits and loans and the liquid assets -which
Figures 3] and JJ allow to trace the dynami
E. Pruyt and C. Hamarat, 2010. The Concerted Run on the DSB Bank
liquid deposits and loans lost liquid deposits and loans
43 6B
3B 4sB
3B
1B LsB
\
0 sf é
o 6 2 Ws rr a) o 6 2 2 m0
liquid assets fixed assets
6 18 as 30 36 42S oe 2 6 rs rd
“oe (Day) Tine (Das)
Suid asc: DSBO_so_soncered_ny —— fed asses: DSB0_no_conceted nun
gud anets: DSBI_concested. a fowe feed etes :DSBI_convered ri bs
{quid anc: DSBD_ concerted na median, xed arses :DSB2_conecrted rat median
Aqidaset: DSBS_concerted nigh fied ase: DSB3_concered_ra gh
liquidation liquidation losses
2 400M
1B
S ib
5 com \ ih \ {/\
o | +s \
o 6 12 18 M4 30 36 42 48 $4 60 o fi _—— i
Time (Das) os 0p 6 3 ua 48 55 60
Tae Das)
fasion: DSBO comer nn
pasion: DSB_conerad nn, bw gai Ise DEB cone 0
Epsion:DSR2 concerted m_nedim ———————__Sedatelisce Do
fakin Seed = amelie
total asset total liability ratio perecived likelihood solvency failure
Ls os
1 — Ios
\ he
os|_| i ons
ELT TAA EE EL
0 0
oe ae eo vee
EAE seed ae Subs se ee
Figure 3: Behaviour of different scenarios for the ‘concerted bank run’ model (1/2)
E. Pruyt and C. Hamarat, 2010. The Concerted Run on the DSB Bank 9
perceived likelihood liquidity failure perceived likelihood bank failure risk
o 6 2 W of 30 38 42 48 84 60 o 6 2 W of 30 3 42 @ 84 60
“Tue (Day) Te Das)
liquid fraction running DNB bank failure declaration
=
F 02 os
oa 02s
|
ole 0
° 6 2 OW Tr) . 6 18 a8 oo
Figure 4: Behaviour of different scenarios for the ‘concerted bank run’ model (2/2)
are replenished by liquidation of fixed assets— until it pushes the perceived likelihood of a bank
failure up causing a second bank run and a sudden collapse of the bank (see the DSB1 scenario
displayed in blue in Figures (3) and [d). In this case, liquid deposits and loans are lost during 3
weeks before the second bank run finishes off the bank. In that case, there may still be enough
time to save the bank. They could for example raise interest rates paid on (deposits and) loans
in order to raise ‘fresh’ money to compensate the liquid deposits and loans lost.
The DSB2 scenario (displayed in orange in Figures 3] and 4) shows that the collapse occurs
sooner with a liquidation premium of 25%. And the DSB3 scenario (displayed in red) shows that
the concerted bank run is followed immediately by a full collapse of the bank in case of 100%
anger, 100% expected hindrance of a bank failure, and a liquidation premium of 25%. In that case,
the second bank run follows so fast upon the first concerted run, that there is little the bank can
do to stop the bank run: there is simply not enough time to react unless preventive measures had
been taken beforehand. Figure|5|shows clearly that the peaks in liquid deposits and loans lost are
actually caused by the depletion of the stock of liquid deposits and loans.
Although the bank —at least for this particular ESD model formulation and for the parameter
values used~ seems to collapse sooner or later after an initial perturbation of sufficient amplitude,
the delay with which the second run follows upon the concerted run makes a big difference for
enarios DSB1 and DSB2 there seems to be some time for strategies/policies
s management, but not in scenario SDB3, in which the second run follows
° there may only be time for preventive mechanisms
put in place in the past, emergency measures (such as increasing the withdrawal time or limiting
the amounts that can be withdrawn per account per day) and reactive crisis management, or an
‘emergency measure’ that places the bank under legal restraint.
However, the fact that the modelled bank seems to collapse sooner or later may partly be
due to the fact that this version of the model is a crisis model without any protective checks
those involved: in sc
and anticipative c
immediately upon the first run, in which ¢
E. Pruyt and C. Hamarat, 2010. The Concerted Run on the DSB Bank 10
6 9 2 1S 18 a ys 38 69S SSCS
Tae Day)
Figure 5: liquid deposits and loans and liquid deposits and loans lost following the concerted bank
runs
and balances and/or policies for dealing with such crises. The causal loop diagram in Figure [3]
shows indeed that the positive liquidity and solvency loops make that the likelihood of a bank
failure keeps on increasing —unless actively stopped until the bank collapses. This could have
been expected given the fact that revenues and profits are not generated or added to the asset
base here: in this version there is only a reinforcing drain without replenishment (sce below for
replenishment options).
a a a alle
9 fraction
‘amg
ater
perceived prrczived Pane’, aa
cd liquid liquid de {5 hindrance bank
Pa ie Gepostis NG) ana nears last. failures
and bans >
solvency +
Sailure concerted liquid.
wen q fraction running
liquid assets lost +
liquidation
F premium
liquid assets:
Figure 6: Main feedback loops responsible for the ¢
run
‘cond bank run induced by the concerted bank
automated Monte-Carlo simulations, scenario analyses, what-if
s, and policy analyses are traditionally performed in SD modelling to check whether the
ive to small parameter changes, to ¢
probabilistic parameter inputs, to 2 the modes of behaviour of different
and to explore the change in behaviour given the occurrence of events, chang
implementation of polici
These traditional SD analyses may be slightly less useful —at least in their traditional form, for
their traditional purposes, and in their traditional interpretation for exploratory SD.
Take for example a traditional Monte-Carlo analysis: based on the the aggregated outcomes
of 1000 runs sampled using Monte-Carlo sampling from normal distributions for the variables
anger and expected hindrance possible bank failure, both N(0.5,0.1) displayed in Figure [7) some
and visualise the confidence bounds given
ets
in conditions or
of conditions,
E. Pruyt and C. Hamarat, 2010. The Concerted Run on the DSB Bank i
may conclude that the bank will collapse sometime between 32 and 75 days after the call for
the concerted bank run — and most likely between 48 and 57 days after the call. But from an
exploratory point of view, that cannot possibly be concluded from this exploratory model and this
rather narrow and intuitive analysis.
