FINANCIAL SYSTEM TRANSFORMATION - A NETWORK APPROACH -
Lyubomir Mirchev1
Velina Slavova2
Hristian Elefteridis3
May 2010*
Abstract The objective of this work is to establish a conceptual and mathematical model that allows the development of strategies and measures for ensuring security and stability in the financial system. The aim is to achieve effective organizational and operational transformation, combined with early warning systems for possible crisis situations. The theme is inspired by the problems related to the global crisis. The team proposes the application of a network approach to the banking system and simulates the behavior of such a network-system under the influence of an external shock. The model and the simulation show that the behavior of a banking system is predictable and the parameters that influence are limited, highly measurable and verifiable. The authors propose the adoption of the banking system as a separate critical infrastructure and the inclusion of the banking and financial supervisory authorities as key elements in a decentralized network for financial regulation on a supranational level.
JEL Classification: G21, G15, C63, C90, G28 Keywords: financial system, network, transformation, critical infrastructure
* This work was partially developed within the regional project of the Francophone University Agency (AUF), "College Doctoral Regional es Sciences de Gestion", coordinated by the "Institut de la Francophonie pour l'administration et la gestion" in Sofia 1
Lyubomir Mirchev –University of Nice – Sophia Antipolis, GREDEG/CNRS, France; University of National and World Economy – Sofia, Bulgaria,
[email protected] 2 Velina Slavova – Professor in New Bulgarian University, Sofia, Bulgaria,
[email protected] 3 Hristian Elefteridis – New Bulgarian University, Sofia, Bulgaria,
[email protected]
Table of Contents Introduction................................................................................................................................. 3 1. European Commission initiative and concepts ......................................................................... 5 1.1. Project for the new regulatory system ............................................................................... 5 1.2. A European Program for Critical Infrastructure Protection ................................................ 7 2. Contemporary approaches, methods and practices for achieving stability in the financial system ......................................................................................................................................... 9 2.1. Network approach for solving the basic problems associated with global crisis ................. 9 2.2. Application of a Network model for banking system stability analysis ............................ 11 Modeling the banking system............................................................................................. 12 Shock simulation ............................................................................................................... 14 Simulation results .............................................................................................................. 16 Mark-to-market accounting................................................................................................ 22 Systemic events ................................................................................................................. 24 2.3. Ways for improving the network approach for ensuring stability and efficiency of the banking system ...................................................................................................................... 27 Network model results using scale-free networks............................................................... 29 Network (conceptual) model for critical infrastructure protection....................................... 30 Simulation model results for Network protection strategies................................................ 32 Conclusions............................................................................................................................... 36 References................................................................................................................................. 37
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Introduction The world is in a global economic crisis. In contrast to previous financial crises, this time the phenomenon is global. G-20 leaders agreed on the need for transformation of financial institutions and in particular for increased regulation of the financial system. This transformation opens up new opportunities for overcoming the crisis in the financial area through prevention based on early warning systems and ensuring sustainability and viability of the system of financial institutions. Regardless of this new structures and opportunities, the problem of developing a comprehensive approach for achieving greater security and stability in the financial sector is on the agenda. In this regard, we propose: o Broadening the scope of the critical infrastructure in the area of financial markets by considering the banking system as a separate critical infrastructure; o Include the financial regulation and supervision as a key element in a decentralized network on a supranational level; o The application of modern network approach to solve the essential problems of the global crisis. The recent global experience highlights the need to monitor systemic risks arising from both the macroeconomic developments in the economy and from the global financial markets. Integration of economies and modern technology opens up new challenges to the global stability. This requires new concepts, methodologies and models for financial system transformation and network crisis management. Such opportunities are provided by the project for new regulatory system, proposed by the European Commission, and its initiative to develop and implement a European Program for Critical Infrastructure Protection - EPCIP. The application of a network approach to the financial system could be the key for finding solutions the global crisis. In the literature more and more researchers acknowledge the impact of network structures on many social and financial activities. By applying the theory of networks, one can understand and influence the functioning of the financial systems. The new European regulatory structures – the European Systemic Risk Board and the European System of Financial Supervisors, are elements of an EU-level network. The inclusion of these structures and the banking system in a single framework will form a complex multilevel 3
system, called network of networks, where its characteristics are synergetic result of the relevant characteristics of their constituents, thus it acquires qualitatively new properties impossible to be achieved by its various parts – it achieves greater viability and operational efficiency. The objective is to achieve an effective organization and a functional transformation combined with early warning systems for possible crisis situations. To understand the functioning of this system of systems and to benefit from these potential new characteristics of the financial system we should understand how its elements are working. We already know that the banking system is highly interconnected and complex structure. For revealing its behavior, the application of a network model is most appropriate. We are applying a contagion model simulation, which shows us the reactions of the system when a shock is introduced – its resilience and fragility. We find that depending on the level of network integrity and the structure of the individual banks, a shock could be absorbed or could lead to near collapse of the whole system. Given the fragility of the banking system we propose the application of the Critical Infrastructure Protection paradigm for ensuring better protection of the interests of the whole society. We define the banking system as a new, high level “economic infrastructure”, regarding its important role in today’s economy. The critical infrastructure protection paradigm allows the construction of fundamentally new types of models for ensuring stability and efficiency. To be able to better protect the banking system in this context we are drafting a framework model for analyzing and strengthening the stability of the banking market.
