Financial Networks and Bank Liquidity

Financial Networks and Bank Liquidity✩ Thiago Christiano Silvaa,b,c,∗, Marcos Soares da Silvab , Benjamin Miranda Tabakc a University of São Paulo, São Paulo, Brazil Bank of Brazil, Brası́lia, Brazil c Catholic University of Brası́lia, Brası́lia, Brazil b Central Abstract Our paper is the first work that links banking liquidity performance and core-periphery network structures. We show that the core-periphery structure can improve liquidity performance of banks. We find that network centrality plays also a major role in the liquidity performance of banks. In special, central players often have better liquidity performance than peripheral members do. The results are relevant for policy making and financial regulation. Keywords: liquidity, core-periphery, network topology, financial stability, banking regulation, Basel III JEL Classification: D85, G21, G28, G38. 1. Introduction The recent international financial crisis has attracted increasing attention of bank regulators and of the banking community to the need of developing new mechanisms for monitoring and managing liquidity risk, both in the bank-specific and systemic levels. Following this line, Basel III has included guidelines for a new standard of policy recommendations that addresses issues related to liquidity. In special, Basel III now requires banking institutions to maintain high-quality liquid assets that can be easily converted to cash, so as to cover their liquidity needs in scenarios of stressed cash flows for a horizon of 30 days (cf. the liquidity coverage ratio in BCBS (2013)). In addition, banks should have sufficient liquid assets to ensure long-term liquidity needs by programming the liquidity flow for a one-year horizon (cf. the net stable funding ratio in BCBS (2014)). It is expected that the introduction of these new standard will confer more resilience to financial institutions against liquidity shocks. Bhattacharya & Thakor (1993) highlight that the main question about liquidity within a financial system relates to the role that banks exert in manipulating and matching different shortterm liabilities and assets maturities. Kashyap et al. (2002) argue that banks operate as liquidity ✩ Thiago C. Silva and Benjamin M. Tabak gratefully acknowledge financial support from the CNPq foundation. author. Address: Banco Central do Brasil, Depep/Conep, Andar 13, Setor Bancário Sul (SBS) Quadra 3 Bloco B - Ed. Sede, CEP: 70074-900, Brası́lia, Distrito Federal, Brazil. Telephone: +55 (61) 3414-3870. Email addresses: [email protected] (Thiago Christiano Silva), [email protected] (Marcos Soares da Silva), [email protected] (Benjamin Miranda Tabak) ∗ Corresponding Preprint submitted to Journal Of Network Theory In Finance August 30, 2016 providers through the use of short-term funds raised from the public. This fact can cause maturity mismatches, exposing banks to non-diversified shocks, which can ultimately lead them to bankruptcy (Diamond & Dybvig (1983)). Another important topic related to liquidity is of interbank networks. In their seminal work, Allen & Gale (2000) show that liquidity shocks can be further amplified in the financial system via contagion processes that can propagate through interbank relationships. Following their research, several works explore the influence of different network topologies in establishing a more robust or fragile financial system. For instance, De Masi & Gallegati (2012) use the interbank network to investigate the credit relationships between banks and firms in the Italian market, while Fujiwara et al. (2009) provide a similar study for the Japanese interbank market. Castro Miranda et al. (2014), in turn, explore the network topology of the Brazilian payments system. Guerra et al. (2014) study how network interconnectivity is relevant to explain bank efficiency and Anand et al. (2013) examine the role of macroeconomic fluctuations, asset market liquidity, and network structure in determining contagion in financial systems. A very relevant question is how the network topology formed by financial operations between market participants influences banking liquidity performance.1 In this line of research, Craig et al. (2015) investigate the role of private information and interbank relationship lending in determining the price of liquidity in the German financial market. Similarly, Cocco et al. (2009) use the same type of data to study the bank relationship lending using bilateral interbank data from the federal funds market in the Portuguese case. All of these works use network theory to explain how bank liquidity behaves. However, these works limit their investigation to bank-level network measures, such that there is still a gap in the literature pertaining the role that the global network structure plays in determining bank liquidity. Our work is the first to try to fill in this gap. Several researches across jurisdictions report that interbank markets have a core-periphery structure, such as the domestic interbank networks of the USA (Markose et al. (2012)), of the Netherlands (in ’t Veld & van Lelyveld (2014)), of Germany (Craig & von Peter (2014)), of Italy (Fricke & Lux (2015)), among many others. These findings suggest that financial institutions (FI) seem to self-organize in core-periphery structures. To better understand the underlying formation mechanism of these networks, Lux (2015) shows that the resulting equilibrium state of an endogenous network formation process realized by banks is effectively reached when banks are disposed in a core-periphery structure. In this way, we focus on this particular network structure when studying bank liquidity. Core-periphery structures present two perceptible mesoscale structures: the core and the periphery. Core members intermediate financial operations between members of the periphery and are also strongly connected to other core members. In contrast, periphery members can only establish a few connections with core members and not among similar peers. Though the theoretical and structural aspects of core-periphery networks are clear, the consequences that core-periphery structures bring for the banking liquidity performance stand as an important question in the research agenda. This is the first work that attempts to shed light in this question by analyzing how network topology, in special core-periphery, relates to the banking liquidity performance. 1 Krause & Giansante (2012) show that the characteristics of interbank lending network is an important determinant of contagion within financial markets. 2 We build our empirical model using a dynamic panel that employs unique supervisory and accounting data of the Brazilian interbank market from 2008 to 2014. We control for changes in the macroeconomic scenario and for bank-specific characteristics. We also use controls for network measurements to capture whether banks are located at the network core or periphery. To the best of our knowledge, this is the first paper that makes use of a comprehensive set of network measurements to describe banking liquidity. We also contribute to the literature by presenting a thorough network analysis of the Brazilian interbank network. In this analysis, we focus on understanding the banks’ roles and the network structural properties. We employ the liquidity coverage ratio (LCR) as in Basel III (BCBS (2013)) as a proxy to liquidity performance of banks. Essentially, LCR measures the amount of liquid resources that is available for an institution to withstand expected and unexpected cash flows in the next 30 days, under severe stress scenarios. With this setup, we are able to capture operational requirements that are effectively demanded by the Brazilian jurisdiction. These stress scenarios simulate ruptures in historical trends of variables related to cash flow estimates. We mold these scenarios by employing parameters that are extracted from historical references of experienced past crises. In general terms, we consider the potential cash flow that banks need to face the following stress situations: 1) wholesale and retail deposits run-off; 2) market risk stress on liquidity, including firesales, variation on prices, interest rates, foreign currencies, and stocks; and 3) 30-day contractual cash flows, including private securities and repos. In order to explain the liquidity performance of FIs, we select a comprehensive set of network measurements to extract structural information of the network from different aggregative viewpoints, ranging from local to global perspectives. For clarity, we follow Silva & Zhao (2015) who classify network measurements into three intuitive classes: strictly local, quasi-local, and global network measures. Strictly local measures are vertex-level indices that only use information of FIs in an isolated manner from the remainder of the network. Quasi-local network indicators, in turn, are vertex-level measures and use both information of the FI itself and also of its direct neighborhood to derive information. Finally, global measurements are network-level indices that make use of all of the network structure. Our paper is the first work that links liquidity performance of banks and core-periphery network structures. Even though core-periphery structures are found in several domestic interbank networks, little is known on the economic implications of this peculiar network structure. We here address this gap by giving one implication of such network structure on the liquidity performance of banks. Also, we show that the core-periphery network structure can improve the liquidity performance of banks. As the mainstream in the literature advocates that banks join interbank markets mostly to adjust their liquidity positions, this finding suggests that the core-periphery structure that emerges from financial operations between market participants enhances, on average, the liquidity positions of banks. In addition, since core-periphery is a common network structure across jurisdictions, our results may be of general interest to the community. In addition to that main finding, we also use a comprehensive set of network measures to explain the factors that increase or decrease the liquidity performance of banks. This study per se has also not been performed in the literature. For instance, we see that network centrality plays also a major role in the liquidity performance of banks. In special, central players often have better 3 liquidity performance than peripheral members do. Considering that core-periphery structures can unchain large liquidity deficits in the network in case a bank in the core defaults, our results on centrality have strong implications in the financial stability area. This is because central players are often those that are in the network core. Thus, our results show that the liquidity performances of core banks are, on average, enhanced. Consequently, the systemic risk of the financial system as an entirety is reduced. With respect to strictly local measures, we analyze the Brazilian interbank network using the degree and strength measurements. We find that both funding and investment diversifications are lower for non-large banks, revealing that these institutions, on average, assume secondary roles in the interbank market. In addition, we verify that the average funding amount of large banks is larger than their average investment, because they diversify more in the lending perspective. In what concern quasi-local measures, we employ centrality measures (closeness and betweenness), criticality, and dominance indicators. Our results signal that non-large banks are peripheral in the sense of centrality measures. In contrast, large banks have the largest centrality measures, corroborating the fact that they are members of a network core. Banks in this core act as intermediaries to other entities; hence, they are easily reachable from any point in the network. In addition, we show that non-large banking institutions are critical during 2008 in the Brazilian interbank market, but that criticality diminishes after that period. Large banks, in contrast, present significant criticality during the entire studied period. Two factors contribute to the maintenance of the considerable criticality of large banks: 1) they have larger out-strength in the interbank market; and 2) they are frequently funded by non-large banks, which in turn are more leveraged and present lower capital buffers. Furthermore, we find that non-banks do not have an effective dominance as lenders nor borrowers. Opposed to that, the dominance of large banks in both perspectives constantly increases from 2008 to 2014. With reference to global measures, we utilize the density, diameter, rich-club coefficient, and assortativity. We show that the Brazilian interbank network is very sparse during the period under analysis. The network diameter is very small, fluctuating around 3 or 4 intermediation chains. We also confirm the existence of a “rich-club” of banking institutions that have large degree. In addition, we find that the interbank network shows a clear disassortative mixing pattern. All of these facts suggest the presence of a solid core of large banking institutions that are strongly interconnected to the remainder of the network. Since they can easily reach most banks in the network, they act as liquidity providers in the interbank market. We find that banks have moderate cost for adjusting their liquidity performance in the interbank market. Moreover, the short-term adjustment costs for liquidity strongly depend on the liquidity performance of banks. For instance, when we consider all of the banking institutions, we verify that a liquidity shock takes about four quarters to absorb roughly 95% of its initial impact. Now, when we only consider banks with low liquidity performances in the analysis, we find that they need about two years to recover from an identical liquidity shock. In contrast, banks with high liquidity performance only take two quarters to recover from that same liquidity shock. Therefore, banks with better liquidity performances have lower adjustment costs against liquidity shocks. This finding suggests that banks with low liquidity performance that are at the verge of becoming illiquid may be very prone to external liquidity shocks, as they take longer to recover or adjust their balance sheets. In this way, they are more susceptible of defaulting. Conversely, banks with high 4 liquidity performance that display the same liquidity positions can better withstand these external liquidity shocks, as they can adjust their balance sheets with more flexibility. In our dynamic panel models, we use Silva et al. (2016b)’s methodology to capture the coreperiphery network structure. The authors show that networks that present a strong disassortative mixing together with the presence of the rich-club effect have core-periphery topology. Therefore, we employ the assortativity and the rich-club coefficient as proxies to extract how well the network fits into a core-periphery network structure. Though this network topology leads to better banking liquidity performance, it comes with costs in terms of financial stability. According to a comparative analysis between different types of network structures performed by Lee (2013), a core-periphery network with a deficit core bank gives rise to the highest level of systemic liquidity shortage, implying greater systemic risk. To identify how compliant the network realization is to a compliant core-periphery structure, we combine the network measures (i) assortativity and (ii) rich-club coefficient. Considering that large banks are usually located in the core