Ds8_MC_N
Sos SSSA S oo
Siued deposi and ba
ISB
° cy <0 a 700 6 7 7) 7 700
Time Dey) Tine (Day)
Figure 7; 1000 Monte-Carlo runs with anger ~ N(0.5,0.1) and hindrance bank failures ~
N(0.5,0-1)
— psp. — -
DSB_MC_N
perceived Weelnsod bank Sue ike
t
° w sa 7 100 ° er % 7" 100
Tine Dey) Tene Dey
Figure 8: 1000 individual traces of Latin Hypercube sampled runs with anger ~ U(0,1) and
expected hindrance of a possible bank failure ~ U(0, 1)
The bounds in Figure [7| cannot possibly -from an exploratory point of view— be interpreted
as likelihoods: the exploration is much too narrow ~in terms of distributions, sampling tech-
nique (Monte-Carlo 1000), and uncertainties explored (only parametric uncertainty of just two
variables)~ for exploratory purposes. By just changing the sampling technique (to Latin Hyper-
cube), the distributions sampled from (to Uniform distributions U(0,1)), and displaying individual
traces instead of confidence intervals, a different picture already emerges (sce Figure 8).
It looks as though there are two slightly different types of behaviour in Figure|8|—which was not
se in Figure/7}- and that there is tion between runs in which the bank immediately
and runs in which the bank only collapses after a ‘bleeding’ time.
a. bifui
Neither can exploratory SD models be used for meaningfully answering traditional what-if
questions: exploratory SD outputs cannot be interpreted in a (strongly or weakly) predictive
sense which means that outputs of what-if analyses can at most be considered to be ‘plausible out-
comes if this or that happens in this particular model with these particular values’. Exploratory
what-if analyses and exploratory scenario analyses are nevertheless very useful from an exploratory
point of view for exploring plausible futures as already illustrated above (DSB1, DSB2 and DSB3
scenarios discussed and displayed above).
E. Pruyt and C. Hamarat, 2010. The Concerted Run on the DSB Bank 12
Traditionally, the effectiveness of policies/strategics for dealing with undesirable behaviours
(in this case all scenarios but the green one) is then tested. Such policy analyses certainly make
sense from an exploratory point of view, but the conclusions cannot be more than indicative, most
certainly not predictive, prescriptive and/or conclusive.
We expect relatively simple, adaptive, conditional closed-loop policies/strategies to be most
effective over the entire ensemble of futures, and therefore to be more robust, as well as under-
standable and intuitively most appealing.
MultplicationFactorPolicyA
perceived likelihood Siliiins
DNB bank faiture ce a
declaration i “Sg:
credibility denials lig fuica =O
running withdrawal time
loss of credibtty 4 inkl credibility
DSB DSB
organised rn
concerted percentage running —®”
concerted liquid
expected
fraction running
ee
cclihood.
at new fixed loan as
new fixed loan percentage
ihre of initial deposits and loans ii a
rest Switch
itotal asset total ¥ PolicyB
lability ratio i earned tie ng fixed
SwitchPolieyc “fixed loan and foaxs
ted [| liquid
liquid asset deposits |) deposits
ability ratio alien |iend iar, “a derest ane
loans lost
initial valve quid
deposits and loans
= quid assets fixed assets
new liquid assets Pt guidation
* ¥. liquidation losses
SwitehPoticyD ‘ p ahs 3
<new liquid asset liquidation
new liquid | depo Habilty target premium
equity liquid liquidation time
assets
‘ost
Figure 9: SFD of the ‘concerted bank run’ model with four policies (displayed in red)
Following simple policies are tested here —mainly for illustrative purposes~ for the exploratory
DSB Bank model (the necessary structures are included in Figure [3] in red):
¢ Policy A is a simple closed loop policy for slowing the -or decreasing the amount of- liquid
deposits and loans lost by influencing the withdrawal timé™, This policy seems to have been
applied to some extent in the real DSB Bank crisis too: its e-banking site became terribly
slow during the crisis, ‘officially’ because the site was attacked by hackers. Although not
included here, this policy may also create an unintended positive ‘panick’ feedback effect.
Policy B ensures that a fraction —50% in thi
replaced at each and any time by fired depos
e— of the liquid deposits and loans lost arc
and loans.
S cast
T withdrawal time = 1 + liquid fraction running * MultiplicationFactorPolicyA; with Multiplication FactorPoli-
cyA = 20.
E. Pruyt and C. Hamarat, 2010. The Concerted Run on the DSB Bank 13
Policy C ensures that a new onetime fixed loan equal to the initial value liquid deposits
and loans times the new fixed loan percentage of initial deposits and loans (here equal to
20%) is contracted if (and only if) the perceived likelihood liquidity failure rises above 50%.
« Policy D ensures that new liquid equity amounting to €250000000 is added if (and only if)
the perceived likelihood of a solvency failure rises above 50%.
Figure/10| visualises the impacts of these four polici
and the perceived likelihood bank failure risk for scenarios
be seen that:
strategies on the liquid deposits and loans
DSB1, DSB2, and DSB3. There it can
e Policy A just slows the fall, but does not prevent it from happening;
« Policy B stops the fall by gradually substituting liquid deposits and loans by more expensive
fixed deposits and loans in case of DSB1 and DSB2, but not in the longer run in case of
DSB3;
« Policy C allows to deal with the threat but may require multiple fixed loans while gradually
losing liquid deposits and loans;
¢ Policy D allows to stabilise the bank in time by solving the solvency problem, except in
scenario DSB3 where the solvency crisis is solved after the liquidity has resulted in a collapse
(the black and green line coincide). However, by combining policies A and D, the acute
liquidity problem is dealt with by policy A and the solvency problem by policy D.
