Scholarly article on topic 'Evaluating the effectiveness of the new EU bank regulatory framework: A farewell to bail-out?'

Evaluating the effectiveness of the new EU bank regulatory framework: A farewell to bail-out? Academic research paper on "Economics and business"

CC BY-NC-ND
0
0
Share paper
Academic journal
Journal of Financial Stability
OECD Field of science
Keywords
{"Banking regulation" / "Banking crisis" / "Capital requirements" / Bail-in / "Resolution funds"}

Abstract of research paper on Economics and business, author of scientific article — Peter Benczur, Giuseppina Cannas, Jessica Cariboni, Francesca Di Girolamo, Sara Maccaferri, et al.

Abstract In response to the economic and financial crisis, the EU has adopted a new regulatory framework of the banking sector. Its central elements consist of new capital requirements, the single rulebook, and rules for bank recovery and resolution. These legislations have been adopted to reduce the call for government bail-out of distressed banks in future crises. The present study performs a detailed quantitative assessment of the reduction in public finance costs brought about by the introduction of these rules. We use a microsimulation portfolio model, which implements the Basel risk assessment framework, to estimate the joint distribution of bank losses at EU level. The approach incorporates the complete safety-net set up in EU legislation to absorb these losses, explicitly modelling enhanced Basel III capital rules, the bail-in tool and the resolution funds. Using a near-full sample of commercial, cooperative and savings banks in the EU, we quantify the cumulative effects of this safety-net and the contribution of each individual tool to the total effect. Considering a crisis of a similar magnitude as the recent one, our results show that potential costs for public finances decrease from roughly 3.7% of EU GDP (before the introduction of any new tool) to 1.4% with bail-in, and finally to 0.5% when all the elements we model are in place. This latter amount is very close to our estimate of leftover resolution funds and the size of the Deposit Guarantee Scheme. This exercise extends the quantitative analyses performed by the European Commission in its Economic Review of the Financial Regulation Agenda by developing additional scenarios, crucial robustness checks, simulations for different annual data vintages, and by implementing some methodological improvements.

Academic research paper on topic "Evaluating the effectiveness of the new EU bank regulatory framework: A farewell to bail-out?"

ARTICLE IN PRESS

Journal of Financial Stability xxx (2016) xxx-xxx

ELSEVIER

Contents lists available at ScienceDirect

Journal of Financial Stability

journal homepage www.elsevier.com/locate/jfstabil

Evaluating the effectiveness of the new EU bank regulatory framework: A farewell to bail-out?

Peter Benczur, Giuseppina Cannas, Jessica Cariboni, Francesca Di Girolamo, Sara Maccaferri *, Marco Petracco Giudici

Financial and Economic Analysis Unit, Institute for the Protection and Security of the Citizen European Commission, Joint Research Centre, Via E. Fermi 2749,21027 Ispra, VA, Italy

ARTICLE INFO

ABSTRACT

Article history: Received 29 July 2015 Received in revised form 12 December 2015 Accepted 8 March 2016 Available online xxx

JEL classification:

Keywords: Banking regulation Banking crisis Capital requirements Bail-in

Resolution funds

In response to the economic and financial crisis, the EU has adopted a new regulatory framework of the banking sector. Its central elements consist of new capital requirements, the single rulebook, and rules for bank recovery and resolution. These legislations have been adopted to reduce the call for government bail-out of distressed banks in future crises.

The present study performs a detailed quantitative assessment of the reduction in public finance costs brought about by the introduction of these rules. We use a microsimulation portfolio model, which implements the Basel risk assessment framework, to estimate the joint distribution of bank losses at EU level. The approach incorporates the complete safety-net set up in EU legislation to absorb these losses, explicitly modelling enhanced Basel III capital rules, the bail-in tool and the resolution funds.

Using a near-full sample of commercial, cooperative and savings banks in the EU, we quantify the cumulative effects of this safety-net and the contribution of each individual tool to the total effect. Considering a crisis of a similar magnitude as the recent one, our results show that potential costs for public finances decrease from roughly 3.7% of EU GDP (before the introduction of any new tool) to 1.4% with bail-in, and finally to 0.5% when all the elements we model are in place. This latter amount is very close to our estimate of leftover resolution funds and the size of the Deposit Guarantee Scheme.

This exercise extends the quantitative analyses performed by the European Commission in its Economic Review of the Financial Regulation Agenda by developing additional scenarios, crucial robustness checks, simulations for different annual data vintages, and by implementing some methodological improvements.

© 2016 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND

license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

1. Introduction

The world has experienced in recent years the most severe economic and financial crisis since the Great Depression of 1929. It started in 2007 in the US, with the collapse of the residential mortgage market and the collapse of Lehman Brothers. The crisis sent shock waves to the financial system worldwide: for the first time, giants of the financial world faced severe distress and some of them went into bankruptcy (see e.g. Blanchard, 2009; Claessens et al., 2010; Laeven and Valencia, 2013).

* Corresponding author. Tel.: +39 0332 783832; fax: +39 0332 785752.

E-mail addresses: peter.benczur@jrc.ec.europa.eu (P. Benczur), giuseppina.cannas@jrc.ec.europa.eu (G. Cannas), jessica.cariboni@jrc.ec.europa.eu (J. Cariboni), francesca.di-girolamo@jrc.ec.europa.eu (F. Di Girolamo), sara.maccaferri@jrc.ec.europa.eu (S. Maccaferri), marco.petracco@jrc.ec.europa.eu (M. Petracco Giudici).

As a first response to the crisis, many governments and central banks intervened and bailed out failing banks. In the period 2008-2012, the total costs borne by European governments to support the financial sectors in the forms of capital injection and asset relief (excluding guarantees) amounted to 600 billion D, corresponding to 4.6% of 2012 European GDP (see European Commission, 2014b).

These numbers explain why a strong consensus emerged that ad-hoc ex-post financial support is no more sustainable, and one must find ways to resolve failing banks at no or limited costs to taxpayers and society (e.g. Huertas, 2010). There is a clear agreement on the need for a better designed, more efficient and more integrated framework to improve the stability of the banking sector and to protect public finances (Schoenmaker and Gros, 2012; Huertas and Nieto, 2012), capable of dealing effectively with a crisis situation, together with a more centralized supervision (Beck, 2012; Goyal et al., 2013; Dewatripont, 2014).

http://dx.doi.org/10.1016/jjfs.2016.03.001

1572-3089/© 2016 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/ by-nc-nd/4.0/).

ARTICLE IN PRESS

P. Benczur et al. / Journal of Financial Stability xxx (2016)xxx-xxx

Regulators have proposed and adopted a number of different measures to limit the effects of bank losses and failures on the whole financial and economic system, in the case of future crises. The set of these financial instruments is generally referred to as the financial safety-net. A comprehensive summary of the financial reforms adopted by the European Union (EU) is discussed in the Economic Review of the Financial Regulation Agenda (from here onwards: ERFRA; see European Commission, 2014a). These reforms do not only address the banking sector, but they also look at financial markets and their infrastructure, shadow banking, the stability and resilience of the insurance sector.

In this paper, we model the impact of the following major reforms dealing with the banking sector:

• The new Capital Requirement Regulation and Directive IV (CRR/CRD IV, European Parliament and Council, 2013), which transposes the Basel III Accord into EU legislation and enhances the quality and quantity of capital that banks should set aside to tackle unexpected losses.

• The Bank Recovery and Resolution Directive (BRRD, European Parliament and Council, 2014), which sets up a series of rules and resolution tools, such as the sale of the business or shares of the institution under resolution, the setting up of a bridge institution, the separation of the performing assets from the impaired or under-performing assets of a failing institution, and the bail-in of shareholders and creditors of a failing institution. National resolution funds are also established to resolve distressed banks at national level.

• The Single Resolution Mechanism Regulation (European Council, 2014), which foresees that the resolution funds of countries participating in the banking union1 are pooled into a single resolution fund.