because they intermediate more financial operations, we expect that non-large banks will compose the periphery. In a perfect core-periphery structure, the periphery only connects to the core, which in turn intermediate and provide liquidity to the system to another peripheral member. Therefore, core-periphery networks must have a clear disassortative pattern. However, the network will not have a perfectly disassortative network because core members also connect to each other (similar peers). Considering that only a small fraction of banks are large, the overall network disassortativity will be strongly negative for core-periphery financial networks with heterogeneous bank size distributions. To enforce the strong interconnectedness of core members, we inspect rich-club coefficient. We expect that strongly connected cores will have large rich-club coefficients. In this paper, we also contribute to the literature by providing insights as to how centrality and distance network measurements influence the liquidity performance of banks. We relate centrality with how often banks intermediate financial transactions. We find that central players, in general, have better liquidity performances than those players that are located in the periphery. In addition, we relate how easy liquidity can flow within an interbank network to the network diameter. We find that, as the network diameter gets larger, the harder is to liquidity to flow from one extreme to the another, leading to a decrease in the overall liquidity performance of banks. Our results also corroborate that the Brazilian interbank market effectively plays the role of liquidity provider for its constituent members. We also study how the investments diversification impacts the liquidity performance of banks. We find that banks with less concentrated investments portfolios, on average, present better liquidity positions. In addition, we relate market discipline to the positive association we unveil between the default probability and the liquidity performance of banks.2 Honga et al. (2014) find similar results for the US industry. This finding suggests that banks with potential solvency problems make strong efforts to emit signals or actions with the purpose of conveying the apparent information that their liquidity positions are satisfactory. Intuitively, banks with relative large default probabilities must maintain larger liquidity buffers against unexpected external shocks because they do not have wide access to the interbank market 2 The computation of the default probability only takes into account credit and market risks, hence it does not have a liquidity component. 5 and have higher costs for adjusting against external liquidity shocks. The paper proceeds as follows. In Section 2, we present the employed data set, as well as some of its structural characteristics. In Section 3, we supply a topological analysis of the Brazilian interbank market by using several complex network measurements that capture different aggregative structural viewpoints of the network topology. In Section 5, we define the empirical econometric model to explain banking liquidity performance. In Section 6, we discuss the results from our econometric models. In Section 7, we present robustness tests to check our empirical model. In Section 8, we explore policy implications based on our results. Finally, in Section 9, we draw some conclusions. 2. Data In this work, we merge together unique databases with supervisory and accounting data maintained by the Central Bank of Brazil that contain bilateral exposures between pairs of financial institutions and balance sheet statements.3 We report qualitative and quantitative aspects of the Brazilian financial network on a quarterly basis from the beginning of 2008 to the end of 2014. We consider all types of unsecured financial instruments registered in the Central Bank of Brazil. Due to domestic regulatory norms, financial institutions must register and report all securities and credit operations, which reinforce the data representativeness and quality. Among examples of financial instruments, we highlight credit, capital, foreign exchange operations and money markets. The money market comprises operations with public and private securities. Both types of operations are registered and controlled by different institutions. We collect and match bilateral information between financial institutions using several financial systems in the Brazilian jurisdiction. We have information on operations with private securities provided by the Cetip,4 on operations between FIs with credit characteristics supplied by the SCR,5 and on swaps and options registered by the BM&FBOVESPA.6 There is a total of 107 types of active operations based on unsecured financial instruments in the Brazilian market. In order to facilitate the understanding of the total amount flowing in 3 The collection and manipulation of the data were conducted exclusively by the staff of the Central Bank of Brazil. 4 Cetip is a depositary of mainly private fixed income, state and city public securities and other securities representing National Treasury debts. As a central securities depositary, Cetip processes the issue, redemption and custody of securities, as well as, when applicable, the payment of interest and other events related to them. The institutions eligible to participate in Cetip include commercial banks, multiple banks, savings banks, investment banks, development banks, brokerage companies, securities distribution companies, goods and future contracts brokerage companies, leasing companies, institutional investors, non-financial companies (including investment funds and private pension companies) and foreign investors. 5 Among several other types of legal attributions, SCR (Sistema de Informações de Crédito do Banco Central), which is operated by the Central Bank of Brazil, holds operations and securities with credit characteristics and associated guarantees contracted by FIs. 6 BM&FBOVESPA is a Brazilian-owned company that was created in 2008 through the integration of the São Paulo Stock Exchange (Bolsa de Valores de São Paulo) and the Brazilian Mercantile & Futures Exchange (Bolsa de Mercadorias e Futuros). As Brazil’s main intermediary for capital market transactions the company develops, implements and provides systems for trading equities, equity derivatives, fixed-income securities, federal government bonds, financial derivatives, spot FX and agricultural commodities. 6 each type of market, we aggregate these 107 financial instruments into relevant macro-groups, as illustrated in Table 1. In order to group different financial instruments into macro-groups, we take into account their total gross amount of active operations, as well as a logical relationship among them. Table 1: Unsecured financial instruments that are traded in the Brazilian financial network. We cluster them together in macro-groups, such that financial instruments in the same group share logical relationships with respect to the nature of the financial operation. Acronym Description of the macro-group # Financial instruments DI Mandatory DI Credit Financial bill CCB FDS Swap Debenture Transfer Others Interfinancial deposits Mandatory interfinancial deposits Credit operations Financial bills Bank credit bills Social development fund shares Swap operations Debentures Interfinancial transfers Other financial instruments 1 10 1 7 1 1 1 1 1 83 TOTAL 107 We consider financial exposures that exist among different financial conglomerates or individual FIs that do not belong to conglomerates. We remove intra-conglomerate exposures in the analysis. We contemplate all banking institutions in the Brazilian financial market, which encompass the following macro-segments that are defined on a legal basis: • Banking I: commercial banks, multiple banks with commercial portfolio, or federal savings banks. • Banking II: multiple banks without commercial portfolio and investment banks. • Banking IV: development banks. Since large banks have different characteristics in relation to non-large banks—such as additional capital requirements and better opportunities in the market in general—we report our results by discriminating large and non-large banks. We first build a cumulative distribution function of the financial institutions’ total assets in the financial system and rank them in descending order. Then, we classify as large or as non-large depending on the region that the financial institutions fall in that ranked distribution. We consider as large banks those first institutions that fall into the 0% to 75% of the total assets of the system. Otherwise, we classify them as non-large banks. Figure 1a displays the number of financial institutions that are active in the interbank market from 2008 to 2014. We can see that the total number of participants remains roughly constant 7 throughout the period, specially for large banks. In special, the number of large banking institutions is, on average, 7.32, while of non-large banks, 120.43. Figure 1b portrays the total market shares of the large and non-large banks. While non-large banks have a roughly constant share in the interbank market, the market share of large banks suffers a large increase in the period of June 2010 to June 2011. This increase is due to the large injection of onlending by the government via development banks. Figure 1c indicates the average capital buffers of large and non-large financial institutions as a function of time. We consider the capital buffer as the amount of capital that exceeds the minimum capital requirements that Basel III recommends. We can see that large banks detain the most liquidity of the financial system mainly because of their relative size. Figure 1d shows the average within-network leverage of large and non-large banks. We compute the within-network leverage of a financial institution as the ratio of its liabilities inside the network and its capital. More leveraged entities have more external financing and therefore can impact more the financial system in case they default. In average, we see that non-large banks are more leveraged than large banks. The large change on the average within-network leverage from June to September 2010 on both large and non-large banks happens on account of the massive amounts of onlending that large development banks provided to the banking system at that time. Among other factors, the considerable decrease on the within-network leverage of large banks from December 2011 to March 2012 occurs because of the beginning of increase cycle of the domestic policy rate in Brazil that remained until the end of our sample. The increase on the domestic policy interest rate provides incentives for substitution of financial assets to federal bonds as their yields increase. Since our sample only deals with unsecured financial instruments—which does not encompasses federal bonds—we verify this large decrease on the within-network leverage of large banks as a consequence of this substitutive effect. Figure 2 displays the total amount of unsecured operations in the Brazilian interbank market. Since the amount of transfers is prevalent against all of the others financial instruments, in Fig. 2a we highlight how the transfers amount compares to the sum of all of the others financial instruments. In turn, Figure 2b exhibits the evolution of all of the financial instruments except transfers. We note a vertiginous increase in the transfers amount in September 2010, which is due to transfers of major development banks to other banking institutions.7 This finding is consistent with the Financial Stability Report of the Central Bank of Brazil published in the first semester of 2011 BCB (2011), which explains that the large amounts of transfers to banking institutions occurred to overcome the liquidity shortage of the last international financial crisis. Except for operations related to transfers, we can also see that interfinancial deposits are the majority and remain roughly constant until the end of 2012, period in which they start to reduce. Exposures related to credit operations, in contrast, assume an expansive behavior. Exposures due to operations related to financial bills take on significant values in the interbank market operations after the start of 2012, which coincides with the decline of operations related to interfinancial deposits. Figure 3 depicts exposure networks in the Brazilian interbank market for September 2008, 7 Figure 1b shows a clear evidence of this fact as there is a steep increase in the total market share of large banking institutions exactly in September 2010, which is due to these large transfers amounts. 8 140 x 10 10 16 100 Market Shares [US$] Number of FIs 120 Large banks Non−large banks 80 60 40 14 12 10 Large banks Non−large banks 8 6 4 20 0 03/2008 06/2008 09/2008 12/2008 03/2009 06/2009 09/2009 12/2009 03/2010 06/2010 09/2010 12/2010 03/2011 06/2011 09/2011 12/2011 03/2012 06/2012 09/2012 12/2012 03/2013 06/2013 09/2013 12/2013 03/2014 06/2014 09/2014 12/2014 0 (a) Total number of FIs 03/2008 06/2008 09/2008 12/2008 03/2009 06/2009 09/2009 12/2009 03/2010 06/2010 09/2010 12/2010 03/2011 06/2011 09/2011 12/2011 03/2012 06/2012 09/2012 12/2012 03/2013 06/2013 09/2013 12/2013 03/2014 06/2014 09/2014 12/2014 2 (b) Total market shares 1.4 10 Large banks Non−large banks 1.2 Large banks Non−large banks 9 10 Avg. Leverage Avg. Capital Buffer [US$] 10 1 0.8 0.6 0.4 0.2 8 03/2008 06/2008 09/2008 12/2008 03/2009 06/2009 09/2009 12/2009 03/2010 06/2010 09/2010 12/2010 03/2011 06/2011 09/2011 12/2011 03/2012 06/2012 09/2012 12/2012 03/2013 06/2013 09/2013 12/2013 03/2014 06/2014 09/2014 12/2014 03/2008 06/2008 09/2008 12/2008 03/2009 06/2009 09/2009 12/2009 03/2010 06/2010 09/2010 12/2010 03/2011 06/2011 09/2011 12/2011 03/2012 06/2012 09/2012 12/2012 03/2013 06/2013 09/2013 12/2013 03/2014 06/2014 09/2014 12/2014 10 (c) Average capital buffer (d) Average leverage Figure 1: Aggregate descriptive indicators related to the Brazilian interbank network and to the accounting data of financial institutions. The y-axis of (b) and (c) are in log-scale. December 2011, and December 2014. For each of these dates, we apply three filtering criteria so as to better visualize the amounts that are being lent and borrowed within the network. The filters are for exposures larger than USD 10 million, 100 million, and 1 billion. We see a distinctive and much sparser network with exposures larger than USD 1 billion in September 2008 in relation to the other networks in December 2011 and 2014. These, in turn, seem to be similar to each other. This suggests that, in September 2008, the great majority of lending and borrowing operations were in smaller amounts. Moreover, we see that large banks intermediate and also concentrate a large portion of unsecured financial operations, which hints us to the fact that they are members of a network core. We will quantitatively confirm this claim using network analysis tools in Section 3. 9 10 18 x 10 Total Amount [US$] 16 Transfer Remainder 14 12 10 8 6 4 0 03/2008 06/2008 09/2008 12/2008 03/2009 06/2009 09/2009 12/2009 03/2010 06/2010 09/2010 12/2010 03/2011 06/2011 09/2011 12/2011 03/2012 06/2012 09/2012 12/2012 03/2013 06/2013 09/2013 12/2013 03/2014 06/2014 09/2014 12/2014 2 (a) Transfer vs. remainder 10 x 10 4.5 Total Amount [US$] 4 3.5 3 2.5 2 1.5 1 Debenture DI Mandatory DI Financial Bill Credit Swap FDS CCB Others 0 03/2008 06/2008 09/2008 12/2008 03/2009 06/2009 09/2009 12/2009 03/2010 06/2010 09/2010 12/2010 03/2011 06/2011 09/2011 12/2011 03/2012 06/2012 09/2012 12/2012 03/2013 06/2013 09/2013 12/2013 03/2014 06/2014 09/2014 12/2014 0.5 (b) All instruments, except transfers Figure 2: Total amount of unsecured exposures in the Brazilian interbank market. We discriminate the curves using the macro-groups as defined in Table 1. 