It should be noted that the cost of these policie: have not
been explored systematically here.
not equal and that the polic
Although scenario analyses, risk analyses, and policy analyses and their the exploratory inter-
pretation make more sense from an exploratory point of view than the corresponding traditional
analyses and interpretations, it could still be argued that they are not sufficiently broad and
systematic to firmly base policy making under deep uncertainty on. Indeed, just exploring the
(combined) effect of three parametric uncertainties by means of four scenarios can hardly be called
systematic. A more systematic exploration of uncertainties is the topic of the following section.
E. Pruyt and C. Hamarat, 2010. The Concerted Run on the DSB Bank
liquid deposits and loans
4
perceived likelihood bank failure risk
ws
o 0
gud deposts and ons
‘Bued depose and loess
tid depose sn ess
IR depose alos
‘bed deporte aed lesne
psa
DSIDueva
DsBieoio’
DeBlevleye
DSBleelegD
liquid deposits and loans
. iW 29 30 4 30 6 7 80 99 100
Time (Day)
Perceved Hidiicodtank Buhrersk DSSIPsicyD
perceived likelihood bank failure risk
tid deposit ad eons
‘uid depts and leans
Inj epost dome
‘Guid depose aad loess
Haid depen md loms
st
Deaienira
DSRS
Dewveleve
DSReleD
liquid deposits and loans
perceived Heeihood tank fers: Dst
Prcesed Keeiood bank furersk- DSS2Poicr
Peceved ditcadbank biurersk DSS2Psho
Paced Hivodbaak fuensk DS@Dvlere
Percened diicodEank Btbrersk DSS22sieyD
perceived likelihood bank failure risk
‘uid deposit and eens
Tu deposts and loans
[uid depen dls
sot
Dsaieolera
Deel
Deesvolieve
DSBIPRlD
liquid deposits and loans
o 0 39 30 4 S000 708090 100
Tine (Dey)
pecevedHhdnood bank firersk. D509
PeceredIeeood bank fre rsk DSS3Poicy
Peceved idiieodtank biurersk DSSiesien
[Pecevel Hahivod bak fuse rsh DSBSDvleve
Percened HbdiicodEank brersk. DSESPsievD
perceived likelihood bank failure risk
o 10
Iii deposit and eons
Haid depen males
sob
Dsaieolova
Damieelarola
2: DSBSPALADAIC
DSBIEMIAPID
o 020 30 40 708090100
Time Day)
perceived Hieliood tank fire: DSBS
Peveredlesinood tank frenst DS2SPSiera
Percened iaiseadbant Burersk DSSiPsL Peis
Deceved Hedcod bak tse nak: DSESDOLAPHIC
Perceived Kbdibood ant fsrerak. DSS:PS1APeID
Figure 10: Four different policies and one combined policy applied for three different scenarios
E. Pruyt and C. Hamarat, 2010. The Concerted Run on the DSB Bank 15
4 ESDMA: Systematic Exploration of Uncertain Behaviours
and Policy Robustness
The ESDMA discussed here is kept as simple as possible: only one ESD model is used to ex-
plore the influence of ‘simple’ uncertainties (parametric uncertainties and uncertainties related to
the formulation of the three lookup functions) in terms of the resulting dynamic behaviours and
bifurcations, and test the effectiveness and robustness of some policy options given these
ple’ uncertainties. The input for this analysis co} of thousands of full factorial samples from
broader parameter ranges (e.g. 0-1 instead of 0.15-0.25) and from parameterised functions, with-
out fundamentally changing the model structure (see for an example
of ESDMA with slightly different models).
The two logistic lookup functions displayed in Figures [2(b) and[2{c) are replaced —in order to
explore the influence of uncertain (lookup) functions on the model behaviour- by the parameterised
(logistic) functions displayed in Figure II] parameters for the inflection point, the skewness, and
the decay rate of these functions are varied.
‘im-
Figure C.1 shows 25 graphs of the dynamics of the liquid deposits and loans for different
inclination points of the perceived likelihood of solvency failure and perceived likelihood of liquidity
failure functions, with 900 (full factorial) samples of the skewness of the latter functions per graph.
(a) perceived likelihood of a solvency (b) perceived likelihood of a liquidity
failure function used in Figures C1 and failure function used in Figures Cl and
C2 in app C C2 in app C
(c) perceived likelihood of a solvency (d) perceived likelihood of a liquidity
failure function underlying Figures C3, failure function underlying Figures C3,
C4, C5 in app C C4, C5 in app C
Figure 11: Fully parameterised contimious ESDMA functions (replacing two of the lookup fune-
tions in Figure (2)
Figure C.2 zooms in on the apparent ‘bifurcation’ of the dynamics of the liquid deposits and
loans as displayed in the first column of Figure C.1, between the graphs in the second and third
rows. This ‘filmstrip’ shows the behaviour for various degrees of skewness of the perceived likelihood
of solvency failure and perceived likelihood of liquidity failure functions for different x-values of
the inflection point of the perceived likelihood of liquidity failure function ranging from 0.185 to
E. Pruyt and C. Hamarat, 2010. The Concerted Run on the DSB Bank 16
0.200 and for a fixed value of the inclination point of the perceived likelihood of solvency failure
function of 0.8. The film strips show that more and more clusters of trajectories start to drop as
the x-value of the inflection point of the perceived likelihood of liquidity failure increases.
Hence, Figures C.1 and C.2 show that the different shapes and shifts of the inclination points of
these two uncertain functions matter a lot for the resulting dynamics of the bank run and the time
available for intervention. However, the importance of the outcomes of the uncertainty analy.
for these two functions should not be overemphasized: within the bigger uncertainty picture, thes
functions are just two of the uncertainties and more of them should be explored.
Before exploring the combined effect of even more uncertainties, it makes sense to check whether
clear structures can be discerned in the trajectory data generated while changing several uncertain-
ionless resemblance plot! displayed in Figure C.3 shows that clearly
lusters of similar trajectories can be discerned (in a sample of 5000 out of 40000 tra-
considered. The dimer
Now that we know that there is enough structure in the data to pursue further detailed analys
of the behaviours, it makes sense to visualise the outcomes of the 40000 trajectories generated by
combining different values of the uncertainties considered, more precisely:
for liqskew = 0.0 - 0.1 - 0.2 - 0.3- 0.4
for solskew = 0.9 - 1.0- 1.1-1.2-1.3-14
for liqgrow = 10 - 15 - 20 - 25
for solgrow = 10 - 15 - 20 - 25
for anger = 0.2 - 0.4 - 0.6 - 0.8 - 1.0
for exp. hindrance = 0.2 - 0.4 - 0.6 - 0.8 - 1.0
for loss cred. = 0.2 - 0.4 - 0.6 - 0.8.