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1. European Commission initiative and concepts 1.1. Project for the new regulatory system In October 2008 the European Commission (EC) mandated a group of high level experts, chaired by Jacques de Larosière, to formulate recommendations for the future of European financial regulation and supervision. Based on the recommendations from the report “de Larosière” and the discussions at the European Council, the EU Council and European Parliament found large consensus on the need for reform and the objectives to be achieved. The final report submitted by the group "de Larosière" on February 25, 2009 contained measures to achieve greater efficiency in a new system of European financial supervision. The report sets out proposals for new approaches to enhance cooperation and coordination among the national supervisory authorities, including the establishment of new supervisory authorities at European level. Their framework is presented in Chart.1.
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Chart.1. A new European supervisory framework Based on recommendations from the “de Larosière” report, an action plan is prepared to reform the regulatory and supervisory practices in the financial markets including an accelerated timetable for its implementation. The adopted framework introduces: - the European Systemic Risk Board (ESRB) which will monitor and assess potential threats to financial stability that arise from macro-economic developments and from developments within the financial system as a whole ("macro-prudential supervision"). To this end, the ESRB would provide an early warning of systemwide risks that may be building up and, where necessary, issue recommendations for action to deal with these risks. The creation of the ESRB will address one of the fundamental weaknesses highlighted by the crisis, which is the vulnerability of the financial system to interconnected, complex, sectoral and cross-sectoral systemic risks; and
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– the European System of Financial Supervisors (ESFS) consisting of a robust network of national financial supervisors working in tandem with new European Supervisory Authorities to safeguard financial soundness at the level of individual financial firms and protect consumers of financial services ("micro-prudential supervision"). The new European network will be built on shared and mutually reinforcing responsibilities, combining nationally based supervision of firms with centralization of specific tasks at the European level so as to foster harmonized rules as well as coherent supervisory practice and enforcement. This network should be based on the principles of partnership, flexibility and subsidiarity. It would aim to enhance trust between national supervisors by ensuring, that host supervisors have an appropriate say in setting policies relating to financial stability and consumer protection, thereby allowing cross-border risks to be addressed more effectively. The European supervisory authorities in ESFS will consist of three independent European authorities: European Banking Authority (EBA), a European Insurance and Occupational Pensions Authority (EIOPA) and European Securities Markets Authority (ESMA). The project for a new regulatory system, proposed by the European Commission, actually is a decentralized system of systems involved in the supervisory and regulatory processes.
1.2. A European Program for Critical Infrastructure Protection Considering the financial structures as an element of the critical infrastructure, according to the Opinion of the European Central Bank of 13 April 2007 on a proposal for Council directive on the identification and designation of European Critical Infrastructure and the assessment of the need to improve their protection / (CON/2007/11), allows the application of network systems methodology with all their opportunities to achieve viability, stability and efficiency of operation and prevention, preparedness and response to threats involving critical infrastructures and interdependencies between sectors. The proposed Directive establishes the procedure for identification and designation of European critical infrastructures, disruption or destruction of which would significantly affect two or more Member States or one Member State if the critical infrastructure is located in another Member State. The ECB has concluded that particular attention in this regard should be given of the operation and supervision of infrastructure and systems for clearing and
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settlement of payments and securities by the central banks of the European System of Central Banks (ESCB) and the contribution of central banks to the stability of the financial system. In the legislative Resolution of the European Parliament on April 22, 2009 on the proposal for a Council decision for Critical Infrastructure Warning Information Network (CIWIN) (COM (2008) 0676 - C6-0399/2008 - 2008/0200 (CNS)) is recorded that: The Council supported the Commission's plan to propose a European Program for Critical Infrastructure Protection (EPCIP) and approved the establishment of CIWIN by the Commission. This Decision establishes a secure system of information and communications - Critical Infrastructure Warning Information Network to assist Member States to exchange information on vulnerabilities and appropriate measures and strategies to reduce risks associated with the critical infrastructure protection (CIP). The legislative Resolution of the European Parliament on April 22, 2009 gives a contemporary definition of a "Critical infrastructure": those assets, systems or parts thereof located in Member States which are essential for the maintenance of vital societal functions, health, safety, security, supply chain, economic or social wellbeing of people, and the disruption or destruction of which would have a significant impact in a Member State as a result of the failure to maintain those functions.
