Network Formation and Community Structure in a Simulated Banking System

Transcription

1 Network Formation and Community Structure in a Simulated Banking System Peter C. Anselmo 1,2 anselmo@nmt.edu Max Planck 1,3 mplanck@icasa.nmt.edu Institute for Complex Additive Systems Analysis 1 Department of Management 2 Department of Computer Science 3 New Mexico Institute of Mining and Technology Socorro, New Mexico USA Abstract An analysis of differences in community structure and impacts on system solvency and changes in household lending in a simulated banking system is presented. Communities are formed as interbank loans are made, and are defined at any point in time based the methodology presented by Newman (2006). As we have done in earlier work (Anselmo and Planck, 2012), we simulate an evolving balance-sheet agent-based banking system where banks are in one of three risk classes that are defined according to the amount banks invest in a risky, non-household asset. At each step of the simulation, these agent/banks make simulated decisions about lending and/or borrowing based on a simple decision model. Defaults in these investments often lead to drastic changes in solvency and borrowing from other banks in the overnight-loan market. These interbank loans lead to networks are formed either randomly or based on a simple familiarity measure. In either case, potential lending banks must be members of the subset of all banks offering the best rate to a would-be borrower, and must be offering sufficient funds so that the number of interbank loans made by a would-be borrower at any point in time is less than or equal to 3. 1

2 Overview We study the impacts of both individual agent/bank betweeness centrality and community betweeness centrality on solvency and network risk in two contexts: a randomly-formed interbank network and a network formed based on a model of interbank familiarity. Our analysis is based on the use of the betweeness centrality (Freeman, 1977, 1979) measure for individual banks to assess network risk as a function of both community structure and the banks themselves. We use Newman s (2006) method for finding community structure on a dynamic basis, and we compute the average betweeness of community members at each iteration of the simulation. We then assess the imacts of these measures on average system solvency and infer network riskiness from comparisons between betweeness measures. Network analyses using measures originating in graph theory have been done in varying contexts for some time. Centrality-based methodologies have been discussed by White and Borgatti (1994), and Borgatti (2005, 2006) following the seminal work of Freeman (1977 and 1979). Network modeling and analysis techniques have been successfully applied to banking systems, both in isolation (Boss, et. al., 2004; Minoiu and Reyes, 2011; Martinez-Jaramillo, et. al., 2012) and as part of larger global financial systems (Battiston, 2012; Vitali and Battistion, 2013). Our work begins with a stylized model of a banking system where banks participate in the interbank lending market as a result of anticipated reserve-requirement shortfalls for the upcoming period. In this paper, the concern is a comparison of network risk measures that are based on betweeness centrality observations at each step of the simulations. We present data that suggest that interbank overnight loan networks formed as result of past loan experiences between banks the notion of familiarity are riskier than overnight loan networks formed when banks randomly select lending partners from a pre-selected set of qualified banks. The next section of the paper contains an abbreviated presentation of our balance-sheet based model. This is followed by a section in which the process by which the two network-formation methods is defined. The familiarity and random-based network formation methods are very similar and differ in only one respect, the addition of the familiarity criterion to the randomselection criteria. A section summarizing our results, in which we suggest that the addition of the familiarity criterion results in riskier networks, is followed by brief concluding remarks. 2