S
Figure C.4 contains the trajectories of the liquid deposits and loans of 48000 runs split out in
1600 runs in each of the 30 graphs according to different combinations of inflection points of the
perceived likelihood of liquidity failure and perceived likelihood of solvency failure functions.
Looking at the overall picture, four patterns can be clearly distinguished for high parameter
values of the solvency and liquidity inclination points. Very low values for both parameters only
generated a gradual decline. In between there is a clear transition zone where more and more
clusters of trajectories break down.
Information about the timing of the simulated bank failur
should not be interpreted in a probabilistic sense. This figure displays shows 22755 bank failures
within the first three months out of a total of 40000 runs — the remaining 17245 trajectories do
not collapse (entirely) within this time horizon. However, these graphs and numbers cannot be
interpreted in a probabilistic sense because of the exploratory nature of the model, the extreme
uncertainty about the real underlying probabilities, the full factorial design together with the
uniform density functions used, etc. Based on the outcomes of the bank failure declaration, they
show that this model together with th generate four dominant types of runs: the
modelled bank either collapses immediately, or it collapses in the short term (after 10 to 20 days
in this model), or it collapses in the medium term (after two to four months in this model), or it
does not collapse within the time horizon considered.
These detailed analyses are ~given the fact that probabilistic interpretations for this exploratory
model are not possible~ only really useful as a starting point for an exploratory policy anal
both for designing (adaptive) policies and testing their effectiveness and robustness, and for com-
paring them with the outcomes of the no-intervention base case.
splayed in Figure {I2|-which
uncertaint:
The same simple policies that were tested in the ESD policy analysis in section 3] are tested
here in this ESDMA policy analysis. In the full factorial design of the ESDMA poli
8We are very grateful to Jan Kwakkel for generating this plot and his critical reflections on our work on ESDMA.
°The scripts and techniques to determine automatically what the clusters represent are currently under devel-
opment. As for now, we can only guess what the shape of this particular resemblance plot really means.
E. Pruyt and C. Hamarat, 2010. The Concerted Run on the DSB Bank 17
4000]
2000
1000
Figure 12: Bar graph of 22755 bank failures out of 40000 runs ~ the remaining 17245 trajectories
do not collapse (entirely) within the time horizon simulated here
liquidity premium is varied (0.10 ; 0.15 ; 0.20, 0.25 ; 0.30) on top of previous variations. Adding
the variations of the liquidity premium makes the clusters of trajectories slightly less distinctive.
In stead of displaying the trajectories, we immediately display the bank failures as in Figure [T2)
Figure [13] gives a visual impression of the effectiveness of these policies, in other words, whether
they help to avoid or delay a bank failure. Starting with the base c
of runs collapses immediately, or in the short term, or spread out over the medium term, or not
at all (103508 out of 200000 runs). Policy A delays the immediate collapses from the very short
term to the short term and only leads to a minor reduction (about 1%) of the number of collap
in the time horizon considered. Policy B leads to slightly more immediate collapses, but almost
climinates short term and medium term collapses by solving the liquidity problem. Policy C
outperforms policy B in the very short term and over the entire horizon, but not in the short and
medium term. And policy D reduces compared to the base case~ the number of collapses over the
whole line, but not as much as policies B and C. Policy D helps to solve solvency problems, but
is less appropriate for solving acute liquidity problems. That problem could be partly solved by
combining policy D with policy A (see Figure [I3{f)). This combined policy eliminates immediate
collapses, and strongly reduces all other types of collap
For real it is interesting at this point to compare the efficiency, effectiven
ss of these policies and to to experiment with policies of different strength as well as with
different combinations of polici
It would also be really interesting to explore the scenario spaces for which policies are not
afective yet wing for easiple the PRIM algorithm (se (Bryant and Lempert 2009)). This,
however, is work in progres:
, a considerable number
and ro-
bustne:
10]¢ is extremely likely that we will have made all currently known changes and improvements, and will have
implemented /applied promising algorithms and new coding to perform more advanced analyses and obtain better
visualisations.
E. Pruyt and C. Hamarat, 2010. The Concerted Run on the DSB Bank 18
(a) No policy — 103508 runs out of 200000 do not collapse (b) Policy A — 105104 runs out of 200000 do not collapse
within the time horizon — first bar = 16345; second bar within the time horizon
= 10437
a * = 7 Wit sssain mel La A a na
(c) Policy B — 167968 runs out of 200000 do not collapse (d) Policy C — 173800 runs out of 200000 do not collapse
within the time horizon — first bar = 16345; second bar within the time horizon — first bar = 7440
= 12020
(e) Policy D — 163738 runs out of 200000 do not collapse (f) Policy A + D — 180564 runs out of 200000 do not
within the time horizon — first bar = 9710; second bar = collapse within the time horizon
8920
Figure 13: No Policy, Policy A, Policy B, Policy C, Policy D, Policies AxD ~ all applied to an
ensemble of 200000 scenarios, over 200 days, and with a maximum Y-axis value of 5000 [runs]
E. Pruyt and C. Hamarat, 2010. The Concerted Run on the DSB Bank 19
5 Conclusions
Many banks collapsed in 2008-2009. At least one of them collapsed after a public call for a bank
run. This paper presents an Exploratory System Dynamics (ESD) model of such a concerted bank
run. The model is a rather traditional ‘dynamic bank run model’ with an exogenous call possibly
triggering a second run. The model was developed the same morning of the call in order to explore
possible behaviours and consequences. Hence, the model is really modelled as a short term crisis
model. It is exploratory in terms of its goals, size, scope, and level of aggregation /simplification.
Keeping in mind that the model used is a simplistic and rather ideal model, it may be concluded
from the ESD simulations that:
© The public call for a run may seriously endanger the stability of a bank if sufficient depositors
follow the call.
