Journal of Network Theory in Finance

Structural systemic risk: evolution and main drivers

Nuno Azevedo and Vitor Oliveira

  • Overall the results show that the structural systemic risk of the Portuguese banking system has reduced from 2007 and 2017 with some peaks in 2010 and 2011.
  • This paper support the role played by capital in mitigating structural systemic risk.
  • The methodology behind the analysis could be used to analyse other type of shocks and adverse scenarios as well as to build up stress tests with a macroprudencial dimension.
  • The model could also be used to calibrate structural systemic buffers such as O-SII buffer and/or SRyB.

This paper analyzes how systemic risk structurally evolved between 2007 and 2017. The main contributions of the paper to the literature include the methodology, analysis and potential use for macroprudential policies. The methodology, known as network analysis, comprises direct (credit and liquidity risk) and indirect (concentration risk) contagion channels as well as other specificities that improve the methodologies exploited so far in the literature. Using a consolidated sample, which varies between 14 and 17 banks over the period 2007–17, we show that the structural systemic risk of the Portuguese banking system reduced between 2007 and 2017. Further, in line with most of the literature, this paper highlights that direct contagion is not significant compared with contagion that stems from banks’ common exposures to asset classes. Finally, this paper supports the role played by capital in mitigating structural systemic risk, and the model behind the analysis can be used to perform stress tests with a macroprudential dimension as well as to calibrate structural capital buffers such as the other systemically important institutions and systemic risk buffers.

1 Introduction

Until the 2007–9 financial crisis, supervision focused on the soundness and strength of individual financial institutions, and neglected, to a certain extent, the interconnectedness between them stemming from direct and indirect exposures. In the aftermath of the crisis, it became clear that the stability of the financial system must be addressed by taking the system as a whole and not just focussing on each unit of the system. Therefore, it is of the utmost importance to augment the analysis of the probability of default of each institution with the probability of contagion in the financial system, ie, the impact of the default of one institution on other financial institutions and, ultimately, on the remaining sectors of the economy.

There is a wide range of definitions of systemic risk. For the purpose of this paper, systemic risk describes a situation when many (if not all) financial institutions fail as a result of a common shock or a contagion process. In this vein, contagion refers to the risk that the failure of a financial institution leads to the default of other financial institutions through a domino effect in the interbank market or payments system or through asset prices (Allen et al 2012).

One of the best known and most used methodologies to better understand and measure systemic risk as a domino effect is network analysis. This reduces the financial system to a set of nodes and relationships (Levy-Carciente et al 2015). Thus, it allows for a broad range of analyses, from the identification of the type and properties of the network to the capability of the financial system to withstand certain types of shocks, given the structure of its network, in order to identify inherent risks and devise policy proposals to mitigate them.

Within the network, we can identify two main channels of possible contagion:

  1. (1)

    direct interbank linkages between financial institutions (known in the literature as direct contagion), which has been covered by a large strand of the literature (Furfine 2003; Upper and Worms 2004; Elsinger et al 2006a; Solé and Espinosa-Vega 2010; Mistrulli 2011); and

  2. (2)

    contagion via changes in bank asset values, known in the literature as indirect contagion (Levy-Carciente et al 2015).

Following the seminal studies of Elsinger et al (2006a, 2006b), several studies emerged aimed at assessing the contagion and the propagation of potential losses within a network through both direct and indirect channels (Arinaminpathy et al 2012; Gauthier et al 2012; Fink et al 2016; Bargigli et al 2015; Bookstaber and Kenett 2016; Montagna and Kok 2016; Halaj 2017).

This paper assesses the systemic risk in the Portuguese banking system using network analysis to answer the following question: how has structural systemic risk evolved over time in the Portuguese banking system? Note that the assessment of systemic risk carried out in this paper is based on the concept mentioned above. Thus, our proposal is to gauge systemic risk from the perspective of the domino or cascade effect within the banking sector, and it does not take into account the impacts on the wider economy, eg, in the private nonfinancial sector, which is covered by other definitions of systemic risk. In addition, while we acknowledge the two (cyclical and structural) components of the systemic risk, we will focus our analysis on the structural dimension.

The main contributions of this paper are threefold. First, this paper introduces some specificities that improve the network models exploited so far in the literature. This more encompassing methodology could be extrapolated to perform similar analysis of other banking systems, after the adjustment of some parameters outlined further in this paper. Second, the paper applies our methodology to a specific banking system, using rich microdata that comprises both bilateral exposures between banks and elements of their balance sheets throughout a reasonable period of time (2007–17) in order to gauge how systemic risk has evolved, which gives a significant improvement over the use of a much shorter period, as is commonly found in the literature. Finally, the paper sheds some light on the application of the methodology presented to macroprudential policies.

Our model contains, to the best of our knowledge, the most encompassing methodology to so far have been constructed. It integrates credit risk and liquidity (funding) risk as well as direct and indirect contagion channels, going further than other studies such as Levy-Carciente et al (2015), which considers only credit risk and indirect contagion channels; Halaj (2017), which, albeit focusing only on credit risk, analyses the impacts of direct and indirect contagion channels; and Gorpe et al (2019) and Sun and Chan-Lau (2017), which study only the direct channel of contagion, but consider credit and liquidity (funding) risk and the impact of fire sales prompted by funding needs not covered by the liquidity provided by the central bank (Gorpe et al 2019) or other banks (Sun and Chan-Lau 2017). Note that, in the latter two studies, the haircuts applied to the assets sold are exogenously ascribed, whereas in our paper they are a function of the volume of securities placed in the market.

In addition, the methodology used in this paper introduces the role played by the central bank, which complements the role of other banks in the system in mitigating liquidity (funding) risk. Our methodology goes beyond the work by Gorpe et al (2019) and Sun and Chan-Lau (2017), which handled the banking roles separately: Gorpe et al (2019) only considers the role played by the central banks, while Sun and Chan-Lau (2017) neglect this and take into account only the role played by the other banks in the system.