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2. Contemporary approaches, methods and practices for achieving stability in the financial system 2.1. Network approach for solving the basic problems associated with global crisis The network approach can be an effective tool for solving problems posed by the global crisis. It is associated with the introduction of the information paradigm of security and stability in the financial system, including key elements such as bodies for banking and financial supervision and regulation. A paradigm is seen as a key model or method for achieving certain type of goals. The aim is to achieve effective organizational and operational transformation. This transformation offers new opportunities for prevention based on early warning systems, and ensures sustainability and viability of the system of financial institutions in case of failure of some of its units (bankruptcies and etc.). There is a growing consensus in the economics literature for recognition of the impact of network structures on many social and financial activities. Using the theory of networks, one can improve the functioning of the financial systems. The application of Network approach to the financial systems is especially important in assessing financial stability. For example, the resilience of a banking system to shocks can be evaluated according to the network structure that connects the financial institutions. Modern networking concepts are created in connection with the possibility of applying the benefits of information technology primarily in the security systems. The construction of an early warning system as a network structure at the highest level, matching its work with the networks of the European regulators and the national supervisors at their respective levels, and linking them with the network of banks and other non-bank institutions, allows the realization of a network system. This is a system of systems (network of networks), where its characteristics (properties) are synergetic result of the relevant characteristics (or properties) of their constituents. This makes it possible to achieve new states of the integrated (European or global) financial system in which the system as a whole acquires qualitatively new properties impossible to be achieved by its various parts. The achievement of viability, stability and operational efficiency is ensured. The need of implementing a network approach and an early warning system has been outlined in several paragraphs of the report and recommendations “de Larosière”.
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The adopted framework introduces: surveillance on macro-level (surveillance on financial stability), through the creation of the European Systemic Risk Board in the European Central Bank, and supervision on micro-level, implemented by the European System for Financial Supervisors. Individual national supervisors interact with each other on a decentralized basis within the supervisory colleges or on the basis of the signed bilateral or multilateral memorandums of understanding (MoU). Meanwhile the three supervisory authorities on EU level, which form the ESFS, coordinate and facilitate the work of the national supervisors and synchronize the financial regulations and supervisory practices which are the fundament for the financial markets integration. From another point of view ESRB and ESFS interact with each other and with the ECB and the European institutions, responding to potential threats to the stability of the financial market, thus forming a system of higher level.
t
B ba ank In nki ing sti ng an tu tio Fin d N ns an on ci a l
fec y ef erg Syn
isi lat on ion Le ve l
E
ar In ly an tern wa d a (c t rn S i oo u on Na ing rd pe al t r i a n io n a vi R sy tio sio eg d na ste Su l R n) n L ula m pe eg ev tio el n rv u
This system is actually a system of systems. The advantage of such network structures with decentralized management is that they are more resistant to crisis situations and to disruption of their integrity. Based on this concept we can be outline a four layer network architecture for financial supervision and crisis management
Chart.2. – Network Financial Crisis Management & New System Architecture
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The network approach presumes the development of concepts, methods, practices and new organizational structures for financial processes transformation and in particular for improved regulation of the financial industry. A network, linking the hierarchical or geographical spread organizational structures, provides opportunity for exchange of operational information, cooperation, and establishes a centralized shared awareness. This in turn leads to synchronization of the system as a whole. The result is increased efficiency, improved resistance to destructive influences and viability in crisis situations. The need of network implementations in the financial domain arises from the Memorandum of understanding on cross-border financial stability, signed in June 2008 by the financial supervisory institutions, central banks and finance ministers from the EU, and from the general practical guidelines for crisis management. The recommendations set forth in these documents create opportunities for the application of network approach for transformation of the financial system. By ESRB, the ECB will have access to supervisory information on micro-level. With the implementation of a modern model of a network for crisis management and with the cooperation on international level, effective mechanisms crisis situations resolution could be created. Information will be exchanged in real time and will provide relevant data for decision making in crisis situations. We propose the inclusion and development of these opportunities as necessary basic elements of a common network model for transformation, stability and efficiency of the financial system.
2.2. Application of a Network model for banking system stability analysis For better analyzing the financial stability of a system we should first take a look at its structure. Financial markets are largely integrated complex network structures. In the next chapter we will call them “economic infrastructure”. So most appropriate is to use a network approach when describing the banking market. This market is composed of number of banks connected by interbank linkages (debt or equity exposures). For safeguarding and maintaining the stability of this economic infrastructure, first we have to find the answer to the question: what is the banking system behavior in a crisis situation? There are many factors affecting the banking system behavior but
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we will focus on one of the main sources for systemic risk – the interbank connections. For this reason we are constructing a simulation model, describing a network of banks, connected with debt exposures, following the methodology of Nier, Yang, Yorulmazer and Alentorn (Nier 2008). For simplicity at this stage we will assume that we have a homogeneous banking system i.e. the banks are randomly connected to each other and each bank has the same chance to be connected to any another bank. Modeling the banking system The shock, we are simulating, is individual, hitting one bank at a time. Nevertheless that most of the external shocks would affect several or all banks simultaneously (like credit risk), hitting one bank (common for operational risks) will give us a clear view of the knock-on effect of the shock, transmitted throughout the system. At this stage of the model the shock is affecting the banks’ solvency and we assume perfect liquidity i.e. the shocked bank could sell all its remaining assets without any price reduction and repay its obligations up to the amount of assets in disposition, and perfect information symmetry i.e. excluding the information contagion effect. Both liquidity and information effects could amplify the simulated contagion in the paper. We are constructing a random graph with predefined number of nodes (banks) N which have lent to one another with probability of p. So pij is the probability that bank i has lent to bank j. So if we use p=0.2 this means that we will have 20% interconnected graph with N nodes. The number of connections will be equal to Z = N*(N-1)*0.2.