A concerted bank run may —depending on the conditions~ cause an immediate bank run, or
a first run followed by a ‘bleeding time’ and a second run in the very short, medium or long
term (or never at all).
An isolated policy to slow the loss of liquid deposits and loans does little to prevent a second
run from happening. A policy to make up for (a big) part of the liquid deposits and loar
losses by gradually obtaining fixed deposits and loans (for example by raising the inter
rate on those products) may work, but not in case of a high liquidation premium. A policy
in which large fixed loans are sought for dealing with the liquidity problem may work, but
may nevertheless lead to a gradual loss of liquid deposits and loans. And an equity policy
may help to deal with the solvency problem, but does not seem to be enough for dealing
with the liquidity problem. However, that may be solved by combining the latter policy with
policies to deal with acute liquidity problems.
Later, this simple ESD model was used to test and (further) develop ESDMA which allows
for a more systematic and broader exploration of uncertainties and policy robustness. From the
ESDMA, it can be concluded that:
e It scems to be necessary in case of a concerted bank run (i) to be able to buy time by
delaying the follow-up run such such that any acute solvency problem can be dealt with,
and/or (ii) to put the necessary mechanisms in place that allow to deal almost ins
with acute liquidity problems.
¢ The ESDMA confirms the applied conclusions reached with the ESD. Different values for
the policy parameters may still be explored, as well as the cost efficiency of these polic
The ESDMA described in this paper is also exploratory in the sense that it was our first EMA
on an ESD model using the Python language/package. Hence, all scripts and coding were de-
veloped and/or used for the first time. This is also the main reason for the lack —in the current
version of the paper- of an systematic ex-ante design of the uncertainty explorations: one of the
major lessons learned is that a decent ex-ante ESDMA design is needed to make the exploration
process more efficient.
Still it can be concluded from a methodological point of view that:
¢ ESD is useful for very quickly and somewhat intuitively exploring uncertain dynamically
complex issues. It may for example be used for generating —very different plausible dynamic
behaviours that may support the reflection process ~ as ‘tools for thinking’. It may also be
used to reason about policies. But in isolation, it may also be criticised for being too intuitive,
narrow and unsystematic to base real world policies on.
ESDMA is useful for systematically exploring possible behaviours of uncertain dynamically
complex issues as well as the efficiency and effectiveness/robustness of potential solutions
E. Pruyt and C. Hamarat, 2010. The Concerted Run on the DSB Bank 20
under deep unc > all
possible behaviours that can be generated by taking parametric and structural uncertainties
seriously into account.
srtainty. It may for example be used to systematically scan and analys
In the near future, we will work on cases of increasing complexity in order to gradually advance
our work on ESDMA. In this paper, we already included uncertainty ranges and different formu-
lations/functions. Simple analysis and visualisation techniques were good enough here because
the behaviours generated with the DSB model were clearly distinctive. In the next stage, we will
simultaneously explore different model formulations (see (Pruyt and Hamarat 2010). Future work
will include considering different world views with very different models and preferences. Each of
these steps will lead ~at first sight and without good ana sation techniques~ to more
and more chaotic behaviours. We will therefore also explore better ways to deal with problems
of combinatorial complexity, and develop better and more user-friendly methods, techniques, and
tools, starting from existing analysis methods, data mining techniques, mathematical and control
theory techniques, formal modelling methods, and multi-dimensional visualisation techniques.
References
Agusdinata, D. (2008). Exploratory Modeling and Analysis. A Promising Method to Deal with
Deep Uncertainty. Phd dissertation, Delft University of Technology, Delft. (http://www. |
{next generationinfrastructures .eu/index . php?page1D=17&itemID=433706| (3)
Bryant, B. and R. Lempert (2009). Thinking inside the box: A participatory, computer-assisted
approach to scenario discovery. Technological Forecasting & Social Change 77(2010), 34-49.
(17)
Forrester, J. (1968). Principles of Systems. Cambridge, MA: Wright-Allen Press, Inc. 3]
Lempert, R., S. Popper, and S$. Bankes (2003). Shaping the next one hundred years: New
methods for quantitative, long-term policy analysis. RAND report MR-1626, The RAND
Pardee Center, Santa Monica, CA. |http://www.rand.org/pubs/monograph_reports/|
'2007/MR1626. pdf] [3)
MacDonald, R. H. (2002). The Dynamics of Federal Deposit Insurance: A Feedback View of
System Behavior. Phd dissertation, University at Albany, State University of New York,
New York. [5] 22]
MacDonald, R. H. and A. M. Dowling (1993, July). The savings and loan crisis:
Dynamics
A System
spective. In Proceedings of the 11th International Conference of the System
Cancun, Mexico. [5]
Meadows, D. and J. Robinson (1985). The Electronic Oracle. Computer Models and Social
Decisions. Chich John Wiley & Sons. [3] [23]
Pruyt, E. (2007). Dealing with Uncertainties? Combining System Dynamics with Multiple Crite-
ria Decision Analysis or with Exploratory Modelling. In Proceedings of the 25th International
Conference of the System Dynamics Society, Boston, MA, USA. System Dynamics Society.
(www. systemdynamics . org/conferences/2007/proceed/papers/PRUYT386 . pdf|
Pruyt, E. (2009a, July). Making System Dynamics Cool? Using Hot Testing & Teaching
C cedings of the 27th International Conference of the System Dynamics So-
ciety, Albuquerque, USA. System Dynamics Society. [ttp://www.systendynamics.org/]
{conferences/2009/proceed/papers/P1167.pdf| [23]
Pruyt, E. (2009b, July). Saving a Bank? The Case of the Fortis Bank. In Proceedings of the 27th
International Conference of the System Dynamics Society, Albuquerque, USA. System Dy-
namics Society. {http://www. systemdynamics . org/conferences/2009/proceed/papers/|
Pi275-pat]
E. Pruyt and C. Hamarat, 2010. The Concerted Run on the DSB Bank 21
Pruyt, E. (2010). How to Become a System Dynamics Modeller? Hop Step and Jump Towards
Real-World Complexity. Delft: Delft University of Technology. (forthcoming — based on
current SPM2313 exercises book). [23]
Pruyt, E. (2010b, July). Making System Dynamics Cool II: New hot testing and teaching cases
of increasing complexity. In Proceedings of the 28th International Conference of the System
vics Society, Seoul, Korea. System Dynamics Society. http://www. systemdynamics .
