“Too central to fail” systemic risk measure using PageRank algorithm

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“Too central to fail” systemic risk measure using PageRank algorithmR Tae-Sub Yun a, Deokjong Jeong b, Sunyoung Park c,∗ a

Department of Industrial & Systems Engineering, Korea Advanced Institute of Science and Technology (KAIST), 291 Daehak-ro, Yuseong-gu, Daejeon 34141, Republic of Korea b School of Business & Technology Management, Korea Advanced Institute of Science and Technology (KAIST), 291 Daehak-ro, Yuseong-gu, Daejeon 34141, Republic of Korea c Korea Capital Market Institute, 143 Uisadang-daero, Yeongdeungpo-gu, Seoul 07332, Republic of Korea

a r t i c l e

i n f o

Article history: Received 31 December 2017 Revised 20 September 2018 Accepted 19 December 2018 Available online xxx JEL codes: C63 C90 D85 E44 G21 G28 Keywords: Systemic risk Network structure Centrality Too central to fail Simulation PageRank

a b s t r a c t Following the popularity of the concepts of “too big to fail” and “too connected to fail” after the global financial crisis, the concept of “too central to fail” has garnered considerable attention recently. In this study, we suggest a “too central to fail” systemic risk measure, Rank, using the PageRank algorithm. Then, adopting a centrality perspective, we compare this measure, which effectively captures network relationships among financial institutions, with other well-known systemic risk measures, conditional value at risk (CoVaR) and marginal expected shortfall (MES). First, we model a simulation that generates bilateral connections among financial institutions. Second, we use real market data representing United States financial institutions. We show that Rank can capture the network structure among financial institutions better than CoVaR and MES. Further, Rank does not have procyclical properties; therefore, it is not dependent on market conditions. This study contributes to the development of a timely measure using publicly available market data. The measure also overcomes the shortcomings of the balance sheet-based approach, which is subject to time lags, because financial institutions release balance sheets quarterly basis. We also include equity and liability-type assets, in which systemic risks mainly propagate through intricately connected liability obligations. The findings will help regulators and policy-makers understand the implications of monitoring systemic risks from a network perspective. © 2018 Elsevier B.V. All rights reserved.

“The recent crisis showed that some financial innovations, over time, increased the system’s vulnerability to financial shocks that could be transmitted throughout the entire economy with immediate and sustained consequences that we are still working through today. Some of these vulnerabilities were a consequence of innovations that increased the complexity and interconnectedness of aspects of the financial system.” Chair of the Board of Governors of the Federal Reserve System (2014–2018), Janet L. Yellen at the American Economic Association/American Finance Association Joint Luncheon, San Diego, US on January 4 2013.1

R This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government(MSIT)(No. NRF2013R1A1A1076066). ∗ Corresponding author. E-mail addresses: [email protected] (T.-S. Yun), [email protected] (D. Jeong), [email protected] (S. Park). 1 See Yellen (2013) for the full speech.

https://doi.org/10.1016/j.jebo.2018.12.021 0167-2681/© 2018 Elsevier B.V. All rights reserved.

Please cite this article as: T.-S. Yun, D. Jeong and S. Park, “Too central to fail” systemic risk measure using PageRank algorithm, Journal of Economic Behavior and Organization, https://doi.org/10.1016/j.jebo.2018.12.021

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T.-S. Yun, D. Jeong and S. Park / Journal of Economic Behavior and Organization xxx (xxxx) xxx Table 1 Indicator-based measurement approach. Category (weight)

Individual indicator

Indicator weight

Cross-jurisdictional activity (20%)

Cross-jurisdictional claims Cross-jurisdictional liabilities Total exposures as defined for use in the BaselⅢ leverage ratio Intra-financial system assets Intra-financial system liabilities Wholesale funding ratio Assets under custody Payments cleared and settled through payments systems Values of underwritten transactions in debt and equity markets OTC derivatives notional value Level 3 assets Held for trading and available for sale value

10% 10% 20% 6.67% 6.67% 6.67% 6.67% 6.67% 6.67% 6.67% 6.67% 6.67%

Size (20%) Interconnectedness (20%)

Substitutability/financial institution infrastructure (20%)

Complexity (20%)

Source: Basel Committee on Banking Supervision (2011) Notes: This table shows the assessment methodology for the identification of SIFIs. The methodology depends on an indicator-based measurement approach that employs indicators to cover the different aspects of a financial institution. The Basel Committee on Banking Supervision released the revised methodology, following its decision to review the framework every three years (BCBS, 2011, 2013, 2017, 2018). The amendments support our argument proceeding from “too big to fail” or “too connected to fail” to “too central to fail.”

1. Introduction Managing financial systemic risks from a network perspective has become a major concern since the global financial crisis. To maintain financial stability, the International Monetary Fund (IMF), the Bank for International Settlements (BIS), and the Financial Stability Board (FSB) have identified systemically important financial institutions (SIFIs) that must be subject to higher capital buffer requirements under strengthened regulations (IMF, BIS, and FSB, 2009). In November 2017, BIS published an updated list of SIFIs (FSB, 2017).2 As per the list, JP Morgan Chase is classified under bucket four and is required to have 2.5% higher capital buffers, while the Bank of America, Citigroup, Deutsche Bank, and HSBC are allocated to bucket three and will have to maintain 2.0% higher capital buffers, effective January 2019. The identification of SIFIs significantly impacts both regulatory agencies and individual financial institutions. However, we note two shortcomings in the current SIFI criteria. First, the assessment methodology does not consider complex network relationships among financial institutions.3 The current methodology relies on an indicator-based measurement approach that employs selected indicators to reflect the different aspects of a financial institution (Table 1).4 Further, the criteria do not cover the dynamic forms of network relationships, such as common exposure among financial institutions, although the interconnectedness category accounts for intra-financial system assets and liabilities. However, the other categories, do not fully reflect the systemic importance of a financial institution beyond interconnectedness (i.e., whether a financial institution is critical to the stability of the financial system). Second, assessments based on balance sheet data do not reflect the latest circumstances of financial institutions. That is, balance sheet data are subject to time lags because financial institutions generally release their balance sheets on a quarterly basis. Thus, assessments that use balance sheet data are not reliable signals of alarm or progress, which is inconsistent with the objective of preventing crises by identifying SIFIs. Next, we discuss the concept of “too central to fail” and note the gaps between “too big to fail,” “too connected to fail,” and “too central to fail”.5 Although a financial institution could have significant assets, it may not be closely connected with other financial institutions in the financial system (i.e., “too big to fail” = “too connected to fail” ). To elaborate, a firm dealing in regulated mutual funds could be very large, but it might have transparent and simple relationships with others (Ragan, 2009). Similarly, a financial institution could take a critical position, although it is small or not closely connected with others (i.e., “too big to fail” = “too central to fail” or “too connected to fail” = “too central to fail”). For example, mortgage insurers in general, and Bear Stearns in particular, are relatively small but had substantial externalities on the system. This is because numerous factors could contribute toward making an institution systemically important (for a further 2 In addition to publishing policy measures for SIFIs, the FSB has been identifying global systemically important banks (G-SIBs) since 2011 and global systemically important insurers (G-SIIs) since 2013. 3 De Bandt and Hartmann (20 0 0) and Nier et al. (2007) discuss the role of complex networks when mechanisms causing the failure of multiple banks simultaneously emerge, as follows: direct bilateral lending and borrowing between banks, a common source of risks from correlated exposure among banks, feedback effects with an endogenous fire sale, and informational contagion. Their work underpins the main argument of this study, that is, the current SIFI criteria do not fully capture financial networks. 4 Following its decision to review the framework every three years, the Basel Committee on Banking Supervision (BCBS) recently released the revised methodology to assess G-SIBs (BCBS, 2018; see BCBS, 2011, 2013, 2017 for changes in the assessment methodology). The recent amendments support our argument proceeding from “too big to fail” or “too connected to fail” to “too central to fail.” For example, enhancing the substitutability/financial institution infrastructure category warrants the introduction of trading volume and modification of weights, which capture the systemic importance of a bank (i.e., the systemic impact of a bank’s distress or failure or the extent to which a bank offers financial institution infrastructure). 5 There is no standard or consensus distinguishing the three terminologies. Bernanke (2009) and Cecchetti (2012), for instance, mention “too big to fail” and “too interconnected to fail” in their speeches, although they use “too big to fail” in the broader sense. Later, Dudley (2014) used the term “too big to fail” in his speech.