3 Model The discussion in this section is a summary of the detailed model presented in Anselmo and Planck (2012) 1. Haldane, et. al. (2011) presents a model that is similar in several aspects, and the model itself falls into the general agent-based modeling and simulation category that has been and is being pursued by many researchers. We assess the daily financial well-being of I individual banks, as well as the overall health of the system, using our solvency measure that is grounded in simulated balance sheets for each bank: (1) where denotes all other banks remaining in the system, and k denotes off-topology loans (which are balance-sheet assets A) in the form of mortgages, credit cards, and other conventional bank assets. Financial relations with the non-bank entity are considered as on-topology assets in this model. The subscript C denotes cash.the letter L denotes on-topology liabilities, which are overnight obligations to other banks and/or the bank of last resort (BLR). The average system solvency measure, that we use in the regression models discussed below. is the aggregate measure of system risk Modeling daily net bank cash flows (see Anselmo and Planck, 2012 for a detailed discussion) leads to the definition of for all banks at time t. denotes funds available for household lending and, for middle-risk and risky banks, investing in risky assets at time t. Because encompasses demand deposits D, implies borrowing to cover overnight reserve requirements. Assets are amortized over time, and as deposits change according to a random-walk model, banks must either hoard cash or make cash-flow inducing loans in order to maintain solvency. If banks borrow in the interbank network (if for some j), then they must increase assets proportionally to maintain the same solvency level. In this discussion we assume that banks only borrow in the interbank market to meet demand-deposit liquidity requirements, and inspection of 1 Simulation similar to those described here and in the first paper may be run from the New Mexico Tech Institute for Complex Additive Systems Analysis website: 3

4 (1) shows that borrowing to meet interbank obligations will only make the solvency situation worse. Major features of the bank/agents in this model are: Three types of banks risk types: least-risky, middle-risk, and risky. Least-risky banks do not invest in the risky asset offered by the non-bank entity (NBE), middle-risk banks allocate up to 1% of their available capital to the NBE, and risky banks allocate 10% of available capital to the NBE. At each iteration of the model, banks allocate funds (if ) to short-term loans, mortgage loans, the interbank market, and, if they are in middle-risk or risky categories, the risky NBE. All non-nbe loans are at the same (variable and loan-specific) levels of risk, and the mix between each non-nbe category is the same for all banks regardless of risk position The bank of last resort (BLR) maintains solvency standards that banks are aware of. Banks maintain a liquidity safety margin, and if their solvency level is below the sum of the solvency standard and the safety margin, banks will hoard cash but pay interbank claims until their solvency level is above the sum. Banks subject to liquidity events caused by claims on other (usually, risky) banks will either hoard cash but meet interbank claims, or will hoard cash and not meet interbank obligations, thereby initiating the potential for contagion across the system. Banks will not resume household lending activity until their solvency levels return to the level of the sum of the BLR solvency requirement and the bank safety margin. Interbank market liquidity sources determined according to either a random or familiarity-based set of criteria, and are subject to available capital at candidate banks Banks borrow in the interbank market to meet anticipated next-day reserve requirements only Banks wish to limit the information content of their borrowing efforts, and this is done by seeking 3 loans in the amount of for all desired borrowing amounts. Banks prefer to borrow from each other, and will only borrow from the BLR if two or fewer banks have the amount on offer. Banks do not learn; their decision behavior does not change throughout the process 4

5 Major features of the simulation model itself are: 300 banks; 100 each in the least-risk, middle-risk, and risky categories to start One NBE and one bank of last resort (BLR), which has the power to close and/or merge banks and also is a liquidity provider as necessary Balance-sheet based; balance sheet items and bank liquidities (which are based on balance-sheet measures) are computed at each iteration of a simulation Variable loan rates for all loans, each loan tracked and amortized throughout Mergers between randomly-selected banks every 400 iterations The BLR has the ability to shut down banks not meeting the solvency cutoff for 180 days or iterations Weighted betweeness centrality and individual solvencies for all banks, along with community structure (and membership for each bank) and average solvency computed at each step (along with other variables) simulation runs The weighted betweeness centrality measure, adapted from Freeman (1979) and computed using the Brandes (2007) algorithm at each iteration is: Banks that are on many shortest paths between many pairs of banks will have relatively high measures, and will be considered relatively risky for the stability of the overall system in the context of this discussion. On the other hand, banks that are either on very few paths between other pairs of banks (relatively small measures), or are connected to the system by either a claim or a loan ( = 0) are considered relatively non-risky with regard to the system as a whole. Note that banks with one large liability to one other bank, but no other system connections, will have a betweeness centrality measure = 0 the same weighted measure as a similarly-situated bank with a much smaller liability to another bank. This measure is the cornerstone of the analysis described in this paper. At each step we compute the betweeness centrality for every agent with respect to the entire network; we refer to this 5