We quantify the cumulative effects of the adopted pieces of legislation on government contingent liabilities, i.e., on public finance costs conditional on a (severe) financial crisis. Starting from publicly available balance sheet data of nearly all commercial, cooperative and savings banks in the EU, we use a microsimulation portfolio model (originating from De Lisa et al., 2011), which implements the Basel risk assessment framework, to estimate the joint distribution of bank losses at EU level. This model, which is referred to as SYMBOL (SYstemic Model of Bank Originated Losses), allows simulating the joint distribution of bank-level losses in excess of capital under various minimum capital requirement levels and safety-net tools such as bail-in and resolution funds. The model can thus be used to assess the reduction in the amount of losses that remains uncovered after the intervention ofthe available tools, and that could potentially hit public finances. Aggregating data over the entire banking system, our method allows assessing the overall reduction in potential public finance costs deriving from the adopted policies.

SYMBOL has been used by the European Commission as a tool for ex-ante quantitative impact assessments of a number of legislative proposals (see Marchesi et al., 2012; European Commission, 2011b; Cariboni et al., 2012; Cannas et al., 2013c), for the cumulative evaluation of entire financial regulation agenda (ERFRA, European Commission, 2014a), and for the assessment of contingent liabilities linked to public support to the EU banking sector during the crisis (European Commission, 2011a, 2012a; Benczur et al., 2015).

1 The banking union transfers the banking supervision from national to European level and provides for a more centralised management of banking crises. It is made up of a single rule book for financial institutions, the Single Supervisory Mechanism, and the Single Resolution Mechanism, all of which are mandatory for all euro area Member States and open to all other countries in the EU.

Besides presenting a more detailed, formal and thorough version of the ERFRA exercise (European Commission, 2014a; Cariboni et al., 2014), our paper extends its results along three major lines. First, it models the single resolution fund for countries participating in the banking union. Second, it performs the simulation using data from multiple years (2007, 2009, and 2012), documenting the impact of recent bank balance sheet trends on the results, and analysing the sensitivity of the findings to different data vintages. Third, it allows for a richer correlation structure among banks and evaluates its impact on the results.

This latter aspect is particularly important. De Lisa et al. (2011) demonstrated that the degree of commonality (correlation) among the shocks hitting banks has a major impact on the extreme tail percentiles of the distribution of deposit guarantee scheme losses, which increase strongly as the correlation coefficient increases. One of our main objectives with this paper is to explore the robustness of the Commission's ERFRA exercise to this key ingredient. This overall commonality among bank shocks can come from two main sources: exposure to common shocks and forms of contagion. Though we do not explicitly model contagion effects through the interbank market (direct contagion), our framework can represent different degrees of commonality by different shock correlation structures.

For our quantitative exercise, we make the following main assumptions. First, results are calibrated to match the gravity of the 2008-2012 crisis,2 i.e. a severe and systemic crisis event. Second, we work under the conservative assumption that all simulated bank excess losses and recapitalization needs that cannot be covered by the safety-net fall on public finances.3 Third, we assume that full bail-out prevents the spreading of contagion through the interbank market. Fourth, the safety-net is considered able to fully rule out direct contagion effects; more specifically, we assume that all distressed banks are resolved and recapitalized.4

Our results show that potential costs for public finances of a crisis similar to the recent one decrease from roughly 3.7% of EU GDP (before the introduction of any new tool) to 1.4% with bail-in, and finally to 0.5% when all the elements we model are in place. We view this as a major reduction. According to these findings, bail-in is the tool that contributes most to the reduction in the potential costs for public finances. This reinforces results of Breuss et al. (2015), who find that bail-in is effective in reducing the fall of GDP in the Euro Area core countries, and thus has also advantages from a macroeconomic perspective.

At the same time, our results imply that the modelled safety-net design would still leave the possibility of some public finance costs in case of a very extreme crisis event. This is partly due to our conservative modelling approach to the safety-net, i.e. allowing the use of available tools at their minimum levels (see more details in Section 2). More importantly, supervisors have additional tools to absorb these residual losses, including among others the leftover resolution funds and parts of the Deposit Guarantee Scheme. We have estimated the additional capacity of these two tools to be around 0.3-0.4% of EU GDP, almost equalling our estimated 0.5%.

The discussion on the true effectiveness of the proposed tools is still ongoing. Avgouleas and Goodhart (2015) discuss in details the economic and legal pros and cons of bank bail-in regimes and in

2 Bank losses and recapitalization needs triggered by the last crisis are proxied by state aid data, in particular the total recapitalization and asset relief provided to banks over 2008-12 (around 600 bn euro), see European Commission's DG Competition State Aid Scoreboard, European Commission (2014b) and Benczur et al. (2015).

3 The severity of the systemic crisis assessed in this exercise is higher than that ofthe "2014 EU-wide stress test" performed by the EBA and results cannot directly be compared due to different methodologies.

4 Potential contagion across banks through bail-in is disregarded due to scarce data. Some preliminary results are already available in Fontana et al. (2015b).

ARTICLE IN PRESS

G Model

JFS-423; No. of Pages 17

P. Benczur et al. / Journal of Financial Stability xxx (2016) xxx-xxx

particular the potential risks they may pose in domestic and cross-border frameworks. They also argue that one may want to keep a last layer of public insurance for the financial system. A similar case is made by Dewatripont (2014). A different view is taken by the Five Presidents' Report (Juncker et al., 2015), which proposes to complete the banking union by adding a fiscally neutral common backstop (i.e. reaching a public finance cost of zero in the future).

Despite the recognized need to establish a safety-net for banks, to the best of our knowledge academic research has so far concentrated on individual tools, and few quantitative approaches have been proposed to analyse the cumulative effects of such tools. One exception is Breuss et al. (2015), using a DSGE model to simulate the counterfactual response of euro area GDP to a large adverse financial shockunder different safety-net setups. The paper finds that the drop in GDP would have been smaller by 10-40%, depending on the set of mechanisms adopted. Apart from the fact that our approach is not meant to assess linkages to the rest of the economy, the main difference lies in our granularity of modelling the safety-net and thus these results cannot be easily compared with the findings of this paper. Breuss et al. (2015) follows a macro approach, and model the safety-net as a certain part of banking losses being directly picked up by creditors, the government and/or the single resolution fund. In contrast, we implement the fine details of each safety-net element on a bank-by-bank basis, which allows us to obtain results on the relative contribution of each actor in absorbing losses.

There is a rich literature on making the case for and evaluating the effects of higher capital requirements. Examples include Macroeconomic Assessment Group (2010), Miles et al. (2012), Bank of England (2012) and European Commission (2012b). A detailed survey can be found in Annex 1 of European Commission (2014a). The focus of this literature is in general the impact on GDP and on financial stability, and not on the issue of government bailouts, thus it is not straightforward to compare the outcome of this literature with the present paper.

The research on deposit insurance modelling is well developed, as this type of insurance was set in place long time ago. The first paper dates back to Merton (1977) and since then a number of quantitative studies have been developed to assess their features (among the others Bennett, 2002; Duffieetal., 2003; Kuritzkesetal., 2002; Sironi and Zazzara, 2004; Maccaferri et al., 2013). The contribution by Acharya et al. (2010) presents a setting for a deposit guarantee scheme which also takes into account systemic risk, while the original paper developing SYMBOL (De Lisa et al., 2011) quantifies an optimal target level for the Italian deposit guarantee scheme fund based on the simulated distribution of bank losses and corresponding failures. Finally the recent work by Anginer et al. (2014) examines the relation between deposit insurance and a banking crisis in the years before and during the crisis. This literature focuses in general on the estimation of the loss distribution of deposit insurance and the evaluation of fund adequacy via credit risk models, while we assess the added value of similar tools in funding bank resolutions in case of a severe crisis.

Concerning the bail-in, Galliani and Zedda (2014) include this tool in a framework based on the SYMBOL model to assess the possible circular effects between a distressed banking system and public finances. They find that the bail-in tool is very effective in reducing public finance costs. Although their analysis is limited to a subset of countries and not in a systemic crisis situation, Section 4.2 contains a comparison with our results.