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discussion on these factors, see Ragan, (2009)). Referencing the evolution of network analysis helps us link it to complex financial systems from a network approach.6 “Too big to fail” examines large-scale financial institutions in a financial system (Fig. 1(a)). This first level focuses on information from big nodes (i.e., large-scale financial institutions) in the network structure. The concept of “too connected to fail” emphasizes the complex relationships among large-scale financial institutions (Fig. 1(b)). This second level pays attention to information from edges (“relationships”) with big nodes in the network structure. Information from both a node and an edge is important in the network structure. The third level utilizes both approaches in a complementary manner (Fig. 1(c)). The “too central to fail” approach examines the network structure for financial institutions that have a crucial influence on the entire financial system. Rather than focusing on information from only big nodes or edges connected to big nodes, this top-level approach considers information from all nodes and edges in the network structure. In other words, the “too central to fail” approach uses information from both node and edge while considering all financial institutions in the system. We argue that the “too central to fail” perspective can replace the “too big to fail” and “too connected to fail” approaches to fully understand the network structure of the financial system. The key objective of this paper is to propose a new method to quantify network relationships between financial institutions from the “too central to fail” perspective. We compare the proposed measures with well-known systemic risk measures using stock data. First, we model a hypothetical banking system for simulations. We assume a stylized balance sheet that includes assets and liabilities. Financial institutions in the simulations have a complex interbank network through their asset-type assets and liability-type assets. They may also default from shocks and financial distress propagates to an entire financial system through the interbank network. Second, we conduct an empirical analysis to check if the measure can capture the network structure. We then conduct a panel regression analysis using both simulations and real market data. To represent centrality in terms of the most relevant examples, we sample US financial institutions and compare Rank with two well-known systemic risk measures: conditional value at risk (CoVaR) and marginal expected shortfall (MES) (Fig. 2). The size of the nodes implies the level of Rank, CoVaR, and MES, while the edges denote connections among financial institutions. Owing to limitation of space, we have replaced the names of financial institutions with tickers (e.g., “STT” and “JPM” denote State Street Corp and JP Morgan, respectively; see Table A1 in the Appendix for details). State Street Corp and JP Morgan have been on the list of SIFIs since 2011, proving their centrality in the financial system (FSB, 2011, 2012, 2013, 2014, 2015, 2016, 2017). We find that the centrality captured by the three measures is inconsistent. We assume that each measure has a different focus and captures various attributes in the financial system. We then identify the main factors affecting each measure by conducting a simulation and an empirical analysis. The inconsistency between the measures highlights the need to develop a systemic risk measure from the “too central to fail” perspective.7 This study makes the following three contributions to the literature. First, we consider the direction of a financial institution’s influence on another financial institution and vice versa. Using the PageRank algorithm to determine financial systemic risks, Dungey et al. (2012) suggest correlating a firm’s stock price movements with its network. Thus, the authors make the restricted assumption that the effect on one financial institution is the same as that on another financial institution. Second, we account for both equity and liability connections to fully capture network relationships among financial institutions. Battiston et al. (2012a) propose a method to quantify networks using equity investment. However, equity connections based on equity stakes only include partial network channels because systemic risks mainly propagate through intricately connected liability obligations (“domino effects” in Upper and Worms, 2004; Gai and Kapadia, 2010; Nier et al., 2007; Battiston et al., 2012). Third, we support the validity of new network measures through simulations and using real financial data. Previous studies propose measures from a network perspective; however, they mainly perform a descriptive-level analysis (Battiston et al., 2012b; Kuzubas et al., 2014; Demirer et al., 2017). The remainder of this paper is organized as follows. In Section 2, we provide a theoretical background through a literature review. In Section 3, we explain the sample data and variables for the analysis. In Section 4, we present a simulation model to construct a hypothetical banking system. In Section 5, we present the empirical results. We conclude in Section 6 by summarizing the research and discussing the potential for future studies. 2. Literature review The global financial crisis has provoked an approach toward financial systemic risks from a network perspective. Following Allen and Gale (20 0 0) and Freixas et al. (20 0 0) work on the structure of financial networks, understanding financial systems through networks has drawn much attention since the collapse of Lehman Brothers. Theoretical analyses suggest that the more financial institutions are connected through various channels, the more resilient the financial system will be to shocks (Brunnermeier and Pedersen, 2009; Geanakoplos, 2010). A shock can be dispersed to each financial institution in a densely connected financial system. However, the learning from the global financial crisis changed this understanding; financial systems can be vulnerable to shocks when financial institutions are excessively connected. As the intermediation chains of financial institutions lengthen, small exogenous shocks are amplified to big endogenous ones that can affect an en-

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See Section 2 (literature review) in this paper and Battiston et al. (2010) for a further discussion on the evolution of network analyses. The centrality measure of Rank can help understand the behaviors of financial institutions and the entire financial system. Other centrality measures such as degree, closeness, betweenness, and eigenvector centrality can be complementary when monitoring financial vulnerability. 7

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Fig. 1. Scheme of “too big to fail,” “too connected to fail,” and “too central to fail”.

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Fig. 2. Centrality of US financial institutions. Notes: Edges denote connections among financial institutions, while the size of nodes implies the level of Rank, CoVaR, and MES in 2008Q2. Owing to limitations of space, we replace the names of financial institutions with tickers (e.g., “STT” and “JPM” denote State Street Corp and JP Morgan, respectively; see Table A1 in the Appendix for details).

tire financial system (Shin, 2010). Caballero (2015) and Minoiu et al. (2015) also empirically support that high connectedness between financial institutions can increase the probability of a banking crisis.8 The increasing interest in financial networks has led to the development of a systemic risk measure to reflect network characteristics. However, the quantification and representation of a financial network as a measure differ by the feature under focus.9 Well-known systemic risk measures used in financial networks include the principal components analysis,

8 For a literature review of recent finance and economics papers from a network perspective, see Glasserman and Young (2016), Langfield and Soramäki (2016), Aldasoro et al. (2017), Benoit et al. (2017), Battiston and Martinez-Jaramillo (2018), Caccioli et al. (2018), and Neveu (2018). 9 Measuring systemic risks while considering a financial network is somewhat new. Numerous studies have suggested and explored measures. Kara et al. (2015) divide network measures into direct and indirect approaches; a direct approach follows bilateral obligations between financial institutions, while an indirect one estimates relationships between financial institutions using real market data. In this research as well, Rank estimates the complex

