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Bank Capital Shock Propagation via Syndicated Interconnectedness

Abstract

Loan syndication increases bank interconnectedness through co-lending relationships. We study the financial stability implications of such dependency on syndicate partners in the presence of shocks to banks’ capital. Model simulations in a network setting show that such shocks can produce rare events in this market when banks have shared loan exposures while also relying on a common risk management tool such as value-at-risk (VaR). This is because a withdrawal of a bank from a syndicate can cause ripple effects through the market, as the loan arranger scrambles to commit more of its own funds by also pulling back from other syndicates or has to dissolve the syndicate it had arranged. However, simulations also show that the core-periphery structure observed in the empirical network may reduce the probability of such contagion. In addition, simulations with tighter VaR constraints show banks taking on less risk ex-ante.

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Notes

  1. For instance, as the market collapsed during the first year of the global financial crisis from approximately $800–$300 billion in quarterly issuance volume (Gadanecz 2011), international trade experienced the most sudden, severe, and globally synchronized collapse on record (Antonakakis 2012). On the sensitivity of the syndicated loan market to banks’ balance sheets and its rapid speed of adjustment, see Chui et al. (2010), Ivashina and Scharfstein (2010a) and De Haas and Van Horen (2012a).

  2. Credit risk is the largest risk type for risk-weighted-asset (RWA) calculation on the banking book, with corporate (including syndicated) loans dominating this category; RWAs are in turn used to calculate capital requirement for banks, see BCBS (2013b).

  3. Using data from from Q2 1991 to Q2 2012, Adrian and Boyarchenko (2012) estimate a correlation coefficient of 0.7 between the Chicago Board of Exchange Option Implied Volatility Index (VIX) and tightening of lending standards by US banks.

  4. See, for example, BCBS (2012, 2013a).

  5. We rely on the Dealogic Loan Analytics database to draw out stylized facts about syndicated loan market dynamics and for parameter calibration.

  6. Specifically, from 2007 through 2009, about 80 % of the contraction came from the reduction in the number of loans, and only 20 % from the average loan size. The total number of unique tranches declined from 15,070 to 11,556, while average tranche size declined only by 13 %, from $305 to $266 million.

  7. These numbers are comparable with those of Allen and Gottesman (2006) who show that the loan share held by lead arrangers has on average been 27 %, compared with the average loan share of 3 % held by syndicate participants.

  8. This approach contrasts, for example, with He and Krishnamurthy (2013), who use log utility with risk-averse agents and derive a feature whereby leverage is countercyclical.

  9. More generally, a robust empirical relationship between bank capital and lending, as well as the ability of equity capital to serve as a buffer against negative shocks, are found by Gambacorta and Mistrulli (2004), Berrospide and Edge (2010), Cornett et al. (2011), Gambacorta and Marques-Ibanez (2011) and Carlson et al. (2013).

  10. In terms of geographic proximity, De Haas and Van Horen (2012a) use more traditional empirical tools to find that banks continued to lend more to geographically close countries, where they are integrated into a network of domestic co-lenders, and where they have more lending experience. Such bank-borrower closeness may matter especially in times when a firm’s net worth drops (Ruckes 2004) or for carving out local captive markets (Agarwal 2010).

  11. At the more aggregate, banking system or country level, the network analysis of cross-border banking can also be done using the BIS banking statistics: Hattori and Suda (2007) and Minoiu and Reyes (2013) examine international banking networks using BIS consolidated and locational banking statistics respectively.

  12. Not too surprisingly, simulation results show that a common, rather than idiosyncratic, component to bank capital shocks is the most evident driver of rare events in this market (these are defined as an aggregate rate of decline in loan syndication in excess of 30 %). While, in the absence of a common component to bank equity shocks, the market is quite stable, when a common component is introduced the distributions of withdrawals from lending and of dissolved syndicates shows a long tail.

  13. This differs from the results of Caballero and Simsek (2013), who study the propagation of liquidity shocks through interbank markets with the uncertainty about the network itself (e.g., Knightian uncertainty) serving as a key driver.

  14. Specifically, we look at the distribution of the Euclidean distance between each pair of banks based on their portfolio overlaps using the methodology of Cai et al. (2011).