Concerning the main contributions to the analysis, this paper builds as far as possible on a network structure based on historical data and potential shocks based on the financial statements of banks, rather than on an endogenous network based on algorithms, as used by Halaj (2017) and Montagna and Kok (2016). This mitigates the caveats already identified in the literature, mainly those identified by Mistrulli (2011) related to overestimation of the vulnerability to contagion and thus systemic risk.

Using a consolidated sample of between 14 and 17 banks (representing, on average, 90% of the total assets of the Portuguese banking system, which includes resident banks and subsidiaries of foreign banks) over the period 2007–17, we conclude that systemic risk of the Portuguese banking system reduced between 2007 and 2017. In addition, as shown in most of the literature, contagion through direct links is not significant, unlike indirect contagion (common exposures).

Finally, the results presented in the paper support the important role of capital in mitigating structural systemic risk, and suggest useful avenues for our methodology in carrying out macroprudential stress tests and calibrating structural buffers.

2 Related literature

There are several definitions of systemic risk, which all have as a common denominator the relevance of their materialization, that is, in order for the risk to be considered systemic it is necessary that the impacts of its materialization affect not just one but several institutions of the financial system, as well as the functioning of this system relating to the provision of financial intermediation services to the economy, significantly impairing economic growth and social welfare. In this sense, European Central Bank (2009) defined systemic risk as “the risk that financial instability will become so widespread that it impairs the functioning of the financial system to the point where economic growth and social welfare suffer materially.” In the same vein, Federal Reserve Chairman Ben Bernake defined systemic risk as (Boles 2009) “developments that threaten the stability of the financial system as a whole and consequently the broader economy, not just that of one or two institutions.”

Systemic risk comprises two dimensions: a cyclical dimension and a structural dimension (European Systemic Risk Board 2013). The cyclical dimension corresponds to the accumulation of systemic risks during the expansive phase of the economic cycle, often accompanied by the expansion of credit and excessive growth of asset prices. The structural dimension refers to the distribution of risk across the financial system and potential contagion, which in turn depends on the structure of direct and indirect interlinkages in the system. The analysis carried out in this paper addresses only the structural component of systemic risk, particularly as regards contagion. According to Allen et al (2012), contagion is understood as the risk that the default of one financial institution leads to the default of others through a domino effect, through interbank exposures, the payments system or asset prices.

The more significant the direct or indirect interlinkages between institutions, the greater the effect of contagion. Direct interlinkages result from exposures between institutions, with the simplest case being the short-term claims of one financial institution on another financial institution. Indirect interlinkages result from the correlation of exposures to financial and nonfinancial markets, as well as exposures to the same types of asset, counterpart and country.

Network analysis is the most popular methodology for the evaluation of systemic risk, particularly contagion, from a structural perspective. First, it allows the evaluation of systemic risk through the contagion effect via its two channels (direct and indirect). Second, it does not require market data, which can be scarce for some markets or countries and thus can be significantly influenced by characteristics of the market, such as liquidity and efficiency.11 1 These methodologies include the contingent claim approach, which takes into account the work developed by Merton (1974); extreme value theory, which is used to calculate the probability of steep falls in the equity prices of a particular bank conditional on falls in the quotations of other banks or even the market; and the contribution of an institution to the value-at-risk (VaR) of the entire financial system, which can also be measured by conditional VaR (CoVaR), proposed by Adrian and Shin (2008).

This methodology is also useful to test the several transmission channels of contagion, such as counterparty risk, liquidity risk (which results from the fact that a given institution is unable to roll over its short-term financing from another institution) and the risk of indirect contagion resulting from exposures common to the same types of asset, which might result in the recognition of losses mainly through fire sales and their respective haircuts.

The analysis of networks applied to the financial system has its origin prior to the financial crisis of 2007–9 with the studies carried out by Boss et al (2004, 2006) and Elsinger et al (2006b, 2006a). These studies are based on a contagion process on the capital market triggered by an exogenous shock, negatively impacting the equity of each credit institution. In a subsequent step the shock propagates to other financial institutions through the interbank exposures to the financial institutions that defaulted in the first shock.

This type of analysis has gained increasing relevance since the global financial crisis, particularly after the failure of Lehman Brothers, which, in exposing the failures of relevant and complex institutions having direct and indirect interlinkages with the rest of the financial system, likely contributed to the systemic financial crisis, negatively affecting the economies of several countries. One of the difficulties in studying the domino effect underlying the contagion empirically is the small number of historical observations related to it. This is due to the fact that the authorities normally do not wait passively for the collapse of the financial system, but intervene in some way, which in turn undermines the assessment of the potential contagion of an institution to the financial system. Against this background, the studies involving networks commonly rely on simulation exercises (Summer 2013).

In general, the methodology of networks commonly starts with an exogenous shock to the financial system. Some more fragile institutions will not be able to meet their commitments, which usually stems from the fact that the value of their capital, after recognizing the losses resulting from the shock, falls below a certain limit. Thus, the default of some institutions may generate losses in other institutions with whom they have direct links and may also lead to their default. In addition to the credit risk related to counterparty default, there is also a risk of nonrollover of short-term financing by some institutions when the lending institution also defaults. Then the institution affected by the liquidity shock will have to sell part of its assets to balance its balance sheet.22 2 In any balance sheet the balance between assets and their funding has to be maintained, ie, the total assets must be equal to total debt and equity. In the event of nonrenewal of a portion of the debt, the institution will either have to sell assets or increase capital to maintain their balance. As this type of contagion exercise takes into account an adverse scenario, where capital increase is very difficult, this option commonly relies on forcing the sale of assets. Since the sale of assets may be cross-referenced to several institutions, it might result in a devaluation of assets, which will negatively impact institutions exposed to the same types of asset.

The contagion exercise ends when the default of an institution does not cause any further default in the system. The limit imposed on capital for an institution to default, the rate of recovery of direct exposures (and therefore the amount of losses), the rate of renewal of the funding and the haircut rate on the asset price are parameters that may be exogenous or modeled on the characteristics of the agents, macroeconomic and market environment and the regulatory framework.