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interbank exposure, and cross-border linkages (Bisias et al., 2012). The principal component analysis gauges the degree of commonality and associates significant factors with systemic risks.10 The interbank exposure illustrates entities as nodes and relationships as edges, based on graph theory.11 The cross-border linkages focus on the funding of global banks and examine risk transmission.12 Regulatory agencies such as the IMF, FSB, and central banks have also noted systemic risk measures from a network perspective to monitor financial systems and maintain financial stability. The IMF examines four methods, including a network approach, to assess the systemic implications of financial linkages (IMF, 2009).13 In addition, it analyzes three indicators by calculating the contribution of an institution to systemic risks (IMF, 2011).14 Arregui et al. (2013) review tools to measure interconnectedness and analyze the systemic risk of interconnectedness from a surveillance perspective.15 Chan-Lau (2010) suggests a way to impose additional regulatory capital charges on the basis of interconnectedness. Admati et al. (2013) and Federal Reserve Bank of Minneapolis (2016) support additional capital requirements to end the “too big to fail” problem and reduce the need for government bailouts. The interest of regulatory agencies in centrality further supports the present research in the concept of “too central to fail” (European Central Bank, 2010; Arregui et al., 2013). Examining the evolution of network analysis helps develop a systemic risk measure using a financial network approach. Network methodologies have been developed at three levels in the field of network analysis (Battiston et al., 2010). The first level depends on a topological approach in which the links between entities may simply exist or not. The second level includes weights or weights with directions to links. Direct interaction between entities is represented as a link, which can be a transaction, ownership, or credit relation, in the case of financial institutions.16 The top level assigns a degree of freedom to nodes that proceed to a non-topological variable to shape the network. This is in line with recent research that accounts for the dynamics of nodes through centrality. Degree, closeness, betweenness, and eigenvector centrality are the most commonly used centrality measures derived from a social network analysis.17 In finance and economics, Battiston et al. (2012b) DebtRank identifies systemically important nodes in loans, while Soramäki and Cook’s (2013) SinkRank determines systemically important banks in a payment system. Kuzubas et al. (2014) claim that centrality measures perform well in predicting SIFIs. In addition, Thurner and Poledna (2013) suggest that centrality measures can be effectively used to select a counterparty, which could decrease the number of failed firms and the total loss. The existing literature uses simulations owing to the lack of information on bilateral relationships between financial institutions. In particular, micro-level bilateral information (from one financial institution to another) rather than aggregate-level bilateral information (from one country to another) is not publicly released. Thus, researchers have constructed hypothetical financial systems with economic agents on the basis of theory and examined the effects of financial networks on financial vulnerability. Nier et al. (2007) analyze the impacts of various banking network structures on systemic risk and Erol and Ordoñez (2017) examine the effects of regulation levels on systemic risk in interbank networks. In addition, recent studies on financial networks conduct simulations to overcome limited data. The model and assumptions used in the simulations differ by the purpose and focus of the research. For example, Gai and Kapadia (2010) and Gai et al. (2011) develop a model of contagion in financial networks and demonstrate the amplification of fragility as a result of complexity and concentration in a financial network. Krause and Giansante (2012) show that a network of interbank lending can be a transmission mechanism of bank failures. The authors allow for different bank characteristics and interactions with others to capture a more realistic financial network. Elliott et al. (2014) and Acemoglu et al. (2015) analyze the contagion of failures among interdependent financial organizations and the impacts of network structure on stability.18 Simulation research originated as a result of the regulatory objective of central banks to maintain a stable financial market. For instance, the National Bank of Belgium simulates consequences of the non-repayment of interbank loans by demonstrating the time-varying structure of the Belgian interbank market (Degryse and Nguyen, 2004). The Austrian National Bank developed the Systemic Risk

network relationships among financial institutions by mainly using the stock returns of financial institutions as real market data. See Kara et al. (2015) for detailed taxonomy on financial network measures. 10 The applications of principal components analyses include the absorption ratio (Kritzman et al., 2011) and PCAS (Billio et al., 2012). 11 Chan-Lau et al. (2009) and the IMF (2009) show network models in terms of interbank exposure. Billio et al.’s (2012) Granger-causality network is also based on this property. 12 The cross-border linkages include the bank funding gap highlighted in Fender and McGuire (2010). 13 The IMF’s (2009) Global Financial Stability Report, published after the global financial crisis, represents a network approach, co-risk model, distress dependence matrix, and default intensity model. 14 The IMF’s (2011) Global Financial Stability Report analyzes the performance of CoVaR, joint probability of distress (JPoD), and the Diebold–Yilmaz index (Diebold and Yilmaz, 2009, 2014). 15 The measures include CoVaR, return spillovers, distress spillovers, JPoD, conditional probability of default, and systemic contingent claim analysis (Arregui et al., 2013). 16 The finance literature using network analysis includes, for instance, interbank markets (Boss et al., 2004; Iori et al., 2006; Iori et al., 2008) and corporate control or ownership (Almeida and Wolfenzon, 2006; Vitali et al., 2011). 17 Degree centrality estimates the number of immediate neighborhood nodes and finds a highly connected node. It counts incoming links (in-degree), outgoing links (out-degree), or all links (degree). Closeness centrality measures the shortest path between one node and the others, implying that a node with shorter paths to other nodes is more central. Betweenness centrality measures the number of times a node passes the shortest path and identifies nodes that act as “bridges.” Eigenvector centrality assigns scores to all nodes and determines connections to high-scoring nodes. Simply put, an important node is connected to important neighbors. An application of eigenvector centrality is Google’s PageRank. 18 See Upper (2011) for a summary of other simulation studies on financial networks.

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Table 2 Variable definitions and data sources. Variables Measurement

Definition

Rank

Measure of centrality of individual financial institutions Author’s calculation based on Page et al. (1999) from “too central to fail” perspective and Billio et al. (2012) Extent of contribution to systemic risk of individual Author’s calculation based on Adrian and financial institutions Brunnermeier (2016) Average stock return of individual financial institutions on Author’s calculation based on the condition that financial market is in the worst return Acharya et al. (2017)

Conditional value at risk (CoVaR) Marginal expected shortfall (MES)

Sources

Firm characteristics Stock price Size Leverage Liquidity Network connection

Daily stock price for the sample financial institutions Total asset in book value of individual financial institutions Liability to equity ratio of individual financial institutions Sum of cash and short-term investment to total asset ratio of individual financial institutions Bilateral network relationships between financial institutions distinguishing effects to and from another financial institution

Center for Research in Security Price Compustat Compustat Compustat

Index of Standard and Poor’s 500 Volatility index on S&P 500 stock index option prices Difference between three-month London Interbank Offered Rate (LIBOR; based on the US dollar) and three-month Treasury bill rate Difference between three-month Treasury bill and 10-year Treasury bond rate Difference between 10-year Treasury bond and Baa-rated corporate bond yield

Center for Research in Security Price Chicago Board Options Exchange Federal Reserve Bank of St. Louis Board of Governors of the Federal Reserve System

Author’s calculation based on Billio et al. (2012) and Jeong and Park (2018)

Macroeconomic variables S&P 500 VIX TED spread

Maturity spread Credit spread

Board of Governors of the Federal Reserve System Board of Governors of the Federal Reserve System Federal Reserve Bank of St. Louis

Notes: This table shows variable definitions with data sources. We calculate measurement variables (Rank and two well-known systemic risk measures, conditional value at risk (CoVaR) and marginal expected shortfall (MES)) and network connection using real market data. We collect balance sheet data for firm characteristics and macroeconomic data to reflect the US economic situation.

Monitor (SRM) (Boss et al., 2006) and the Bank of England set up the Risk Assessment Model for Systemic Institutions (RAMSI) (Alessandri et al., 2009).19

3. Data and variables 3.1. Data We focus on US financial institutions to analyze the notion of “too central to fail” in the financial system. Following Adrian and Brunnermeier (2016), we select our sample financial institutions from among companies whose standard industrial classification (SIC) code is between 60 and 65 and whose headquarters are located in the United States. To exclude non-financial holding companies, we omit financial institutions whose SIC is 67. We also exclude small-scale financial institutions whose market capitalization was less than $US 5 billion as of June 2007, that is, before the global financial crisis. Thus, the final sample comprises 92 financial institutions (see Table A1 in the Appendix for the list of institutions). We collect daily stock price and quarterly balance sheet data of the sample companies for 20 0 0–2016 from the Center for Research in Security Price (CRSP) and Compustat (Tables 2 and 3). The balance sheet data include total assets in book value, leverage (ratio of liability to equity), and liquidity (ratio of the sum of cash and short-term investments to total assets). In addition, we employ daily macroeconomic variables to reflect the US economic situation. We include data on the S&P 500 from CRSP to capture the overall stock market conditions. To represent volatility in the financial market, we adopt the volatility index (VIX) with data from the Chicago Board Options Exchange (CBOE). In addition, for money market variables, we obtain the three-month London Interbank Offered Rate (LIBOR; based on the US dollar) and the three-month Treasury bill rates from the Federal Reserve Bank of St. Louis and the Board of Governors of the Federal Reserve System. We then collect data on 10-year Treasury note and Baa-rated corporate bond yields as capital market variables from the Board of Governors of the Federal Reserve System and the Federal Reserve Bank of St. Louis.

19 Fearing that the European banking crisis will prove pervasive, central banks are mamking advances in simulation analyses to emphasize stress testing. In addition to Austria and England, other countries developing or upgrading their stress testing methods include Brazil, Canada, Chile, the Czech Republic, France, Germany, Italy, Japan, the Netherlands, Norway, Spain, Sweden, Switzerland, the United States, and the European Central Bank (Schmieder et al., 2011; Ong, 2014).