6 measure as individual global betweeness, or IGB. We also consider the average of all community-member betweeness centrality (IGB) measures, which we refer to as Global Community Betweeness Centrality (GCAB): We consider two types of banking networks that are defined by short-term interbank liabilities (loans; claims). The first type are random networks, in which candidate lender banks are selected by would-be borrower banks in a random fashion once screening criteria have been met. The second type of banking network is one in which lending banks are selected, subject to the same screening criteria, based on familiarity that is defined by a simple model we present below. Banks seek loans from other banks based, initially, on cost and available funds from an offering bank. At each timestep, offering banks are sorted according to the quoted interbank rate for all banks j i at time t. We define for possible rate classes k = 1,..,K as the number of banks in rate-class meeting the offer-volume requirements for bank i at time t. Z it < 0 denotes that borrowing bank i has a shortfall, and therefore its desired borrowing amount at time t. This is the first step in the process of selection of a lending bank in both network-formation cases. The second step, that is also common to both bank-selection processes, is establishment of the sufficiency of funds offered by potential lending banks in each class. 2 Once potential lending banks are classified according to rates and fund availability, they are selected by would-be borrowing banks based on either random or familiarity criteria. Random Networks We define the interbank network at any time t in terms of directional edges between nodes as follows: 2 Some of what follows in the discussion is taken directly from Anselmo and Planck (2012). 6

7 Once banks in rate-class q have been determined by any bank at time t, the second screening criterion applied to all would-be lending banks is that the lending amount devoted to the interbank market must be true. The probability that an interbank loan is made, that is for a borrowing bank and for the corresponding lender, is a function of whether an interbank liability already exists (if so, our model does not allow the new loan to occur) and the size of the remaining interbank pool within the rate class. The probability of a loan also depends on the size of the pool of banks with the same, lowest rate on offer and the total assets are sufficient to satisfy the borrowing bank s demand In the event that and, where the number of banks from the pool already selected in the current iteration, as the bank effectively selects lending banks without replacement from the pool of available banks in the best-rate pool. Other scenarios for interbank connectivity that defines the topology include: and with the remainder - allocated to the first randomly-selected bank in the set of banks with rates if and the first two randomly selected banks if. For the next rate class,, 7

8 with and so on as bank I systematically considers each rate class according the rates on offer. If or or then for all system banks. In cases where for a selected lending bank, the amount borrowed by bank i will be and the remainder either ( after the most recent loan at time t) or ( will be sought from other qualifying banks. As noted earlier, the BLR will fill any outstanding borrowing requests once the entire set of offering banks is parsed and the borrowing bank will risk BLR shutdown if the loan is not repaid. Naturally, when an overnight loan is repaid, = 0 for the loan in question, and the topology continues to evolve as the edge between banks i and j is removed:. For the purposes of this work, we make the simplifying assumption that a bank desiring funds from the interbank market searches only within the top tier of banks as defined by their rate offerings banks in set. If then bank i will borrow all available funds from the banks offering the best rate, and will get the remainder up to - from the BLR. Familiarity Networks Familiarity networks are an extension of random networks because of a single additional qualifying criterion that is measured using a simple familiarity measure. Recalling the time and edge-based definition of e t above, we define 8