Another difficulty that arises is the absence of data from bilateral exposures; this data is often present only in reports sent to the supervisor, which are confidential. This fact led to the use of an estimation technique known as the maximum entropy method (Elsinger et al 2006b, 2006a). Note that, according to Mistrulli (2011), the use of this estimation technique leads to the overestimation of losses resulting from the contagion process and thus the overestimation of systemic risk.

Following the seminal studies developed prior to the global financial crisis, the literature on systemic risk assessment using networks analysis has been growing, including an increasing number of transmission channels in a single contagion exercise as well as the modeling of some parameters.

The studies carried out by Solé and Espinosa-Vega (2010), Mistrulli (2011) and Sun and Chan-Lau (2017) consider only the contagion stemming from the direct exposures of one institution to another, which results in two types of risk: credit risk, ie, contagion resulting from noncompliance by the institutions in their bilateral exposures to other institutions, and liquidity or funding risk, which arises from the difficulty in replacing short-term sources of funding at the time of a default of a financial institution acting as a lender to another financial institution or institutions. Solé and Espinosa-Vega (2010) use cross-border bank data gathered through the Bank for International Settlements database. They simulate a contagion exercise with two shocks, one related to credit risk and another related to liquidity. In relation to credit risk, they simulate the default of a banking system in a given country and tackle the effect of contagion on the other banking systems. With regard to liquidity risk, they present the possibility of default of a banking system that is lending to another system; the latter will only be able to renew 65% of its funding needs, and the remainder will lead to fire sales of assets with a haircut of 50%. The contagion exercise evidences that the UK and US banking systems are globally systemically important. In addition, the consideration of credit and liquidity risks is relevant, otherwise the risk of contagion will be underestimated.

Mistrulli (2011) applies an exercise of contagion relying only on the Italian banking system, using the database of bilateral exposures between banks reported to the Bank of Italy as of 2003. Each contagion exercise starts with the default of one bank at a time. Subsequently, losses are calculated from each bank that has exposures to the bank that defaults, with a loss given default varying from 10% to 100% in multiples of 10. If the losses are greater than the regulatory capital, the bank defaults. The simulation continues after the first iteration as long as the failures of the failed banks lead to failures of other banks. Using this simulation exercise, Mistrulli concludes that the severity of contagion in the Italian banking system is low, and therefore its systemic risk is low. In addition, Mistrulli (2011) compares the results of an endogenous network (using the maximum entropy method) with those from the exogenous network and shows that the maximum entropy method overestimates contagion results compared with the network based on the interbank exposures.

Sun and Chan-Lau (2017) use the interbank exposures of the Chilean banking system, reported to the Chilean central bank, in order to analyze their systemic risk. However, they introduce two novel methodologies. First, they exhaustively characterize the network of the Chilean banks, using, among other measures, the network’s density, corresponding to the ratio of the number of existing connections to the number of potential connections, which depends on the number of banks in the network (n×(n-1)), where n stands for the number of banks, and the network’s reciprocity, that is, the probability that some connection has a correspondence in the opposite direction. For example, bank A is exposed to bank B, which in turn is exposed to bank A.

Another distinctive aspect of this study is that, instead of using an arbitrary parameter for the percentage of funding that is rolled over in a liquidity shock (as in Solé and Espinosa-Vega (2010)), Sun and Chan-Lau (2017) estimate the parameter as a function of the capital ratio of the bank that needs to renew its funding, with this ratio also being used to calculate the additional cost of the new funding. Thus, the parameter is a function of a nonlinear relationship between the capital ratio observed for the bank and the value of the optimal capital ratio for the banking system. The haircut applied to the assets placed on the market by banks that cannot roll over all of their funding needs reaches 20% of liquid assets and 60% of nonliquid assets, replacing the 50% applied by Solé and Espinosa-Vega (2010). Although the assumptions and data used by Sun and Chan-Lau (2017) are different from those used by Solé and Espinosa-Vega (2010), their conclusions are similar. The contagion that stems from fire sales due to a liquidity shock contributes to the domino effect to a greater degree than just losses resulting from a default event due to direct exposures between banks.

One of the other aspects under debate regarding this type of analysis is the relationship between the magnitude of the systemic risk and the network structure of a certain banking/financial system. On the one hand, a highly interconnected financial system may facilitate risk sharing and make the system more resilient to exogenous shocks: a certain exogenous shock over a strongly interconnected system may be more easily dissipated because it is absorbed by a greater number of parts within this system. On the other hand, if the parts of a system are more interconnected, it is natural that the probability of contagion from shocks increases (Summer 2013). The results of the studies carried out so far do not point in a specific direction in relation to this particular aspect. Part of the explanation for this lack of definition lies in the variability in assumptions and databases used in the studies, which result in different conclusions regarding the effect the network structure has on the likelihood of contagion.

A study by Gorpe et al (2019) using a large data sample of bilateral exposures from around 200 European banks as of 2017 Q3 concluded that the magnitude of bilateral exposures, coupled with bank-specific characteristics, is a key driver of the total number of defaults resulting from the simulation exercise. Their paper includes many new features that enhance the state-of-the-art studies performed so far in this field and was an inspiration for our work regarding the role played by the central bank in limiting liquidity risk and the indicators used to measure systemic risk. One of the main aspects brought to the contagion analysis by Gorpe et al was the use of a unique prudential data set from which the authors could draw real interbank exposures. Another feature related to the network methodology was the consideration of the role played by the central bank in mitigating liquidity risk. Gorpe et al also introduced indicators that could be used to measure systemic risk, such as the contagion index, contagion level and amplification ratio. Finally, their methodology provides a decomposition of the contagion in credit and funding shocks that can be used to calibrate bank-specific capital and liquidity requirements as well as large exposure limits.

Nevertheless, it is not only the network of interbank exposures that determines the risk of contagion, but also common exposures across assets and sectors of the economy (known as indirect contagion).