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Table 3 Descriptive statistics for the variables investigated. Variables Measurement

Observation

Mean

Standard deviation

Min

Max

Rank CoVaR MES

5272 5272 5272

0.0123 0.0147 0.0333

0.0055 0.0111 0.0272

0.0038 −0.0026 −0.0070

0.0593 0.0882 0.2159

5711 5711 5711 5272

169,596.1 7.1622 0.1375 1

352,538.2 5.7796 0.1402 0.9683

207.5180 0.0320 0.0012 0

2,577,148 50.8369 0.9081 9.3729

6256 6256 6256 6256

20.7412 0.4159 1.9110 2.1159

7.0320 0.3506 1.0777 0.5999

12.6349 0.1621 −0.2482 1.3035

49.3615 1.6226 3.4266 4.6473

Firm characteristics Size (million USD) Leverage Liquidity Network connection Macroeconomic variables VIX TED spread (%) Maturity spread (%) Credit spread (%)

3.2. Measurement variables In this subsection, we present the concept of calculating Rank and compare it with well-known systemic risk measures, CoVaR (Adrian and Brunnermeier, 2016) and MES (Acharya et al., 2017), after quantifying the three measures.20 3.2.1. Rank We quantify the centrality of individual financial institutions from a “too central to fail” perspective. Rank represents the link between one financial institution and another while considering the other financial institution’s weight. Therefore, Rank is a relative value rather than an absolute value. First, we calculate an “effect matrix” that shows the extent to which each financial institution is connected to other financial institutions. We apply Billio et al. (2012) and Jeong and Park’s (2018) Granger-causality network to create the effect matrix. Dungey et al. (2012) construct an effect matrix on the basis of the correlation of stock returns. However, the correlation of the effect matrix cannot capture direction. That is, in terms of correlation, the effect of financial institution i on financial institution j is the same as that of financial institution j on financial institution i. Thus, we distinguish between the effect of financial institution i on financial institution j and that of financial institution j on financial institution i. Whereas Billio et al. (2012) apply a p-value to calculate each financial institution’s connectedness, we use the F-statistics of the Granger causality network as the entity of the effect matrix (eijt ). The use of F-statistics, rather than p-values, allows us to be more specific by accounting for wider variations. Second, we calculate the value of financial institutions’ centrality. Based on entity (i, j) of the effect matrix, we normalize the effect weight of each financial institution as follows:

ei jt Ei jt =  i ei jt where eijt denotes the extent of the effect by financial institution i on financial institution j at time t and Eijt is the effect weight on financial institution j by financial institution i at time t. Next, we apply the PageRank algorithm (Page et al., 1999) to obtain Rank.21

Rankit =

(1 − α ) N

+α



Ei jt Rank jt

where Rankit is the Rank of firm i at time t, α is a damping factor and is generally set to 0.85, and N is the total number of firms in the system.22 Rank always has a positive value and a higher Rank value denotes that the firm has a greater contribution to systemic risks in the network structure. There are two types of financial risk measures: vertical (time series) and cross-section. The authorities can monitor the financial system through vertical measures, recognizing the trend of risks in the financial markets, and comparing the increase or decrease in risk with past trends. In contrast, cross-section measures allow authorities to concentrate their

20 We choose CoVaR and MES from among popular systemic risk measures for the control group. As with Rank, we can calculate CoVaR and MES using real market data. 21 The Economist (2004) explains PageRank with an example. See The Economist (2004) for an explanation of the concept and mechanism of PageRank. 22 A damping factor is the probability at each web page that internet users are not satisfied and request another random page (Brin and Page, 1998). In computer science, the damping factor is generally set to 0.85. Mathematically, a damping factor ranges between zero and one, which results in an inverse matrix of Rank.

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surveillance on certain financial institutions. Since supervisory resources such as personnel and infrastructure are limited, critical institutions are identified in advance, allowing for rapid activation of contingency plans in case of economic shock. 3.2.2. Conditional value at risk Conditional value at risk (CoVaR) measures an individual firm’s contribution to systemic risk. Following Adrian and Brunnermeier (2016), we conduct a quantile regression to calculate CoVaR. We can reflect extreme market situations by relaxing the assumption of the error term’s normal distribution. The quantile regression model to calculate CoVaR is as follows:

Xti =

α i + γ i Mt−1 + εti

Xtsystem =

α system/i + β system/i Xti + γ system/i Mt−1 + εtsystem/i system

where Xti is firm i’s stock return at time t, Mt−1 is the vector of state variable at time t–1, and Xt is the index return at time t. Our selection of the following state variables is based on Adrian and Brunnermeier (2016): VIX, TED spread, changes in three-month T-bill rate, maturity spread, credit spread, and returns on S&P 500. Table 2 presents the details on the variables. We obtain the estimated values for α i , γ i , α system/i , β system/i , and γ system/i using quantile regression. Using the estimated parameters from the regression, we obtain the value at risk (VaR) and conditional value at risk (CoVaR) for each firm. Then, we calculate CoV aRti using the following equation:

V aRti (q ) = αˆ i + γˆ i Mt−1 CoV aRti (q ) = αˆ i

system/i

+ βˆ i

system/i

V aRti (q ) + γˆ i

system/i

Mt−1

C oV aRti (q ) = C oV aRti (q ) − C oV aRti (50% ) where CoV aRti is a proxy for contribution to systemic risk. Hereinafter, we simply denote CoVaR by convenience. CoVaR generally has a negative value and a small CoVaR could be interpreted as a greater contribution to systemic risk. 3.2.3. Marginal expected shortfall Marginal expected shortfall (MES) is another measure of an individual firm’s contribution to systemic risk (Acharya et al., 2017). Compared to CoVaR, the MES averages a firm’s stock returns on the condition that the financial market is based on the lowest returns. The formula for MES is as follows: i ME S5% = −E [Xti

| I5% ]

Xti

where is firm i’s stock returns at time t and I5% denotes index returns when the index is in the lowest 5%. MES is generally greater than 0 and a larger MES value can be interpreted as a greater contribution to systemic risk. 4. Simulation methodology We construct a simple yet reasonable simulation model to show whether Rank reflects network information better than other measures. We attempt to prove it theoretically or empirically to check if the measure truly reflects network information. However, given the complexity of network relationships among multiple financial institutions, as noted by Krause and Giansante (2012), it is difficult to derive analytic solutions to show that the measure illustrates network information. Thus, we could not empirically demonstrate the effectiveness of Rank using real market data because information on bilateral exposure between financial institutions is not available to the public. 4.1. Banking system We assume a hypothetical banking system using a simulation model, with each financial institution holding primitive assets (e.g., any factors of production or other investments) as part of their portfolio.23 The values of financial institutions depend on those of the primitive assets (hereinafter, assets). We can track the varying values of financial institutions on the basis of the changing asset values. We set the number of financial institutions and assets in the banking system. There 23 There can be two starting points in the design of a hypothetical banking system. In one method, we assume the distribution of size and structure of the balance sheet of financial institutions. (Nier et al., 2007; Gai and Kapadia, 2010; Battiston et al., 2012a). Although we can assume various distributions of size and balance sheet structure, the results can be arbitrarily biased depending on the settings. In the other method, we consider primitive assets and assume random assignment of assets for institutions during the initial phase of the simulation (e.g., primitive assets in Elliott et al., 2014; units of capital units of capital in Acemoglu et al., 2015). Drawing on Elliott et al. (2014), the notion that each financial institution has a primitive assets portfolio in the banking system simplifies the development of simulations. Primitive assets can extend to debts and other contracts. We can imitate any type of real-world asset using combinations of primitive assets that follow the GBM. We can also include various cases in the experiments; for example, we can examine various types of financial institutions, assets, or balance sheet structure. In addition, we can prevent problems in the model selection that can manipulate the simulation results.

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Fig. 3. Price movement of assets using the GBM. Notes: We assume that there are N assets whose price movements follow the GBM. The price movements of the assets are independent of each other. The x-axis denotes time and the y-axis denotes price of assets.