Turning the focus from public finances to holders of bank liabilities, Conlon and Cotter (2014) make use of historical consolidated balance sheet data from the financial crisis to assess the counterfac-tual impact of bailing-in different categories of liabilities during the crisis. Beyond general differences in the methodology (simulation versus historical data), the different focus leads to additional differences. Conlon and Cotter (2014 analyse a "worst case scenario"

for senior bondholders: all losses exceeding the available equity and subordinated debt are absorbed by senior debt, i.e. there are no limits on bail-in, and no additional resolution tools. In contrast, we analyse a worst case scenario for public finances: we implement the full safety-net, with a limit on bail-in.

Finally, there is already some literature on the advantages of a single resolution fund over national resolution funds. The main aspects are the possibility of breaking the vicious loop between banks and sovereigns, and a better internalization of cross-border externalities. Related papers include Brunnermeier et al. (2011), Alter and Schüler (2012), Schoenmaker and Siegmann (2013) and Fontana et al. (2015a).

Relative to existing analyses, our paper features numerous advantages. On the conceptual side, we cover nearly all EU banks, assess the EU-wide distribution of various notions of banking losses, in particular the part which might have to be picked up by public finances (bail-out), taking into account detailed components of the banking safety-net. On the technical side, we perform robustness analysis to data vintages, different levels of consolidation and correlation structures.

In the context of our exercise, we refer to the reduction in contingent liabilities as the benefits of the implemented tools. Let us stress upfront that our exercise is limited to assessing this particular benefit and no other macro costs and benefits. Though we recognize the importance of assessing the costs, their assessment is very complex and would require the estimation of the behavioural response of banks to various pieces of legislation. There is nevertheless a stream of existing literature performing macroeconomic cost-benefit analysis of the introduction of safety-net tools (e.g. Breuss et al., 2015; Macroeconomic Assessment Group, 2010; Miles et al., 2012; Bank of England, 2012; European Commission, 2012b), which finds relatively small costs. This is reinforced by initial expost studies (Cecchetti, 2014; Bridges et al., 2014).

Our results are also informative for this macro modelling setting, since they can be used as calibration inputs in two ways. First, modelling each safety-net tool individually allows determining their contribution to total loss absorption. This can replace the exogenous assumption about these shares in Breuss et al. (2015). Second, although not presented in this study, the SYMBOL modelling framework allows some assessment in the reduction of the probability of a systemic crisis due to the introduction of the safety-net,5 which is a necessary ingredient to assess its macroeconomic benefits (e.g. Bank of England, 2012; European Commission, 2012b).

The remaining of this work is organized as follows. Sectio 2 presents the methodology, including a summary of the modelling assumptions and a description of the way the safety-net is implemented in our framework. Section 3 presents the dataset. Section 4 shows the results and robustness checks, while the last section concludes. Finally, the Annexes present a technical description of the SYMBOL model, some additional results, and technical details on the construction of one of our correlation matrices.

2. Methodology

2.1. The SYMBOL model

We use the SYMBOL model to simulate losses in a given banking system. The model fits within the Basel framework for banks' minimum capital requirements. The loss distribution of an individual bank depends upon an estimated (average) implied obligor probability of default (IOPD) in each bank's portfolio. The IOPD is basically a function of an adjusted Risk-Weighted Asset (RWA)

5 See the discussion related to the reduction in the probability of excessive public

finance costs of a banking crisis (risk heat-map) in Benczur et al. (2015).

ARTICLE IN PRESS

4 P. Benczur et al. / Journal of Financial Stability xxx (2016) xxx-xxx

Total capital Ball-in tool Resolution fund (up to 5% TA) Possible additional tools Bail-in, RF and/or DGS

Together 8% TA

Fig. 1. Order of intervention of the safety-net tools. Note: TA: total assets, RF: Resolution Funds, DGS: Deposit Guarantee Scheme.

density (its ratio to Total Assets, TA). Failure of a bank is determined by comparing the size of simulated losses and the regulatory capital available to absorb the shocks. Correlated bank losses are generated via Monte Carlo simulations using the Basel Internal Rating Based (IRB) function (see Basel Committee on Banking Supervision, 2005, 2006, 2010 rev. 2011, 2013; Vasicek, 2002; Merton, 1974).The correlation exists either as a consequence of the banks' exposure to common borrowers or, more generally, to a particular common factor (for example, the business cycle); and it can also represent contagion among the banks.6 De Lisa et al. (2011) highlight the importance of this assumption in shaping the extreme tails of loss distributions. One of our objectives with this paper is to explore the robustness of the Commission's ERFRA exercise to this key ingredient. Section 4.3.2 discusses the correlation structures we apply, and Annexes 1 and 3 contain additional technical details.

For the purpose of the present exercise, each Monte Carlo simulation ends when 100,000 runs with at least one bank failure are obtained. The large number of runs with at least one bank failure ensures a sufficient degree of stability in the extreme tail of the loss distributions. As a consequence, the model needs to run for a few hundreds of thousands of iterations for more than 3000 banks, which is a major computational challenge (Muresano and Pagano, 2014).

The loss distribution is simulated based on the following assumptions:

• SYMBOL approximates all risks as if they were credit risk; no other risk categories (e.g. market, liquidity or counterparty risks) are explicitly considered.

• SYMBOL implicitly assumes that the IRB formula adequately represents (credit) risks that banks are exposed to.

• All events happen at the same time, i.e. there is no sequencing in the simulated events.

The technical steps of the SYMBOL model are detailed in Annex 1. Benczur et al. (2015) also contains some further details and extensions.

2.2. The safety-net cascade

The full array of safety-net tools that can intervene to cover losses and recapitalization needs, hence protecting public finances, includes bail-in, Resolution Funds (RF), Deposit Guarantee Schemes (DGS), and the improved standards on minimum capital requirements and capital conservation buffer set up in the CRR/CRD IV package.

Their modelled order of intervention, reflecting the adopted Directive (European Parliament and Council, 2014), is sketched in Fig. 1. Countries in the EU will have to implement the bail-in tool

6 The SYMBOL model includes an optional module forsimulating direct contagion between banks, via the interbank market. When the module is turned on, additional losses proportional to interbank market exposures to an insolvent bank are added on top of the losses generated via the Monte Carlo simulation, potentially leading to further bank insolvencies. In the current analysis, we do not consider direct interbank contagion, as explained in Section 3.3.

by January 2016, national resolution funds will be collected over a time period of 10 years, starting from 2015, and the single resolution fund will be collected over an 8 years period, starting from 2016.

According to the BRRD, under the bail-in tool, a minimum amount of losses, equal to 8% of total liabilities plus own funds (here measured by total assets) needs to be covered by shareholders and unsecured creditors (first two boxes in Fig. 1) before other tools can intervene. Then, if the minimum threshold of 8% TA is satisfied and if the resolution authority agrees to intervene, the RF can contribute to the resolution by absorbing losses up to 5% of the total assets of the failing bank (third box in

Fig.1).

The total size of RF ex-ante funds equals 1% of the country-level amount of covered deposits.7 In the present exercise we will consider two possibilities: one where the single resolution fund is in place for countries participating in the banking union, and another where each country has its national resolution fund.

After this, the order of intervention of the remaining tools is subject to the discretion of the resolution authority. For instance, additional bail-in tools could be used, the residual resolution funds could be called to cover losses above 5% total liabilities (including own funds) and/or parts of the deposit guarantee schemes could also intervene as the last tool, though their funds cannot be used for recapitalizing banks. For the purpose of the present exercise, we consider only the tools in the grey boxes, as the remaining ones are subject to the authorities' discretion. Moreover, one would also need bank-level data on covered deposits for assessing the intervention of the DGS, which is not publicly available.

Given this regulatory framework, our analysis is based on the following assumptions for the design of the safety-net:

• As no data is available on the amount of unsecured liabilities held by each individual bank, we assume that all banks comply with the minimum 8% TA threshold of capital plus unsecured liabilities. In practice all banks with total capital lower than the 8% TA threshold are assumed to meet it via bail-inable liabilities. In case a bank holds capital higher than this threshold, there would be no bail-in, and the whole capital will be used to bear losses. Additional unsecured liabilities on top of this minimum is not accounted in the analysis, as our dataset contains no data on its size. One should note that the BRRD requires that banks meet a minimum requirement for own funds and liabilities eligible for bail-in. This amount will be set on a case-by-case basis by resolution authorities, based on selected criteria set out in the BRRD. It could thus be expected that the resolution authority will require banks, and especially large ones, to hold more than our assumed minimum threshold. This is also aligned with the discussion on the total amount of loss absorbing capacity for global systemi-cally important banks launched by the Financial Stability Board (2014).