In this vein, Levy-Carciente et al (2015) developed an analysis of indirect contagion in the Venezuelan financial system between 1998 and 2013 with the main aim of using this type of analysis in stress tests with macroprudential characteristics. Their methodology starts with an exogenous shock (equal to 30%) that impacts a certain class of assets. Taking into account the exposures of each bank to that asset class, some will be severely impacted by the shock and go bankrupt, due to the fact that their capital ratio falls below a certain limit. Bankruptcies will affect the asset classes in the market in proportion to the assets each bank holds as a fraction of the total market. This devaluation due to the reduced liquidity of the assets will in turn impact other banks, which may also fail at a later stage. The contagion effect ends when no more banks fail. Note that the parameters relating to the initial shock and to the discount applied to the assets are fixed arbitrarily. Levy-Carciente et al (2015) conclude that the concentration of certain types of assets is very relevant to the evaluation of contagion, and therefore of the systemic risk, an aspect that could intensify the initial shocks even if they are considered to be small.

The combination of direct and indirect contagion is the main novelty of a more recent study by Montagna and Kok (2016). In this analysis, known as the multilayered interbank network model, each layer corresponds to a type of network: the network formed by bilateral exposures between financial institutions; the network resulting from common exposures to a particular type of asset or sector of the real economy; the network that stems from the use of the same type of collateral; and the network formed by the exposures through derivative instruments. In particular, Montagna and Kok (2016) focus on the network of short- and long-term direct exposures as well as those common to the same types of asset (indirect exposures).

Note that, regarding direct contagion, Montagna and Kok (2016) did not have access to observed bilateral exposures, but built them according to a probability matrix, inspired in turn by the geographical distribution of the activities of each bank, disclosed by the European Banking Authority during stress test exercises at the European level. Concerning indirect contagion, the transmission mechanism is based on fire sales that occur when a given institution breaches its liquidity buffer due to the default of an institution that secured part of its funding (as in Solé and Espinosa-Vega (2010)) or through the devaluation of its assets’ market value due to fire sales of other banks (as developed by Levy-Carciente et al (2015)).

Another important novelty brought to the literature by Montagna and Kok (2016) is the modeling of the haircut parameter applied to assets as a function of the value placed on the market instead of using fixed values as in previous studies. Using a sample of the 50 largest banks at European level, they conclude that considering only one type of network in isolation will lead to an underestimation of the contagion results and therefore of the systemic risk. Only a methodology that simultaneously considers the various types of network, as well as the transmission of the shocks between them, can lead to a holistic view of systemic risk. In a more recent study, instead of using the maximum entropy method to determine bilateral exposures, Halaj (2017) uses the values reported to supervisors by banks, with their main conclusions being in line with Montagna and Kok (2016).

3 Data and descriptive statistics

3.1 Data

We use consolidated data from financial reports (balance sheet), prudential reports (own funds and large exposures) and the central credit register (CCR) from 2007 to 2017. The sample of banks varies between 14 and 17 in total (representing, on average, 90% of the total assets of the Portuguese banking system, which includes resident banks and subsidiaries of foreign banks).

We use the financial and prudential reports from 2007 to 2013 from Banco de Portugal, and the financial reporting requirements (FINREP) and the common reporting requirements (COREP) from 2014 to 2017. Despite the improvements introduced in the latter, they are very similar to the earlier reports, and the differences do not impair our analysis, namely the identification of the bilateral interbank exposures and the main classes of assets on each bank balance sheet.

FINREP, whose implementation is steered by the implementation technical standards (ITS) (European Commission 2014) issued by the European Banking Authority (EBA), apply to all credit institutions and investment firms across the European Union (EU) that consolidate their financial reports based on International Financial Reporting Standards and cover balance sheet and income statements, comprehensive income and equity, disclosure of financial assets and liabilities and financial asset disclosures, and off-balance-sheet activities and nonfinancial instrument disclosures. In this paper the use of FINREP allows for the identification of banks’ exposures to each type of asset and counterparty.

COREP, also subject to the EBA ITS mentioned above, were introduced as part of the Capital Requirements Directive (CRD IV) in order to standardize the reporting of capital requirements and prudential regulatory information by regulated investment firms and credit institutions across the EU. COREP allow for the analysis of the interbank exposures and comprise information related to credit risk, market risk, operational risk, own funds and capital adequacy ratios. Finally, the CCR database permits the assessment of the concentration of banks’ exposures to industry sectors with respect to their nonfinancial corporations (NFC) counterpart. The data from large exposures (in both Banco de Portugal’s own reports and COREP) is key for the analysis carried out in this paper.

The large exposure reporting represents, to the best of our knowledge, the most comprehensive and up-to-date data set that captures (on a quarterly basis) granular bank- and exposure-level information of the euro area banking system covering all economic sectors: credit institutions, financial corporations, nonfinancial corporations, general governments, central banks and households. In this paper, however, we focus primarily on the interbank exposures within domestic banks. This allows for the creation of networks of interbank exposures. One drawback is the fact that this data includes only exposures that meet Capital Requirements Regulation (CRR) and EBA requirements for large exposure reporting.

3.2 Descriptive statistics

This section provides basic descriptive statistics for our database. The summary statistics are presented in Table 1. We observe that the sample of banks is quite heterogeneous regarding, in particular, total assets, whose amount varies from €6 million (the smallest bank) to €106 billion (the largest bank), and the capital ratio, which ranges from 8% to 45%. In addition, banks are mostly credit providers (the median of the loans/total assets ratio reaches 0.799).

Table 1: Summary statistics for the full sample, 2007–17. [TCR, total capital ratio. EI, equity instruments. TA, total assets. DSI, debt securities instruments. SD, standard deviation.]
  TCR EI/TA DSI/TA Loans/TA TA (€ bn)
Max 0.451 0.641 0.961 0.998 106.09
Q3 0.163 0.028 0.379 0.884 037.32
Median 0.128 0.011 0.183 0.799 009.92
Mean 0.127 0.022 0.268 0.710 023.54
Q1 0.105 0.003 0.083 0.581 001.84
Min 0.081 0.000 0.001 0.004 000.06
SD 0.068 0.053 0.246 0.252 028.84
Interbank exposures as of (a) 2008 Q4 and (b) 2016 Q4.
Figure 1: Interbank exposures as of (a) 2008 Q4 and (b) 2016 Q4.