Fig. 4. Framework of balance sheet of financial institutions in simulation. Notes: We suppose a simple balance sheet framework. The total assets of financial institutions are composed of two types of assets: equity-type and liability-type. The asset composition of financial institutions is randomly decided in the initializing simulation and will remain fixed.

exist i = 1, 2, . . . , N financial institutions in the banking system and j = 1, 2, . . . , M assets whose price movements follow the geometric Brownian motion (GBM). The price movements of the assets are independent of each other. Each financial institution chooses whether to hold each asset at random. If the institution chooses to hold, it also chooses how much to hold of each asset at uniform distribution. Therefore, financial institutions can have several assets. Fig. 3 depicts the price movement of assets using the GBM. The total assets of financial institutions are composed of two types of assets (Fig. 4): equity-type and liability-type.24 The asset composition of financial institutions is randomly decided in the initializing simulation and will remain fixed. The total equity-type asset of financial institution i is the sum of assets that follows the GBM (Fig. 5).

EtAssetit =



Pjt wi j

j

where EtAssetit is the sum of institution i’s equity-type assets at time t, Pjt is the price of asset j at time t, and wij is the amount of asset j that belongs to financial institution i. 4.2. Interbank network In the simulation model, financial institutions have liability relationships with each other. That is, one financial institution may lend capital to another at random. The total liability-type asset of financial institution i is the sum of liability connections considering depreciation such as loan loss provision (Fig. 6).

LtAssetit =

 j



ci j min



E jt −1 , 1 E j0

where LtAssetit is the sum of institution i’s liability-type assets at time t, cij is the debt obligation of firm j that belongs to institution i, and Ejt is financial institution j’s total equity at time t. 24 Extending Nier et al. (2007) and Krause and Giansante (2012), we construct a stylized balance sheet for individual financial institutions. Rather than all types of assets and liabilities, we focus on assets and liabilities that connect financial institutions.

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Fig. 5. Equity-type asset movement in simulation. Notes: We assume that the total equity-type assets of financial institutions are the sum of assets that follow the GBM. The x-axis denotes time and the y-axis denotes the price of equity-type asset.

Fig. 6. Liability-type asset movement in simulation. Notes: We assume that total liability-type assets of financial institutions are the sum of debt obligation considering depreciation (loan loss provision). The x-axis denotes time and the y-axis denotes the price of liability-type asset.

The initial state of liability and equity for each firm will be determined by randomly selected leverage. Then, the liability will be fixed.

Et Assetio + Lt Assetio = Ei0 + Li where Ei0 is financial institution i’s total equity at time 0 and Li is financial institution i’s total liability. Each firm’s market value is equal to the book value of its equity (Fig. 7). We note that a liability-based connection among financial institutions is more important than an equity-based one because the latter is easy to unwind. Recall that equity investors are free to sell stocks at any time. However, Battiston et al. (2012b) and Elliott et al. (2014) focus on equity-based connections among financial institutions. Therefore, their value for a firm’s connections linearly depends on each firm’s market value. Therefore, our simulation model includes liability-type price functions (Fig. 8). The value of liability-type assets only changes if the firm’s equity is lower than its initial value. The equity-based connection can also be explored using equity-type assets. 4.3. Shock and default mechanism A shock influences multiple financial institutions through financial linkages. If a financial institution’s equity becomes zero, we define this as a default. We define a "shock" as a plunge in the equity-type assets of a financial institution. Thus, the probability of a default increases if the level of the shock is disruptive, and vice versa. Please cite this article as: T.-S. Yun, D. Jeong and S. Park, “Too central to fail” systemic risk measure using PageRank algorithm, Journal of Economic Behavior and Organization, https://doi.org/10.1016/j.jebo.2018.12.021

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Fig. 7. Equity value changes in simulation. Notes: The equity of financial institution changes as equity-type and liability-type assets change. The x-axis denotes time and the y-axis denotes the equity price of a financial institution.

Fig. 8. Function of liability value changes. Notes: The value of liability-type assets only changes if the equity of the financial institution is lower than the initial value.

Fig. 9. Shock and default mechanism.

The simulation model focuses on default in both assets and liabilities (Fig. 9). Financial institutions are more likely to default when they do not hold sufficient assets and liabilities. For example, if the equity-type assets of financial institution 1 become fragile because of a shock from the GBM, its equity may plunge in the first round. In the second round, this impairs the liability-type assets of financial institutions 2 and 3 that have claims on financial institution 1. While depreciation, such Please cite this article as: T.-S. Yun, D. Jeong and S. Park, “Too central to fail” systemic risk measure using PageRank algorithm, Journal of Economic Behavior and Organization, https://doi.org/10.1016/j.jebo.2018.12.021

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Table 4 Panel regression for the impact of network connection on Rank in simulation-based analysis. (1) Constant

0.00692 (0.00)

(2) ∗∗∗

0.0326 (0.00)

(3) ∗∗∗

0.00678 (0.00)

(4) ∗∗∗

0.0324 (0.00)

(5) ∗∗∗

0.0324 (0.00)

(6) ∗∗∗

0.00986∗ ∗ ∗ (0.00)

Firm characteristics 0.0 0 0528∗ ∗ ∗ (0.00) −0.0 0 0 0836 (0.39)

Size Leverage Liquidity

0.0 0 0974∗ ∗ ∗ (0.00) −0.0 0 0 0777 (0.41) −0.0318∗ ∗ ∗ (0.00)

0.0 0 0531∗ ∗ ∗ (0.00) −0.0 0 0 0849 (0.39)

0.0 0 0 0179∗ (0.06)

Network connection

0.0 0 0977∗ ∗ ∗ (0.00) −0.0 0 0 0792 (0.41) −0.0318∗ ∗ ∗ (0.00) 0.0 0 0 0194∗ ∗ (0.03)

0.0 0 0977∗ ∗ ∗ (0.00) −0.0 0 0 0792 (0.41) −0.0318∗ ∗ ∗ (0.00) 0.0 0 0 0194∗ ∗ (0.03)

0.0 0 0 0173∗ (0.06)

10,0 0 0 0.0646

2.791 (0.84) 10,0 0 0 0.0646

10,0 0 0 0.0 0 04

Macroeconomic variable Market volatility Observations R-squared

10,0 0 0 0.0024

10,0 0 0 0.0641

10,0 0 0 0.0028

Notes: This table shows the estimates of a panel regression on the impact of network connection on Rank. We show the estimates of these regressions, with numbers in parentheses denoting p values. Estimates with ∗ ∗ ∗ , ∗ ∗ , ∗ denote statistical significance of the estimate at the 1%, 5%, and 10% level, respectively.

as loan loss, occurs in liability-type assets, the equity of financial institutions 2 and 3 may plunge. This chain reaction continues across neighboring financial institutions, rendering the entire financial system vulnerable.25

5. Empirical analysis 5.1. Simulation-based analysis We simulate stock data, firm characteristics, and network structure following the simulation methodology described in the previous section. For each simulation trial, we set the financial institutions at N = 10 0 0, the number of assets at M = 100, and the window length at 300 days. Then, we conduct the simulation 100 times to consider various cases. We then perform the simulation 10,0 0 0 times for robustness and find that the results remain qualitatively the same. We report the empirical results of the 100 simulations in this study. The baseline model for the regression analysis is as follows:

Measur eit =

α + β F irm characteristicit + γ Macroeconomict + εit

where Measureit is firm i’s calculated measures (i.e., Rank, CoVaR, or MES) at trial t and Firm characteristicit includes a firm’s size, leverage, liquidity, and network connections. We use size as a logarithm for the book value of total assets; leverage as liability over equity; liquidity as the ratio of equity-type assets to total assets; and network connections as the number of liability connections, where the amount of liability-type assets exceeds 0.5% of total assets. Macroeconomict includes volatility, which is defined as the standard deviation of the index (a summation of all assets is considered the index in the simulated financial system). The estimation results in Table 4 show the impact of firm characteristics and network structure on Rank. The results indicate that firm size has a significantly positive effect on Rank, that is, as a financial institution increases in scale, it tends to hold a higher Rank, which is in accordance with being “too big to fail.” On the contrary, liquidity has a significantly negative effect on Rank. Here, we infer that Rank assigns less value to firms with sufficient cash or a cash equivalent. These results are consistent with those in previous research. When a financial institution has sufficient liquidity, the shock may not propagate to other financial institutions. In addition, network connections have a significantly positive effect on Rank, which is the most remarkable result. In other words, Rank assigns greater weight to financial institutions that have more connections with other financial institutions. This result supports the “too central to fail” argument. Note that we mention CoVaR and MES are not associated with network connections in the following results. We argue that Rank is the only measure that captures the network structure from stock data. Finally, the results illustrate that market volatility has no significant effect on Rank. Thus, we can say that Rank is not a procyclical measure, that is, Rank can detect systemic risk equivalently in both normal and crisis periods. Please cite this article as: T.-S. Yun, D. Jeong and S. Park, “Too central to fail” systemic risk measure using PageRank algorithm, Journal of Economic Behavior and Organization, https://doi.org/10.1016/j.jebo.2018.12.021