  15. We look at new syndicated loans during year 2005 reported by Dealogic.

  16. The syndicated loan market follows an “originate-to-distribute model,” whereby the originating bank, dubbed lead arranger or lead manager, retains about a third of each syndicated loan on average (Allen and Gottesman 2006; Ivashina and Scharfstein 2010b). The remaining share is sold to a syndicate of investors including banks, pension funds, mutual funds, hedge funds, and sponsors of structured products. The lead arrangers screen and monitor the borrower and typically have an informational advantage based on their long-term relationship with the borrower (Allen et al. 2012). The lead arrangers choose the participant lenders and administer the loan/syndicate, whereas participant lenders essentially just fund the loan. Large loans are typically structured in multiple facilities. All facilities are covered by the same loan agreement; however, they may have different maturity or drawdown terms. One of the most obvious benefits of loan syndication has to do with a reduction in agency problems and informational asymmetries (Dennis and Mullineaux 2000; Ivashina 2009). See Wilson (1968) for a general theory of syndication and Pennacchi (1988) for a more general model of bank loan sales.

  17. Note that in the autarky case we assumed that banks could invest in only one project as lead arrangers. Thus, they were not able to spread investments across different loans and achieve benefits of diversification this way. In a simple world of only one project per lead bank, syndication offers advantages by allowing banks to buy shares in other lead banks’ loans. We note that similar gains may be obtained by allowing banks to diversify by investing in different projects as lead arrangers. However, as we are interested in exploring the implications of different network topologies when allowing banks to interact through syndication, we maintain the assumption of only one project per bank as lead arranger and abstract from the possibility of diversifying loan portfolios as lead arrangers.

  18. This maximization problem has a solution when \(\sigma ^2\) and \(\sigma _c^2\) are sufficiently large relative to \(R\). Note that \(l_{\!j}\) is chosen from the set of positive integers.

  19. Thus, banks are not allowed to optimize their withdrawals in a similar manner to how they optimize their initial investments.

  20. Since the weight \(\theta \) on the common component of equity shock is a free parameter, the standard deviation of \(\epsilon _c\) is effectively a normalization parameter in the simulations. The situation where the standard deviations differ between the common and idiosyncratic components can be expressed by adjusting the value of \(\theta \).

  21. Note that \(\theta =0\) corresponds to the benchmark case of no common equity shock.

  22. The Dealogic database has 706,385 observations from 2005 through 2007. We limit the bank sample to the largest 131 banks. Combined, they account for 63.98 % of all observations during this sample period. However, we are able to match only 82 banks with Bankscope’s balance sheet data.

  23. As we do not observe the life of the loan in Dealogic, only information at the origination, we do not have accurate information on the number of defaulted loans. Therefore, we use an institution-level default likelihood measure from Bloomberg, which averages 2.3 % for our sample of banks during the crisis period (year 2008).

  24. This type of network is sometimes called the configuration model in the network literature.

  25. This is similar to the “coherent noise” mechanism proposed by Sneppen and Newman (1997), where the maximization behavior of banks replaces the function of the extinction dynamics in the coherent noise mechanism.

  26. While Cai et al. (2011) compute the distance measure using syndicated portfolio commonalities based on cross-syndication in same industries (2-digit SIC code) or countries, we apply the same measure to cross-syndication at the loan level, \(j\). This is possible because the degree of cross-syndication in this market is relatively high.

  27. Following Ivashina and Scharfstein (2010a), if a bank’s role is that of an administrative agent, arranger, bookrunner, documenting agent, facility agent, mandated arranger, or syndication agent, the bank is designated as a lead arranger. In most cases, one lead arranger assumes most of these roles, while the database identifies other banks only as participants.

  28. See Fig. 12 in Appendix, which shows histograms of \(deg_{m}\) for selected years.

  29. Namely, there are 8 banks that lead projects with 1 participant, 8 banks with 2 participants, and so forth. This approach ensures an average number of participants of 6.

  30. In a different context, such core-periphery topology has been found to be a robust feature of interbank networks across different jurisdictions. See, for example, Soramäki et al. (2007) for the Fed Funds market, Craig and von Peter (2014) for the German banking system, and Fricke and Lux (2014) for Italian payment system.