3. Topological analysis of the interbank network We provide the mathematical underpinnings of how we compute the network measurements in Appendix A. In this section, we focus on providing their economic meaning in the context of financial networks. For the sake of clarity, we inform the descriptive statistics of the local, quasilocal, and global network measures in Tables 2, 3, and 4, respectively. We examine each of them in the following. 10 Table 2: Summary results for local network measurements. All Banks Network Measure Large Banks Non-large Banks Avg. Std. Min. Max. Avg. Std. Min. Max. Avg. Std. Min. Max. Out-degree 9.03 0.74 7.53 10.32 49.32 5.46 36.63 56.86 6.60 0.94 4.94 8.29 In-degree 9.03 0.74 7.53 10.32 24.71 2.02 20.67 30.29 8.08 0.78 6.62 9.53 Out-strength (x USD bi) 1.94 0.79 0.80 3.10 30.38 13.10 9.77 46.12 0.23 0.06 0.15 0.33 In-strength (x USD bi) 1.94 0.79 0.80 3.10 20.23 6.32 31.51 0.84 0.29 0.42 1.25 9.13 Table 3: Summary results for quasi-local network measurements. All Banks Network Measure Large Banks Non-large Banks Avg. Std. Min. Max. Avg. Std. Min. Max. Avg. Std. Min. Max. Avg. shortest path 2.01 0.02 1.96 2.05 1.54 0.06 1.48 1.69 2.04 0.02 1.99 Closeness (×10−3 ) 0.40 0.01 0.38 0.43 0.52 0.02 0.48 0.57 0.39 0.01 0.37 2.08 0.42 Betweenness (×10−3 ) 0.70 0.06 0.60 0.84 10.09 1.76 5.55 12.43 0.14 0.04 0.08 0.23 Criticality 0.97 0.17 0.68 1.29 1.54 0.28 0.91 2.27 0.93 0.19 0.63 1.32 Lender dominance 0.12 0.02 0.08 0.16 0.13 0.03 0.09 0.18 0.12 0.02 0.08 0.16 Borrower dominance 0.86 0.04 0.80 0.92 4.47 0.58 3.00 5.73 0.64 0.04 0.59 0.71 Table 4: Summary results for global network measurements. Network Measure Avg. Std. Min. Max. Assortativity -0.33 0.04 -0.39 -0.25 Rich-club coefficient -0.33 0.04 -0.39 -0.25 Density 0.07 0.01 0.06 0.08 Diameter 3.73 0.26 3.00 4.00 Network-level shortest path distance 2.01 0.02 1.96 2.05 11 (a) September 2008 (> 10M) (b) September 2008 (> 100M) (c) September 2008 (> 1B) (d) December 2011 (> 10M) (e) December 2011 (> 100M) (f) December 2011 (> 1B) (g) December 2014 (> 10M) (h) December 2014 (> 100M) (i) December 2014 (> 1B) Figure 3: Snapshots of the unsecured exposure network that represents the Brazilian interbank market. The shapes convey the bank macro-segments. The circles denote institutions classified as Banking I, the squares, Banking II, and diamonds, Banking IV. The colors illustrate the bank control types. The green color portrays domestic private institutions; the red color, government-owned institutions; the blue color, private with foreign control institutions; and the black color, private with foreign participation institutions. The vertices’ sizes are proportional to the corresponding institutions’ sizes. 3.1. Degree (strictly local measure) We can conceive the in- and out-degree of a vertex as measures for quantifying the liabilities and assets diversification, respectively, of market participants. As these indices increase, FIs become more diversified in terms of funding (liabilities side) or investments (assets side). In addition, FIs with large degrees are more susceptible to within-network events, as they are more susceptible to impacts that connect the origin of the event to the refereed FI. This is true because there are potentially several paths through which the impact can travel. Among several examples of possible financial events studied by the literature, we highlight the occurrence of idiosyncratic or joint defaults. However, the topological aspects of the network play a crucial role in the propagation of such kinds of events. As such, an FI with large degree will not necessarily suffer a larger impact than an FI with small degree as the interbank connectivity pattern may amplify or reduce the impact accordingly to the direct or indirect neighborhoods of these FIs. Figures 4a and 4b depict the evolution of the average out-degree and the average in-degree, 12 35 50 30 Large banks Non−large banks 30 20 25 20 10 10 0 5 (a) Out-degree Large banks Non−large banks 15 03/2008 06/2008 09/2008 12/2008 03/2009 06/2009 09/2009 12/2009 03/2010 06/2010 09/2010 12/2010 03/2011 06/2011 09/2011 12/2011 03/2012 06/2012 09/2012 12/2012 03/2013 06/2013 09/2013 12/2013 03/2014 06/2014 09/2014 12/2014 40 Avg. In−Degree 60 03/2008 06/2008 09/2008 12/2008 03/2009 06/2009 09/2009 12/2009 03/2010 06/2010 09/2010 12/2010 03/2011 06/2011 09/2011 12/2011 03/2012 06/2012 09/2012 12/2012 03/2013 06/2013 09/2013 12/2013 03/2014 06/2014 09/2014 12/2014 Avg. Out−Degree respectively, of the Brazilian interbank network. Both funding and investment diversifications are lower for non-large banks, revealing that these institutions, on average, assume a smaller number of financial operations than large banks in the unsecured interbank market. This is expected because non-large banks have lower amounts of external and internal financing in relation to large banks. As such, they maintain financial operations with a smaller number of counterparties to contain monitoring costs. We also notice a slight downward trend for the funding and investment diversifications for non-large banks, suggesting that they are concentrating more financial operations on a subgroup of banks. In contrast, the within-network funding and investment portfolios of large banks roughly assume an upward trend in the studied period. The number of borrowing and lending operations largely increases from December 2008 to March 2009. The increase on the borrowing and investment portfolios of banks in this period may be related to the uncertainties of financial agents that were brought by the global financial crisis. In this way, banks were less willing to be overly exposed to few banks and therefore diversified more. After this date, the in- and out-degree of large banks tends to stand still until the end of the sample. Still regarding large banks, we see that average out-degree is larger than the average in-degree throughout the entire sample, showing that large banks prefer to diversify more on their investment side rather than their funding side. Both the investment and funding diversification profiles here are biased downwards because we are only considering interrelationships that happen inside the financial network composed of financial institutions. On the one hand, we are not considering retail and wholesale deposits that account for a large parcel of the external financing banks receive and would increase the funding diversification estimates. On the other hand, we are not considering loans to the real sector—such as to firms and households—that would increase the investment diversification estimates. Since the main topic of this paper is to understand how the network structure relates to bank liquidity, we focus on the interbank market that is the main channel of liquidity management of banks. (b) In-degree Figure 4: Evolution of the in- and out-degree of the participants in the Brazilian interbank network. We discriminate the trajectories by bank sizes (large or non-large). 13 3.2. Strength (strictly local measure) In a network of exposures, the out-strength represents the amount of money that an FI has invested in that market, providing a measure of total exposure or dependence of that entity to a specific market segment. Note that as the out-strength of an institution increases, it is more likely that it will be more and more susceptible to impacts due to its potential higher vulnerability in that market. In contrast, the in-strength symbolizes the amount of money an FI has received from players of that market segment. As the in-strength of an entity grows larger, it is more likely that it will be more and more dominant in the borrower perspective in the market. 11 11 10 10 In−Strength [US$] Large banks Non−large banks 9 Large banks Non−large banks 9 10 10 8 8 10 03/2008 06/2008 09/2008 12/2008 03/2009 06/2009 09/2009 12/2009 03/2010 06/2010 09/2010 12/2010 03/2011 06/2011 09/2011 12/2011 03/2012 06/2012 09/2012 12/2012 03/2013 06/2013 09/2013 12/2013 03/2014 06/2014 09/2014 12/2014 10 10 10 10 (a) Out-strength 03/2008 06/2008 09/2008 12/2008 03/2009 06/2009 09/2009 12/2009 03/2010 06/2010 09/2010 12/2010 03/2011 06/2011 09/2011 12/2011 03/2012 06/2012 09/2012 12/2012 03/2013 06/2013 09/2013 12/2013 03/2014 06/2014 09/2014 12/2014 Avg. Out−Strength [US$] 10 (b) In-strength Figure 5: Evolution of the in- and out-strength of the participants in the Brazilian interbank network. We discriminate the trajectories by bank sizes (large or non-large). We report the y-axis in log-scale. While the degree subsides in determining how diverse are the funding and investment portfolios of an FI, the strength indicates the total amount that is being funded or invested in the network. Figures 5a and 5b display the average out-strength and the average in-strength, respectively, in the interbank market. For both indicators, we see upward trends during this period, with predominance of amounts invested and funded by large banks. In addition, the ratio of the average total amount invested and funded remains roughly constant at 1. Putting together this fact with the observation that the investment diversification is larger than the funding diversification of large banks (remind Fig. 4), we conclude that the average funding that large banks receive is larger than their average investment in the interbank market. This suggests that large banks prefer to diversify more in their investment portfolio management in relation to their funding portfolio management. We can visualize this fact in Figs 6a and 6b, which depict the average amount lent to each neighbor and the average amount borrowed from each neighbor in the financial market. 3.3. Closeness (quasi-local measure) We can relate the concept of closeness to the efficiency in complex networks (Latora & Marchiori (2002)), in the sense that efficiency measures how well information propagates throughout 14 8 16 10 8 6 2 0 x 10 8 14 12 10 8 Large banks Non−large banks 6 4 2 0 03/2008 06/2008 09/2008 12/2008 03/2009 06/2009 09/2009 12/2009 03/2010 06/2010 09/2010 12/2010 03/2011 06/2011 09/2011 12/2011 03/2012 06/2012 09/2012 12/2012 03/2013 06/2013 09/2013 12/2013 03/2014 06/2014 09/2014 12/2014 4 Large banks Non−large banks Avg. In−Strength / In−Degree x 10 03/2008 06/2008 09/2008 12/2008 03/2009 06/2009 09/2009 12/2009 03/2010 06/2010 09/2010 12/2010 03/2011 06/2011 09/2011 12/2011 03/2012 06/2012 09/2012 12/2012 03/2013 06/2013 09/2013 12/2013 03/2014 06/2014 09/2014 12/2014 Avg. Out−Strength / Out−Degree 12 (a) Out-strength / out-degree (b) In-strength / in-degree Figure 6: Evolution of the in- and out-strength to in- and out-degree ratios of the participants in the Brazilian interbank network. We discriminate the trajectories by bank sizes (large or non-large). We report the y-axis in logscale. the network. In this way, FIs with a large closeness indices are efficient in propagating information, both at global and local scale. From a liquidity point of view, these types of FIs have facility in obtaining funding from other players in the market, as they play a central role in the network. Figure 7a shows how the closeness index varies for large and non-large banks in the interbank market network. We note that the closeness displayed by large banks is larger than of non-large banks. In addition, the trajectories of the closeness indices for both large and non-large banks seems to be stable, with considerable fluctuations. 3.4. Betweenness (quasi-local measure) We can understand the betweenness as how active banks are in intermediating financial operations between different market participants. Banks that are very active in this function can be regarded as liquidity providers in the financial network. The between is a centrality measure that relies on the number of shortest paths that pass through a given vertex. In the literature, there are other centrality measures that relies on feedback and the spectrum of the graph (Silva & Zhao (2016)). However, they are highly correlated to each other. In this way, we select the betweeness to give a sense of large and non-large banks relate to network structure in terms of structural centrality. Figure 7b depicts the betweenness for large and non-large banking institutions that participate in the interbank market. We note that non-large banks are mainly peripheral in the sense that they almost do not take part in the communication through the shortest path of other two entities in the network. In contrast, large banks have the largest betweenness values and show an upward trend in the period. The increase in the centrality played by large banks corroborates the fact that they are members of a network core. Banks in this core act as intermediaries to other entities; hence, they are easily reachable from any point in the network. 15 3.5. Dominance (quasi-local measure) We can interpret the dominance as how important one bank is for their neighbors in terms borrowing and lending operations. If a bank is dominant, then it is responsible for a large fraction of the funding or investment portfolios of its neighborhoods. The removal of dominant FIs may cause large impacts on their direct neighbors, as they play a central role in their funding or investment operations. Figures 7c and 7d display the dominance of large and non-large banks acting as lenders and borrowers, respectively, in the interbank market. Non-banks do not have an effective dominance as lenders nor borrowers in any given time of the studied period. However, the dominance as lenders and borrowers of large banks constantly increases from 2008 to 2014. We can give special attention for the interval from September 2008 to December 2008, in which the dominance of large banks acting as borrowers and lenders significantly increased. 3.6. Criticality (quasi-local measure) We can conceive the criticality as a quasi-local measure of transmission of liquidity shocks between FIs. Note that, in the spectrum of the criticality, the local importance of an FI is not directly related to its size; rather, it is represented by its creditors’ vulnerabilities, measured by their net liabilities to capital buffer ratios. Figure 7e reports the criticality indices for large and non-large banks in the period from 2008 to 2014. Except for a large portion of 2008, on average, non-large banking institutions are not critical for the given sample and show a downward trend, suggesting that their neighbors are not vulnerable to them. Opposed to that, on average, large banks are critical, with a slight upward trend during the studied period, with a prominent peak in December 2008. Two factors contribute to the maintenance of the considerable criticality of large banks: 1) they have larger out-strength in the interbank market; and 2) they are frequently funded by non-large banks, which in turn are more leveraged and present lower capital buffers. 