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Table 5 Panel regression for the impact of network connection on CoVaR in simulation-based analysis. (1) Constant

0.0178 (0.09)

(2) ∗

0.0466 (0.00)

(3) ∗∗∗

0.0183 (0.08)

(4) ∗

(5)

(6)

0.00387 (0.78)

0.0366∗ ∗ ∗ (0.00)

0.00364∗ ∗ ∗ (0.01) −0.0 0 0485 (0.68) −0.0356∗ ∗ (0.02) −0.0 0 0 0596 (0.59)

0.00373∗ ∗ ∗ (0.00) −0.0 0 0351 (0.73) −0.0332∗ ∗ (0.01) −0.0 0 0 0759 (0.44)

−0.0 0 0 0646 (0.56)

10,0 0 0 0.0012

8293.7∗ ∗ ∗ (0.00) 10,0 0 0 0.2381

10,0 0 0 0.0 0 0 0

0.0470 (0.00)

∗∗∗

Firm characteristics Size Leverage

0.00315∗ ∗ (0.02) −0.0 0 0496 (0.67)

Liquidity

0.00365∗ ∗ ∗ (0.01) −0.0 0 0490 (0.68) −0.0356∗ ∗ (0.02)

0.00314∗ ∗ (0.02) −0.0 0 0492 (0.67)

−0.0 0 0 0613 (0.58)

Network connection

Macroeconomic variable Market volatility Observations R-squared

10,0 0 0 0.0 0 06

10,0 0 0 0.0012

10,0 0 0 0.0 0 06

Notes: This table shows the estimates of a panel regression on the impact of network connection on conditional vale at risk (CoVaR). We multiplied the dependent variables by 10,0 0 0 to make the coefficients of the variables easier to recognize. We show the estimates of these regressions, with numbers in parentheses denoting p values. Estimates with ∗ ∗ ∗ , ∗ ∗ , ∗ denote statistical significance of the estimate at the 1%, 5%, and 10% level, respectively.

Table 6 Panel regression for the impact of network connection on MES in simulation-based analysis.

Constant

(1)

(2)

(3)

(4)

(5)

(6)

0.156 (0.45)

1.871∗ ∗ ∗ (0.00)

0.164 (0.43)

1.877∗ ∗ ∗ (0.00)

0.752∗ ∗ ∗ (0.00)

0.855∗ ∗ ∗ (0.00)

−0.00859 (0.74) 0.150∗ ∗ ∗ (0.00)

0.0212 (0.41) 0.150∗ ∗ ∗ (0.00) −2.126∗ ∗ ∗ (0.00)

−0.00871 (0.74) 0.150∗ ∗ ∗ (0.00)

0.0211 (0.42) 0.150∗ ∗ ∗ (0.00) −2.125∗ ∗ ∗ (0.00) −0.0 0 0889 (0.68)

0.0234 (0.24) 0.154∗ ∗ ∗ (0.00) −2.064∗ ∗ ∗ (0.00) −0.00133 (0.43)

−0.0 0 0876 (0.69)

10,0 0 0 0.0092

216,338.2∗ ∗ ∗ (0.00) 10,0 0 0 0.4230

10,0 0 0 0.0 0 0 0

Firm characteristics Size Leverage Liquidity

−0.0 0 0987 (0.65)

Network connection

Macroeconomic variable Market volatility Observations R-squared

10,0 0 0 0.0042

10,0 0 0 0.0092

10,0 0 0 0.0042

Notes: This table shows the estimates of a panel regression on the impact of network connection on marginal expected shortfall (MES). We multiplied the dependent variables by 10,0 0 0 to make the coefficients of the variables easier to recognize. We show the estimates of these regressions, with numbers in parentheses denoting p values. Estimates with ∗ ∗ ∗ , ∗ ∗ , ∗ denote statistical significance of the estimate at the 1%, 5%, and 10% level, respectively.

Tables 5 and 6 show the results when the dependent variable is changed to CoVaR or MES. In particular, firm size has a significantly positive effect on CoVaR and leverage has a positive effect on MES. CoVaR represents market pressure when a firm is experiencing bad days, while MES is a firm’s average return when the market is in a bad situation. It is reasonable that size rather than leverage is the dominant factor in CoVaR. By contrast, leverage rather than firm size is the dominant factor in MES. In addition, the results show that liquidity has a significantly negative effect on both measures. We can interpret these results in the same manner as before. Finally, the results show that network connections have no significant effect on either measure. Thus, we can say that CoVaR and MES are less capable of capturing network information.

25 Learning from the global financial crisis has led us to model simulations conservatively. In reality, financial institutions can endure a longer shock by selling assets at a discounted price, i.e., a fire sale. However, financial institutions in simulations are much more vulnerable to a shock. That is, they are directly exposed to drops in asset prices because the structure including assets and liabilities is fixed in the simulation model. In other words, in the simulations, there is no buffer to maintain liquidity in case of a shock.

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Table 7 Panel regression for the impact of network connection on Rank in empirical analysis. (1) Constant

0.0124 (0.00)

(2) ∗∗∗

0.0117 (0.00)

(3) ∗∗∗

0.0128 (0.00)

(4) ∗∗∗

0.0121∗ ∗ ∗ (0.00)

Firm characteristics −0.0 0 0 0506 (0.49) 0.0 0 0 0 0442 (0.83) 0.0 0 0351∗ ∗ ∗ (0.00)

Size Leverage Network connection

−0.0 0 0 0948 (0.22) 0.0 0 0 0225 (0.30) 0.0 0 0353∗ ∗ ∗ (0.00)

−0.0 0 0 0835 (0.26) 0.0 0 0 0104 (0.65) 0.0 0 0353∗ ∗ ∗ (0.00)

−0.0 0 0136∗ (0.09) 0.0 0 0 0334 (0.16) 0.0 0 0356∗ ∗ ∗ (0.00)

Macroeconomic variables −0.0 0 0 0104 (0.63) −0.00136∗ ∗ ∗ (0.00) −0.0 0 0 0435 (0.61) 0.0 0 0906∗ ∗ ∗ (0.00)

VIX TED spread Maturity spread Credit spread

−0.0 0 0 0157 (0.47) −0.00133∗ ∗ ∗ (0.00) −0.0 0 0 0323 (0.70) 0.0 0 0951∗ ∗ ∗ (0.00)

Firm classification dummy Non-depositories Insurances Broker-dealers Observations R-squared

5256 0.0036

5256 0.0106

−0.0 0 0508 (0.11) 0.0 0 0221 (0.41) −0.0 0 0216 (0.63) 5256 0.0059

−0.0 0 0501 (0.11) 0.0 0 0254 (0.34) −0.0 0 0315 (0.47) 5256 0.0131

Notes: This table shows the estimates of a panel regression on the impact of network connection on Rank. We show the estimates of these regressions, with numbers in parentheses denoting p values. Estimates with ∗ ∗ ∗ , ∗ ∗ , ∗ denote statistical significance of the estimate at the 1%, 5%, and 10% level, respectively.