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Chart.3. – Simulation model interface – written on Microsoft Visual C# Express
Next we have to do is to fill the balance sheets of all banks. We denote the individual bank assets by a. So ai = ei + ii where e is the external assets i.e. loans and other investments to non-bank counterparties, and i denotes the interbank assets, i.e. exposures to other banks in the system. On the other side of the balance sheet we have the liabilities, denoted by l, so li = ci + di + bi , where ci is the capital of bank i, di are the deposits (from nonbank customers) of bank i, and bi denotes the borrowings (from other banks) of bank i. As every balance sheet, ai = li. The interbank assets i of one bank are the borrowings b of another – these linkages will be used as a shock transmitting channel. We generate the banks balance sheets by starting with the external assets of the banking system as a whole (E). Then we chose the percentage of the external assets in the total assets of the banking system (A). The proportion is E/A. Knowing that A
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= E + I, where I is the total interbank assets in the system and having E and E/A as an input, we can find A and I. A = E / (E/A) and I = A – E. Now, knowing the total size of the interbank exposures, we calculate the weight of each link by dividing I to the total number of links: link = I / Z. From there we can find the individual bank’s interbank assets and borrowings by multiplying link to the number of outgoing and incoming connections to each node (bank) in the graph. To find the external assets e we use a two-step approach. We know that the assets side should be equal to the liabilities side: e + i = b + c + d. So, to have positive capital and deposits we need e + i ≥ b. First we take eint + i = b, where eint is the interim value of the external assets of a bank. On the second step we distribute the remaining external assets equally to each bank: e = eint + (E-Σ eint)/N. The bank’s capital c is set as a percentage of the bank’s assets (c/a). This proportion is an input to the model and it is close to the supervisory capital adequacy ratio (CAR): c = (e + i)*(c/a). The final balance sheet item - deposits fills the remaining gap in the liabilities site: d = e + i – b – c. So initially we construct the model’s banking system by using the following inputs: N – number of banks; p – probability of connection; E – total external assets of the system; E/A – percentage of system’s external assets to system’s total assets; c/a – percentage of bank’s capital to total bank’s assets. Shock simulation The shock reduces by certain percent the external assets of the bank, showing that the initial shock is external to the system. Further the shock is transmitted through the interbank assets and borrowings of the banks, internalizing the shock to the system. When the shock is introduced to the banks, the capital is the first to absorb the losses: s – c, where s is the size of the shock. If the shock is greater than the capital s > c than the bank defaults and the borrowings are the next to absorb the losses: s – c – b. If the shock is enough big to wipe out the whole borrowings, the 14
final absorber is the customer deposits: s – c – b – d. The amount of the shock transmitted to the banks to which the shocked banks have links is limited to its borrowings (Chart.4.). So if the shock could be absorbed by the banks borrowings, the transmitted shock would be s – c. If it is bigger than the borrowings, the transmitted shock would be the whole amount of b. The shock for the banks neighbors depends of the link weight (size of each interbank exposure), but as all links in the model at this stage has the same weight, we will be calculating the shock simply by dividing the shock to be transmitted by the number of incoming links (the number banks which have lent to the shocked bank) snew = (s – c) / k, where snew is the shock to be transmited to one of the creditor banks and k is the number of creditor banks. The banks from the second round effect first absorb the shock by their capital and if it is not enough, with their borrowings and distribute further shock along the connecting links. This procedure is repeated until there are no new defaulted banks.
Capital Borrowings Deposit
s
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Chart.4. – Shock absorption and transmission For each simulation we change one of the parameters between certain limits. As the graph representing the banking system is random we make 100 runs with the same setting but with new generated graph and calculate average of the number of defaults for all the iterations, then we change the step and make again 100 iterations and so on. By so doing we avoid a biased result if the randomly generated graph isolates the shocked bank by making strange connections pattern. First we will see how the size of the shock is affecting the banking system. This means to what extend the banking system is resilient to certain amount of shock, transmitted through the interbank linkages. The size of the shock is measured by percentage of the external assets of the initially shocked bank. We use the following fixed values for the model parameters: N = 10; p = 20%; E = 100 000; E/A = 70%; c/a = 5%; and we change the shock between 10% and 100%.