3.7. Density (global measure) The density give us a sense of how connected the financial network is. Large values for density indicate a high number of financial operations between market participants. In practice, we observe in the literature that interbank networks (Silva et al. (2016b,a)) are often very sparse and payment transfer networks are somewhat dense (Castro Miranda et al. (2014)). Figure 8a shows the density of the interbank market from 2008 to 2014. The network density varies over the interval [6.4%, 7.7%]. Interestingly, the network diameter reaches its maximum value in September 2008. Inspecting the exposure network in Fig. 3, we verify that there are fewer financial operations that are greater than USD 1 billion in relation to the other network snapshots taken in December 2011 and December 2014, suggesting that banks diversified more their lending portfolios during the crisis period. We also see that the Brazilian interbank market is very sparse. The sparseness in these networks may arise because banks incur in operational expenses to maintain relationships with other counterparties. As such, banks often create relationships with only a small subset of possible candidates so as to minimize costs (relationship lending). The selection among the candidates follows 16 the banks’ utility functions that normally rely on a tradeoff among past transactions, offered return rates, and market creditworthiness. 3.8. Average network-level shortest path distance (global measure) In the interbank networks, the network measurement hpi can be seen as the average length of the intermediation chains that are taking place among the market participants. Longer intermediation chains arise when hpi is large, which effectively contribute to slowing down the market transactions between participants and consequently harming the liquidity allocation between FIs. In contrast, when p is small, the information between the market participants flows quickly in the network, giving rise to a well-functioning liquidity allocation in the market. Figure 8b shows the evolution of the network-level shortest path distance in the interbank market from 2008 to 2014. We can see a downward trend of the network-level shortest path distance, raveling that the length of intermediation chains between banks tends to get smaller. In this way, the liquidity allocation turns to be more efficient, due to the fact that banks can communicate with each other easier. Looking side by side Figs. 8a and 8b, we see an interesting phenomenon. Normally, as networks get sparser, the tendency of the network-level shortest path distance is to increase, as there are fewer feasible paths in the network. Interestingly, we verify in our simulations that as the network gets sparser, the network-level shortest path distance decreases. This suggests that financial institutions are concentrating a large portion of their financial operations in a subgroup of banks that in turn have facility in communicating with the remainder of the network. This subgroup of vertices is an evidence of a core-periphery structure in the Brazilian interbank market, which we quantitatively will show when describing the identification strategy of core-periphery structures in the following sections. 3.9. Diameter (global measure) The diameter indicates the largest intermediation chain that is possible in the financial network. It is therefore an upper bound of the liquidity velocity inside the network in case a financial institution needs liquidity to satisfy its short-term needs. Figure 8c shows the network diameter of the interbank network from 2008 to 2014. From March 2008 to March 2011, the diameter remains constant at T = 4. After March 2011, the network diameter generally oscillates between T = 3 and T = 4, reflecting the steady decrease of network-level shortest path distance observed in Fig. 8b. In a perfect core-periphery structure, we would expect a network diameter of 2, which corresponds to the path (i) lender periphery member to core member and (ii) the corresponding transfer channeling to a borrowing peripheral member. Perfect core-periphery structures therefore can allocate resources from the lending periphery to the borrowing periphery with a single intermediator. In the Brazilian case, the network diameter of 4 reflects that core members are not fully connected to themselves nor to periphery members. As such, we observe the existence of funds transferring between core members so that liquidity can travel from any pairs of members inside the network. The network diameter can thus gives us a sense of an upper bound of liquidity velocity inside the financial network. 17 3.10. Rich-club coefficient (global measure) The rich-club coefficient conveys the notion of associativity between different market participants that meet some connectivity criterion. Subgroups or communities of banks that have large rich-club coefficients indicate that they maintain financial operations among every other participant in that group. It is therefore an indicative of well-connectedness among a sub-group of vertices in the network. We rich-club coefficient at level k roughly represents the density of the network that is formed by only vertices with degree not smaller that k. Therefore, we can understand how the most connected vertices in the network are linked altogether if we take large values of k. The rich-club coefficient assumes values in-between [0, 1], in which 0 denotes the absence of a rich-club and 1 represents a perfect rich club. Figure 9a portrays the rich-club coefficient for the Brazilian interbank market for four values of the degree k ∈ {2, 10, 20, 30}. We can inspect if large banks form a “rich club” inside the financial network by looking at the rich-club coefficient for large values of k. We see the existence of a strong rich club in the network that is mainly composed of large banks. This observation implies that all large banks are roughly interconnected to each other and therefore can transmit liquidity to one another in a direct manner. We also verify that the financial network does not present dense structures in the periphery. We do this exercise by computing the rich-club coefficient for small values of k. Therefore, liquidity transfer between non-large banks is normally intermediated by large banks that have ease connection to the entire network. Therefore, while large banks seem to form near-clique structures with other large banks in a small region, the network as a whole has, in general, sparse structures. 3.11. Assortativity (global measure) The assortativity gives us a sense of how similar pairs of banks tend to connect to each other. We define similarity here in terms of the number of connections that each counterparty has inside the financial network. We declare as closely similar two banks with similar number of connections. The assortativity measure provides values in-between [−1, 1]. In a financial system, large banks tend to have more connections because they have more resources to manage and also have to control for counterparty risk (concentration vs. diversification dilemma). Non-large banks tend to have smaller connections in view of their limited resources. If large banks tend to connect to alike and so do non-large banks,8 then the network is assortative in the sense that the network assortativity yields a value inside the positive interval (0, 1]. In case there is a pattern in which non-large banks tend to connect to large banks and vice versa, then we declare the network as disassortative such that the network assortativity resides in the negative interval [−1, 0). If there is no clear pattern discriminating the linkages between the financial institutions, then the network assortativity nears 0. Figure 9b depicts the network assortativity of the interbank network from 2008 to 2014. Although the Brazilian interbank network shows a clear disassortative mixing pattern, we can see 8 Silva et al. (2016a) provide several evidences corroborating the fact banks with dissimilar sizes tend to connect to each other in a financial system. 18 two distinct regions in the graph with respect to the assortativity behavior. First, from December 2007 to December 2012, the network gets more and more disassortative. Now, from March 2013 onwards, the network starts to becomes less disassortative (more assortative). Considering that the fraction and the total number of large and non-large banks remain the same throughout the entire period as Fig. 1a reveals, then changes in the network assortativity are due to link rearrangements, such as deletion, creation, or modifications. A network with a negative momentum on the assortativity—such as from the period from 2008 to 2012—indicates that the participants are connecting more and more to dissimilar peers. Given that there are few large banks in the network, peripheral banks may be exchanging large bank counterparties to non-large banks. We expect exchanges with more concentration instead of more diversification because both the out- and in-degree of non-large banks have a negative tendency in the period. This fact suggests a search for yield in the period, as non-large banks normally are more risky counterparties. At the beginning of 2013, we see a positive momentum on the assortativity, which indicates that banks are now connecting to similar banks. Again, given the small fraction of large banks and the more concentrated portfolios of non-large banks throughout time, non-large banks seem to be rearranging their active financial operations from non-large to large banks, suggesting that they are readapting their investment and funding portfolios to less riskier counterparties. We can relate this change on the risk perception of banks to the negative macroeconomic perspectives in Brazil. From 2013 onwards, Brazil experienced a period of monetary policy tightening with consecutive increments in the domestic policy rate in view of the negative prospectives in the economy. For instance, in the end of the first semester of 2013, the prices in the stock market started to plunge and the economy began to suffer from a cycle of currency devaluation. Given the smaller margin non-large banks have to operate in view of their resources, they may have adjusted their investments and funding sources to less risky portfolios to contain and control for possible market volatilities. 4. How can we identify core-periphery structures? Our goal in this paper is to understand how network structure—in particular core-periphery structures—affect bank liquidity. We discuss a strategy to identify the compliance of network realizations to perfect core-periphery structures. This identification will be useful during the econometric exercises that we perform in the next section. Silva et al. (2016b) propose a new way to check how compliant a network topology is to a perfect core-periphery structure by using information on the network assortativity and rich-club structure. There are some positive points in employing this methodology in relation to the traditional approach in Craig & von Peter (2014). First, Craig & von Peter (2014)’s methodology assumes that the network has a single core, otherwise the underlying process of the methodology fails in attempting to identify core members. Second, the output is stochastic as Craig & von Peter (2014)’s methodology relies on an optimization process whose solution depends on the initialization setup. These points are overcome in Silva et al. (2016b) as the procedure is deterministic—i.e. it does not depend on initialization parameters—and also allows for multiple cores in the financial 19 network.9 A drawback of Silva et al. (2016b)’s methodology is that it supposes that the underlying network has at least weak traces of a core-periphery structure. It therefore only checks how compliant or how far the analyzed network is to a perfect core-periphery structure. This requirement is satisfied by our data as Silva et al. (2016b) show that the Brazilian interbank network has a core-periphery structure. We can identify the core members in the network through the rich-club coefficient. We declare as core members those vertices that survive the filtering process for a large k when we compute the rich-club coefficient.10 This process is effective in pinning down the core banks because core members have large degrees, are central in the sense that they intermediate financial operations of other banks, and are tightly interconnected to other large banks. The periphery regions mainly correspond to financial institutions that are either only borrowers or lenders and are sparsely interconnected (rich-club coefficient analysis with small k). In our regressions, we use both the network disassortativity11 and the rich-club coefficient as regressors to explain bank liquidity. The disassortativity measure gives a sense of how non-large banks in the periphery tend to connect to large banks in the core. Violations linking two peripheral members would decrease the overall disassortativity, while compliant links would increase that value. The rich-club coefficient captures how strong core members are interconnected. Violations of two core members not being connected decrease the rich-club coefficient, while the existence of these connections increase that value. We also interact the network disassortativity and the richclub coefficient to understand the role that a strongly interconnected core perform to bank liquidity in case we already have a core-periphery network. We do not use Craig & von Peter (2014)’s methodology in our panel estimates to identify perfectly compliant core-periphery structures because it does not disentangle the violations (i) linkages between two peripheral members and (ii) absence of linkages between core members. In contrast, we can capture these two effects using Silva et al. (2016b)’s strategy by analyzing the network disassortativity and the rich-club coefficient. 5. Econometric model In this section, we define the empirical specification that we employ to identify and assess the determinant factors of liquidity performance in the Brazilian interbank market. We use the following dynamic panel: (1) (2) (3) LCRi,t = α + β0 LCRi,t−1 + β1 Xi,t + β2 Xi,t + β3 Xt 9 The + β4 Dt + υi + εi,t , (1) fitness function of Craig & von Peter (2014)’s methodology is the error score that is defined as the fraction of connections between two members in the periphery. Silva et al. (2016b) show that the correlation of this error score to the assortativity measure is more than 90% for the Brazilian interbank market when the network has a core-periphery structure. They also compare the core composition and find that both approaches identify the same core sub-group of financial institutions. 10 As Silva et al. (2016b) show, this methodology provides essentially the same results as those in Craig & von Peter (2014)’s methodology. 11 Since the Brazilian interbank network assumes negative values throughout the entire period, we opt to employ the disassortativity that we define as the absolute value of the assortativity value. 