org/cgi-bin/sdsweb?P1026+0| [23]
Pruyt, E. (2010c). Scarcity of minerals and metals: A generic explorato! amics
model. In Proceedings of the 28th International Conference of the System Dynamics Soci-
ety, Seoul, Korea. System Dynamics Society. http://www. systemdynamics .org/cgi-bin/|
ql
Pruyt, E. (2010d, July). Using Small Models for Big Issues: Exploratory System Dynam-
ics for Insightful Crisis Management. In Proceedings of the 28th International Conf
ence of the System Dynamics Society, Seoul, Korea. System Dynamics Society.
|//www. systemdynamics.org/cgi-bin/sdsweb?P1266+0] 3) (4)
Pruyt, E. and C. Hamarat (2010). The Influenza A(HIN1)v Pandemic: An Exploratory System
Dynamics Approach. In Proceedings of the 28th International Conference of the System
's Society, Seoul, Korea. System Dynamics Society. |http://www.systemdynamics .
org/cgi-bin/sdsweb?P1389+0| {4| (15) (20)
Rafferty, M. (2008, July). Northern rock ple: A case study in banking policy during tim
ings of the 26th International Conference of the System Dynamics Soc
5)
ardson, G. (1997). Problems in causal loop diagrams revisited. System Dynamics Re-
view 13(3), 247-252. [22]
Richardson, G. P. (1991). Feedback thought in social science and systems theory. Philadelphia:
University of Pennsylvania Press. [22)
Scheltema, M., L. Graafsma, K. Koedijk, E. du Perron, et al. (2010, 23 June). Rapport van
de commissie van Onderzock DSB Bank. Onderzocksrapport, Commissie Scheltema, Den
Haag. [1
Sterman, J. (2000). Business dynamic:
Trwin/McGraw-Hill: Boston. [3)
systems thinking and modeling for a complex world.
Sterman, J. (2002). All models are wrong: reflections on becoming a systems scientist. System
Dynamics Review 18(4), 501-531. [3)
E. Pruyt and C. Hamarat, 2010. The Concerted Run on the DSB Bank 22
A System Dynamics and Diagrammatic Conventions
SD models consist of specific structural elements causally linked into feedback loops. These models
only contain direct causal relations (e.g. the blue links in Figure [I4). For SD to be of any use,
it is required that possible causal links can be perceived or hypothesised. Causal influen
cither positive or negative. A positive causal influence —indicated by a blue arrow with a ‘+’ sign
in Figure (14 means that if the influencing variable increases (decreases), all things being equal,
the influenced variable increases (decreases) too above (under) what would have been the case
otherwise, or AY B => 28 > 0. In other words, ‘a positive arrow from A to B means that A adds
to B, or, a change in A causes a change in B in the same direction’ p249). A
negative causal influence indicated by a blue arrow with a‘ sign in Figure{14}- means that if the
influencing variable increases (decreases), all things being equal, the influenced variable decreases
(increases) under (above) what would have been the case otherwise, or A> B = 22 <0. In
other words, ‘[flor a negative link from A to B one says A subtracts from B, or a change in A
a change in B in the opposite direction’ (ibidem).
A feedback loop consists of two or more causal influences between elements that are connected
in such a way that if one follows the causality starting at any clement in the loop, one eventually
returns to the first element. In other words, the variable feeds back after some time- to itself,
which makes that its behaviour is (partly) shaped by its own past behaviour. Feedback loops are
cither positive or negative. A feedback loop is called positive or reinforcing if an initial increase
in a variable A leads after some time to an additional i
are
causes
ease in A and so on, and that an initial
ck loops in isolation
called negative or balancing if an initial
decrease in A leads to an additional decrease in A and so on. Positive feedba
generate exponential growth or decay. A feedback loop i
increase in variable A leads after some time to a decrease in A, and that an initial decrease in A
leads to an increase in A. Negative feedback loops in isolation generate balancing or goal-secking
behaviour and can be used for automat:
Feedback loops give
linear. Feedback loop:
connected, and their r
se to nonlinear behaviour, even if all constitutive causal relationships are
everal feedback loops are often strongly
change over time. The feedback concept is a fundamen-
almost never exist in isolation:
ective strength
tally important characteristic of SD.
weak or
perccived solvency 44 meena
of the bank conditions
solvency of S
the bank ge
- fear of
f tb) t+) batik failure
liquid bank
reserves _ Ny
A_ tendency to withdraw +
personal savings
Figure 14: Causal loop diagram of a traditional bank run, based on (Richardson, 1991; MacDonald,
2002)
Causal Loop Diagrams (CLD) are often used by System Dynamicists to map (systems of) feed-
back loops and strongly simplified and aggregated CLDs are often used to ease the communication
of the main feedback effects. Following symbols are mostly used in CLDs: 7 represents a positive
causal influence; — represents a negative causal influence; and~ represent a positive and a
| influence with a delay; (and represent negative feedback loops; and @ and @
represent positive feedback loops.
Figure (14) displays for example a CLD (based on (Richardson 1991) and (MacDonald 2002
p67-77)) of a traditional bank run. It reads as follows: The weaker or more uncertain the eco-
negative caus
E. Pruyt and C. Hamarat, 2010. The Concerted Run on the DSB Bank 23
nomic conditions are, the higher the fear of bank failure will be, and the higher the tendency to
withdraw personal savings. A higher tendency to withdraw personal savings leads directly to a
lower perceived solvency of the bank but also indirectly over lower liquid bank reserves and a lower
solvency of the bank. This lower perceived solvency of the bank will in turn increase the fear of
bank failure above what would have been the case, and so on.