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Simulation results While increasing the shock, the extent of contagion is also increasing to a certain point where the shock is distributed to enough banks so it could be absorbed. This mechanism depends on the level of bank interconnectedness. In more connected banking system the contagion effect is greater (Chart.5a.). Nevertheless the contagion pattern is different: while the shock is relatively small, the more connected network is absorbing the shock better as it is distributing small fractions of the shock to many neighbors. But after certain point the effect of contagion is prevailing over the effect of diversification and the contagion sequence rolls over. After a certain point of saturation the increase in the size of the shock is not provoking additional failures because the shock is distributed to sufficiently many nodes in the system. Defaults by size of the shock
number of defaults
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Chart.5a. – Defaults by size of shock and connection probability
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Chart.5b. – Defaults by size of shock and connection probability The change in the level of concentration in the banking system is giving us similar effect as the increase in its interconnectedness. We compare two systems with 10 and 30 banks. Having more banks we acquire more linkages and greater possibility of contagion (Chart.5c.). Despite of this similarity we have different levels of saturation so when we have more banks in the system, the absolute number of the affected by the contagion effect banks will be higher, but as a percent of the total banks we will have lover default level, because of the effect of diversification. Defaults by size of the shock
number of defaults
6 5
defaulted banks (N=30)
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defaulted banks (p=0,2)
3 2 1 0 10%
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size of the shock
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Chart.5c. – Defaults by size of shock and number of banks The different capital levels are also strongly affecting the contagion behavior. When the banks have less capital buffers they are more prone to contagion (Chart.5d.). This could be due to riskier business model or due to previous shocks which affected certain or all banks in the system. Defaults by size of the shock 8
number of defaults
7 6 5 4 3
defaulted banks (p=0,4; c=0,3)
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Chart.5d. – Defaults by size of shock, connection probability and size of capital The portfolio structure of the banks assets is also affecting their contagion sensitivity. Banking system with more interbank exposures and less exposures to non-financial entities will have lesser chance for external shock (and initially the effect of diversification will be stronger), but the higher weight of the interbank linkages allows them to transmit more stress to their neighbors in the system, and in a situation with a higher size of the initial shock, the number of defaults will be also higher (Chart.5e).
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Defaults by size of the shock 7
number of defaults
6 5 4 3
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Chart.5e. – Defaults by size of shock, connection probability and size of external assets From Chart.6. we can clearly see that the capital buffers play crucial role in the banks stability. The relationship between the capital levels and the contagion effect is clearly negative. When the capital is set to 1% almost all of the banks fail, but as the capital increases, the contagion effect becomes weaker. After certain level of capital the banks are resilient to interbank contagion because the shock is distributed to sufficiently large number of banks, and only the initially shocked bank fails. The contagion behavior is affected also by the level of interbank connections. Less connected network could bear less damages form an external shock initially as the contagion paths are fewer, but on the other hang, if the shock spreads, the system will need more capital to absorb the losses. Highly interconnected system have greater chances of contagion but the more links it has the more the effect of diversification is prevailing so the banks could absorb the shock with less capital needed. The lower level of capital could be explained by riskier business model, previous shocks which affected certain or all banks in the system or moral-hazard behavior in a situation where the government has announced explicit engagement to bail-out any troubled bank.
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Defaults by size of capital 11
bank defaults (p=0,4)
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number of defaults
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bank defaults (p=0,2)
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bank defaults (p=0,6)
7 6 5 4 3 2 1 0 1% 2%
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8% 9% 10% 11% 12% 13% 14%
capital / assets
Chart.6a. – Defaults by size of capital and connection probability
Chart.6b. – Defaults by size of capital and connection probability The effect of the portfolio structure is shown on Chart.7. Initially when the interbank assets prevail, the effect of diversification is stronger than the effect of contagion. Increasing the external assets we increase the size of the potential shock and thus the number of defaults goes up. At certain point the level of interbank 20
exposure goes enough low, the system is practically disintegrated, the shocked bank stays isolated and the contagion mechanism becomes ineffective.
number of defaults
Defaults by size of External Assets 6
bank defaults (p=0,4)
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bank defaults (p=0,6) bank defaults (p=0,2)
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10 % 15 % 20 % 25 % 30 % 35 % 40 % 45 % 50 % 55 % 60 % 65 % 70 % 75 % 80 % 85 % 90 %
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Chart.7. – Defaults by size of external assets The structure of the banking network has an important role in defining the contagion behavior. We have a reversed u-turned curve (Chart.8.). While the system is practically not integrated (the probability of connection is 0%), the shock cannot spread and only the shocked bank fails. Increasing the interconnectedness the contagion effect increases to the point where we have enough connections so that the diversification effect could outweigh the contagion by distributing the shock to sufficiently high number of banks. We can see that a complete system (with high enough probability of connection) is capable of absorbing the shock and again only the initial bank fails. The threshold (equilibrium between the contagion and diversification effects) depends on banks profiles. A banking system with less buffers (for example capital) will bear higher damage in terms of failed banks because higher amount of shock will be transmitted between the banks and the system will need higher level of interbank linkages to survive and absorb the shock. We can draw a conclusion that the lower level of capital or other buffers is increasing the destructive power of the interbank linkages, and in a banking system with more capital buffers, the interbank linkages will be more shock-absorbers and less shock-transmitters, thus improving the system resilience.