20 in which LCRi,t portrays the liquidity performance of bank i at time t, which we proxy by the (1) Liquidity Coverage Ratio (LCR) of Basel III. We detail its computation in Appendix B. Xi,t is feature vector that carries the network measurements. In our analysis, we control for bank-specific (2) features and external macroeconomic factors that we model using the features vectors Xi,t and (3) Xt , respectively.12 We also control for time fixed effects using time dummies Dt . The term υi represents the non-observable individual factors. Finally, the term εi,t is the error term that, by hypothesis, is identically and independently distributed with zero mean and constant variance σε2 , i.e., εi,t ∼ IID(0, σε2 ). We expect the liquidity structure of a bank to persist over time, as its balance sheet structure cannot be quickly adjusted. This is the reason we opt to use a dynamic rather than a static panel model. We effectively model the short term adjustment cost by including the lagged dependent variable LCRi,t−1 among the regressors. The associated coefficient β0 represents the speed of adjustment to equilibrium. Short-term adjustment costs for banks arise due to rigidities in their balance sheets, which unable them to raise liquidity in a short notice in response to negative liquidity shocks. Values of β0 between 0 and 1 imply persistence of LCR and also stability, as the liquidity performance is damped over time until it returns to its normal level. As the autoregressive coefficient β0 approximates 1, the more rigid or the more inefficient is the bank to raise liquidity in a short notice due to external shocks. Conversely, banks with β0 nearing 0 can adjust their liquidity needs with relative easiness, as their liquidity positions can be modified with less inertia on their past positions. There are three main questions that our empirical model in (1) seeks to test: • Are the short-term adjustment costs for liquidity (autoregressive coefficient β0 ) significant when we have already controlled for network-based measurements, bank-specific controls, and macroeconomic variables? In addition, we seek to investigate how these costs behave for different financial institutions that participate in the interbank market. Institutions with large inertia in this coefficient can have difficulties to absorb external liquidity shocks, because they may not be able to accommodate their liquidity needs in the short run. • Is the network structure one of the drivers of the liquidity performance of banks and does the network topology explains liquidity performance? • Interbank markets are the focus of central banks’ implementation of monetary policy and also have a significant impact on the entire economy. Does financial regulation policies adopted by the Central Bank of Brazil in the interbank market improve the overall liquidity of the financial system? We investigate this by only considering the network layer of regulatory assets rather than all of the unsecured assets. Given the dynamic nature of our empirical model, least squares estimation methods yield biased and inconsistent estimates (cf. Baltagi (2001)). In this way, we use a dynamic panel estimation that is able to deal with the biases and inconsistencies of our estimates. A further challenge 12 We observe that the external macroeconomic factors are global time-dependent events. For a fixed time, they are homogeneous among banks. Hence, we only use the subscript t in the corresponding feature vector. 21 for the estimation of LCR is of the presence of potential endogeneity problems, which can arise when there is correlation between the explanatory variables and the error term. Endogeneity can occur as a result of measurement error, autoregression with autocorrelated errors, simultaneity and omitted variables. To address these problems, we employ the Generalized Method of Moments (GMM) for linear dynamic panel-data estimation put forward by Arellano & Bover (1995) and Blundell & Bond (1998). The Blundell–Bond estimator is well suited to account for the model’s dynamic structure and it also has two additional properties. First, Blinder et al. (2003) show that the Blundell-Bond estimator does not break down in the presence of unit roots. Second, it accommodates the possible endogeneity between our dependent variables and some of the explanatory variables in our models by means of appropriate instruments. In particular, the system GMM estimator uses lagged values of the dependent variable in levels and in differences as instruments, as well as lagged values of other regressors, which could potentially suffer from endogeneity. The latter problem would lead to a correlation between those endogenous variables and the error term and hence to inconsistent estimates if not properly taken care of. With respect to the potential endogeneity of our regressors, we consider that our explanatory variables, as well as the lagged dependent variable, are endogenous. For those endogenous variables, we make use of their lagged values as instruments, as discussed in Arellano & Bover (1995) and Blundell & Bond (1998). Note that the system GMM estimator also controls for unobserved heterogeneity and for the persistence of the dependent variable. All of our reported results are based on the one-step system GMM estimator, using robust standard errors. Even though the two-step estimator is asymptotically more efficient, the two-step estimates of the standard errors tend to be severely downward biased, as Arellano & Bond (1995) and Blundell & Bond (1998) draw attention to. Returning to our empirical specification shown in (1), we use the following network measure(1) ments to compose the feature vector Xi,t :13 • Strictly local measure: in-strength. • Quasi-local measures: Herfindahl-Hirschman index (HHI) for intra-network assets and betweenness. • Global measures: disassortativity,14 rich-club effect with k = 30,15 diameter and density. Note that network measurements are known to be highly correlated to each other.16 As such, we must carefully choose those measures that are not highly correlated, while still being able to 13 Refer to Section 3 for details. the assortativity evolution in the Brazilian interbank market in Fig. 9b, we see that it assumes strictly negative values. In this way, for clarity, we opt to use the disassortativity that we define as the modulus or absolute value of the assortativity. 15 We select k = 30 so as to capture the connectedness of the network core, which is only composed of those FIs with large degree. To select such value, we use both the rich-club coefficient curve in Fig. 9a and the degree values of the most connected FIs in Fig. 4. 16 To name a few, the pairs out- and in-strengths, degree and strength, closeness and betweenness, betweenness and degree are often highly correlated. 14 Inspecting 22 capture local, quasi-local, and global structural features of the network. The network measure(1) ments that compose our feature vector Xi,t satisfy these restrictions. (2) We build up the attribute vector Xi,t , which accounts for defining the bank-specific properties, using following descriptors: • Control type: we make distinction between private domestic and foreign institutions. • Size: we distinguish between large and non-large institutions. • Main activities: we consider three activity segments: wholesale, investmen, and universal. The universal activity segment only applies for large banks that hold multiple portfolios with two or more segments and that operate nationwide. • Probability of default (PD): we employ the model described in Tudela & Young (2003). Therein, the default probability is modeled via a hybrid model, which employs a combination of the classical Merton structural approach and additional financial information. The original Merton model relies on several simplifying assumptions about the structure of the typical FI’s finances. The event of default is determined by the market value of the FI’s assets in conjunction with its liability structure. When the assets value falls below a certain threshold (the default point), the firm is considered to be in default. A critical assumption in the original Merton structural model is that the event of default can only take place at the maturity of the debt when the repayment is due. In contrast, Tudela & Young (2003) modifies this strong and restrictive assumption to allow for defaults to occur at any point in time and not necessarily at debt maturity. • Accounting variables: we use aggregate accounting variables that are extracted from FIs’ balance sheets. In special, we characterize FIs in accordance with their funding costs, operational costs, and ROE. With regard to the funding costs variable, it encompasses expenditures with deposits, repurchase agreements, securities, loans, onlending, sales operations and assets transfers. In turn, operational costs include administrative expenditures, such as with personnel (including social charges), communications, publicity, energy, and non-recurrent operations. (3) For the attribute vector Xt that holds macroeconomics variables, we use: • Brazil’s quarterly GDP. • Domestic policy rate (Selic). 6. Discussion of the results Tables 5, 6, and 7 report the estimated coefficients of the econometric panel in (1) for the full set of FIs, for the sub-sample comprising only FIs with low liquidity performance, and for the subsample composed of FIs with high liquidity performance, respectively. We establish the borders 23 of the sub-samples that only have FIs with low and high liquidity performances using the lower and upper quartiles of the liquidity performance of banks, respectively. The consistency of the system GMM estimator depends on the validity of the assumption that the error terms do not exhibit serial correlation and on the validity of the instruments. To address these issues, Arellano & Bond (1995) and Blundell & Bond (1998) present two specification tests that we employ in our simulations. In the first one, termed as the Hansen test, we verify overidentifying restrictions. In essence, it tests the overall validity of the instruments by analyzing the sample analogue of the moment conditions that we use in our estimation process. In the second test, we examine the hypothesis that the error term is not serially correlated. We test whether the differenced error term has a second order serial correlation. By construction, the differenced error term probably has a first order serial correlation even if the original error term does not. Failure in rejecting the null hypotheses of both tests should give support to our models. We note that the autoregressive coefficient suggests a moderate cost for adjusting the liquidity performance of banks. For all of the banks, on average, a liquidity shock would take four quarters to absorb roughly 95% of the initial impact. Banks with lower liquidity performance, however, would need almost two years to recover from an identical liquidity shock. In contrast, banks with high liquidity performance would need only two quarters to absorb a liquidity shock. In this way, we see that the short-term adjustment costs for liquidity are significant. In special, banks with lower liquidity performance have more difficulty in accommodating their balance sheets when external liquidity shocks happen. The in-strength can be understood as a proxy of how active is a bank in the interbank market when it comes to borrowing resources. We expect that, on average, if banks are getting funded by large amounts in the interbank market, they will have better liquidity positions. In fact, we see that the Brazilian interbank market effectively plays the role of liquidity provider for its members, as we can infer from the positive and statistically significant coefficient associated to the in-strength. We have several evidences from Section 3 that the Brazilian interbank network has a coreperiphery structure. Now we verify how the core-periphery topology affects banking liquidity performance. Note that core-periphery structure seems to be a common finding in several domestic interbank networks, implying that our results may have wide implications. Recall that we can check the core-periphery topological property by inspecting the interaction among the disassortativity and rich-club coefficients. Besides the interactions between these two network measurements, we also report their individual coefficients, so that we can understand which one prevails. We can clearly see that the core-periphery structure seems to enhance the liquidity performance of banks due to the positive sign and statistically significant values of the aforementioned variables. We also see that the disassortativity prevails over the rich-club coefficient, implying that the existence of two mesoscale structures, the core and the periphery, leads market participants to much better liquidity performances in relation to the existence of a near-clique structures inside the core and sparse structures between periphery-periphery and periphery-core. We give an intuition behind that in the following. We can conceive the strong interconnectedness between core members as a mechanism of resilience and redundancy of the financial system in terms of liquidity shortages. This is true because peripheral members can easily exchange between core members as they are easily reachable and can reach any other participants in the network. In contrast, the existence of the two mesoscale structures contributes to the rapid liquidity flow inside the network, 24 Table 5: Estimation results for the liquidity performance of the full sample of banking institutions. The coefficients and their corresponding standard deviations (in parentheses) are reported. (***) p < 0.01; (**) p < 0.05; (*) p < 0.10. Explanatory variable Spec. (1) Specifications Spec. (2) 0.4895*** (0.0195) 1.0230*** (0.3152) 0.0452* (0.0238) 0.0318** (0.0117) 0.6194*** (0.1125) 0.0288*** (0.0074) -0.3451*** (0.0904) -0.0996*** (0.0377) -0.1079* (0.0063) 0.4771*** (0.0196) 0.9804*** (0.3649) 0.0551*** (0.0137) 0.0184*** (0.0032) 0.5429*** (0.1670) 0.0258*** (0.0073) -0.3362*** (0.0895) -0.1177*** (0.0377) -0.2065*** (0.0757) 0.0073*** (0.0023) -0.04873*** (0.0186) 0.2091*** (0.0072) -0.0089 (0.0059) 0.0163** (0.0077) Constant -0.8804 (0.7946) -0.6468 (1.0930) Bank fixed effects Quarterly dummies YES YES YES YES Liquidityt−1 Disassortativity Rich-club [Disassortativity] · [Rich − club] Betweenness In-strength HHI-Assets Diameter Density PD Funding cost Adjusted ROE Operational cost GDP Domestic private Foreign Wholesale segment Investment segment Universal segment Small-sized FI Order 2 Abond Sargan (p-value) Wald test (p-value) Number of instruments Number of samples 0.4666 0.48 0.0000 141 3346 25 0.3462 0.6516 0.0000 153 3346 Spec. (3) 0.4686*** (0.0196) 0.9993*** (0.3411) 0.0419*** (0.0110) 0.0626*** (0.0104) 0.5355* (0.2810) 0.0234*** (0.0074) -0.3153*** (0.0039) -0.1196*** (0.0375) -0.1883** (0.0579) 0.0080*** (0.0024) -0.0507*** (0.0187) 0.1864*** (0.0072) -0.0091 (0.0058) 0.0158** (0.0076) -0.2598 (0.5186) -0.3879 (0.5450) 0.3328*** (0.1271) 0.0326 (0.1506) 1.4785** (0.5834) -0.2019 (0.1251) -0.3021 (1.2020) YES YES 0.3580 0.7291 0.0000 141 3346 Table 6: Estimation results for the liquidity performance of the sub-sample of banking institutions with low liquidity performance. The coefficients and their corresponding standard deviations (in parentheses) are reported. (***) p < 0.01; (**) p < 0.05; (*) p < 0.10. Explanatory variable Spec. (4) Spec. (5) Spec. (6) 0.6740*** (0.0253) 0.9028*** (0.2692) 0.0951*** (0.0231) 0.0184*** (0.0094) 0.8813*** (0.2121) 0.0132*** (0.0056) -0.1896*** (0.0700) -0.0950*** (0.0302) -0.2282*** (0.0618) 0.6979*** (0.0305) 0.8459*** (0.2738) 0.1124*** (0.0287) 0.0196** (0.0079) 0.8100*** (0.2876) 0.0132** (0.0064) -0.1702** (0.0818) 0.0821** (0.0331) -0.4183*** (0.0894) 0.0036 (0.0181) -0.0438*** (0.0035) 0.4460*** (0.1203) -0.02396*** (0.0072) 0.0291*** (0.0089) Constant 0.3552 (0.9836) 4.1823*** (1.2175) 0.7151*** (0.0347) 0.8520*** (0.2510) 0.0833*** (0.0175) 0.0154*** (0.0013) 0.8714*** (0.2637) 0.0100* (0.0042) -0.0857 (0.0827) 0.2960** (0.1202) -0.1883** (0.0579) 0.0072 (0.0215) -0.0221*** (0.0036) 0.7015*** (0.1337) -0.0214*** (0.0082) 0.0225** (0.0109) -1.9553*** (0.6996) -1.5120** (0.6685) 0.1661 (0.1041) 0.8372*** (0.2334) 0.7979 (1.0866) 0.3581** (0.1403) 4.4302*** (1.4901) Bank fixed effects Quarterly dummies YES YES Liquidityt−1 Disassortativity Rich-club [Disassortativity] · [Rich − club] Betweenness In-strength HHI-Assets Diameter Density PD Funding cost Adjusted ROE Operational cost GDP Domestic private Foreign Wholesale segment Investment segment Universal segment Small-sized FI Order 2 Abond Sargan (p-value) Wald test (p-value) Number of instruments Number of samples 0.4161 0.1739 0.0000 134 645 26 YES YES 0.4374 0.2036 0.0000 162 645 YES YES 0.4782 0.3647 0.0000 151 645 Table 7: Estimation results for