Risk measures using stock data generally have procyclical properties. “Procyclical” means that the measure strongly correlates with market conditions. In other words, a particular measure tends to grow with a rise in the economy and declines when the economy shows a decreasing trend. We note that market volatility has a significant effect on CoVaR and MES but not on Rank. Therefore, Rank is the only measure that does not have procyclical properties. Thus, the contribution of financial institutions to systemic risks can be captured effectively, regardless of market conditions. 5.2. Analysis based on real market data We examine whether Rank captures network relationships using real market data. We quantify Rank, CoVaR, and MES for the sample US financial institutions. We calculate each measure across a one-year window. The baseline model of the panel regression is as follows:

Measur eit =

α + β F irm characteristicit + γ Macroeconomict + εit

where Measureit denotes calculated measures (Rank, CoVaR, and MES) and Firm characteristicit includes the size, leverage, liquidity, and network connections of financial institution i at time t. We use size as a logarithm for the book value of total assets, leverage as the ratio of liability to equity, liquidity as the ratio of the sum of cash and short-term investments to total assets, and network connections as the number of connections whose p-value on the Granger causality network is less than 0.05. Macroeconomict includes VIX, Ted spread, maturity spread, and credit spread. In addition, firm classification is a dummy variable based on the SIC classification (for details, see Table A1 in the Appendix). The estimation results in Table 7 show that the network connection has a significantly positive effect on Rank. This result supports the finding that Rank can capture network structure, as indicated by the previous empirical analysis based on the simulation. However, firm size does not have a significant effect on Rank, which is inconsistent with the findings of previous empirical analyses based on simulations. We assume that Rank cannot capture the difference by firm size because we focus on large-scale financial institutions. Focusing on macroeconomic variables, the results indicate that Rank is not a procyclical measure. VIX and maturity spread have no significant effect on Rank. Further, TED has a significantly negative effect, while credit spread has a significantly positive effect. Higher values denote that a financial market is in bad condition, as VIX represents uncertainty and TED Please cite this article as: T.-S. Yun, D. Jeong and S. Park, “Too central to fail” systemic risk measure using PageRank algorithm, Journal of Economic Behavior and Organization, https://doi.org/10.1016/j.jebo.2018.12.021

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Table 8 Panel regression for the impact of network connection on CoVaR in empirical analysis. (1) Constant

0.00325 (0.07)

(2) ∗

−0.0370 (0.00)

(3) ∗∗∗

0.00343 (0.07)

(4) ∗

−0.0367∗ ∗ ∗ (0.00)

Firm characteristics Size Leverage Network connection

0.00106∗ ∗ ∗ (0.00) −0.0 0 0 0382 (0.42) 0.0 0 0 0463 (0.78)

0.00257∗ ∗ ∗ (0.22) −0.0 0 0305∗ ∗ ∗ (0.00) 0.0 0 0 0147 (0.84)

0.00110∗ ∗ ∗ (0.00) −0.0 0 0 0421 (0.41) 0.0 0 0 0312 (0.85)

0.00255∗ ∗ ∗ (0.00) −0.0 0 0311∗ ∗ ∗ (0.00) 0.0 0 0 0129 (0.86)

Macroeconomic variables 0.0 0 0775∗ ∗ ∗ (0.00) 0.00920∗ ∗ ∗ (0.00) 0.0 0 0676∗ ∗ ∗ (0.00) 0.00230∗ ∗ ∗ (0.00)

VIX TED spread Maturity spread Credit spread

0.0 0 0775∗ ∗ ∗ (0.00) 0.00920∗ ∗ ∗ (0.00) 0.0 0 0676∗ ∗ ∗ (0.00) 0.00230∗ ∗ ∗ (0.00)

Firm classification dummy Non-depositories Insurances Broker-dealers Observations R-squared

5256 0.0115

5256 0.7406

0.00103 (0.20) −0.00162∗ ∗ (0.02) −0.00128 (0.25) 5256 0.0209

0.00161∗ ∗ (0.01) −0.00146∗ ∗ (0.01) 0.0 0 0243 (0.79) 5256 0.7558

Notes: This table shows the estimates of a panel regression on the impact of network connection on conditional vale at risk (CoVaR). We show the estimates of these regressions, with numbers in parentheses denoting p values. Estimates with ∗ ∗ ∗ , ∗ ∗ , ∗ denote statistical significance of the estimate at the 1%, 5%, and 10% level, respectively.

denotes market fear in interbank money markets. Maturity and credit spread indicate higher costs for maturity and credit risk. Finally, firm classification has no significant effect on Rank. Thus, we can say that the type of financial institution does not affect Rank. Table 8 presents the estimation results when the dependent variable is CoVaR. We find that firm size has a significantly positive effect on CoVaR. This result is consistent with our previous results in the simulation-based empirical analysis. However, leverage has a significantly negative effect on CoVaR, which differs from the findings obtained from the empirical analysis based on the simulations. Existing research argues that more-leveraged financial institutions tend to make greater contributions to systemic risk. CoVaR does not effectively capture leverage information in our analysis. In addition, the results show that network connection has no significant effect on the measure; thus, we can suggest that CoVaR cannot capture network structure. Further, all macroeconomic variables have a significantly positive effect on CoVaR. In other words, CoVaR is a procyclical measure. Finally, in terms of financial institution type, non-depository institutions tend to have larger CoVaR than depository institutions. Insurance firms have a smaller CoVaR than depositories. Broker-dealers show no significant difference from depositories. Table 9 illustrates the case of a dependent variable MES. The results show that firm size and leverage have a significantly positive effect on MES. However, network connections have a weak negative effect on MES. Intuitively, a highly connected firm makes a larger contribution to systemic risk. To this effect, MES cannot capture network structure well. In addition, all macroeconomic variables have a significantly positive effect on MES. Thus, like CoVaR, MES is a procyclical measure. Finally, the type of financial institution shows no difference for the measure, except for non-depositories, which tend to have a larger MES value than other firm types. In sum, our empirical examination reveals that Rank is the only measure that can consider a firm’s network structure from stock data. We also show that Rank is not a procyclical measure, and thus, it could have a consistent value, regardless of market condition. However, Rank seems unable to capture traditional properties such as size and leverage. We believe that Rank can contribute to maintaining financial stability not only for supervisory authorities, but also for financial institutions. Financial institutions can be motivated to manage their centrality using Rank because additional capital requirements involve costs. CoVaR and MES do not explain how financial institutions can adjust their centrality in the financial system; however, this is possible using Rank, by diversifying or simplifying exposures with counterparties. Please cite this article as: T.-S. Yun, D. Jeong and S. Park, “Too central to fail” systemic risk measure using PageRank algorithm, Journal of Economic Behavior and Organization, https://doi.org/10.1016/j.jebo.2018.12.021

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Table 9 Panel regression for the impact of network connection on MES in empirical analysis. (1) Constant

0.0113 (0.02)

(2) ∗∗

−0.0653 (0.00)

∗∗∗

(3)

(4)

0.00622 (0.22)

−0.0675∗ ∗ ∗ (0.00)

0.00194∗ ∗ ∗ (0.00) 0.0 0 0624∗ ∗ ∗ (0.00) −0.0 0 0356 (0.36)

0.00376∗ ∗ ∗ (0.00) 0.0 0 0112 (0.14) −0.0 0 0360∗ (0.07)

Firm characteristics Size Leverage Network connection

0.00162∗ ∗ ∗ (0.00) 0.0 0 0641∗ ∗ ∗ (0.00) −0.0 0 0311 (0.43)

0.00369∗ ∗ ∗ (0.00) 0.0 0 0129∗ (0.08) −0.0 0 0351∗ (0.07)

Macroeconomic variables 0.00135∗ ∗ ∗ (0.00) 0.0273∗ ∗ ∗ (0.00) 0.00235∗ ∗ ∗ (0.00) 0.00673∗ ∗ ∗ (0.00)

VIX TED spread Maturity spread Credit spread

0.00136∗ ∗ ∗ (0.00) 0.0272∗ ∗ ∗ (0.00) 0.00233∗ ∗ ∗ (0.00) 0.00668∗ ∗ ∗ (0.00)

Firm classification dummy Non-depositories Insurances Broker-dealers Observations R-squared

5,256 0.0292

5,256 0.6868

0.00991∗ ∗ ∗ (0.00) −0.00157 (0.41) 0.00129 (0.67) 5,256 0.0537

0.00912∗ ∗ ∗ (0.00) −0.00229 (0.15) 0.00483∗ (0.05) 5,256 0.7180

Notes: This table shows the estimates of a panel regression on the impact of network connection on marginal expected shortfall (MES). We show the estimates of these regressions, with numbers in parentheses denoting p values. Estimates with ∗ ∗ ∗ , ∗ ∗ , ∗ denote statistical significance of the estimate at the 1%, 5%, and 10% level, respectively.