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Defaults by probability of connection 11
bank defaults (c=0,05)
10
number of defaults
9
standard deviation (c=0,05) bank defaults (c=0,03)
8 7 6 5 4 3 2 1 0 0%
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10% 15% 20% 25% 30% 35% 40% 45% 50% 55% 60% 65% 70% 75% 80% 85% 90%
probability of connection
Chart.8a. – Defaults by connection probability and size of capital
Chart.8b. – Defaults by connection probability and size of capital Mark-to-market accounting So far we have made all simulations under the assumption of perfect market liquidity. Now we will introduce the liquidity effect described by the elasticity of the assets’ price to the assets sales and the mark-to-market accounting effect to the banks’ balance sheet accounts. Under the new framework the assets price is decreasing with the same proportion as the assets sold on the market compared to the total assets in the system. We are introducing a coefficient elasticity, which is 22
affecting the magnitude of the liquidity effect. Value of 0 means no liquidity effect or perfectly inelastic asset price (perfect liquidity), and 1 means full liquidity effect or unitary elasticity of the asset price. % of change in assets price = 1 – elasticity * (asold / A) By introducing the mark-to-market accounting principle, banks’ assets are revaluated on each simulation cycle, taking into account the current assets market price. This means that when a bank defaults it sells all its remaining assets and exerts pressure on the assets prices. In parallel with that the balance sheets of all other remaining banks are revaluated and the amount of assets is decreased in accordance with the new prices. The effect of the mark-to-market accounting principle is that it brings additional shock to the system, weakening all the banks. This shock cumulates over the balance sheet contagion effect and amplifies it. The contagion profile with mark-to-market accounting resembles to a contagion profile of less capitalized banking system (Chart.9.). We have higher number of defaulted banks in any configuration of the network (level of interconnectedness of the graph).
Chart.9. – Defaults by probability of connection and liquidity effect Under this effect we are withnessing earlier defaults even when the shock is relatively small (Chart.10.). The diversification effect starts preveiling on a later stage i.e. the banking system needs more interbank linkages to distribute the shock
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to sufficiently large number of banks so that the contagion effect could be overcome.
Chart.10. – Defaults by size of shock, probability of connection and liquidity effect With the same level of initial shock the banking system needs more capital to withstand the contagion sequence. The liquidity effect is causing higher defaults in equally capitalized banking systems (Chart.11.).
Chart.11. – Defaults by probability of connection, size of capital and liquidity effect Systemic events All the simulations so far were made by initially shocking one bank. Nevertheless that most of the external shocks would affect several or all banks simultaneously. In the model we are introducing the ability to shock several banks at the beginning of the simulation. The contagion profile shows how vulnerable and fragile a banking system is (Chart.12.). We see that by increasing the number of initially 24
shocked banks we have stronger contagion effect (wider contagion area). This is mainly due to the greater shock, introduced to the system. To withstand a systemic shock the banking system needs to be better capitalized and more interconnected.
Chart.12. – Defaults by probability of connection, size of capital and number of shocked banks For better revealing the behavior of the banking network, we are conducted a similar simulation but this time maintaining relatively identical size of the shock in the different scenarios i.e. increasing the number of initially shocked banks while decreasing the shock size for each bank. We can see a slight increase in the contagion area (Chart.13.) due to the fact that the initial shock is spread to more banks and thus we have more contagion channels. By further increasing the number of initially shocked banks, the relative size of the shock for each bank is getting smaller and we see a new three staged contagion profile. First, when the banks have lower capital buffers, the contagion effect works and we have high number of defaults. At some point by increasing the banks’ capital the effect of diversification starts prevailing and the number of defaults is limited only to the initially shocked
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banks. By further increasing the capital level, having in mind that with high number of initially shocked banks the size of the shock is relatively small, the banks are getting able to withstand the shock and the system scores no defaults.
Chart.13. – Defaults by probability of connection, size of capital and number of shocked banks, maintaining fixed shock size By introducing the mark-to-market accounting principle we see again a new contagion profile. By increasing the number of shocked banks while holding the total size of shock identical, this time the contagion area expands rapidly (Chart.14.). The liquidity effect amplifies the contagion effect. With greater number of initially shocked banks we do not observe anymore the three staged profile. Instead of that, having lower interconnectivity, the number of defaults increases gradually while the banks are getting less capitalized. In a higher interconnected network the transition is more rapid – we observe a certain break point where the banks can no longer withstand the initial shock and the contagion effect is leading to rapid system breakdown.
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Chart.14. – Defaults by probability of connection, size of capital and number of shocked banks, maintaining fixed shock size and including the liquidity effect.