the liquidity performance of the sub-sample of banking institutions with high liquidity performance. The coefficients and their corresponding standard deviations (in parentheses) are reported. (***) p < 0.01; (**) p < 0.05; (*) p < 0.10. Explanatory variable Liquidityt−1 Disassortativity Rich-club [Disassortativity] · [Rich − club] Betweenness In-strength HHI-Assets Diameter Density Spec. (7) Spec. (8) Spec. (9) 0.3808*** (0.0041) 0.5488*** (0.1428) 0.0011* (0.0004) 0.0084*** (0.0020) 0.0291*** (0.0081) -0.0009*** (0.0002) -0.0114*** (0.0034) -0.0037*** (0.0008) -0.3901* (0.0451) 0.3913*** (0.0483) 0.5713*** (0.1635) 0.0025 (0.0019) 0.0096* (0.0052) 0.0204*** (0.0072) -0.0027* (0.0015) -0.0048 (0.0329) -0.0107 (0.0175) -0.6785* (0.3725) 0.0009 (0.0017) -0.0009*** (0.0003) 0.0006*** (0.0002) -0.0000 (0.0000) 0.0057* (0.0035) 0.9897*** (0.0594) 0.4754*** (0.0607) 0.3842*** (0.0496) 0.6973*** (0.2179) 0.0044 (0.0067) 0.0054*** (0.0013) 0.0534*** (0.0042) -0.0010* (0.0026) -0.0196 (0.0356) -0.0087 (0.0179) -0.6760** (0.3794) 0.0015 (0.0018) -0.0009*** (0.0003) 0.0008 (0.0006) -0.0015 (0.0024) 0.0059* (0.0036) 0.0546 (0.0742) -0.0363 (0.0706) 0.0708 (0.0576) 0.0170 (0.0358) -0.2786 (0.2522) -0.0528 (0.0414) 0.4959 (1.2020) YES YES YES YES YES YES PD Funding cost Adjusted ROE Operational cost GDP Domestic private Foreign Wholesale segment Investment segment Universal segment Small-sized FI Constant Bank fixed effects Quarterly dummies Order 2 Abond Sargan (p-value) Wald test (p-value) Number of instruments Number of samples 0.4656 0.2495 0.000 151 505 27 0.615 0.3314 0.0000 145 505 0.7253 0.5332 0.0000 159 505 as the core shortens the effective network distance between borrowers and lenders in the periphery. By reducing the rich-club effect inside the network, we may reduce the redundancy inside the core, however, we still can find other similar core members to reaccommodate or rearrange the financial operations. Now the reduction in the network dissasortative pattern may lead to the degradation of the structural properties of the core and the periphery. Eventually, these two mesoscale structures may cease to exist. In this case, the liquidity flow would decrease as core members would be less central and therefore their shortest path distances would increase. This would happen because, in a core, large banks are easily reachable by all of the market members in the network and effectively play the role of liquidity providers. When this core cannot easily communicate with the remainder of the network anymore, liquidity on average would take longer to flow inside the network. In this way, periphery members with low liquidity performance that assume debtor positions in the interbank market would not be able anymore to gather funds directly from core banks that play the role of liquidity distributors. Centrality also plays an important role in explaining liquidity performance of banks. We can see that by inspecting the coefficient of the betweenness, which is positive and statistically significant. In special, we see that banks that intermediate more financial operations are likely to have better liquidity performance. Large banks are the ones with larger centrality or betweenness indices. Periphery members are often only borrowers or lenders in the interbank market; hence, they do not intermediate financial operations. Even though the magnitude of the betweenness coefficient is large, the disassortative pattern of the network is stronger in providing better liquidity performance for banks because of its large coefficient. Interestingly, in the results for only banks with high liquidity performance, we see that the rich-club effect is insignificant. This may happen because almost all of the banks with high liquidity performance are large banks, which in turn are members of a core. In this way, the “rich-club” effect turns out to be insignificant in this configuration. In contrast, the disassortativity seems to be a very important factor regardless of the sample we use in our simulations. We also see that the betweenness in the sample of only banks with low liquidity performance plays a much important important role in enhancing liquidity performance that in the sample that is composed of only banks with high liquidity performance. Therefore, centrality plays a key role for members that are roughly at the periphery. However, it is not very relevant when we analyze banks with high liquidity performance. Diversification is an essential element in what concerns liquidity performance of banks. We can see that banks, whose relationships in their active interbank operations are less concentrated, on average, present better liquidity positions. This is captured by the statistically significant negative coefficient of the HHI-index, which measures the assets concentration of banks. With respect to the network members, we see that large institutions present diversified portfolios both in the borrowing and lending perspective. Non-large financial institutions, in contrast, on average, often present more concentrated borrowing and lending portfolios. In addition, as the network diameter increases, the efficiency of liquidity transfers is reduced as the number of intermediation chains gets larger. With this respect, the less likely are the occurrences of interbank operations related to liquidity shortfalls when the network diameter is small. As we have seen, the Brazilian interbank market shows, on average, a small network diameter of 4. This characteristic means that banks that are not connected to the core of interbank market have 28 more difficulty in gathering resources from large banks, for large banks are the central players in distributing liquidity in the financial market. From a theoretical point-of-view, if a financial institution has a probability of default higher than the average of its peers, then other agents would see it as a risky institution. As such, they would demand higher yields in financial operations so as to counterbalance the higher assumed risks. Another effect of having relative high probability of default is that the institution suffers from credit restriction. Other institutions, besides establishing higher prices to accept financial contracts, limit the amount that they are willing to lend to that risky institution. In view of this, that institution would have difficulty in funding itself and hence to adjust its liquidity. Interestingly, however, we verify a positive association between the default probability and the liquidity performance of banks. This fact suggests that banks with potential solvency problems make strong efforts to emit signals or actions with the purpose of conveying the apparent information that their liquidity positions are satisfactory. Intuitively, banks with relative large default probabilities must maintain larger liquidity buffers against unexpected external shocks because they do not have wide access to the interbank market and have higher costs for adjusting against external liquidity shocks. We can also observe that the funding costs have negative association with liquidity performance. As such, banks with liquidity shortfalls have to pay more expensively for gathering funds in the interbank market. This feature suggests that market discipline is effective in the credit market. Likewise, banks that have higher operational costs hold, on average, low liquidity performances. The banking liquidity conditions are procyclical, i.e., the liquidity of banks increases in economic expansionary periods, while it contracts in recessions. As we expect, large banks whose activities are related to investment and wholesale credit or that are public are consistently more liquid than banks that are private, foreign, or small. 7. Robustness tests In this section, we perform robustness tests with a focus on regulatory assets that are determined by the Central Bank of Brazil. These regulatory assets are used as a part of Central Bank of Brazil’s regulatory policies to promote liquidity in the financial system. Among these regulatory assets, we can highlight: • DPGE (Time Deposit with Special Guarantee): the DPGE is a fixed income security representing time deposits created to assist small- and mid-sized financial institutions to raise funds. Thus, DPGE confer to holders the right to credit against the issuer. Probably, it is one of the main instruments used by the Central Bank of Brazil in promoting liquidity in the financial system. It was created in April 2009 by the National Monetary Council (CMN) in its Resolution no. 3692. Through Resolution no. 4415, in 2012, the CMN also created a new type of regulatory asset known as DPGE II. This version is distinguished from the DPGE because it is eligible for the Credit Guarantee Fund (FGC). In addition, terms should be adjustable to the respective bank loans to which they are pegged. • Adjustment of reserve requirements: the Central Bank of Brazil can effectively inject liquidity in the financial system by decreasing the reserve requirement levels in periods of distress. 29 • Mandatory interfinancial deposits: there are several types of mandatory interfinancial deposits. In general terms, they enable funds exchanges between financial institutions in order fulfill specific requirements. For instance, the financial instrument “interfinancial deposit linked to microfinance operations” can be used by financial institutions to fulfill the minimum requirements in microfinance operations. These financial instruments are mainly used to force liquidity to flow in the interbank market, as they encourage financial transactions in which one of the parts is small- or mid-sized institutions. • Special types of financial bills: Instrument that allows fundraising term extension for financial institutions. Thus, they provide better management of financial institutions’ assets and liabilities. One of the main advantages of financial bills is the minimum maturity period to maturity, without possibility of partial or total redemption before that period. Another characteristic is that the financial asset has a minimum nominal unit value. Some special types of financial bills are eligible debt instruments for composing the regulatory capital of financial institutions. As robustness exercises, we perform two re-estimations of the discussed econometric model. We again focus only on unsecured financial instruments. In the first, we re-run the model without considering these regulatory assets. In contrast, in the second model, we only consider the network layer constituted of regulatory assets. Table 8 reports the estimates for the panel when we employ the network composed of all of the unsecured assets but regulatory assets. Note that, by removing regulatory assets, we are effectively leaving behind contracts that are induced by the Central Bank of Brazil, and not the FIs themselves. This network layer, thus, is constituted of financial relationships that are solely due to strategies of each of the network participants. Inspecting Specifications (10), (11), and (12) informed in Table 8, we note that the cost of adjusting banking liquidity maintains significant and does not suffer considerable changes in relation to the estimated liquidity cost when all of the unsecured assets are brought into the analysis. These results, however, suggest that the interbank network loses efficiency as to its ability to transmit regular flows of liquidity resources when we exclude financial operations induced by regulatory policies of the Central Bank of Brazil. This observation suggests that the regulatory policies performed by the Central Bank of Brazil do help in promoting a more liquid financial system. We now analyze how the network topology changes due to the removal of regulatory assets. As Fig. 10 reveals, we first note that the total amount of regulatory assets in the network is not representative in relation to the total amount of unsecured assets. The network topology, however, seems to change in a more significative way. Figure 11 portrays the percentage changes observed in the network density, and the in- and out-degrees of large and non-large banking institutions. While the network layer of regulatory assets represents, on average, only 3% of the total unsecured assets, the network density seems to reduce in an amplified way. In order to better analyze the reason of the network density reduction, we inspect the percentage changes in the in- and outdegree of the network members. Interestingly, for large banking institutions, we see that the active funding operations assumes a large reduction of [10, 11]%, revealing that an expressive portion of the large FI’s relationships is exclusively due to regulatory assets. In the other perspective, the 30 Table 8: Estimation results for the liquidity performance of banking institutions when regulatory financial instruments are excluded. The coefficients and their corresponding standard deviations (in parentheses) are reported. (***) p < 0.01; (**) p < 0.05; (*) p < 0.10. Explanatory variable Liquidityt−1 Liquidityt−2 Disassortativity Rich-club [Disassortativity] · [Rich − club] Betweenness In-strength HHI-Assets Diameter Density Spec. (10) Spec. (11) Spec. (12) 0.4802*** (0.0209) -0.0410** (0.0185) 0.9186*** (0.1762) 0.0419* (0.0212) 0.0102* (0.0053) 0.5212*** (0.1022) -0.0120** (0.0062) -0.0093 (0.0486) 0.0839 (0.0534) 0.0408 (0.0560) 0.4414*** (0.0214) -0.0599*** (0.0285) 0.8883*** (0.1648) 0.0492*** (0.0127) 0.0117* (0.0060) 0.5681*** (0.1480) -0.0130** (0.0063) -0.0002 (0.0476) -0.0327 (0.0613) -0.0259 (0.0738) 0.0067*** (0.0017) -0.0010*** (0.0002) 0.0678 (0.1355) -0.0017 (0.0048) 0.0206*** (0.0064) -1.1647** (0.5233) -3.5301*** (0.8777) 0.4476*** (0.0216) -0.0521*** (0.0185) 0.8417*** (0.1731) 0.0446*** (0.0109) 0.0084 (0.0047) 0.5932** (0.2351) -0.0137** (0.0062) 0.0059 (0.0469) -0.0198 (0.0604) 0.0495 (0.0743) 0.0071*** (0.0017) -0.0010*** (0.0002) -0.1426 (0.1341) -0.0025 (0.0047) 0.0189*** (0.0063) -0.3857 (0.2642) -0.1681 (0.2440) 0.4248*** (0.0992) 0.0878 (0.1213) 1.6780*** (0.4405) -0.0984 (0.0289) -3.4532*** (0.8858) YES YES YES YES YES YES PD Funding cost Adjusted ROE Operational cost GDP Domestic private Foreign Wholesale segment Investment segment Universal segment Small-sized FI Constant Bank fixed effects Quarterly dummies Order 2 Abond Sargan (p-value) Wald test (p-value) Number of instruments Number of observations 0.1384 0.6470 0.0000 141 3145 31 0.1729 0.8093 0.0000 151 3145 0.1682 0.7751 0.0000 149 3145 number of active investment operations only reduces [2, 3]%, showing that large banks, on average, only assume investor positions with other banks with contracts that have one or more regulatory assets and at least another unsecured asset. That is, they seem to not invest in peers with only regulatory assets in the relationship. For non-large banking institutions, we see that both the funding and investment operations uniformly reduce to about [6, 7]% of the original number when all of the unsecured assets are considered. Analyzing the global network structure, we see that the network assortativity does not have a perceptible change. This fact indicates that the network relationships correlation is maintained by the removal of regulatory assets. The network diameter does not change as well. Using these two facts, we can see that the network, though sparser, does not change in a structural sense. Another interesting robustness exercise is to study how the network layer composed of only regulatory assets explain liquidity performance of banks. We re-run our econometric model using only that network layer. Table 9 reports the results. An interesting finding is that the assortativity of this network layer is negatively related to liquidity performance of banks, meaning that regulatory assets incentive the formation of less concentrated financial networks that normally occur in core-periphery networks (strongly disassortative networks). This happens because banks are less willing to connect only to core banks, and hence they diversify more. In this way, the network topology formed by regulatory assets contributes to decreasing the systemic risk that is inherently embodied in a core-periphery structure. We can say therefore that the introduction of regulatory assets help at a large extent small- and micro-sized banks to adjust their liquidity positions. 