• According to the BRRD, the final decision on the use of resolution funds is left to the resolution authority. As this discretion cannot be mathematically modelled and since our analysis focuses on a severe crisis, in the present exercise the resolution fund is assumed to intervene whenever necessary.

• In line with the objectives of the BRRD, safety-net tools are assumed to be sufficient, by themselves, to ensure the orderly resolution of banks and thus prevent direct contagion effects in the system. In particular, we assume that all distressed banks are resolved and recapitalized.

7 Covered deposits are obtained from deposits eligible for protection by the DGS afterthe limit of coverage (100,000€ in European countries) is applied.

ARTICLE IN PRESS

P. Benczur et al. / Journal of Financial Stability xxx (2016) xxx-xxx

As already stressed, though not directly considered in this exercise, the additional tools in the dashed box of Fig. 1 are likely to further absorb losses. In Section 4, we also discuss on the amount of leftover funds in the resolution funds and DGS that remains available at the end of the cascade.

2.3. Technical steps of the safety-net cascade

The output of the SYMBOL simulation is a matrix of losses Ln,i, where n denotes a simulation run and i refers to a bank. Let us denote the expected loss for bank i by ELi (see the Annex 1 for further details). Capital is the first source to absorb unexpected losses (first box of Fig. 1). In this framework bank i is assumed to go into insolvency when simulated unexpected losses (Ln i -ELi) exhaust all available capital Ki, or in other terms, when it has positive excess losses:

Under the NRF, in each country C the RF has at its disposal a target fund equal to 1% of the amount of covered deposits (CovDep):

Failure :=ExcLn i = Ln i - EL. - K. > 0.

Moreover, we also consider recapitalization needs up to 8% of risk-weighted assets.8 This reflects the level of minimum capitalization under which a bank is considered viable under Basel rules, and the minimum level to which banks were recapitalized by public interventions in the past crisis.

Formally, the bank is assumed to be undercapitalized when

K - (Ln,i-EL,) < 8% • RWA{,

where RWAi denotes its risk-weighted assets. This leads to a matrix of excess losses plus recapitalization needs (ExcLRni):

ExcLRn i = max{Ln i - EL, - K{ + 8% • RWA{, 0}.

To save on terminology, we refer to these as financing needs hereafter.

In case capital is not sufficient, the bank makes use of its bail-in-able liabilities (Bailing, which are set such that its total loss absorbing capacity (LACi) is 8% of its total assets (TA^:

LAC{:=Bailin{ + K{ = 8% • TA{.

The bail-in able liabilities (second block in Fig. 1) are thus set equal to:

Bailin{ = max{LAC{ - K{, 0},

and leftover financing needs after bail-in-able liabilities intervene are:

LB { = max{ExcLRni - Bailin{, 0}.

In the next step (third block in Fig. 1), the RF intervenes and it can cover financing needs of bank i up to a ceiling equal to 5% of its total assets, thus financing needs of bank i pertaining to RF are:

LRF{ = min{LB,{, 5% • TA{},

while the remaining financing needs (LB { - LRF{) will remain uncovered.

In this step we consider two possibilities for the RF: it can operate via national compartments (NRF, National Resolution Fund) or there can be a single fund for all the banks participating in the banking union (SRF, Single Resolution Fund).

8 Recapitalization needs are estimated also for banks suffering from losses but

not exhausting all their capital (L„i - ELi >0 and Lni - ELi - Ki < 0). However it should be noted that recapitalization needs in simulations where no failure is observed are not included, since losses in these runs are not stored for computational reasons.

tnrf,c = 1% ^CovDep,,

i £ C

and the total financing needs that each NRF is assumed to absorb equal

Under the SRF the target is equal to:

TSRF = 1% • ^ CovDep{,

{£ Bankmg Umon

and the total financing needs that SRF is assumed to absorb equal

{£ Bank{ng Un{on

Ln = n,i

Summarising, in each run n the total leftover financing needs9 not covered by any of the considered tools are:

L^r = £(lb,{ - LRF{) + max{LfS - TSRF, 0} {

+ max{Lf,C - TNRF,C, 0} for the SRF,

C£Banking Union

Leftover = J2 (LBn{- L^) + J2 max{LfC - TNRF,C, 0} for the NRF.

Note that leftover financing needs in general contain both a recapitalization and an excess loss component. Since the former could be recouped later by selling the financial assets acquired, it does not represent a long-run fiscal cost. On impact, however, it still leads to a deterioration of public finances. Benczur et al. (2015) explore this distinction on a country level, and provide a detailed discussion.

3. Description of the data and scenarios

3.1. Description of the sample

The main ingredient to SYMBOL simulations and all the other computations is unconsolidated bank balance sheet data, coming from Bankscope, a proprietary database of banks' financial statements produced by Bureau van Dijk. Our dataset covers a near-full sample of commercial, cooperative and savings banks in EU 27 countries (more than 3000 banks). To maximize the sample size, we use robust imputation procedures of capital and risk-weighted assets variables (see Cannas et al., 2013b for more

9 Though, in case of fund exhaustion, aggregated financing needs remain unchanged, their value at single bank level depend upon the order of intervention of the RF. In case different orders would need to be considered (from largest to smallest banks, vice versa or random), leftover financing needs at single bank level would be given by the following:

LLeftover

Lrf, 0 V , 0 V + max{LB . - 5% • TAu 0},

where the inner max operator represents the residual fund after the RF intervened to cover financing needs of banks prior to bank i; the second addend represent the share of financing needs beyond the scope of the RF, if any.

ARTICLE IN PRESS

6 P. Benczur et al. / Journal of Financial Stability xxx (2016) xxx-xxx

Table 1

Sample used for the simulations: EU 27 aggregated amount of selected variables.

Capital and risk-weighted assets are adjusted for Basel III definitions. Population total assets exclude branches.

Year Banks' sample bn € Population total assets bn €

Number of banks Total assets Risk-weighted assets Capital Coverage ratio

2007 3265 26,848 13,701 1047 76% 35,552

2009 3250 29,214 13,258 1230 78% 37,483

2012 3086 30,086 12,284 1289 75% 40,036

Source: Bankscope and Schoenmaker and Peek (2014).

technical details). European Central Bank data on aggregated banks' total assets for the EU (as reported by Schoenmaker and Peek, 2014) are used as the statistical population to calculate the sample coverage ratio, defined as the share of aggregated total assets in the sample compared to European Central Bank aggregated figures. The sample coverage ratio is used to rescale from the sample to the population losses obtained in the various steps of the exercise.

Table 1 presents some descriptive statistics for selected input variables. Data used for the present exercise are as of 2007, 2009 and 2012, and they refer to EU 27 banks. This choice allows us to run simulations using balance sheet data "before the crisis", "during the crisis", and "after the crisis". The last two columns compare the total assets in the sample with the total assets from the population of banks and figures show that the sample accounts for around 75-80% of the population.

It should be noted that capital levels and risk-weighted assets used in the simulations are adjusted with respect to original balance sheet data to account for the new Basel III definitions (figures in Table 1 account for these corrections), as will be detailed in Section 3.2.

Besides the change in the number of banks over the three years considered, one can observe a general increase of total assets and a much higher increase of capital, together with a reduction of risk-weighted assets. This broad trend of deleveraging and offloading risks is also noted in existing studies and analyses (see for example, the 2014 Banking Structures Report of the ECB). In terms of implications for our exercise, a decrease of risk-weighted to total assets is expected to decrease banking losses, while increased capitalization would further reduce the need for additional safety-net or public finance interventions.

Data on covered deposits at country level are key to determine the amount of funds available to the RF. Since they are only available in supervisory databases, we use the ratios of covered deposits over customer deposits from Campolongo et al. (2011) and Cannas et al. (2013a).