9 where m is the number of consecutive historical timesteps considered by bank i. In this paper, we used m=30 for all banks in both types of networks. The familiarity measure is defined simply defined as the average of the sum of the absolute values of the variables: This criterion, which is bounded by 0 and 1 provides an additional evaluation dimension as borrowing banks parse lending banks according to their respective rate classes. Candidate banks are now classified within rate classes, and within each rate class they are ordered according to f ijt, so that v(f) it is the number of banks within each rate class q with identical f ijt values. Edge and, in the aggregate, network-formation probabilities follow in the same fashion as for random networks with this added criterion. In this work, we used m=30 in all simulations. While borrowing is an evident critical factor in network formation, removal of network arcs by settling interbank claims is also critical as the banking network evolves. In the next section we discuss how we modeled this feature of the problem in light of the notion that the change in the cash position at time t might not be sufficient to pay all claims at time t+1. Results One of the main ideas behind this work is to utilize the GCAB (global community average betweeness) and IGB (individual global betweeness; the weighted betweeness centrality measure) in the context of the random-based and familiarity-based banking networks to gain some insights regarding the relative riskiness of each network. Our analysis is based on the betweeness measures and fundamental ideas about how the two measures can be used to assess relative network risk in terms of an aggregate measure of system solvency. The first idea has to do with the impacts on system solvency of our betweeness measures. In this context, a riskier network would have GCAB and IGB measures that were negatively associated with overall average solvency, as this would be an indication that communities and betweeness are bad for the overall system. The second idea is that high levels of connectivity in an interbank network are riskier than low (or lower) levels of connectivity. The intuition behind this second proposition is that the degree to which risk in the form of events that may precipitate a 9

10 contagion-based liquidity crisis within a banking network will be successfully contained is directly related to the degree of interbank connectivity. GCAB and IGB Regressions We implement the first notion of relative network risk assessment by analyzing the percentage of negative signs on regression coefficients for significant variables. The OLS regression model for GCAB is For IGB: As may be seen below in Tables 1 and 2, the sign ratios for the significant variables for the GCAB regressions were similar across both network typologies, though the middle-risk sign rations appear to be more negative for the random network than for the familiarity network. These regressions were run on surviving banks only (in our model, banks may be randomly merged, and/or may be shut down by the simulated Bank of Last Resort). The number of surviving banks in the regressions for which we present result summaries in this paper ranges from 274 to 280. Results for 5 iterations of 2 GCAB simulation runs (one for each network scenario) and 2 IGB simulation runs are presented below in Table 1 (results for 5 GCAB regressions) and Table 2 (results for 5 IGB regressions). The tables contain the number of significant banks in total for each of the 3 risk categories. The table also contains -/+ columns, which indicate the ratio of negative to positive signs for the significant banks in each risk category. Note the R 2 numbers in both tables the familiarity-network regressions appear to have more explanatory power vis-à-vis the dependent, average-solvency variable. This is due in some degree to the larger number of significant bank variables. However, the disparity persists across the different numbers of significant banks in all 4 summaries. 10

11 With regard to IGB regressions, the negative ratios appear to be higher for risky banks in the case of the random network. This may indicate that the random network is riskier than the familiarity network, as there are no cases where the negative/positive sign ratios for the familiarity-based network are notably larger than for the random network. However, this is mitigated somewhat by the fact that there are far more significant agent/banks in all of the 20 regression results presented, which is also reflected in the large cross-framework disparities in the R 2 measure. At this level of analysis, we cannot conclude that the familiar network is riskier with regard to our system-stability measure - than the random network, though it appears that the GCAB and IGB variables have a much more pronounced impact on average system solvency in the case of the familiarity-based network. This last point leads to our second notion, the idea that connectivity between banks, as measured by the IGB measure, is risky in general. Connectivity, Betweeness, and Risk The next step was to investigate whether individual IGB (individual global betweeness, or betweeness centrality) numbers are larger for the familiar network. Larger IGB numbers for agent/banks in the familiarity-based network would be an indication that there was In order to assess the second proposition about banking-network risk, we assess whether betweeness centrality values for all banks across the network at all iterations of the simulation are different across network types. For all 300 banks, we assessed whether individual IGB numbers are higher for the familiarity-based network, and whether there are more positive IGB numbers for familiarity-based network agents than for random-network agents (there are not). That is, we look at the total number of positive IGB numbers for each of the 300 agents under each scenario. Our initial thought was that the IGB numbers should be higher for the familiaritynetwork agents, and that there would be more positive IGB numbers for the familiarity-network agents than for the random-network agents. Table 3 presents a summary of the IGB comparisons between network typologies. As we initially suspected, average IGB numbers for all three bank categories in the familiar-network case are, on average, about 2 to 2.5 times larger than their random-network counterparts. This 11