Figure 1 displays the network of the interbank exposures in two different periods of analysis: 2008 and 2016. We should start by remarking that the dimension of the nodes reflects the own funds of each bank, whereas the thickness of the edges denotes the exposure values. Figure 1 shows that bank 4 plays a central role as a lender hub in the network in both periods, whereas bank 3 increases its role as a lender in 2016. In 2008 banks are weakly connected, but there are no banks that are completely disconnected. In 2016 we can observe a more connected interbank network; thus, each bank has a more diversified portfolio of interbank exposures in 2016 than in 2008. Being positive at bank level, this evolution may lead to a high propensity of financial systems being affected by shocks, since losses from contagion might propagate more rapidly.

Key network statistics: 2007--17. (a) Network density. (b) Average degree of nodes.
Figure 2: Key network statistics: 2007–17. (a) Network density. (b) Average degree of nodes.

In addition, in Figure 2 we present two network summary statistics (average degree of a node and density), as defined in Sun and Chan-Lau (2017), for the entire period. Regarding the network properties, the average degree of a node is defined as the number of edges directed toward (or originating from) a node divided by the total number of nodes, and network density is computed as the ratio of the number of existing links l to the maximum number of possible edges (the maximum possible number of vertices for a network with n nodes is n×(n-1)), 0l/n(n-1)1. The density can be interpreted as the unconditional probability that two nodes share one link, meaning that the network will be completely disconnected if the density equals 0 and be a complete network if the density equals 1.

With the exception of 2013, Figure 2 shows an increase in the network density since 2010. In the opposite direction, the average degree of the nodes has decreased since 2014.33 3 Note that, for the period before 2007, we do not have this type of data available to elaborate this kind of analysis.

At least two important events in the financial systems during the period between 2007 and 2009 should be highlighted: the US subprime mortgage crisis and the collapse of Lehman Brothers. The freeze of the international interbank markets led to a slight increase in the Portuguese banks’ network density between 2007 and 2009. This occurred because banks with comfortable levels of liquidity (lender banks), searching for higher yields, started to lend more to the resident banks that experienced liquidity shortages (borrower banks), which were unable to access the international wholesale markets. As a result, we can observe a more concentrated domestic interbank network. On top of that, it is also important to note that the number of banks reduced between 2007 and 2009. Most of the literature, as previously mentioned, focuses only on one period, and for this reason it is difficult to make a comparison with other EU countries. However, our results are in line with the conclusions of Gabrieli and Georg (2014), who present empirical findings from the euro area interbank market.

In addition, in 2014, one large bank was the subject of a bank resolution that provoked a significant variation in some ratios.44 4 More details about this event and the application of corrective measures may be found on the Banco de Portugal website, However, the creation of a new bank with the assets, liabilities, off-balance-sheet items and assets under management of the previous bank stabilized the evolution of the systemic risk.

As depicted in Figures 1 and 2, the interbank network of the Portuguese banking system became more interconnected throughout the period 2007–17, characterized by the growth of the network density and a decrease in the average degree of a node. As mentioned in Section 2, the influence of contagion on the network’s structure is not straightforward. On the one hand, a highly interconnected network of financial exposures might facilitate the sharing of aggregate risk, making the financial system more resilient to shocks; in other words, a shock to a highly interconnected system might be more easily dissipated, due to the fact that it can be absorbed by more entities. On the other hand, a highly interconnected system might be more prone to the contagion of shocks (Summer 2013) because not only does this interconnectedness create additional transmission channels for shocks during an adverse scenario, with one institution’s default affecting several institutions at the same time (Allen and Gale 2000), but a high degree of interconnectedness makes adverse shocks dissipate quicker (Chinazzi et al 2013). Only with the results of the application of the methodology described in Section 4 will we see which of the two effects prevails.

In order to assess how the concentration of the banking system to asset classes, counterparts and sectors evolved over the period 2007–17, we compute the Herfindahl index by asset class (Figure 3), by counterpart (Figure 4) and, in the case of NFC, by sector of activity (Figure 5).

Herfindahl index by asset class. (a) Herfindahl index. (b) Structure of asset class.
Figure 3: Herfindahl index by asset class. (a) Herfindahl index. (b) Structure of asset class.
Herfindahl index by counterpart. (a) Herfindahl index. (b) Structure of counterpart.
Figure 4: Herfindahl index by counterpart. (a) Herfindahl index. (b) Structure of counterpart.
Herfindahl index by activity. (a) Herfindahl index. (b) Exposure by year and activity.
Figure 5: Herfindahl index by activity. (a) Herfindahl index. (b) Exposure by year and activity.

Despite the fact that the Herfindahl index declined throughout the period, we may distinguish the different cases: the largest decrease occurs in the asset class structure (Figure 3), which is mainly explained by the increase in debt securities share. Note that the most representative types of debt securities are nonfinancial corporations and general governments (with a significant increase), which represent 52% and 46% on average, respectively. The other types of debt securities considered were central banks, credit institutions and other financial corporations. Counterpart indicators decreased progressively until 2015, remaining flat after that. Finally, the Herfindahl index by sector of activity shows a slight reduction; this result was expected, since it relates to stocks and not cashflows.

4 Methodology

The methodology used in this paper builds on the models developed by Solé and Espinosa-Vega (2010) to gauge the direct contagion to interbank exposures, Levy-Carciente et al (2015) to assess the contagion via exposures to assets, and Sun and Chan-Lau (2017) to model the rollover rate and additional funding costs in the case of liquidity shocks.

The model used in this paper is based on the following assumptions:

  • (A1)

    Banks fail if their total capital ratios fall below Pillar 1 requirements (8%) that are also used for eligibility of credit institutions to access emergency liquidity assistance (ELA).55 5 For further details, see European Central Bank (2017).