The choice of using unconsolidated data for our analyses is based on a series of motivations that we briefly discuss here.10 First, consolidated data can also include non-EU activities of large banking groups, while our focus is on within-EU activities only. Second, consolidated data can be hardly reconciled with safety-net elements defined at the national level, particularly national resolution funds in countries outside the banking union. These are also the two main reasons why existing impact assessments (as listed in the introduction) are based on unconsolidated data. Third, consolidation leads in general to a decrease in risk weighted assets and capital and to a complete pooling of bail-in instruments. Though there is indeed some pooling and sharing of risks within a banking group, including parental support in particular, a complete pooling is unrealistic. Section 4.3 further discusses some quantitative implications of using the consolidated sample and argues that the results

10 We have built a consolidated counterpart sample for 2012 using SNL Financial which includes 235 banks covering 80% of total assets.

Table 2

EU average capital (K) and risk-weighted assets (RWA) adjustments by banking group due to the Basel III rules implementation.

G1 banks G2 banks

QISRWA(2012) 1.128 1.102

QISK(2012) 0.71 0.76

QISRWA(2009) 1.245 1.041

QISK(2009) 0.72 0.82

Source: European Banking Authority (2013), Committee of European Banking Supervisors (2010).

based on the unconsolidated sample represent a more conservative estimate of the performance of the safety-net.

3.2. Capital and risk-weighted assets adjustments

The crisis has brought forward, among other issues, the fact that the quality of banks' capital was poor and that banks' risks weights were not adequately calibrated under Basel II. Basel III rules were introduced to tackle these problems (Basel Committee on Banking Supervision, 2010 rev 2011). Since Basel III definitions of risk-weighted assets and capital better reflect the true risk and capital quality, we adjust the SYMBOL inputs to take into account the differences between the data in the balance sheet and those that would have been declared if Basel III had been already implemented. Corrections are based on the European Banking Authority and the Committee of European Banking Supervisors yearly exercises (Quantitative Impact Study, QIS), assessing and monitoring the impact of the new capital standards on European banks' balance sheet data. In particular, the studies estimate what would be the average correction factor to move from reported capital and risk-weighted assets to a framework compliant with the new rules.

Table 2 shows the multiplicative adjustments applied to the data before running the simulations. As no monitoring exercise was conducted in 2007, capital and risk-weighted assets for 2007 are corrected using 2009 adjustments. Banks are differentiated on the basis of their capital size: G1 banks are those whose Tier1 capital is larger than 3 billion € , while all other banks are G2. In the following capital and risk-weighted assets refer to the adjusted figures.

It is worth noting that, according to figures shown in Table 2, the true amount of capital of good quality (i.e. capable to absorb losses) was indeed much lower than the reported Basel II values, and the definition of risk-weighted assets did not adequately capture some risks potentially faced by the banks. For this reason, we use the adjusted values of RWA and capital also to calculate the IOPD and bank losses (see Sections 2.1 and 2.2).

3.3. Scenarios implemented

The scenarios implemented in the present exercise are chosen to represent the situation in the EU banking sector without any tool in place (baseline), an intermediate situation where we assume that bail-in is implemented (scenario 1), and a final setting (scenario 2) with (nearly) full implementation of the EU legislation.

Scenario Capital Recapitalization levels RWA Bail-in RF

Baseline KBS(T)*QISK(T) 8%RWA(T) RWABS(T)*QISRWA(T) N N

Scenario 1 KBS(T)*QISK(T) 8%RWA(T) RWABS(T)*QISRWA(T) Y N

Scenario 2 max{KBS(T)*QISK(T); 10.5%*RWABS(T)*QISRWA(T)} 8%RWA(T) RWABS(T)* QISRWA(T) Y Y

• The baseline scenario is meant to proxy the situation at the inception of the crisis. Therefore in this scenario we limit ourselves to correct the level of risk-weighted asset and capital based on the QIS adjustments (see Section 3.2). Neither bail-in nor resolution funds are in place.

• In scenario 1 the bail-in tool is introduced.

• Scenario 2 assumes that banks are fully compliant with Basel III rules. This includes correction to the definitions of risk-weighted assets and capital, and topping their capital up to the 10.5% of risk-weighted assets, i.e. each bank is assumed to hold at least the minimum capital requirements (MCR) plus the capital conservation buffer (CCB) in full compliance with CRR/CRD IV rules, while keeping any excess buffer. Both the bail-in tool and the resolution funds are in place.

The choice of the scenarios aims to reflect the timing and main steps of the implementation of the legislation. Table 3 summarizes the details of the scenarios.

Let us stress that we do not allow for direct (interbank) contagion in any of the scenarios. Our baseline scenario aims to reproduce what happened during the financial crisis in 2008, where a full government bail-out took place and prevented domino effects through the interbank market. In the other scenarios the safety-net is assumed to be able to prevent contagion by not allowing any distressed bank to spread losses in the system.

The Commission's ERFRA exercise quantified the reduction in losses between a scenario with no bail-out in place (contagion, no safety-net, Basel II and also Basel III capital requirements) and the case where the safety-net is implemented (and contagion is eliminated). In that case, the overall reduction in losses accounted for two effects: eliminating contagion and including the safety-net tools. Given our interest in assessing the reduction in the need for future bail-outs, our paper only evaluates the second, since the first was actually eliminated by the bail-out itself.

Fig. 2. Simulated distribution of financing needs of EU banks, baseline, as a share of EU GDP.

D was also provided to the financial sector via asset reliefs during the same period. These figures lead to an estimate of total financing needs due to the crisis of up to 600 billion D . A simulated figure compatible with the above is observed between the 99.9th and 99.95th percentiles of the distribution of financing needs as of 2009 (see Table 4).11

4.2. Safety-net scenarios

When evaluating alternative scenarios, we use the baseline as reference for ordering the simulation runs and we sort the values of all other distributions accordingly. More specifically, we implement the following:

4. Results: simulated loss distributions under different safety-net scenarios

4.1. The baseline scenario

Table 4 shows the distributions of financing needs after the use of capital available to banks for 2007, 2009 and 2012. One can see that these distributions are zero up until the 80th percentile, after which there is a steep increase. When using different data vintages, we observe a notable decline in the distribution moving from the inception of the crisis to recent years. This reflects the gradual improvement of the EU banking sector. Fig. 2 offers a graphical comparison of the three distributions.

To facilitate the comparison of financing needs among different scenarios, it is useful to select a particular percentile from the distribution and focus all the analyses in its surroundings: then one can compare individual numbers instead of full distributions. We select a percentile that corresponds to a situation which is similar to the last crisis. To this aim we use data on state aid to the financial sector during the recent crisis (2008-2012): the total amount of recapitalization measures in the period 2008-2012 was 428 billion D (European Commission, 2014b). A total of roughly 180 billion

1. We sort the aggregated distribution of ExcLRnii run under the baseline scenario.

2. In the other scenarios, we order the simulation runs based on the same ranking as in 1; then we implement the safety-net cascade bank by bank; finally we aggregate on the system.

3. As the outcome of the step above may not be monotonically increasing, we smooth the distributions via a Hodrick-Prescott

11 It is important to note that being at the 99.95th percentile does not mean that the event happens with a probability of at most 0.05 percent. It is more appropriate to think about the SYMBOL (and also the Basel) probabilities as "theoretical probabilities". The Basel II criteria are such that an institution is expected to suffer losses that exceed its capital on average once in a thousand years (a confidence level of 99.9%). The regulation acknowledges that "the high confidence level was also chosen to protect against estimation errors, that might inevitably occur from banks' internal probability of default, loss given default and exposure at default estimation, as well as other model uncertainties" (see Basel Committee on Banking Supervision, 2005). Laeven and Valencia (2013) identifies 17 systemic banking crisis episodes in the period 2008-2011 worldwide, and 147 episodes since 1970. Based on this, it is safe to say that the Basel models tend to under predict the actual frequency of bank defaults, which then carries over to model estimates. Theoretical probabilities cannot be thus taken literally as frequencies. Their relative magnitudes, however, can inform us whether one bank or one country is at higher risk than another.