    Fig. 7
    figure 7

    Directed network of banks in the syndicated loan market. A directed link is drawn from a participating bank to a lead bank

  31. This literature generally finds that for the systemic contagion to occur additional factors must be present on top of an idiosyncratic bank shock. For example, Upper and Worms (2004) conclude that a failure of one bank can affect sizeable impact only in association with large loss rates on interbank loans.

  32. While the actual VaR constraint might be more strict, it is not desirable to push the threshold too close to the value of one because numerical implementation can become unstable. Still, this simplified framework is consistent with banks operating at the point at which they feel the restriction binding given the cushion they deem appropriate in terms of their risk management.

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Acknowledgments

We are grateful for the generous support of the BIS Research Fellowship Program. We also thank Tobias Adrian, Douglas Araujo, Dietrich Domanski, Ingo Fender, Blaise Gadanecz, Neeltje van Horen, Francisco Nadal de Simone, Iman van Lelyveld, Goetz von Peter, and the participants of the BIS Monetary and Economic Department Seminar (Basel, Switzerland, April 2013), the Conference on Network Approaches to Interbank Markets (Castellón, Spain, May 2013), and the Banque de France–ACPR–SoFiE conference on Systemic Risk and Financial Regulation (Paris, France, July 2014) for their comments and suggestions. We thank Sergei Grouchko and Michela Scatigna for excellent research support. Any views presented here are those of the authors and do not necessarily reflect those of the BIS or IADB.

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Correspondence to Vladyslav Sushko.

Appendices

Appendix : Simulation Computation Strategy

Our main objective is to obtain the distributions of the number of withdrawals \(\sum _j k_j\) and the number of dissolutions. We obtain the distributions by Monte-Carlo simulations of the equilibrium. The following is the computation algorithm for the case of the homogeneous-degree network, where the degree is given by \(\bar{l}\).

  1. (1)

    Initialize \(f\) and the first-stage policy functions \(a_j, l_j\)

    1. (a)

      Solve for \(f\) so that \(l_j = \bar{l}\)

      1. (i)

        Pick initial \(f\) and set \(p(0)=1\) (there is no withdrawals)

      2. (ii)

        Solve the bank’s first-stage maximization problem

      3. (iii)

        Adjust \(f\) by bisection method until \(l_j = \bar{l}\) is obtained

  2. (2)

    Set \(p\) as a binomial distribution with the probability for a bank to withdraw due to the equity shock and population \(l_j\) (this forms a “naive” expectation in which banks do not take into account the fact that withdrawal behaviors may be correlated)

    1. (a)

      Solve the second-stage maximization and obtain the expected wealth conditional on \(a_j, l_j, h_j\)

    2. (b)

      Solve the first-stage maximization

    3. (c)

      Update \(p\) until \(p\) converges

    4. (d)

      Check if \(l_j\) is still an optimal choice. If not, adjust \(f\) and repeat above

  3. (3)

    Simulations with network

    1. (a)

      Draw a random network with homogeneous degree \(l_j\). Draw equity shocks \(\epsilon _j\).

    2. (b)

      With the policy functions and the network, compute the realized withdrawals and dissolutions.

    3. (c)

      Repeat for many times (10,000) and obtain the simulated distribution of \(h\)

  4. (4)

    Compute a rational expectations equilibrium

    1. (a)

      Replace \(p\) with the simulated distribution of \(h\)

    2. (b)

      Proceed to Steps 2 and 3 above

    3. (c)

      Check if \(l_j\) is still optimal. If not, adjust \(f\) and repeat above

Histogram of Degrees Based on the Euclidean Distance in Loan Portfolios

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Nirei, M., Sushko, V. & Caballero, J. Bank Capital Shock Propagation via Syndicated Interconnectedness. Comput Econ 47, 67–96 (2016). https://doi.org/10.1007/s10614-015-9493-8

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Keywords

  • Syndicated lending
  • Systemic risk
  • Network externalities
  • Value at risk
  • Bank capital shocks
  • Rare event risk