  • (A2)

    The contagion occurs in a stress scenario, as such banks are not able to issue capital, although they can breach the combined buffer requirement.

  • (A3)

    All the assets placed in the market are acquired by other banks or investment funds from the sample considered.

  • (A4)

    The reduction in credit to the economy due to the failure of banks is offset by the credit granted by other banks or investment funds from the sample considered.66 6 This assumption relies on the results obtained by Beck et al (2020), who analyzed the credit supply and real sector effects of bank bail-in following the unexpected failure and subsequent resolution of a major bank in Portugal. They found that, despite some decrease in credit supply after the shock, particularly in small and medium-sized firms, the affected firms were able to respond to this credit contraction by turning to other sources of funding, including new lending relationships.

The starting point is the following stylized balance sheet for bank i{1,,b}:

  DSi+ESi+Loansi=Ki+Li,   (4.1)

where DSi stands for the debt securities, ESi denotes equity securities, Loansi represents the total loans of bank i, Ki stands for bank i’s regulatory capital, Li stands for liabilities and b is the number of banks at the beginning of each period. Considering that bank i owns Bi,m of each asset m{1,2,3} (where 1=Loans; 2=DS; 3=ES), respectively, then the total assets held by bank i is defined as Bi=mBi,m. From the perspective of asset categories, we define the total market value of an asset m as

  Am=iBi,m.   (4.2)

We start by selecting the period from which all balance sheet, large exposures and exposures from CCR data are taken. Then we impose an adverse shock of 2% on each class of assets. The total losses for bank i (Xi) equals 2%, which is similar to the historical asset losses recognized by the Portuguese banking system during a crisis encompassing a sharp decrease in gross domestic product (GDP) coupled with a significant raise in the yields of the sovereign debt. We remark that this assumption is not only reasonable but also realistic, as we can see in Figure 6.

Historical asset losses recognized by the Portuguese banking system, 2007--17. Percentage values have been rounded.
Figure 6: Historical asset losses recognized by the Portuguese banking system, 2007–17. Percentage values have been rounded.

The losses are deducted from the starting balance sheet in the following way:

  DSi+ESi+Loansi-Xi1,2,3=Ki*+Li,   (4.3)

where Ki*=(Ki-Xi1,2,3).

If after the shock Ki*/RWA<8% (where RWA denotes the risk-weighted assets), the bank fails, enters into bankruptcy and puts all of its assets on the market. This will result in a devaluation in the assets’ market value due to common exposures across banks, defined as

  Am,t+1=Am,t-ρmBi,m,tm,   (4.4)


  ρm=1-exp(-αiSiTS),   (4.5)

with TS denoting the aggregate volume of securities held by banks and S=iSi denoting the aggregate sale of the assets.

We also introduce an elasticity factor α>0.77 7 We consider α=20% in this exercise. At the same time, the losses stemming from interbank exposures, namely losses from bank i’s default to j, are defined as

  IBt-1j,i-IBtj,i.   (4.6)

In addition, the failed bank could be financing bank j, as bank j has to roll over this type of funding. This results in a liquidity shock to bank j.

The first line of defense against the abovementioned shock is the funding provided by the central bank, which depends on the amount of unencumbered assets eligible to obtain such funding. When this is exhausted, banks have to resort to funding from other banks, which depends on their level of capital and distance from the optimal capital level (Sun and Chan-Lau 2017). In this regard, inspired by the work carried out by Sun and Chan-Lau (2017), we define two functions of the capital ratio: replacement rate (η) and an incremental funding cost (θ). The replacement rate is defined as

  η(KiRWA)={1if K0RWA<KiRWA,1-(K0/RWA-Ki/RWA)2(K0/RWA-K/RWA)2if KRWA<KiRWAK0RWA,0otherwise.   (4.7)

The incremental funding cost is defined as

  θ(KiRWA)={0if K0RWA<KiRWA,β(K0RWA-KiRWA)3if KRWA<KiRWAK0RWA.   (4.8)

The coefficient β is obtained by the following regression:

  spreadit=β(13.5-(KiRWA)it)3,   (4.9)

where K0/RWA denotes the optimal capital ratio and K/RWA is the minimum capital ratio.

For the purpose of this paper, banks that are unable to renew their funding (either that provided by the central bank or that granted by other financial institutions) have to sell assets: in this vein they will primarily sell those assets in a class for which a lower fire sale loss is expected. In other words, they will sell their most liquid assets. To this end, it is foreseeable that banks will probably withdraw the claims on other banking institutions first, followed by equity, debt securities and loans (Montagna and Kok 2016). Nevertheless, given the liquidity requirements (in particular from 2015 onward), namely the liquidity coverage and net stable funding ratios, we impose the condition that banks first sell nonsovereign debt securities, since sovereign debt securities are commonly considered high-quality liquid assets, a type of asset necessary to comply with the aforementioned liquidity requirements.

Therefore, the potential losses from liquidity and funding stem from two components: one resulting from the assets the banks need to sell to rebalance the amount they were unable to replace, given by

  (1-η)×Li×ρm;   (4.10)

and another stemming from the incremental cost of funding, given by

  η×Li×θ,   (4.11)

where θ is defined in (4.8).

The last stream of losses stems from the devaluation of the assets’ market value due to the liquidation of assets that occurs after each bank’s failure and/or fire sales carried out by banks that withstand difficulties in renewing their wholesale funding. Therefore, the losses that stem from assets’ market devaluation (marked-to-market (MtM) losses) are defined as

  Bi,m,t+1=Bi,m,t×Am,t+1Am,t.   (4.12)

Therefore, we end up with four types of losses:

  1. (1)

    fire sales losses (stemming from the nonrollover of funding; see (4.10)),

  2. (2)

    incremental cost of funding (see (4.11)),

  3. (3)

    credit default losses (see (4.6)), and

  4. (4)

    MtM losses (see (4.4) and (4.12)).