2.3. Ways for improving the network approach for ensuring stability and efficiency of the banking system Until recently, the banking system was considered as a set of financial institutions competing in a specific market – the banking market. In this respect, their role was not considered different from any other market player on the financial and nonfinancial markets. When a bank fails, the law provides protection to the creditors and in most cases to those entrusted their money to the banks - the depositors. But the crisis has shown us that the disturbance occurred in the financial market is rapidly transmitted to the rest of the economy. All the entities, relying on the banks services for conducting their businesses, are also affected adversely. The social function of the banks comes into focus - their role as financial intermediaries in the economy. The significance of this function is increasing more and more. The banking system can be seen as a meta-infrastructure. It is the economic 27
infrastructure connecting the market participants in the economy and facilitating the processes of financial resources transformation.
Banks are:
regular economic agents or
key intermediaries in the economy
Banking market is: set of banks
or
interconnected system (economic infrastructure)
Protection in bed times:
or
all stakeholders, including consumers of financial cervices dependant from the functioning of the financial network
creditors, employees
Chart.15. – Today’s banks Financial markets are largely integrated, but the institutions responsible for their supervision and safeguarding the financial stability remain divided along the national lines. Banking markets are complex network structures. Studies on the stability of financial systems (Allen 2000, Nier 2008) used the assumption that the participants are equal, and the distribution of links is a random – Chart.16(a). Studies on social networks (as are the banking/financial markets) show that their structure is considerably more complex (Lewis, 2009). These networks have the characteristics of scale-free networks4 and small-world networks5. There can be observed a higher level of clustering, where some nodes called "hubs" have much more connections than others. Hubs in the banking system are the systematically important banks. Scale-free network are networks whose degree distribution follows a power law - probability of a node to make connection to other depends on 4
A scale-free network is a connected graph or network with the property that the number of links originating from a given node exhibits a power law distribution. A scale-free network can be constructed by progressively adding nodes to an existing network and introducing links to existing nodes with preferential attachment so that the probability of linking to a given node is proportional to the number of existing links that node has. (Wolfram MathWorld: http://mathworld.wolfram.com/Scale-FreeNetwork.html) 5 Taking a connected graph or network with a high graph diameter and adding a very small number of edges randomly, the diameter tends to drop drastically. This is known as the small world phenomenon. It is sometimes also known as "six degrees of separation" since, in the social network of the world, any person turns out to be linked to any other person by roughly six connections. (Wolfram MathWorld: http://mathworld.wolfram.com/SmallWorldNetwork.html)
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the number of connections, which it owns. On the other hand the radius of the network - the number of hops/links between the two most distant nodes, is relatively small (small world effect) – Chart.16(b).
a) Random network
b) scale-free network
Chart.16. – Types of networks
Network model results using scale-free networks For bringing the simulation closer to the reality we modeled a banking system, based on a scale-free network. For this purpose we implemented the Barabási– Albert algorithm for generating random scale-free networks using a preferential attachment mechanism6. The scale-free banking system is prone to stronger contagion effect and the number of defaults rises sharply due to the presence of hubs (Chart.17.). We can observe a less smooth contagion profile reaching higher number of defaults, showing us the fragility of the financial networks. On the other hand, while increasing the interconnectedness of the system, the defaults are dropping rapidly than in a random network. The overall contagion profile of the scale-free network looks sharper and reaching higher number of defaults in all system configurations in terms of capital levels (Chart.18.) especially when the network is less connected. While increasing the interconnectedness of the network, the contagion profile is starting to resemble to the random network profile, due the fact that, by increasing the connections, the structure of the graph is gradually losing its scale-free characteristics, turning into a complete graph at the end.
6
Preferential attachment means that the more connected a node is, the more likely it is to receive new links. Nodes with higher degree have stronger ability to grab links added to the network. http://en.wikipedia.org/wiki/Barabási–Albert_model
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Chart.17. – Contagion profile – number of defaults by probability of connection
Chart.18. – Contagion profile – number of defaults by probability of connection and size of capital
Network (conceptual) model for critical infrastructure protection At EU level for critical infrastructures have been adopted stock exchanges and settlement systems. Considering the importance of the banking market (which dominates over other sectors of the financial market in the EU), we suggest its 30
consideration as a separate critical infrastructure (social networking infrastructure). Unlike those critical infrastructures (stock exchanges and settlement systems) which are mainly technical infrastructures, the banking market is a higher level infrastructure, playing an important role in the development of all sectors in the economy. It operates using technical infrastructures, such as: payment systems, information systems, etc., building on them through the application of economic models and providing financial services to bank customers and thus turning itself into financial infrastructure - a tool for business conduct. The protection of this critical infrastructure would allow the construction of a fundamentally new type of model for ensuring stability and efficiency of the banking market. So the strategy for preserving and strengthening the financial stability will exceed national boundaries. This will allow a more flexible approach than the currently adopted, based on voluntary co-ordination between national supervisors, who was not sufficiently effective. A model for analyzing and strengthening the stability of the banking market, considered as critical infrastructure would include the following steps: (1) Mapping the real topography (banks inter-connectivity) of the banking network. (2) Identification of the hubs in the system – the supervisory efforts could be focused to these nodes depending on their importance. (3) Assessing the extent of the threat / possible damage, which a hub brings to the system. The risk depends on the hub’s size and connectivity with other hubs and nodes in the network. This evaluation is performed through simulations or analysis through the development of a “fault-tree” for spreading the initial shock. (4) Budget analysis – determines the optimum allocation of resources. Possible tool is the "network-wide investment" - after assessing the possible negative effects of each hub in the system, the investments are allocated in such a way that minimizes the overall negative effect. Priority is given to the most important hubs, which have the greatest impact on the network stability. For applying such model there could be implemented and refined few basic principles (Lewis, 2006) with the following interpretation: Principle 1: You need a network to fight a network. This principle applied to the banking system may have the following two meanings: 31