ARTICLE IN PRESS

8 P. Benczur et al. / Journal of Financial Stability xxx (2016) xxx-xxx

Table 4

EU distribution of financing needs, baseline scenario. Percentiles 2007 2009 2012

Billion € GDP share Billion € GDP share Billion € GDP share

80 0.0 0% 0.0 0% 0.0 0%

82 184.3 1.5% 0.0 0% 23.8 0.2%

84 208.9 1.7% 50.6 0% 31.1 0.2%

86 226.2 1.8% 79.0 0.7% 37.0 0.3%

88 242.5 2.0% 94.7 0.8% 43.2 0.3%

90 259.2 2.1% 109.4 0.9% 50.0 0.4%

95 319.0 2.6% 157.2 1.3% 76.7 0.6%

97.5 384.8 3.1% 207.2 1.8% 109.2 0.8%

99 486.1 3.9% 287.8 2.4% 166.3 1.3%

99.5 573.6 4.6% 358.6 3.0% 220.7 1.7%

99.9 815.1 6.6% 562.6 4.8% 385.7 3.0%

99.95 933.6 7.5% 675.3 5.7% 477.7 3.7%

99.99 1239.3 10.0% 939.9 8.0% 723.8 5.6%

99.995 1394.5 11.2% 1072.0 9.1% 884.6 6.8%

99.999 1670.2 13.4% 1282.3 10.9% 1147.3 8.9%

99.9999 2195.0 17.7% 1737.1 14.8% 1478.0 11.4%

100 2253.7 18.1% 1958.7 16.6% 1529.2 11.8%

filter to eliminate any potential noise due to the reordering. This

method has proven to be quite reliable and robust in general.

We focus our analysis on percentiles in the neighbourhood of the crisis (99.95th percentile), to evaluate how the introduction of different tools can reduce the financing needs not absorbed and potentially hitting public finances. Table 5 presents our main results for year 2012 data. The numbers at the 99.95th percentile suggest the following:

• Introducing the bail-in has the effect of reducing leftover financing needs by up to two thirds: from 3.7% to 1.4% of the GDP in scenario 1, and from 2.7% to 1.0% of the GDP in scenario 2.

• Regarding the effect of the increased capital level as of Basel III, we see that when moving from baseline to scenario 2, financing needs are reduced by one-third (from 3.7% to 2.7% of the GDP).

• The introduction of NRF further halves the leftover financing needs after bail-in (from 1.0% to 0.5% of the GDP). The introduction of the SRF has the effect to lower these levels even further (from 67.6 billion € to 59.4 billion €, both being roughly 0.5% of GDP). This is because a pooled system can reallocate unused funds from a country being less severely hit towards another being more severely hit.

Overall, our results show that financing needs not absorbed by the safety-net and potentially leading to a government bail-out decrease considerably when all the tools are in place. In this sense, the new EU bank regulatory framework constitutes a "farewell to bail-out".

Moreover, supervisors have additional tools - and the flexibility on how to use them - to absorb the residual financing needs, including additional capital buffers foreseen in CRR/CRDIV (e.g. buffers for global systemically important banks and the countercyclical buffer), additional bail-in on top of the 8% minimum, the leftover resolution funds plus additional extraordinary ex-post contributions12 and, only when other means deployed, the Deposit Guarantee Scheme funds.

As an example, we have calculated the amount of leftover resolution funds after the entire safety-net has intervened

12 The resolution authority could request banks to provide additional funds for resolution purposes. Looking at a worst-case scenario from a fiscal point of view, we do not model the possibility of ex-post contributions to the national/single resolution fund. Since they can go up to 3 times the ex-ante contributions, this could further reduce the impact on public finances.

Fig. 3. 2012 breakdown of unexpected losses absorbed by available tools, at the 99.95th percentile. Note: In the left bar, the white area refers to the excess capital buffer (above the minimum requirement). The dashed area in the middle is the minimum regulatory capital, while the chequered area refers to excess losses.

(extraordinary contributions are not considered in this estimate). This would be roughly 0.15% of the EU GDP when NRFs are in place, and it would decrease to 0.1% of GDP when the SRF is in place. These loss absorbing capacities would further increase when we consider also the share of the DGS funds that could be used to fund resolutions: in this case the total available funds (part of DGS plus leftover RF) would be around 0.4% and 0.3% of the EU GDP when, respectively, NRF and SRF are in place.

Fig. 3 visualizes the role of the various safety-net tools in absorbing unexpected losses (Ln i - ELi), see Eq.(1).The left bar corresponds to the baseline scenario, where only capital (corrected via the QIS factor) can absorb losses. Its contribution consists of two parts: the excess capital buffer (white area), and the minimum regulatory capital (dashed area). On top of this, we have excess losses (chequered area). Banks need financial assistance not only to cover excess losses, but also to rebuild their minimum capital. This total financing need is indicated by grey. Without the implemented safety-net, this would most likely be covered by a public bail-out. Note that the recapitalization part of the bail-out is a public finance cost in the short term (it would increase the gross debt of the country), but there is a corresponding asset, which can be sold later to recoup this part.

ARTICLE IN PRESS

P. Benczur et al. / Journal of Financial Stability xxx (2016) xxx-xxx 9

Table 5

2012 EU distributions of financing needs for all the scenarios, share of EU GDP.

FN stands for financing needs. Scenario 1 financing needs after capital are identical to baseline financing needs after capital since the capital levels are equal. LAC: loss absorbing capacity, SRF: Single Resolution Fund, NRF: National Resolution Fund.

Percentiles Baseline: no new legislation Scenario1: bail-in Scenario2: bail-in, Basel III, RF

Initial = FN Initial = FN Final = FN after Initial = FN Intermediate» FN Final A = FN Final B = FN

after capital after capital LAC after capital after LAC after SRF after NRF

80 0% 0% 0% 0% 0.0% 0.0% 0.0%

82 0.2% 0.2% 0.0% 0.0% 0.0% 0.0% 0.0%

84 0.2% 0.2% 0.0% 0.0% 0.0% 0.0% 0.0%

86 0.3% 0.3% 0.0% 0.0% 0.0% 0.0% 0.0%

88 0.3% 0.3% 0.1% 0.0% 0.0% 0.0% 0.0%

90 0.4% 0.4% 0.1% 0.0% 0.0% 0.0% 0.0%

95 0.6% 0.6% 0.2% 0.1% 0.0% 0.0% 0.0%

97.5 0.8% 0.8% 0.3% 0.3% 0.1% 0.0% 0.0%

99 1.3% 1.3% 0.4% 0.6% 0.2% 0.0% 0.1%

99.5 1.7% 1.7% 0.6% 0.9% 0.3% 0.0% 0.1%

99.9 3.0% 3.0% 1.1% 2.0% 0.7% 0.2% 0.3%

99.95 3.7% 3.7% 1.4% 2.7% 1.0% 0.5% 0.5%

99.99 5.6% 5.6% 2.3% 4.4% 1.7% 1.2% 1.2%

99.995 6.8% 6.8% 2.7% 5.4% 2.1% 1.5% 1.5%

99.999 8.9% 8.9% 4.3% 8.2% 3.5% 2.9% 2.9%

99.9999 11.4% 11.4% 5.0% 9.5% 4.2% 3.6% 3.6%

100 11.8% 11.8% 5.2% 9.7% 4.3% 3.7% 3.7%

The middle bar, corresponding to scenario 1, shows that the bail-in substantially reduces leftover financing needs. Bail-in takes up part of excess losses and part of recapitalization needs (the split is not shown on the figure), leaving the remaining parts (if any) to a potential bail-out. Finally, when moving to scenario 2, both the increased minimum capital requirements and the additional tools help further reduce leftover financing needs.