MtM losses only impact assets measured at the fair market value, which varies with each bank’s portfolio composition.

The contagion mechanism comprises several interactions, starting with the failure of one or more banks in the network and ending when no more failures are registered.

5 Results

In this section we assess the results from the simulation exercise based on the methodology described in Section 4.

Contagion results. The histogram outlines the percentage of total failures, contagious banks (banks that suffer the first shock and fail), contagious banks that are O-SIIs, banks failing by contagion and banks failing by contagion due to interbank exposures (direct contagion), with the axis on the left-hand side. The solid lines show the percentage of the banking system asset losses incurred due to the contagion exercise (left-hand axis). The dotted line depicts the banking system's average total capital ratio (right-hand axis).
Figure 7: Contagion results. The histogram outlines the percentage of total failures, contagious banks (banks that suffer the first shock and fail), contagious banks that are O-SIIs, banks failing by contagion and banks failing by contagion due to interbank exposures (direct contagion), with the axis on the left-hand side. The solid lines show the percentage of the banking system asset losses incurred due to the contagion exercise (left-hand axis). The dotted line depicts the banking system’s average total capital ratio (right-hand axis).

As depicted in Figure 7, systemic risk, as gauged by the percentage of banks failing by contagion, has experienced a sharp reduction since 2012.

In the period between 2007 and 2009 systemic risk reduced slightly. The percentage of banks that failed by contagion reached 6% of the total banks in the sample in 2007, after two rounds, diminishing to 0% in 2009. Asset losses reached around 50% of the total assets in the sample of banks considered in 2007, declining to around 15% in 2009.

In 2010 and 2011 contagion increased as a consequence of the crisis witnessed in Portugal that combined, among other things, a sharp decrease in GDP and an increase in the yield-to-maturity of the sovereign debt as a result of successive rating downgrades. This, unsurprisingly, negatively impacted banks as a result not only of the rise of nonperforming loans as a consequence of the difficulties in serving their high level of debt in the nonfinancial private sector (households and, in particular, nonfinancial companies) but also of the freeze of the wholesale markets that led to liquidity constraints.

Therefore, Figure 7 shows that the percentage of banks failing by contagion increased from 0% in 2009 to 56% and 60% in 2010 and 2011, respectively. Contagion also led to the wipeout of the total banking system assets in 2010 and 2011. Subsequently, from 2012 onward, the percentage of banks that failed by contagion declined to 0%, albeit with some asset losses resulting from the initial shock. The outlier observed in 2012 is explained by the strengthening of capital ratios of the largest banks following the release of EBA’s recommendation on the creation and supervisory oversight of temporary capital buffers to restore market confidence in 2011 (European Banking Authority 2011) and the subsequent issue of legally binding notices by Banco de Portugal targeted at banks to strengthen their capital ratios.

Besides the clear reduction in systemic risk observed between 2007 and 2017, with peaks in 2010 and 2011, two other aspects deserve our attention. First, this exercise outlines that there is no straightforward relationship between the systemic importance of the contagious banks (banks that failed after the initial shock) and the final results from the contagion exercise, which points to the fact that EBA criteria to identify other systemically important institutions (European Banking Authority 2014) might not address the potential for contagion of this kind of institution. It is important to note that these results do not jeopardize the criteria envisaged in the EBA guidelines; they only highlight that the relevant authorities should strengthen the criteria with other methodologies, as the contagion exercise carried out in this paper considers there to be room for maneuver provided in the guidelines (for instance, the possibility of using supervisory judgment).

Second, contagion through direct interbank exposures is not significant. In this regard we can observe that the percentage of banks that failed by direct contagion was 7% in 2008, 19% in 2010 and 13% in 2011. We do not observe any failure due to the type of shock concerning liquidity constraints stemming from the failure of banks that are financing other banks or from the need to perform fire sales.

Amplification ratio and contagion indicators. The histogram shows the amplification ratio (right-hand axis). The dashed line shows the contagion index and the solid line shows the contagion level (left-hand axis). The amplification ratio is computed as the ratio of the losses incurred on the second round onward to the losses incurred due to the initial shock. A ratio greater than 1 indicates that losses due to contagion dominate initial losses. The contagion index represents the system-wide losses induced by the initial shock as a percentage of the total assets in the system. The contagion level stands for the percentage of banks failing by contagion.
Figure 8: Amplification ratio and contagion indicators. The histogram shows the amplification ratio (right-hand axis). The dashed line shows the contagion index and the solid line shows the contagion level (left-hand axis). The amplification ratio is computed as the ratio of the losses incurred on the second round onward to the losses incurred due to the initial shock. A ratio greater than 1 indicates that losses due to contagion dominate initial losses. The contagion index represents the system-wide losses induced by the initial shock as a percentage of the total assets in the system. The contagion level stands for the percentage of banks failing by contagion.

The results relating to direct contagion (credit and liquidity risks) to some extent contradict the increase in the interbank network density (augmented with the average degree of a node) observed throughout the period. As discussed in Sections 2 and 3, a highly interconnected network of financial exposures may facilitate the sharing of aggregate risk and make the financial system more resilient to shocks, and this effect prevails due to our sample and the structure of the network of banks used in this paper. This result, among others, is in line with those obtained by Mistrulli (2011). In addition, if the interbank exposures constitute a small portion of the total assets, which is the case with our sample of banks, this result is hardly surprising.

The results outlined in Figure 8 are in line with those discussed above: the three indicators increased in 2010 and 2011 compared with 2009 and experienced a sharp decline after 2011, pointing to a reduction in the systemic risk of the Portuguese banking system between 2007 and 2017 with peaks in 2010 and 2011.

We also analyzed how banks’ size and business models influence their probability of being contagious (failing at the first shock) or failing by contagion. We thus split the sample into large banks (banks with total assets above the median) and medium/small banks (banks with total assets below the median). We can identify two types of bank business models: commercial banks and investment banks. Regarding the percentage of banks failing by contagion, we cannot identify any influence of either bank size or business model. As for the probability of being considered contagious, our data shows that small banks are slightly more prone to fail at the first shock than the large banks. We do not observe the same feature regarding banks’ business models, whose potential to fail at the first shock is the same.