(1) Systemic instability in the banking market haves a network nature, so the means to oppose it should have a network character (a network of national supervisors ESFS). (2) Due to the size of European and international banking market only network approach would be effective. It is not economically feasible to protect every link in the system. European Commission studies show that the national Deposit Guarantee Schemes in the EU would not withstand the shock if several hubs (large, systemically important banks) fail. Principle 2: Protect the hubs, not the connections. This principle is directly related to the preceding because the banking market is built on a network basis. Hubs are critical points, therefore they must be protected. Considering the scarcity of resources and the fact that such a network could be enormous in size, it is not possible to protect each node of the system, so efforts should be focused on the critical points. Principle 3: Invest 80/20. The capital in the banking system is not equally allocated. One could say that the majority of the assets in the banking system are held by a small number of banks. This suggests that the 80/20 rule could be applied, i.e. 80% of resources should be invested in 20% of the units (which are critical to the system). Principle 4: Asymmetric thinking. Innovation in the financial sector often is used as a way to avoid certain regulations. In this regard, regulatory approaches must evolve, and adapt to the market situation, and anticipate and manage the development of the system. Principle 5: Dual purpose solutions. The scarcity of government resources raises the question for stakeholders’ involvement in the process of seeking solutions for improving the stability of the banking system. Example, the establishment of joint entities for electronic or cash payments, creation of buffer funds and other initiatives with purely private capital, would increase the stability of the system, but would also help to improve its efficiency. Thus resources optimization could be achieved.
Simulation model results for Network protection strategies In our simulation model we introduced and tested three protection strategies:
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The first consists of proportional allocation of bail-out funds to the banks. This strategy resembles to a theoretical government bail-out program where the banks’ capital is increased. The second one is a derivate of the first, but the bail-out funds are allocated only the biggest banks (the hubs). The third strategy is called “toxic bank” and resembles to a theoretical government bail-out program, where there is a special institution buying the troubled assets from the banks while applying certain discount ratio. For better comparison we are using identical budget amount for all strategies. We can see that the different strategies affect the contagion profile in a different aspect (Chart.19.). The “proportional allocation” strategy reduces significantly the number of defaulted banks when the shock to the initial bank is moderate. The “hubs allocation” strategy gives overall lower number of defaulted banks. Nevertheless, this strategy is more effective when we have a full-scale shock. The “toxic bank” strategy turns out to be the most effective. It gives the lowest number of defaulted banks, independently of the shock size, because this strategy is the most flexible – the funds are allocated on a case-by-case basis covering only the troubled banks. Depending on the regulators or government’s policy and the budget limits, a different discount ratio could be applied while buying toxic assets from the banks. Irrespective to their effectiveness and characteristics, all the strategies are bound with the same budget limits and when the shock gets enough big they cannot save system entirely (Chart.19.). If the funds limit is not sufficient to cope with the shock scale, these strategies can only postpone the system breakdown and give enough time for the economists and politicians to engage in more serious reforms.
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Chart.19. – Contagion profile after protection strategies – defaults by size of shock Looking at the overall contagion profiles of the different strategies, we can notice that the “proportional allocation” strategy is more effective when the system is significantly undercapitalized (Chart.20.). This is due to the fact that the strategy increases directly the capital base of the banks in the system. The “toxic bank” strategy is more effective with moderately capitalized banks because it reduces the toxic portfolios without affecting their capital.
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Chart.20. – Contagion profile after protection strategies – number of defaults by probability of connection and size of capital
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Conclusions 1) The simulation model developed using graphs and algorithms for economic parameters calculation and the propagation wave of the shock in the banking system show an adequate behavior in the sense that the simulation results are easily explicable in terms of parameters and financial and economic dependencies. The model shows that the behavior of a banking network is predictable and there are limited number of influence parameters that are measurable and even controllable. The model reveals that the stability of the system depends not only on the individual bank’s stability, but also on the intensity and the size of interbank linkages i.e. how integrated the banking market is. 2) The results obtained show that the implementation of the network approach to the banking system offers interesting opportunities for reorganizing its structure and predicting its response in crisis situations. This would contribute to the financial system transformation recommended in 2009 by the “de Larosière” group, and for the establishment of a new system for European financial regulation and strengthening the cooperation and coordination between national supervisors. 3) The adoption of the banking system as a high-level economic infrastructure (separate critical infrastructure) allows the development of fundamentally new type of methods for ensuring stability and efficiency.
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2.
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