12 general relationship persists across bank types, with the smallest ratio between least-risky banks and the largest between middle-risk banks. These differences in IGB numbers across network typologies are supportive of the notion that familiarity-based networks are riskier than random-based networks. Additional evidence may be gleaned from the Avg Count columns in Table 3, which contains the average number of positive betweeness centrality observations (out of a possible total of 3650) for each bank-behavior type across the two networks. Note that the average number of connections is always higher for the familiarity-based network data. Not only are banks more connected, they are more connected more often when the basis for interbank network connections is familiarity. There are differences across bank types in the IGB data presented in Table 3. Middle risk banks are notably less connected as measured by IGB than are least-risky or risky banks. In fact, least-risky banks are slightly more connected than are risky banks, and this situation persists across the two network types. The same situation also applies to the total number of instances where a IGB measure exists when a bank is on the shortest path between at least two other banks - during the simulation. An illustration is provided below in Figures 1 and 2. In Figure 1, banks A and C are connected to the network, but are not between any other two nodes. In our formulation of this phenomenon, IGB(A) = IGB(C) = 0. On the other hand, bank B is unconnected to the network, and IGB(B) = -1. IGB measures as computed using the weighted betgweeness centrality measure in () for all other nodes will be positive. Figure 2 depicts a situation where an addition of 4 edges to Figure 1 has resulted in a network where there are inter-node shortest paths that go through each node in the network. All nodes will have an IGB value that is greater than 0. The configuration in Figure 2 is riskier than the configuration in Figure 1. Comparing the IGB values and the instances of IGB > 0 for all agent/banks in the simulation model leads to the conclusion that familiarity-based networks are more likely to be similar to Figure 2, and random-based networks are more likely to be similar to Figure 1; therefore we conclude based on these data that familiarity-based interbank networks are riskier than random-based interbank networks. 12

13 Discussion The first observation, based on Tables 1 and 2, is that there are many more significant banks in the GCAB and IGB regressions in the familiarity-network case(s). There are also more positive coefficients for significant familiarity-network banks than for significant random-network banks in the regressions. Thus average system solvency is more closely related to more banks in the familiarity-based network case, and this may be due to the relatively larger number of connections in the familiarity network. Changes in the solvency of one bank possibly due to a liquidity event caused by a risky loan, are more likely to impact the system as a whole. This also implies that positive liquidity events, such as might be associated with successful risky investments, will also impact the overall system when the banks are connected at a higher level. This connectivity as shown by the larger values for average numbers of non-zero IGB observations is also the reason for the larger IGB values in the case of the familiarity-based network. However, the differences between IGB measures for middle-risk banks and the other two bank risk classes are not directly explained by connectivity levels. This is evidenced by the fact that the pattern of IGB values across bank risk classes is invariant to the network type. In our model (again, see Anselmo and Planck, 2012 for a full explanation of the simulation model and the bank-behavior model), middle-risk banks have limited exposure to high risk/high return investment opportunities available via the Non-Bank Entity (NBE). This limited exposure allows middle-risk banks to grow at a faster rate than their least-risky counterparts, but not as rapidly as risky banks. Thus, middle-risk banks are less likely than risky banks to need to borrow to cover a shortfall because of a default from the NBE. They are also more likely than least-risky banks to possess sufficient cash reserves to satisfy the cash requirements to loan to risky banks. Middle-risk banks may be seen as similar in more iterations of the model than the other two types of banks to nodes A and C in Figure 1. In these instances, these banks provide liquidity without receiving any from the system. 13