We carried out a sensitivity analysis on the parameters used in our methodology, such as the initial shock as a percentage of total assets (2% in (4.1)) and the α used in the fire sales haircut function (see (4.5)).

In this regard, Figures A.1 and A.2 in the online appendix show the results from shocks of 3% and 1% of total assets, respectively. Concerning the shock of 3%, we observe the same trajectory of a decline in systemic risk throughout the 2007–17 period observed in the baseline exercise, with the exception of a peak in 2015. This occurred due to the exceptional decrease in the capital ratio of one bank in 2015 compared with 2014, which reached a level that was not sufficient to absorb the shock of 3%. The same bank built up a buffer that became sufficient to absorb the same level of shock in 2016 and 2017. Relating to the shock of 1%, we conclude that it is not sufficient to trigger contagion in any year.

Figures A.3 and A.4 in the online appendix depict the results of changing the elasticity factor α from 20% to 10% and 30%, respectively. The results are not significantly sensitive to the changes in the values of the elasticity of prices of equity and debt securities.

So, what are the reasons behind the reduction in systemic risk in this exercise? We conclude that the reduction in Portuguese banking system systemic risk arises mainly from two features. First, banks were better capitalized in 2017 (having an average capital adequacy ratio of 15%) compared with 2007 (having an average capital adequacy ratio of 10.0%), allowing them to withstand adverse scenarios. Second, banks reduced their concentration risk, as shown in Section 3, regarding:

  1. (1)

    asset classes (equity, debt securities and loans and advances);

  2. (2)

    counterparties (credit institutions, general governments, nonfinancial companies, other financial corporations and households); and

  3. (3)

    industry sectors within nonfinancial companies.

We must emphasize that these results are also partly explained by the capital buffers introduced in the Basel III Accord. This new regulatory framework enhances the quality and quantity of capital through

  • the build-up of capital buffers and increased scrutiny of the quality of instruments that should be included in common-equity tier 1 and tier 1 capital;

  • a reduction in the procyclicality of leverage with the imposition of a countercyclical capital tool known as a countercyclical capital buffer; and

  • the adoption of a leverage ratio to complement the risk-weighted capital ratios.

In addition, we performed a counterfactual analysis to test which effect is more pronounced. Figure A.5 in the online appendix shows that if the capital ratio had remained stable at the highest level for the 2017 period, we would not have observed any contagion episode in the Portuguese banking system throughout the period considered.

Basel III also introduced two new liquidity ratios, the liquidity coverage ratio (LCR) and the net stable funding ratio (NSFR). These two ratios were developed to achieve two separate complementary objectives: the LCR defines an adequate level of unencumbered, high-quality assets that banks must maintain to meet their liquidity needs for a 30-day time horizon under an acute stress scenario; the NSFR establishes a minimum acceptable amount of stable funding based on the liquidity characteristics of an institution’s assets and activities over a one-year horizon.

It is worth mentioning that, although our methodology could be extrapolated to other banking systems, the results from the analysis carried out in this paper depend on the parameters used, such as the shock, the optimal target capital ratio, and the beta from the econometric model used in the incremental funding cost (see (4.8), (4.9)), which in turn depend on the historical relationship between spreads and the capital level of the Portuguese banking system. Thus, despite some similarities with other studies pointed out in this section, they should not be extrapolated to other contexts, with other parameters.

6 Conclusion and policy implications

This paper raises the question of how systemic risk has evolved, by considering the period from 2007 to 2017, which includes the global financial crisis and, principally, the sovereign debt crisis that affected not only the Portuguese economy as a whole but the Portuguese banking system in particular. In order to perform this assessment, we developed a methodology encompassing several possible channels of direct and indirect contagion: credit, liquidity and concentration risks.

Overall our results show that the systemic risk of the Portuguese banking system reduced between 2007 and 2017, with some peaks in 2010 and 2011. In addition, we conclude that systemic risk, and in particular contagion, definitively extends far beyond direct links between banks. Our results show that the percentage of banks failing due to direct interbank exposures (including liquidity risk) is not significant, highlighting the importance of indirect links through banks’ common exposures to some types of asset.

Finally, considering policy issues, this paper supports the role played by capital in mitigating structural systemic risk. Further, the model behind the analysis could be used to analyze other types of shocks. It could also be used to build stress tests with a macroprudential dimension, characterized by a dynamic balance-sheet analysis, which would complement the micro stress tests, characterized by a static balance-sheet analysis, by introducing the possibility of contagion both between banks and between the banks and the real economy. This would make stress tests more relevant to what actually occurs in a real stress situation without preemptive action by the supervisors. In addition, the model could also be used to calibrate structural systemic buffers, such as the O-SII buffer, and/or a targeted systemic risk buffer, as allowed for in CRD V, by answering the following questions:

  • What type of institutions triggered the contagion event?

  • Which institutions were responsible for the amplification of the contagion?

  • What should the amount of additional capital be to mitigate the contagion event and the subsequent domino effect?

  • Which asset class was most sensitive to the initial shock and contagion?

Declaration of interest

The authors report no conflicts of interest. The authors alone are responsible for the content and writing of the paper. The opinions expressed in the paper are those of the authors and do not necessarily coincide with those of Banco de Portugal or the Eurosystem. Any errors and omissions are the sole responsibility of the authors.


We are grateful for very valuable comments received from participants of the 2019 Joint Česká Národní Banka/European Central Bank/European Systemic Risk Board Workshop, “Sources of Structural Systemic Risk in the Financial System: Identification and Measurement”. We also thank Álvaro Pina, Ana Cristina Leal, Ana Pereira, Diana Bonfim, Fátima Silva, Inês Drumond, Martin Saldias and Maximiano Pinheiro for very useful comments, and Eduardo dos Santos for research assistance.


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