Our finding of the effectiveness of the bail-in tool matches the results of Galliani and Zedda (2014), who find that bail-in is very successful in absorbing bank losses in selected European countries, and in particular it mitigates the banking-sovereign loop. It is nevertheless difficult to perform a direct quantitative comparison of the two sets of results. Galliani and Zedda (2014) present the expected value of financing needs conditional on at least bank failure in each simulation run, while we look at a much more extreme measure, the 99.95th percentile. They thus have much lower financing needs before bail-in, and hence this tool can absorb almost all losses (95/97% of losses depending on the considered country). They also present simulations under a setting where direct contagion via the interbank market is not stopped by the safety-net. In that case, bail-in reduces the average conditional financing needs by 45-75%.

4.3. Robustness checks

We next perform some robustness checks. The first exercise implements the safety-net scenarios using different data vintages, namely 2007 and 2009 data. The second exercise tests different correlation structures among banks. Detailed results are available in Annex 2, here we only discuss the broad results. In particular, we only focus on the 99.95th percentile values.

In addition, we also perform a robustness check to test how results vary when using consolidated data (complete results are not reported but are available upon request). Based on a sample of 235 EU 27 banks accounting for 80% of the population total assets, we find that financing needs in the baseline and in the Basel III scenario are similar to the ones obtained using unconsolidated data. Financing needs after bail-in and after the entire cascade are instead much lower for consolidated data. In terms of the proportional contributions of individual tools, moving to the consolidated sample increases substantially the impact of bail-in. The contribution of the RF also increases but to a smaller degree. The impact of CRDIV remains almost the same.

Fig. 4. Comparison over years of the leftover financing needs after each safety-net tool in each scenario, 99.95th percentile, share of EU GDP.

The main difference is thus in the impact of bail-in, the consolidated sample leading to a much better performance of this tool. While in general we prefer the conservative estimate based on the unconsolidated sample, there are some aspects of the consolidation process which lead to an overestimation of the impact of this tool. In particular the consolidated sample has lower excess capital and thus increased bail-in capacity.13 Moreover consolidation implies that distressed banks in a banking group can make use of any residual bail-in available at group level.14

4.3.1. Different vintages

Fig. 4 displays the impact of the choice of the data vintage on the evolution of leftover financing needs, moving from 2007 (black bars) to 2012 (light grey bars). As expected, financing needs after capital in all scenarios are higher in the earlier years, as the EU banking sector has been continuously becoming less risky (see also

13 The bail-in capacity is in our modelling framework the difference between the 8% total assets threshold and the amount of total capital.

14 Consider two banks, A and B that form a group. Suppose that A is risky, and B is much less so. When looking at them in an unconsolidated way, the financing needs of A would be taken over by bail-in, but it would stop at 8% of its own total assets; Bank B, on the other hand, would be left with unused bail-in capacity. When looking at the group level, bail-inable funds of bank B would be called in to bear losses for bank A.

ARTICLE IN PRESS

P. Benczur et al. / Journal of Financial Stability xxx (2016) xxx-xxx

Fig. 5. Comparison over years of the relative reduction in financing needs due to the various tools, 99.95th percentile.

Bologna et al., 2014; Cohen and Scatigna, 2014). This is also true after bail-in and after RF. Under Basel III capital requirements (scenario 2), the differences are much smaller.

It is also instructive to compare proportional changes between and within scenarios across different data vintages. We look at three such measures. The effect of Basel III capital requirements is obtained by comparing the reduction in financing needs after capital between the baseline and scenario 2. The effect of bail-in can be assessed by calculating the relative difference in (i) financing needs after capital in the baseline and those after bail-in in scenario 1, or (ii) financing needs after capital and those after bail-in in scenario 2 (two different capital levels). The effect of the (S)RF is the relative difference in financing needs after bail-in and after RF in scenario 2.

The left panel of Fig. 5 shows that the effect of increased minimum capital requirements is higher in 2007 and 2009. This is because scenario 2 involved a topping up of capital to Basel III minimum capital requirements (as discussed in Section 3.3), and its size is larger for the earlier years. The effect of the bail-in tool, on the other hand, is almost identical across years (middle panel), while the impact of the RF is similar in 2009 and 2012, and is smaller in 2007.

4.3.2. Different correlation structures

De Lisa et al. (2011) demonstrated that the degree of correlation among banks has a major impact on the extreme tail percentiles of the distribution of DGS losses, which increase strongly as the correlation coefficient increases. In our exercise, however, we are looking at banks from multiple countries, which calls for a distinction between within- and between-country correlations (entering in Step 2 of SYMBOL, as detailed in Annex 1). Results presented so far have been obtained imposing an equal correlation of 0.5 among all banks, regardless of their country of operation. In terms of the full correlation matrix E1:

i =] i=j

The calibration of E1 is based on the analysis of Sironi and Zazzara (2004) for Italy, who estimated this value using asset price developments for Italian banks. This choice was applied in a country by country simulation setup in the Commission's ERFRA exercise, which is our main starting point. Having developed a method to simulate all EU banks together, we then adopted this assumption for all banks.

In this section we consider three other correlation matrices, with the objective of exploring the robustness of the ERFRA results. Our choices are only illustrative, demonstrating potential directions of departure from E1. The correlation matrix E2 sets the correlation factor to 0.5 for all banks belonging to the same country, and to zero among banks belonging to different countries. This means that there is no common component of banking shocks in different countries. The correlation matrix E3 represents an intermediate situation where banks belonging to the same country have a correlation factor equal to 0.6 and banks belonging to different countries have a correlation factor equal to 0.3. This allows for a common component across countries, but banks of the same country are still subject to a higher degree of commonality. The possibility of imposing a different correlation between banks within the same country and banks in different ones represent an improvement over versions of SYMBOL used in all previous applications.

Formally:

[^2lij =

10.5 0

i =j a Ci = Cj i=j A Ci = Cj

[^3lij =

0.6 0.3

i = j A Ci = Cj i =j A Ci = Cj

where i and j are two banks in the sample and Ci and Cj are the corresponding countries.

The fourth correlation matrix E4 tries to refine the pattern of cross-country correlations, by using information on cross-country exposures published by the Bank for International Settlements (BIS).15 The full details of its construction are reported in Annex 3, here we only briefly summarize the main ingredients. Our starting point is E3, and we want to introduce some differences in the degree of co-movements among different countries, guided by the BIS data on cross-country exposures.

First we created a matrix of cross country exposures, as a proportion of total assets in the home country. To obtain a symmetric matrix, we took the average of the i - j and j - i values. Then we divided country pairs into low, medium and high exposure groups, with assumed correlation values of 0.3, 0.4 and 0.5. The within-country correlation was kept at 0.6. The implied matrix, however, is not necessarily a proper correlation matrix.16 To solve this problem, we used the alternating projection method of Higham (2002) to compute the nearest symmetric positive definite ("proper") correlation matrix. The final correlation matrix is similar to E1.

Fig. 6 shows the results for 2012 for all the investigated correlation structures (results for 2007 and 2009 are available upon request). When comparing results with E1 and E2, we find that imposing the same asset correlation within and between countries leads to larger financing needs. For instance, baseline financing needs obtained with E2 (light grey bars) are roughly 40% of those obtained using E1 (dark grey bars). Moreover, final financing needs after the SRF intervention obtained with E2 are 26% of those obtained using E1. Our choice for E3 (medium grey bars) leads to results in between the other two choices. Relative to E1, E3 has a higher within-country correlation and a lower between-country correlation. For the 99.95th percentile, the latter dominates and leads to lower financing needs. Results obtained with E4 are very close to those obtained with E1. Relative to E1, results with E4 are higher, demonstrating again that a higher degree of correlation leads to higher values at extreme tail percentiles.

Though the different correlation matrices have a sizable effect on the absolute level of our results, we find a very different pattern when we look at the proportional changes between and within

15 Available at http://www.bis.org/statistics/consstats.htm.

16 Intuitively, it might happen that country A has high exposures with all other countries, but then this puts a lower bound on the correlation among all other country pairs, which is not necessarily reflected in their direct cross-exposures.

ARTICLE IN PRESS

P. Benczur et al. / Journal of Financial Stability xxx (2016) xxx-xxx

Fig. 6. Comparison over different E ofthe leftover financing needs after each safety-net tool in each scenario, 99.95th percentile, share of EU GDP, 2012.