8. Policy implications The large failure cascades that occurred in financial systems over the world since the financial crisis in 2008 have taught some lessons for financial regulators. A clear lesson from the global financial crisis is that not only capital requirements are enough but there is also a need for liquidity requirements as well. When financial markets suffer from financial instability and huge asymmetric information, liquidity becomes a very relevant policy issue. The development of Basel III can be seen as a response from international financial regulators. It comprehends a set of reform measures, that were developed by the Basel Committee on Banking Supervision and its aims are at strengthening regulation, supervision and risk management of the banking sector. The main goals of these reforms were to improve the banking sector’s ability to absorb shocks, to refine risk management and governance, and to strengthen banks’ transparency and disclosures (BCBS (2010)). The idea of these reforms to financial regulation was to increase the resilience at the bank level, which in turn can reduce systemic risk. It is important to stress that liquidity has played a major role in the development of the crisis and therefore it should be addressed by financial regulation. Our main result suggest that there is a group of banks that have difficulties in adjusting their liquidity after a liquidity shock, which affects their performance. Thus, imposing minimum liquidity ratios seems to be a relevant regulation policy that has to be implemented. The Brazilian financial regulators have been improving these requirements to comply with Basel III. Our results suggest that a core-periphery structure is prevalent in the Brazilian interbank market, which can amplify the propagation of liquidity shocks. As such a better understanding of 32 Table 9: Estimation results for the liquidity performance of banking institutions when only regulatory financial instruments are included. Specification (13) employs the entire sample, while Spec. (14), only non-large banks. Specification (15) utilizes the entire sample and an interactive dummy for small- and micro-sized banks. The coefficients and their corresponding standard deviations (in parentheses) are reported. (***) p < 0.01; (**) p < 0.05; (*) p < 0.10. Explanatory variable Spec. (13) Liquidityt−1  Spec. (14) 0.4538*** (0.0309) 0.4490*** (0.0324) -0.0151** (0.0073) 0.0521 (0.0269) 0.0009* (0.0004) 0.4216 (0.3281) 0.1439** (0.0612) 0.0025 (0.0075) 0.0492 (0.0862) -0.0232 (0.0281) -0.0258*** (0.0044) -0.4458*** (0.1664) 0.0155 (0.0118) 1.8045*** (0.7210) 0.0463*** (0.0149) 0.0305*** (0.0106) 0.1789 (0.2411) -0.0724 (0.2619) -0.3048** (0.1552) -0.0193 (0.1508) 1.0894 (0.5980) -12.7048*** (2.6624) -0.0177** (0.0079) 0.0895 (0.0582) 0.0015 (0.0011) 0.4986 (0.4198) 0.1370** (0.0667) 0.0013 (0.0097) 0.0312 (0.0964) 0.0228 (0.0302) -0.0252*** (0.0046) -0.5101*** (0.1794) 0.0242* (0.0134) 2.4010*** (0.8861) 0.0493*** (0.0161) 0.0321*** (0.0113) 0.1512 (0.2471) -0.1484 (0.2730) -0.3957** (0.1673) -0.0424 (0.1563) 1.3272** (0.6230) -14.9696*** (3.1830) 0.2215*** (0.0219) 0.7524*** (0.0231) -0.0124** (0.0049) 0.0976 (0.0901) 0.0021 (0.0029) 0.4656 (0.2973) 0.1034** (0.0412) 0.0022 (0.0050) 0.0138 (0.0580) -0.0198 (0.0189) -0.0164*** (0.0030) -0.2654** (0.1121) 0.0003 (0.0079) -4.7214*** (0.5258) 0.0278*** (0.101) 0.0221*** (0.0071) 0.2386 (0.1625) 0.0832 (0.1762) -0.3911*** (0.1045) 0.0262 (0.1015) 0.7637* (0.4026) 9.1578*** (1.9194) YES YES YES YES YES YES  Liquidityt−1 · [Small − Sized] Disassortativity Rich-club [Disassortativity] · [Rich − club] Betweenness Density In-Strength HHI-Assets Diameter Funding cost Adjusted ROE PD Size Selic GDP Domestic private Foreign Credit segment Wholesale segment Banking I Constant Bank fixed effects Quarterly dummies Order 2 Abond Sargan (p-value) Wald test (p-value) Number of instruments Number of observations Spec. (15) 0.3617 0.3158 0.0000 149 1649 33 0.3768 0.5094 0.0000 163 1503 0.1752 0.5597 0.0000 151 1649 how this particular network structure emerges and why they are so common across countries goes beyond the scope of this paper and is left for further research. We can infer from our results, nonetheless, that this topology is the result of liquidity management by banks and financial intermediaries in the financial system. In line with the findings of Krause & Giansante (2012), our results suggest that, when designing regulation, one should also consider financial linkages between banks. Recent research has discovered a core-periphery structure in interbank markets for a variety of countries.17 One of the reasons for this trend is that such a topology may facilitate liquidity management. However, it also poses challenges for financial regulators. Also, Capponi & Chen (2015) find that from a policy perspective in a core-periphery structure it is better to design regulation that targets systemically important banks rather than maximizing the total liquidity of the system, which is preferred if the network is random. These results suggest that the network topology matters for the design of appropriate regulation. 9. Conclusion In this paper, we investigate the roles FIs play within the Brazilian interbank market using a comprehensive set of network measurements borrowed from the complex network theory. One prominent advantage of employing network-based theory is that it is able to capture topological and structural characteristics of the players’ relationships from the data representation itself. Our results indicate that the Brazilian interbank network shows strong disassortative mixing patterns, revealing that highly-connected FIs frequently connect to others FIs with very few connections. Moreover, our analysis confirm that the interbank market also presents the “rich-club” effect, which captures the existence of a subgroup of banks that are strongly interconnected. Putting these two evidences together, we conclude that the Brazilian interbank network effectively has a core-periphery structure. This finding is in line with several domestic interbank networks that we find in the literature (in ’t Veld & van Lelyveld (2014); Craig & von Peter (2014); Fricke & Lux (2015)). Moreover, we analyze the liquidity performance determinants of financial institutions in terms of network measurements, controlling for bank-specific and macroeconomic factors. One of our main findings is that the core-periphery structure is able to enhance, in general, the liquidity performance of banks. Having in mind that several evidences point to the fact interbank markets seem to self-organize in core-periphery structures (cf. Lux (2015)), this finding is a positive point as interbank systems seem to drive themselves to an organization that is optimal or at least improves the overall liquidity of the system. However, this optimality has a cost in terms of financial stability. According to a comparative analysis between different types of network structures performed by Lee (2013), a core-periphery network with a deficit core bank gives rise to the highest level of systemic liquidity shortage, implying greater systemic risk. In this way, the banking system may become more vulnerable if a core bank defaults. With this observation in mind, several questions may arise. First, should these core banks have additional liquidity requirements such as to prevent 17 See Fricke & Lux (2015), Langfield et al. (2014), in ’t Veld & van Lelyveld (2014), and among others. 34 their failures? Second, should regulators limit pairwise financial exposures?18 If we consider that, in a core-periphery structure, members of the periphery concentrate financial operations on a small subset of core banks, by limiting pairwise financial exposures we would be effectively forcing periphery members to connect between themselves; hence, distancing the network structure from a core-periphery topology. Our results also show a positive and statistically significant relation among the banking liquidity performance and centrality. This finding suggests that members that intermediate several financial operations, in general, have better liquidity positions. In addition, our results show that the access to the interbank credit is conducted with short distances from the borrowing banks and the large lending banks. Another relevant factor that facilitates the gathering of credit is the level of diversification of the funding sources, with a clear advantage for banks with larger in-strength measures. Finally, it is essential to highlight that the interbank market is able to assess the credit rating of debtor financial institutions, which is captured by our model by the positive association between less liquidity banks and funding costs. Such fact corroborates the thesis that the market discipline efforts is effective. Interestingly, we also find a robust positive association between the default probability and the liquidity performance of banks. This fact suggests that banks with potential solvency problems make strong efforts to emit signals or actions with the purpose of conveying the apparent information that their liquidity positions are satisfactory. Intuitively, banks with relative large default probabilities must maintain larger liquidity buffers against unexpected external shocks because they do not have wide access to the interbank market and have higher costs for adjusting against external liquidity shocks. As future work, we can further study specific mechanisms related to liquidity shortfalls of banks, controlling the maturity of the employed financial assets in transactions whose finality is to adjust the liquidity of banks. References Allen, F., & Gale, D. (2000). Financial Contagion. Journal of Political Economy, 108, 1–33. Anand, K., Gai, P., Kapadia, S., Brennan, S., & Willison, M. (2013). A network model of financial system resilience. Journal of Economic Behavior and Organization, 85, 219–235. Arellano, M., & Bond, S. (1995). Some tests of specification for panel data: Monte Carlo evidence and an application to employment equations. Review of Economic Studies, 58, 277–297. Arellano, M., & Bover, O. (1995). 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Core–periphery structure in the overnight money market: Evidence from the e-MID trading platform. Computational Economics, 45, 359–395. Fujiwara, Y., Aoyama, H., Ikeda, Y., Iyetomi, H., & Souma, W. (2009). Structure and temporal change of the credit network between banks and large firms in Japan. Economics: The Open-Access, Open-Assessment E-Journal, 3, 2009–7. Guerra, S. M., Tabak, B. M., & Miranda, R. C. C. (2014). Do Interconnections Matter for Bank Efficiency?. Working Paper 374 Central Bank of Brazil. Honga, H., Huangb, J.-Z., & Wuc, D. (2014). The information content of Basel III liquidity risk measures. Journal of Financial Stability, 15, 91–111. Kashyap, A., Rajan, R., & Stein, J. (2002). Banks as liquidity providers: an explanation for the coexistence of lending and deposit-taking. Journal of Finance, 57, 33–73. Krause, A., & Giansante, S. (2012). Interbank lending and the spread of bank failures: A network model of systemic risk. Journal of Economic Behavior and Organization, 83, 583–608. Langfield, S., Liu, Z., & Ota, T. (2014). Mapping the UK interbank system. Journal of Banking and Finance, 45, 288–303. Latora, V., & Marchiori, M. (2001). Efficient behavior of small-world networks. Physical Review Letters, 87, 198701. Latora, V., & Marchiori, M. (2002). Economic small-world behavior in weighted networks. European Physical Journal B, 32, 249–263. Lee, S. H. (2013). Systemic liquidity shortages and interbank network structures. Journal of Financial Stability, 9, 1–12. Lux, T. (2015). Emergence of a core-periphery structure in a simple dynamic model of the interbank market. Journal of Economic Dynamics and Control, 52, A11–A23. Markose, S., Giansante, S., & Shaghaghi, A. R. (2012). “Too interconnected to fail” financial network of US CDS market: Topological fragility and systemic risk. Journal of Economic Behavior and Organization, 83, 627–646. Newman, M. E. (2002). Assortative mixing in networks. Physical Review Letters, 89, 208701. Newman, M. E. J. (2003). Mixing patterns in networks. Physical Review E, 67, 026126. 36 Silva, T. C., Guerra, S. M., Tabak, B. M., & de Castro Miranda, R. C. (2016a). Financial networks, bank efficiency and risk-taking. Journal of Financial Stability, 25, 247–257. Silva, T. C., de Souza, S. R. S., & Tabak, B. M. (2016b). Network structure analysis of the Brazilian interbank market. Emerging Markets Review, 26, 130–152. Silva, T. C., & Zhao, L. (2012). Network-based high level data classification. IEEE Transactions on Neural Networks and Learning Systems, 23, 954–970. Silva, T. C., & Zhao, L. (2015). High-level pattern-based classification via tourist walks in networks. Information Sciences, 294, 109–126. Silva, T. C., & Zhao, L. (2016). Machine Learning in Complex Networks. Springer International Publishing. Tudela, M., & Young, G. (2003). A Merton-model approach to assessing the default risk of UK public companies. Working Paper 194 Bank of England. in ’t Veld, D., & van Lelyveld, I. (2014). Finding the core: Network structure in interbank markets. Journal of Banking and Finance, 49, 27–40. Appendix A. Topological analysis of the interbank network In the process of analyzing the network, we extract some network measures from the graph G = hV , E i constructed from the lending and borrowing operations of the interbank market banks. To build up such network, V denotes the set of vertices (FIs) and E , the set of edges (operations). The cardinality of V , V = |V |, represents the number of vertices or banks in the network, while E = |E |, the number of edges. The matrix A denotes the exposures or assets matrix (weighted adjacency matrix), in which the (i, j)-th entry represents the exposure amount of the FI (vertex) i towards j. The set of edges E is given by the following filter over A: E = {Ai j > 0 : (i, j) ∈ V 2 }. In our analysis, there is no netting between i and j.19 As such, if an arbitrary pair of FIs owe to each other, then two directed independent edges linking each other in opposed directions will emerge. An interesting property of maintaining the gross exposures in the network is that, if an FI defaults, its debtors remain liable for their debts. We also define the matrix of liabilities between the FIs as L = AT , where T is the transpose operator. Next, we present the network measurements that we use to extract topological information of the interbank network. We follow Silva & Zhao (2015) and classify these measures with respect to the type of information the index makes use in its computation, as follows: local, quasi-local, and global measures. Appendix A.1. Strictly local measures Strictly local measures are related to the inherent characteristic of a vertex itself. In this way, measures qualified as strictly local do not take into account the neighboring features. We present some of these network measures in the following. Appendix A.1.1. Degree The degree or valency of a vertex i ∈ V , indicated by ki , is related to its connectivity, or number of links, to the remainder of the network. In directed graphs, this notion can be further extended 19 Pairwise exposures are not netted out so as to maintain consistency with the Brazilian law, because financial compensation is not always legally enforceable. 