SD models also contain stock-flow structures. Figure [I] shows a Stock-Flow Diagram (SFD),
which graphically represents a SD simulation model, and more specifically, its stock variables (0),
flow variables ( # ), auxiliary variables (© or no symbol), and constants ( or no symbol) and
other direct causal influences between variables (the blue arrows). A stock variable —also called
a level or a state variable~ could be seen metaphorically as a ‘bath tube’ or ‘reservoir’. During
a simulation, stock variables can only be changed by flow variables (also known as rates). Every
feedback loop contains at least one stock variable or memory (in order to avoid simulation problems
equations).
e the contents of stoc
s are, metaphorically s
Flow variables regulate the states of stock variables. Hence, flow variables are the variables that
need to be targeted by strategies to improve the problematic condition/s|
stock variables.
Mathematically speaking, the stock variable is the integral of the difference between the incom-
ing flows and the outgoing flows over the time interval considered, plus the amount in the stock
at the beginning of the period. SD models are thus ~if seen from a stock perspective- systems of
integral equations, or —if seen from a flow perspective~ systems of differential equations
ate of the more inert
Time delays are also important elements of SD models. They are included in causal loop
diagrams by means of slashed arrows (~), and in stock/flow diagrams by different delay-type
functions and slashed arrows (+). Nonlinear functions may also be important in SD models.
They are often included in computer models by means of (non-linear) table functions —also called
lookup functions or graph functions.
The simulation over time of simulation models of these structural elements gives what
dynamicists are really interested in: the overall modes of behaviour. System Dynami
be used for exact point prediction or path prediction p34).
One of the basic assumptions of SD is that the structure of a system (and model) drives
its behaviour, and hence, that structural policies are needed to effectively and robustly change
(possible) undesirable behaviours. System dynamicists are therefore biased in a sense that they
look for structural solutions by trying to change links, feedback loops, underlying structures, etc.
not to
B_ Another ‘Hot Teaching/Testing’ Case: The Concerted
Run on the DSB Bank
The case description below was given in November 2009 to about 25 first-year MSc students and
in January 2010 to about 70 second year BSc students during their time-constrained ‘Introduction
to System Dynamics’ exam at Delft University of Technology. Although this case is smaller than
most hot teaching/testing cases (see (Pruyt 2009a), (Pruyt 2010b) and (Pruyt 2010a)), students
found it rather demanding because of the lack of a step-wise approach and somewhat difficult
formulations.
B.1 Case Description
Over the last year, newspapers have been reporting about many bankruptcies of banks and financial
institutions. The latest bankruptcy of a Dutch bank, the Dirk Scheringa Bank or DSB, is a very
E. Pruyt and C. Hamarat, 2010. The Concerted Run on the DSB Bank 24
special case, because the bankruptcy was actually caused by a concerted bank run by angry clients
following the call by Picter Lakeman to empty their deposits.
Since you already modelled the fall of the Fortis Bank, you are asked by the Dutch central
bank ‘De Nederlandse Bank’ to model the fall of the DSB. Keep in mind that a crisis model is
not the same as a complete bank model for going concern.
Deposits being emptied are —from the point of view of a bank~ liquid deposits and loans lost.
These liquid deposits and loans lost drained the liquid deposits and loans, which initially amounted
to €4,500,000,000.
Liquid assets lost are equal to the liquid deposits and loans lost because of the double account-
ing system. Liquid assets lost decrease the amount of liquid assets, which initially amounted to
€1,150,000,000. Suppose that there is a liquid asset liquid liability target of 20%, which means
that fixed assets, which initially amounted to €4,600,000,000), need to be liquidated and turned
into liquid assets if less than 20% of liquid deposits and loans are covered by liquid assets. Suppose
that the liquidation time is only 1 day, which means that there are enough interested parties to
almost instantly sell assets to. However, given this haste, there is a liquidation premium of 10%
on these emerger In other words, only 90% of the fixed asset value is turned into liquid
ots in these emergency sales, and 10% of the fixed asset value is lost as liquidation losses. Keep
in mind when you model the liquidation flow that the model you make is a crisis model and not a
complete banking model: there should at most be a net flow from fixed assets to liquid assets, but
not the other way around. Apart from the liquid deposits and loans, DSB also had fixed deposi
and loans worth €1,000,000,000 which remained constant during the crisis because fied depo
and loans cannot be emptied by depositors or lenders before their due date.
as
In a normal bank run, the amount of liquid deposi
running away away times the liquid deposits and loa:
two factors amplified the running away effect in the case of DSB cris
of unacceptable sales practices and the mediatised unwillingness of the bank to compensate the
victims of these practices, and people understood the hindrance of a bank failurd! after having
witnessed bankruptcies of several banks over the past few months. Multiply the previous right
hand side of the equation therefore with following two factors: (1+hindrance of bank failures) and
(1+anger). Suppose that the hindrance of bank failures amounts to 0.5.
Since the DSB bank run was actually to some extent an organised bank run, you have to
add an additional term to take this concerted action into account, for example: concerted liquid
fraction running away times liquid deposits and loans divided by withdrawal time of 1 day. And
do not forget that the maximum amount of liquid deposits and loans lost equals the amount of
liquid deposits and loans divided by the withdrawal time.
and loans lost equals the liquid fraction
divided by the withdrawal time. Howe’
T,
: clients were angry because
Suppose that the liquid fraction running away amounts to 0% if the perceived likelihood of a
bank failure is 0%, that it amounts to 0% if the perceived likelihood of a bank failure is 25%, that
it amounts to 1% if the perceived likelihood of a bank failure is 50%, that it amounts to 10% if the
perceived likelihood of a bank failure is 75%, and that it amounts to 50% if the perceived likelihood
of a bank failure is 100%.
The perceived likelihood of a bank failure may be modelled as (100% - credibility of the denials)
times the maximum of either the perceived likelihood of a liquidity failure or the perceived likelihood
of a solvency failure.
Suppose that the perceived likelihood of a liquidity failure amounts to 100% if the liquid asset
liquid liability ratio equals -1, that it amounts to 100% if the liquid asset liquid liability ratio equals
0, that it amounts to 80% if the liquid asset liquid liability ratio equals 0.1, that it amounts to
40% if the liquid asset liquid liability ratio equals 0.2, that it amounts to 10% if the liquid asset
liquid liability ratio equals 0.3, that it amounts to 1% if the liquid asset liquid liability ratio equals
11Even without losing money (in case of depositor guarantees), depositors have to wait for months to get their
money back.