6. Conclusions Following “too big to fail” or “too connected to fail,” which gained much attention during the global financial crisis, the concept of being “too central to fail” has become increasingly popular. The methodology of the Basel Committee on Banking Supervision (2011, 2013, 2017, 2018) includes the interconnectedness and substitutability/financial institution infrastructure category to identify SIFIs. However, existing measures do not fully consider the centrality of financial institutions. This paper proposes a measure, Rank, capturing the centrality of financial institutions using the PageRank algorithm. First, we construct a simulation model that considers the centrality of financial institutions. We assume the number of financial institutions and that they hold as many assets as they have in their portfolio. This simplifies the simulation model and prevents problems related to model selection. The new method also employs market data to measure a financial institution’s contribution to systemic risk. Analyses based on a balance sheet are unable to consider the complex network of financial institutions. This is because the release of balance sheets is subject to time lags, and thus, they do not reflect current situations. In addition, a balance sheet includes information only on structured formats and does not show implicit connections among financial institutions such as common exposure. Second, we prove that the measure reflects the network structure by conducting a simulation and an analysis using real market data. We compare Rank with two other well-known measures, CoVaR and MES. The results show that Rank captures network structure more accurately than the other two measures. Rank also shows non-procyclical characteristics. Our findings offer policy implications in that regulators should consider an additional measure to reflect financial networks. We suggest that accounting for the centrality of financial institutions can more effectively achieve financial stability. If financial institutions are identified as SIFIs, they should hold capital buffers. This is in line with recent studies, including Admati et al. (2013) and the Federal Reserve Bank of Minneapolis (2016), which argue for further capitalization of banks. The authors also support the argument that bank capitalization, such as the Basel Ⅲ agreement, can be beneficial rather than expensive. In the real world, it is difficult to access proper network information to apply to network structures owing to the opaqueness of financial institutions. Currently, market data can be an alternative to accessing network structures. Policy-makers can utilize the measure Rank and predict possible results when designing financial regulations. In addition, financial institutions can make full use of Rank by checking and adjusting their centrality frequently. They can save costs of Please cite this article as: T.-S. Yun, D. Jeong and S. Park, “Too central to fail” systemic risk measure using PageRank algorithm, Journal of Economic Behavior and Organization, https://doi.org/10.1016/j.jebo.2018.12.021

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additional capital requirements and manage their risk exposures with other financial institutions. Subsequently, use of the “too central to fail” measure Rank by regulators and financial institutions can contribute to maintaining stability in financial markets. This study also offers opportunities for potential future research. For example, studies could improve the centrality measure by including various firm characteristics. Our empirical results suggest that Rank reflects only network structure and does not reflect other firm characteristics such as size or leverage. This problem can be solved using an adapted version of the PageRank algorithm, as suggested by Dungey et al. (2012). Previous analyses have added a firm’s characteristic weight, such as size, leverage, and liquidity, instead of a damping factor. In addition, studies could examine various relationships between Rank and other factors. Investigating the impacts of Rank on important factors can help understand and manage stable financial markets. Acknowledgements The authors thank the editor and the anonymous reviewers for their constructive comments. They are also grateful for the comments received at the “Finance and Economic Growth in the Aftermath of the Crisis” conference in Milan, Italy (September 11–13, 2017). Appendix A. Parameter calibration in the simulation We estimate the parameters to generate asset movements that follow the GBM. The simple GBM used in the simulations is as follows:

St = S0 eXt Xt =

σ B(t ) + μt

where St denotes asset price at time t, S0 is the asset price at time 0, and B(t) is the standard Brownian process. In particular, we use risk-neutral GBM and the drift (μ) and volatility (σ ) terms are as follows:

μ∗ = r − σ 2 / 2 σ∗ = σ Table A1 List of sample financial institutions. Financial institution Depositories SIC = 60

Bank of America Corp Bank of New York Mellon Corp BB&T Corp Comerica Inc Commerce Bancorp Inc/NJ Credicorp Ltd Fifth Third Bancorp Hudson City Bancorp Inc Huntington Bancshares JPMorgan Chase & Co Keycorp M & T Bank Corp Marshall & Ilsley Corp Mastercard Inc National City Corp New York Cmnty Bancorp Inc Northern Trust Corp People’s United Finl Inc PNC Financial Svcs Group Inc Regions Financial Corp State Street Corp Suntrust Banks Inc Synovus Financial Corp U S Bancorp Wachovia Corp Washington Mutual Inc Wells Fargo & Co Zions Bancorporation

Ticker BAC BK BBT CMA CBH CCL FITB HCBK HBAN JPM KEY MTB MI MA NCC NYCB NTRS PBCT PNC RF STT STI SNV USB WB WAMUQ WFC ZION (continued on next page)

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Table A1 (continued)

Non-depository institutions SIC = 61, 62, 65 excluding 6211

Insurance SIC = 63, 64

Broker dealers SIC = 6211

Financial institution

Ticker

American Express Co Blackrock Inc Blackstone Group LP Capital One Financial Corp CBRE Group Inc Cit Group Inc Citigroup Inc CME Group Inc Countrywide Financial Corp Federal Home Loan Mortg Corp Franklin Resources Inc Intercontinental Exchange Invesco Ltd Janus Capital Group Inc Legg Mason Inc nymex Holdings Inc Nyse Euronext Price (T. Rowe) Group PRINCIPAL Financial Grp Inc Schwab (Charles) Corp SEI Investments co Wyndham Worldwide Corp Aetna Inc Aflac Inc Allstate Corp American International Group Anthem Inc Arch Capital Group Ltd Assurant Inc Axis Capital Holdings Ltd Berkley (W R) Corp Chubb Corp Cigna Corp Cincinnati Financial Corp Cna Financial Corp Coventry Health Care Inc Everest Re group Ltd Fidelity Natl Finl Fnf Group Genworth Financial Inc Hartford Financial Services Health Net Inc Humana Inc Lincoln National Corp Loews Corp Marsh & Mclennan Cos Mbia Inc Metlife Inc Progressive Corp-ohio Prudential Financial Inc Safeco Corp Torchmark Corp Travelers Cos Inc Unitedhealth Group Inc Unum Group White Mtns Ins Group Ltd Xl Group Ltd

AXP BLK BX COF CBG CITG CITI CME CFC FMCC FRI ICE IVZ JNS LM NMX NYX TROW PFG SCHW SEIC WYN AET AFL ALL AIG ANTM ACGL AIZ AXS WRB CBH CI CINF CAN CVH

Ameriprise Financial Inc Bear Stearns Companies Inc E Trade Financial Corp Goldman Sachs Group Inc Lehman Brothers Holdings Inc Merrill Lynch & Co Inc Morgan Stanley TD Ameritrade Holding Corp

RE FNF GNW HIG HNT HUM LNC LC MMC MBI MET PGR PRU SAF TMK TRV UNH UNM WTM XL AMP BSC ETFC GS LEHMQ MER MS AMTD

Notes: Following Adrian and Brunnermeier (2016), we select our sample financial institutions from among companies with a standard industrial classification (SIC) code from 60 to 65, whose headquarters are located in the United States. To exclude non-financial holding companies, we do not include financial institutions whose SIC is 67. We also exclude small financial institutions whose market capitalization was less than US$5 billion as of June 2007, before the global financial crisis.

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Table A2 Parameters in the simulation model. Parameter

Definition

Benchmark

Range of variation

A C N E L

Total number of primitive assets in the financial system Proportion of equity in financial institutions Number of financial institutions in the simulation Proportion of equity-type assets in financial institutions Proportion of liability-type assets in financial institutions

10 0 0 20% 100 90% 10%

Fixed 11–25% 5–150 81–99% 1–19%

Notes: This table shows the parameters in the simulation model. We vary one parameter at a time and analyze the effects on the centrality of financial networks using Rank. The sum of equity-type and liability-type assets should be one (E + L = 1).

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