37 (in) (out) into the in-degree, ki , and the out-degree, ki , in a way that the identity ki = kiin + kiout holds. The feasible values of ki are within the discrete-valued interval {0, . . . ,V − 1} if self-loops are not allowed, and {0, . . . ,V } if self-loops are permitted. When ki = 0, vertex i is disconnected from the remainder of the graph. In this case, we say that vertex i is a singleton. Conversely, when ki is large, we say that vertex i is a hub. The out- and in-degree of vertex i ∈ V are defined as follows: (out) = ∑ j∈V 1{Ai j >0} , (A.1) (in) = ∑ j∈V 1{A ji >0} , (A.2) ki ki in which 1{K} represents the indicator or Kronecker function that yields 1 if K, a logical expres(out) sion, evaluates to true, and 0, otherwise. In a network of exposures, the out-degree ki represents the number of FIs in which participant i has invested (is exposed to). With a similar reasoning, (in) the in-degree ki symbolizes the number of participants that are funding i in the market (they are exposed to i). Appendix A.1.2. Strength The strength of a vertex i ∈ V , indicated by si , represents the total sum of weighted connections of i towards its neighbors. Likewise the degree, the notion of strength can be further decomposed (in) (out) out into the in-strength, si , and out-strength, si , such that the identity si = sin i + si holds. The feasible values of si corresponds to the continuous interval [0, ∞). The out- and in-strength of vertex i ∈ V are defined as: (out) si = ∑ Ai j , (A.3) j∈V (in) si = ∑ A ji. (A.4) j∈V Appendix A.2. Quasi-local measures Given a reference vertex, quasi-local measures take into account the neighborhood’s structural or topological characteristics to render information. Appendix A.2.1. Closeness We compute the closeness of vertex i, εi , in accordance with the following expression (Latora & Marchiori (2001)): εi = 1 V (V − 1) 38 ∑ j∈V j 6= i 1 , pi j (A.5) i.e., it is the sum of the reciprocal of all of the shortest path lengths starting from i. For central vertices, the average shortest path distance is expected to be small, resulting in a large closeness index. Opposed to that, for peripheral vertices, we expect shortest paths to the remainder of the network to be relatively large, yielding a small closeness value. Appendix A.2.2. Betweenness The betweenness of vertex i, Bi , is a centrality measure that quantifies the fraction of shortest paths between all pairs of vertices (k, j) ∈ V 2 , k 6= j 6= i, in a network such that i is one of the intermediate vertices in the path. Mathematically, we evaluate the betweenness as follows (Freeman (1977)): ∑ Bi = (k, j) ∈ V 2 k 6= j 6= i σk j (i) , σk j (A.6) in which σk j quantifies the number of shortest paths starting from k and ending in j and σk j (i) denotes the number of shortest paths starting from k and ending in j such that i is an intermediate vertex, i.e., is a member of the geodesic path. Appendix A.2.3. Dominance The dominance of vertex i ∈ V , Di , measures the relative importance of i on its neighbors’ operations. The dominance of i as a lender and as a borrower is given by: (lender) Di = ∑ j∈V (borrower) = ∑ j∈V Di Ai j (in) sj , (A.7) , (A.8) A ji (out) sj i.e., the lender dominance of i evaluates the fraction of funding to be received by i’s neighborhood, while the borrower dominance of i captures the fraction received by i against the total amount invested in the market by its neighbors. Appendix A.2.4. Criticality The criticality of the FI i ∈ V , Ci , quantifies the impact of the i’s liabilities toward its counterparties’ liquid assets. It is the sum of the vulnerabilities of its creditors regarding their exposures to the FI and is given by: Ci = ∑ V ji = ∑ j∈V j∈V Li j , Ej (A.9) in which V ji = Li j/E j quantifies the vulnerability of j with respect to the funding dependence on i, E j indicates the readily available resources or capital buffer of bank j ∈ V . We use as capital buffer the tier 1 capital of banks. 39 Appendix A.3. Global measures Global measures make use of all the relationships contained in the network to derive information. We show some in the following. Appendix A.3.1. Density The network density D, also known as network connectivity, for a directed network, is defined as: D= E = V
2 2E , V (V − 1) (A.10) in which V and E represent the total number of vertices and edges, respectively. The density assumes values in the interval [0, 1]. When D = 0, we say that G is an empty graph. Conversely, when D = 1, G is said to be a complete or maximal clique graph. Often in the literature, we classify networks as sparse when D assumes values near 0. Conversely, when D approaches 1, we term the network as dense. As a rule of thumb, when the number of edges in the networks is of the order of the number of vertices, i.e., E = O(V ), we consider the network as sparse. Appendix A.3.2. Average network-level shortest path distance The average network-level shortest path distance hpi is given by: hpi = 1 V ∑ hpii, (A.11) i∈V in which hpi i represents the vertex-level average shortest path distance of vertex i that we compute as follows: hpi i = 1 V −1 ∑ pi j , (A.12) j∈V j 6= i The domain of hpi is [0,V − 1]. In the interbank networks, the network measurement hpi can be seen as the average length of the intermediation chains that are taking place among the market participants. In average, as p grows larger, longer intermediation chains will emerge, slowing down the market transactions between participants and consequently harming the liquidity allocation between FIs. In contrast, when p is small, the information between the market participants flows quickly in the network, giving rise to a well-functioning liquidity allocation in the market. Appendix A.3.3. Diameter The network diameter T is given by: T = max pi j , (i, j)∈V 2 40 (A.13) i.e., T is the largest geodesic distance of any pairs of vertices in the network. The feasible values that T may assume are [0,V − 1]. We can interpret the diameter as the largest intermediation chain in the network. Appendix A.3.4. Rich-club coefficient The rich-club coefficient measures the structural property of complex networks called “richclub” phenomenon. This property refers to the tendency of vertices with large degree (hubs) to be tightly connected to each other, thus forming clique or near-clique structures. This phenomenon has been discussed in several instances in both social and computer sciences. Essentially, vertices with a large number of links, usually known as rich vertices, are much more likely to form dense interconnected subgraphs (clubs) than vertices with small degree. Considering that E>k is the number of edges among the N>k vertices that have degree larger than a given threshold k ≥ 0, the scaled version of the rich-club coefficient is expressed as (da F. Costa et al. (2005)): φ (k) = 2E>k , N>k (N>k − 1) (A.14) in which the factor N>k (N>k −1)/2 represents the maximum feasible number of edges that can exist among N>k vertices. Appendix A.3.5. Assortativity Assortativity is a network-level measure that, in a structural sense, quantifies the tendency of vertices to link with similar vertices in a network. The assortativity coefficient r is computed as the Pearson’s correlation of degrees of vertices in each connected pair. Positive values of r indicate that edges in the network have vertices in the endpoints with similar degrees, while negative values indicate endpoints with different degrees (Newman (2003)). In general r ∈ [−1, 1]. When r = 1, the network has perfect assortative mixing patterns, while, it is completely disassortative in the case r = −1. Considering that iu and ku represent the origin and destination of the u-th edge of a non-empty graph, respectively, and that l = ∑(i, j)∈V 2 Ai j denotes the total edge weight of the adjacency matrix (in our context, it is the exposures matrix), the assortativity r is evaluated as follows (Newman (2002)): r= l −1 ∑u∈E iu ku − l −1 2 h l −1 2 i2 ∑u∈E (iu + ku ) h ∑u∈E (iu + ku ) −1 ∑u∈E (i2u + ku2 ) − l 2 i2 . (A.15) According to Silva & Zhao (2012, 2015), understanding the assortative mixing patterns in complex networks is important for interpreting vertex functionality and for analyzing the global properties of the network components. 41 Appendix B. Liquidity performance We define banking liquidity as the ability of FIs to honor their short-run liabilities, to how ease they can convert assets to money and to raise funds, or even to roll-over or emit short-term debts. The inadequate structure of resources held by FIs relates to their liquidity risk, which also encompasses the difficulties for obtaining credit or for raising funds with interest rates comparable to the market reference. The inadequate structure of resources is a risk factor that is associated with the structure of liabilities held by an entity. It measures how adequate this structure is in terms of funding needs, bearing in mind the aspects of possible mismatches with the concentration and the volatility of the funding sources held by FIs. We evaluate liquidity performance by means of banks’ liquidity coverage ratios (LCR). LCR measures the amount of liquid resources that is available for an institution to withstand expected and unexpected cash flows in the next 30 days, under severe stress scenarios. These stress scenarios simulate ruptures in historical trends of variables related to cash flow estimates. We mold these scenarios by employing parameters that are extracted from historical references of experienced past crises. In these situations, it is assumed that these sudden adverse shocks will raise the disbursements of FIs above the expected levels. The liquidity index LCR is given by the ratio of the liquidity buffer and the stressed cash flow for a horizon of 30 days. The liquidity buffer is the amount each bank can raise in short time and is basically composed of unencumbered sovereign bonds. The stressed cash flow is the potential cash flow each bank would need to face stress situations, such as retail and wholesale deposit run-off, market stress, and potential losses on liquid assets and derivative positions. 42 6 5.5 5 x 10 −3 (a) Closeness Large banks Non−large banks Large banks Non−large banks 03/2008 06/2008 09/2008 12/2008 03/2009 06/2009 09/2009 12/2009 03/2010 06/2010 09/2010 12/2010 03/2011 06/2011 09/2011 12/2011 03/2012 06/2012 09/2012 12/2012 03/2013 06/2013 09/2013 12/2013 03/2014 06/2014 09/2014 12/2014 Avg. Betweenness 0.14 0.12 0.1 0.08 0.06 0.04 0 6 5 4 3 2 1 0 (b) Betweenness Large banks Non−large banks Large banks Non−large banks (d) Dominance as Borrower Large banks Non−large banks 03/2008 06/2008 09/2008 12/2008 03/2009 06/2009 09/2009 12/2009 03/2010 06/2010 09/2010 12/2010 03/2011 06/2011 09/2011 12/2011 03/2012 06/2012 09/2012 12/2012 03/2013 06/2013 09/2013 12/2013 03/2014 06/2014 09/2014 12/2014 0.02 Avg. Dominance as Borrower 03/2008 06/2008 09/2008 12/2008 03/2009 06/2009 09/2009 12/2009 03/2010 06/2010 09/2010 12/2010 03/2011 06/2011 09/2011 12/2011 03/2012 06/2012 09/2012 12/2012 03/2013 06/2013 09/2013 12/2013 03/2014 06/2014 09/2014 12/2014 4.5 4 3.5 14 12 10 03/2008 06/2008 09/2008 12/2008 03/2009 06/2009 09/2009 12/2009 03/2010 06/2010 09/2010 12/2010 03/2011 06/2011 09/2011 12/2011 03/2012 06/2012 09/2012 12/2012 03/2013 06/2013 09/2013 12/2013 03/2014 06/2014 09/2014 12/2014 8 6 4 2 0 2.6 2.4 2.2 2 1.8 1.6 1.4 1.2 1 0.8 03/2008 06/2008 09/2008 12/2008 03/2009 06/2009 09/2009 12/2009 03/2010 06/2010 09/2010 12/2010 03/2011 06/2011 09/2011 12/2011 03/2012 06/2012 09/2012 12/2012 03/2013 06/2013 09/2013 12/2013 03/2014 06/2014 09/2014 12/2014 (c) Dominance as Lender Avg. Criticality (e) Criticality 43 Figure 7: Evolution of several quasi-local topological network measurements extracted from the Brazilian interbank network. Avg. Closeness Avg. Dominance as Lender 0.085 0.08 0.075 0.07 0.065 0.06 0.055 4.5 4 3.5 3 2.5 2 1.5 1 0.5 03/2008 06/2008 09/2008 12/2008 03/2009 06/2009 09/2009 12/2009 03/2010 06/2010 09/2010 12/2010 03/2011 06/2011 09/2011 12/2011 03/2012 06/2012 09/2012 12/2012 03/2013 06/2013 09/2013 12/2013 03/2014 06/2014 09/2014 12/2014 Avg. Network Shortest Path 2 1.95 03/2008 06/2008 09/2008 12/2008 03/2009 06/2009 09/2009 12/2009 03/2010 06/2010 09/2010 12/2010 03/2011 06/2011 09/2011 12/2011 03/2012 06/2012 09/2012 12/2012 03/2013 06/2013 09/2013 12/2013 03/2014 06/2014 09/2014 12/2014 1.9 1.85 (b) Network-level shortest path 03/2008 06/2008 09/2008 12/2008 03/2009 06/2009 09/2009 12/2009 03/2010 06/2010 09/2010 12/2010 03/2011 06/2011 09/2011 12/2011 03/2012 06/2012 09/2012 12/2012 03/2013 06/2013 09/2013 12/2013 03/2014 06/2014 09/2014 12/2014 (a) Density Network Diameter 0 −0.24 −0.26 −0.28 −0.3 −0.32 −0.34 −0.36 −0.38 −0.4 (b) Assortativity 03/2008 06/2008 09/2008 12/2008 03/2009 06/2009 09/2009 12/2009 03/2010 06/2010 09/2010 12/2010 03/2011 06/2011 09/2011 12/2011 03/2012 06/2012 09/2012 12/2012 03/2013 06/2013 09/2013 12/2013 03/2014 06/2014 09/2014 12/2014 Density (c) Diameter Assortativity Figure 8: Evolution of several global topological network measurements extracted from the Brazilian interbank network. 1 0.9 0.8 0.7 0.6 K=2 K = 10 K = 20 K = 30 03/2008 06/2008 09/2008 12/2008 03/2009 06/2009 09/2009 12/2009 03/2010 06/2010 09/2010 12/2010 03/2011 06/2011 09/2011 12/2011 03/2012 06/2012 09/2012 12/2012 03/2013 06/2013 09/2013 12/2013 03/2014 06/2014 09/2014 12/2014 0.5 0.4 0.3 0.2 0.1 (a) Rich-club coefficient 44 Figure 9: Evolution of assortativity and rich-club coefficient, which are global network measurements. When looked together, they give us a sense of how close is a network to a core-periphery structure. Rich−Club Coefficient Regulatory Assets All Assets 0.055 0.05 0.045 0.04 0.035 0.03 03/2008 06/2008 09/2008 12/2008 03/2009 06/2009 09/2009 12/2009 03/2010 06/2010 09/2010 12/2010 03/2011 06/2011 09/2011 12/2011 03/2012 06/2012 09/2012 12/2012 03/2013 06/2013 09/2013 12/2013 03/2014 06/2014 09/2014 12/2014 0.025 0.02 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.1 0.09 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01 Large banks Non−large banks (c) Percentage change on out-degree 03/2008 06/2008 09/2008 12/2008 03/2009 06/2009 09/2009 12/2009 03/2010 06/2010 09/2010 12/2010 03/2011 06/2011 09/2011 12/2011 03/2012 06/2012 09/2012 12/2012 03/2013 06/2013 09/2013 12/2013 03/2014 06/2014 09/2014 12/2014 (a) Percentage change on network density Large banks Non−large banks k (out) −k ′(out) k (out) 03/2008 06/2008 09/2008 12/2008 03/2009 06/2009 09/2009 12/2009 03/2010 06/2010 09/2010 12/2010 03/2011 06/2011 09/2011 12/2011 03/2012 06/2012 09/2012 12/2012 03/2013 06/2013 09/2013 12/2013 03/2014 06/2014 09/2014 12/2014 D−D′ D Figure 10: Fraction of active operations due to regulatory assets against total unsecured assets. 0.13 03/2008 06/2008 09/2008 12/2008 03/2009 06/2009 09/2009 12/2009 03/2010 06/2010 09/2010 12/2010 03/2011 06/2011 09/2011 12/2011 03/2012 06/2012 09/2012 12/2012 03/2013 06/2013 09/2013 12/2013 03/2014 06/2014 09/2014 12/2014 0.12 0.11 0.1 0.09 0.08 0.07 0.06 0.05 0.04 0.03 (b) Percentage change on in-degree 45 Figure 11: Percentage changes on the network density and in- and out-degree when we remove established contracts that are due regulatory assets determined by the Central Bank of Brazil. k (in) −k ′(in) k (in)