E. Pruyt and C. Hamarat, 2010. The Concerted Run on the DSB Bank 25
0.4, that it amounts to 0% if the liquid asset liquid liability ratio equals 0.5, and that it amounts
to 0% if the liquid asset liquid liability ratio equals 1.
Suppose that the perceived likelihood of a solvency failure amounts to 100% if the total asset
total liability ratio equals 0, that it amounts to 100% if the total asset total liability ratio equals
0.8, that it amounts to 90% if the total asset total liability ratio equals 0.9, that it amounts to
50% if the total asset total liability ratio equals 1, that it amounts to 10% if the total asset total
liability ratio equals 1.1, that it amounts to 0% if the total asset total liability ratio equals 1.2,
and that it amounts to 0% if the total asset total liability ratio equals 2.
The liquid asset liquid liability ratio is of course equal to the amount of liquid as.
amount of liquid deposits and loans. And the total asset total liability ratio equals the sum of
the fixed assets and the liquid assets over the sum of the liquid deposits and loans and the fixed
deposits and loans.
The central bank issues a bank failure declaration (forcing a bank into bankruptcy) if the liquid
asset liquid liability ratio falls below 0.05 or the total asset total liability ratio falls below 0.9.
over the
B.2 Case Questions
1. (/8) Make a System Dynamics simulation model of this issue on your computer. Verify the
model. Save the model.
2. (/1) Simulate the model first of all over a time horizon of about 60 days without any anger
or an ‘organised’ bank run. In other words, set anger equal to 0, concerted liquid fraction
running away away equal 0%, and the credibility of the denials equal to 90%. Make graphs
of liquid deposits and loans lost and the perceived likelihood of a bank failu
eo
. (/5) Now, adapt the model to simulate a bank run following Pieter Lakeman’s call for an
concerted bank run. Suppose for example that the concerted liquid fraction running away
jumps to 5% on day 2 and falls down to 0% on day 4 and that the credibility of the denials
falls from 90% to 10% from day 2 on. Suppose also that on top of these changes the variable
anger amounts to 0.5 and the liquidation premium to 25%. Save the model.
(a) Simulate the model over a time horizon of 60 days. Make graphs of liquid deposits and
loans lost and the perceived likelihood of a bank failure.
(b) Explain the behaviours obtained, especially if you obtain strange behaviours.
(c) Briefly de
tibe whether and what the bank could do to prevent this bank run.
4. (/3) Simulate a bad case scenario, again over a time horizon of 60 days, in which anger is
1, hindrance of bank failures is 1, and the liquidation premium is 25%.
(a) Make graphs of the liquid deposits and loans lost and perceived likelihood of a bank
failure.
(b) Briefly describe the differences with the previous behaviour?
(c) Briefly describe whether and what the bank could do to prevent this bank run.
5. (/1) Validate the model extremely briefly. Use maximum 2 (different) validation tests. List
the tests used and briefly describe the conclusions of the tests.
6. (/4) Draw a causal loop diagram of the system to help you communicate the main feedback
effects responsible for the bank run.
7. (/1) Explain the link between structure & behaviour briefly (c.g. for the ‘bad case’ scenario).
8. (/1) Save your model again and add a simple closed loop policy (in colour) that prevents
the bank from collapsing. Describe the policy briefly. Test the policy at least in case of the
‘bad case’ scenario and sketch the resulting dynamics on your exam copy.
9. (/1) How do we call variables like hindrance of bank failures and anger?
E. Pruyt and C. Hamarat, 2010. The Concerted Run on the DSB Bank 26
C ESDMA Results
a Wes WAN
Tolvency =O. Sliquidity=00
= solvency =1O-liquidity=
i
T0_| salvency a1 Tiquidity=00.
Wa
Bolvency=l Squidity=0.0,
ay
solvency SOE Nquidity=o-T
solvency 1 Osliquidity=t
01_| salvency=T iquiaity=0-T
Tener guany=OT
Lit
TEE
dolvency =o STiquianiy=oz
Solvency =O TTquiaiy=oz
UE:
solvency =10-liquidity=t
Ua_|_walvency=T Tlquidity=02,
wolvency=1 2 liquidity=02,
of the sol
functions per graph
RSs NAR ‘a y
Figure C.1: trajectories of the liquid deposits and loans for 5x5 variation of the inclination point
ency and liquidity functions, with 900 (full factorial) samples of the skewness of these
~ PS JT
liguidity=0.185 | _tiquiaity=0.186 | _tiquiai
I>
Hquidity=0-188
mS
liguiaity=o.180 | _tiquidity=0.190
Sa
Liquidity=0.200
Figure C.
0.8 (first column of table C.1)
Filmstrip of the “bifurcation” between a Liquidity of 0.185 and 0.2 for a Solvency of
Figure C.3: Two-dimensional resemblance plot of 5000 out of 40000 EMA trajectories indicating
E. Pruyt and C. Hamarat, 2010. The Concerted Run on the DSB Bank 27
the existence of structures in the data.
Tiquidity
Tiquidiy =o:
Solvency =1
Liquidity = 00
Solvency Lr
7 Tigard
0 Solvency =
Solvency
Tiguidiey
Solvency
T Tiquiaiey
9 Solvency
Tiquidiy
Solvency
Tiquidiy
Solvency
Tigard
Solvency
Tiquidiy
Liquidity = 07 =U2 Tiquidiy Tigard
Solvency = 1.0 Solvency = 1-1 Solvency Solvency
Tiguidiy = 0.8 Liquidity = 03 Tiquidiy = 03 Tiquidiey
Solvency Solvency = 1.0 Solvency = 11 Solvency. Solvency
Tigard
Solvency
Liquidity = 0-4
Solvency = 1.0
Tiquidiy
Solvency =
Tigray
Salveney =
Figure C&: Full uncertainty exploration for the trajectories of the liquid deposits and leans split
out in 25 graphs according to combinations of the inflection points of the perceived likelihood of
liquidity failure and perceived likelihood of solvency failure functions