14 This situation will happen for all banks in the simulation, and middle-risk banks are often between other banks with regard to their network connections. But, because of the structure of the model, these banks are more likely to be in the network without being pass-through agents. On the other hand, risky banks are similar to least-risky banks with regard to average betweeness, but spend more time connecting banks to each other may also be seen as an artifact of the fact that risky banks are more likely to borrow in the interbank market and also, risky banks with solid balance sheets are very likely to lend to other risky banks in the interbank market. Least-risky banks have average IGB measures that are larger than those for risky banks regardless of network configuration. These banks also have the fewest instances of being on a shortest path between two other banks. Unlike middle-risk banks, which seem to be the most likely to be connected without having a IGB measure or with limited connectivity as reflected by their smaller IGB measure least-risky banks appear to be well-connected members of their respective networks when they are connected. The model also offers an explanation for this phenomenon. Least-risky banks are, as the system evolves, the smallest because they do not speculate in NBE assets. They do participate in the interbank market by providing liquidity, and because of the small relative size of loans they originate their claims are the last ones to be filled by borrowing banks. This in turn results in least-risky banks needing to, on occasion, utilize liquidity opportunities in the interbank market to meet reserve requirements. The presence of least-risky banks with positive IGB measures may be an indication of a liquidity event impacting larger banks that, first, forces these banks into the interbank market to meet short-term liquidity requirements. If the liquidity event persists, least-risky banks with claims on the larger banks will also be forced into the interbank market to meet short-term liquidity requirements thus the very similar average IGB numbers vis-à-vis risky banks, but the lower average number of positive IGB values. From a regulatory perspective, identification of least-risky banks and attention to their borrowing behavior may be a clue to unfolding liquidity-event-driven contagion in the interbank market. Based on our work, the situation where least-risky banks borrow to meet liquidity reqirements 14

15 caused by larger-bank liquidity issues appears to be insensitive to whether the basis for the interbank network is random or familiarity-based interbank loan connections. Conclusion We may generally think of network risk in terms of aggregate connectivity an exposure in our simulated interbank loan network. Using this idea of risk, the betweeness-centrality-based analysis seems to support the notion that familiarity-based networks are riskier than interbank overnight loan networks formed on a random basis. We base this on the large number of significant banks in the GCAB and IGB regressions, as well as on the magnitude of average IGB differences and the average number of IGB observations between the two network types. Of particular interest is the fact that these differences seem to be largely independent of the risk orientation of simulated banks. Differences in IGB measures between banks across risk categories, particularly with regard to middle-risk banks, were consistent for both types of networks, and IGB and connectivity numbers for least-risky banks may be useful initial indicators of network risk though that possibility must be verified with more analysis. A major next step for our overall banking-system modeling effort includes additional work on a hybrid network, where smaller (in this model, largely least-risk banks) banks do not participate directly in the interbank overnight loan market. Instead, these banks participate indirectly via a corresponding bank, also known as a banker s bank. For a rate that is a fraction of the interbank overnight rate, smaller banks in effect establish short-term deposits with corresponding banks, which then treat the pool of participating bank funds as an investable asset. Correspondent banks may allocate these funds to the interbank market or not. Our extension will therefore be in the form of a hybrid network-formation model, where smaller, less-risky banks invest for the short term with corresponding banks rather than in the interbank market. The corresponding banks, along with other larger banks, participate in the overnight interbank market using a variant of the familiarity model. The model will also be extended to more complex measures and implementations of bank levels of risk aversion, as well as a less naïve model of bank borrowing and lending behavior. We also are extending the model to include multiple NBEs, with connections between those NBEs so that 15

16 the dual network that we currently have is extended to the more realistic case where the system is really a series of interconnected subsystems, each with their own agent and network-risk characteristics. 16

17 References Anselmo, P. and M. Planck, Solvency Dynamics of an Evolving Agent-Based Banking System Model, Working Paper available at: Battiston, S., M. Puliga, R. Kaushik, P. Tasca, and G. Caldarelli, DebtRank: Too Central to Fail? Financial Networks, the FED, and Systemic Risk. Scientific Reports 2: 541, 1-6. Borgatti,S. P., M. G. Everett, and L. C. Freeman, UCINET 6 for Windows: Software for Social Network Analysis. Harvard, MA: Analytic Technologies. Borgatti, S. P., Centrality and Network Flow, Social Networks 27, Borgatti, S. P. and M. Everett, A Graph Theoretic Perspective on Centrality, Social Networks 28, Boss, M., H. Elsinger, M. Summer, and S. Thurner, 2004, The Network Topology of the Interbank Market, Quantitative Finance 4 (2004). Brandes, U A Faster Algorithm for Betweeness Centrality, Journal of Mathematical Sociology 25, Freeman, L. C., A Set of Measures of Centrality Based on Betweeness. Sociometry, 40, Freeman, L. C., Centrality in Social Networks Conceptual Clarification, Social Networks 1, Haldane, A. G. and R. M. May, Systemic Risk in Banking Systems, Nature 469, Martinez-Jaramillo, S., B. Bravo-Benitez, B. Alexandrova-Kabachova, and J. P. Solarzano-Margain, An Empirical Study of the Mexican Banking System s Network and its Implications for Systemic Risk. Banco de Mexico Working Paper Minoiu, C. and J. Reyes, A Network Analysis of Global Banking: , Journal of Financial Stability, 2, Neuman, E. J., G. F. Davis, and M. S. Mizruchi, (2008) "Industry consolidation and network evolution in U.S. global banking, ", Advances in Strategic Management, 25, Vitali, S. and S. Battiston, The Community Structure of the Global Corporate Network, White, D. R. and S. P. Borgatti, Betweeness Centrality Measures for Directed Graphs. Social Networks 16,

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19 Table 1. GCAB Regression Data GCAB Regressions Summary for 5 Trials 3-Day Overnight Loan Payback Period Random Interbank Networks Total Significant Risky Banks Middle Risk Banks Least Risky Banks Adjusted Trial Banks -/+ Share of Total -/+ Share of Total -/+ Share of Total R % % % % % GCAB Regressions Summary for 5 Trials 3-Day Overnight Loan Payback Period Familiar Interbank Networks Total Significant Risky Banks Middle Risk Banks Least Risky Banks Adjusted Trial Banks -/+ Share of Total -/+ Share of Total -/+ Share of Total R % % % % % 19

20 Table 2. IGB Regression Data IGB Regressions Summary for 5 Trials 3-Day Overnight Loan Payback Period Random Interbank Networks Total Significant Risky Banks Middle Risk Banks Least Risky Banks Adjusted Trial Banks -/+ Share of Total -/+ Share of Total -/+ Share of Total R % % % % % IGB Regressions Summary for 5 Trials 3-Day Overnight Loan Payback Period Familiar Interbank Networks Total Significant Risky Banks Middle Risk Banks Least Risky Banks Adjusted Trial Banks -/+ Share of Total -/+ Share of Total -/+ Share of Total R % % % % % 20

21 Table 3. IGB Averages and Number of Observations Non-Zero IGB Data for 5 Trials 3-Day Overnight Loan Payback Period Random Interbank Networks Trial Least Risky Middle Risk Risky Average Average Count Average Average Count Average Average Count Non-Zero IGB Data for 5 Trials 3-Day Overnight Loan Payback Period Familiar Interbank Networks Trial Least Risky Middle Risk Risky Average Average Count Average Average Count Average Average Count

22 Figure 1. An 8-agent/bank network. Bank 3 is connected, but has no shortest paths between any other banks passing through. The IGB measure for bank 3 is 0. Bank B is unconnected to the network, and will have a IGB measure of -1. All other banks have IGB values greater than 0. These figures were drawn using UCINET software (Borgatti, et. al., 2002). Figure 2. A second 8-agent bank network with 4 additional edges vis-à-vis the network in Figure 1. All agent/banks will have values for IGB > 0 if this is the network configuration. From the perspective of system solvency and the overall integrity of the interbank network, this configuration is riskier than the network depicted in Figure 1. 22

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