Fig. 7. Comparison overdifferent E ofthe relative reduction in financing needs due to the various tools, 99.95th percentile, share of EU GDP, 2012.

scenarios. As shown in Fig. 7, the relative impact of the various elements of the safety-net is remarkably stable across the four different correlation matrices.

Overall, the robustness exercises show that though estimated percentiles may depend sizably on various modelling choices, the proportional changes are remarkably stable. This is particularly true about the standalone impact of the bail-in tool: in all cases, it leads to a roughly 60% reduction in public finance costs. At the same time, we do not view any of the implemented correlation structures as adequately capturing the commonality in banking shocks and believe that further work is warranted on this issue. We are currently working on two main improvements: using better interbank network data to refine the direct contagion module of SYMBOL; and extending Sironi and Zazzara (2004) to all EU banks in order to assess the broad co-movement of bank asset values. However, both would be out of the scope of our current exercise.

bail-in and resolution funds. We assumed that the safety-net is able to resolve every distressed bank, hence there would be no bank failure and direct contagion through interbank market. Then we looked at a particular percentile of this distribution (99.95), corresponding to a systemic crisis comparable to the recent one.

We find that the introduction of this safety-net leads to a "farewell to bail-out" by bringing about a sizable reduction in the financing needs not absorbed by available tools, which could potentially be covered by public finances during periods of severe financial distress. The estimated total reduction in financing needs not absorbed by any tool is around 90%. Within this overall reduction, increased capitalization, including the capital conservation buffer, seems to be able to decrease financing needs by about 30%. Bail-in seems to play an even larger role, reducing them by around 60%. The resolution fund helps further, with a single resolution fund being slightly more efficient than a set of national resolution funds.

In our analysis we have also checked that results remain robust with different data vintages and with different correlation structures among banks. It is particularly true about the standalone contribution of bail-in.

Though we view this as a strong justification for the recent financial sector reform agenda, our analysis does not address two important issues. First, where would the very large amount of financial needs, and especially of excess losses, potentially absorbed by bail-in end up (see Fontana et al., 2015b)? In case the holders of bail-in liabilities were still in the banking or the shadow banking sector, or they were systemically important financial institutions, bail-in could in fact re-introduce contagion among financial institutions.

Second, what are the costs of the safety-net? Ex-ante studies seem to rather unanimously find limited macro-economic costs of the reforms (see Macroeconomic Assessment Group, 2010; Miles et al., 2012; Bank of England, 2012; European Commission, 2012b). This is reinforced by initial ex-post studies (Cecchetti, 2014; Bridges et al., 2014). In our view, however, patterns of lending activities and funding costs of banks will need to be monitored continuously once the reforms will be fully implemented. In particular, even limited impacts could be felt asymmetrically in certain segments of the banking sector, its customers or its investors (small and medium enterprises, for example). We believe that further research in these areas is needed.

Disclaimer

The views expressed are the author's alone and do not necessarily correspond to those of the European Commission. Possible errors and omissions are those of the authors.

Acknowledgements

The authors wish to thank the editor and two anonymous reviewers for helpful comments, which led to substantial improvements in the paper. The authors would also like to thank Andrea Pagano for the valuable support to the development of this paper.

5. Conclusions

Annex 1: Steps ofthe SYMBOL model.

In this work we assessed how the safety-net tools proposed in the EU legislation strengthening the financial system reduce financing needs (excess losses and recapitalization needs) that originate in the banking sector and can potentially hit public finances. We built upon a well-established micro-simulation model (SYMBOL), which uses banks' balance sheet data to simulate the joint distribution of banking losses. For any realization of banking losses, we applied the safety-net tools in line with the legislation adopted by EU institutions, in particular increased capital requirements,

STEP 1: Estimation ofthe Implied Obligor Probability of Default of the portfolio ofeach individual bank.

The main ingredient of the model is the average implied obligor probability of default of a bank. It is a single parameter describing its entire loss distribution. It is obtained by numerical inversion of the Basel IRB formula for credit risk, based on total minimum capital requirements declared in the balance sheet. Individual bank data needed to estimate the implied obligor probability of default are

ARTICLE IN PRESS

P. Benczur et al. / Journal of Financial Stability xxx (2016) xxx-xxx

banks' risk-weighted assets and total assets, which can be derived from the balance sheet data. We present a brief overview of the main ingredients below. Benczur et al. (2015) offer some additional details and discussion.

For each exposure l in the portfolio of bank i, the IRB formula derives the corresponding capital requirement CR, i needed to cover unexpected losses17 over a time horizon of one year, with a specific confidence level equal to 99.9% (see Fig. A1.x):

crij (pdij) =

lgd • n

1 -r(pdij)

n-1(pdu)

+V î-SPDL n-1(0 999)J-pd^lgd

•m(pdij ),

where PDi,l is the default probability of exposure l, R is the correlation among the exposures in the portfolio, defined as

1 e-50PD ( i e-50PD

R(PD) = 0.12 • „ +0.24 •( 1 - e

1- e-50

1- e-50

-0.04 • 1 -

S-5 ~45T

with obligor size S =50.

Here LGD is the loss given default18 and M(PD,j) is an adjustment term, defined as

M(PDu ) =

(1 +(M -2.5) •biJ) -1.06 1 -1.5 •bil

with bil = (0.11856 - 0.05478 • ln(PDu))2 and maturity M = 2.5. Note that here all parameters are set to their regulatory default values.

The minimum capital requirement of each bank i is obtained summing up the capital requirements for all exposures:

MCRj = CRi,l • Ai.l

where Ai,l is the amount of the exposure l.

As there are no available data on banks' exposures towards each obligor, the model estimates the default probability of a single obligor (implied obligor probability of default, IOPD) equivalent to the portfolio of exposures held by each bank by inverting the above formulas. Mathematically speaking, the model computes the IOPD by numerically solving the following equation:

CR(!OPDi) = MCRi,

where MCRi and ^iA,i are respectively the minimum capital requirement, set equal to 8% of the risk-weighted assets, and the total assets of the bank. Note that capital and RWA are QIS-adjusted, as detailed in Section 3.2.

STEP 2: Simulation of correlated losses for the banks in the system

Given the estimated IOPD, SYMBOL simulates correlated losses hitting banks via Monte Carlo, using the same IRB formula and imposing a correlation structure among banks.19 The correlation

17 Banks are expected to cover their expected losses on an ongoing basis, e.g. by provisions and write-offs. The unexpected loss, on the contrary, relates to potentially large losses that occur rather seldom. According to this concept, capital would only be needed for absorbing unexpected losses.

18 Set in Basel regulation equal to 45%.

19 The asset value of each bank's debtors evolves according to XAik = + л/l

A) + у/1 - RAZAk. Here ZA,k is the idiosyncratic shock to the debtor, ßA is

Fig. A1.x. Individual bank loss probability density function. Note: MCR: minimum capital requirements, VaR: value-at-risk.

exists either as a consequence of the banks' exposure to common borrowers or, more generally, to a particular common factor (for

example, the business cycle). In each simulation run n = 1.....No,

losses for bank i are simulated as:

lni = lgd • n

]/т-щющN-1(|OPD') V Ï-S^^

where N is the normal distribution function, and N-1 (ani) are correlated normal random shocks with correlation matrix S (see Section 4.3.2 for its potential definitions).

STEP 3: Determination of bank failure

Given the matrix of correlated losses, SYMBOL determines which banks fail. As illustrated in Fig. A1.x, a bank failure happens when simulated obligor portfolio losses (L) exceed the sum of the expected losses (EL) and the total actual capital (K) given by the sum of its minimum capital requirements plus the bank's excess capital, if any:

Failure:=Ln,{ - EL{ - K{ > 0.

The light grey area in Fig. A1.x represents the region where losses are covered by provisions and total capital, while the dark grey one shows when banks fail under the above definition. It should be noted that the probability density function of losses for an individual bank is skewed to the right, i.e. there is a very small probability of extremely large losses and a high probability of losses that are closer to the average/expected loss. The Basel Value at Risk (VaR) corresponds to a confidence level of 0.1%, i.e. the minimum capital requirement covers losses from the obligors' portfolio with probability 99.9%. This percentile falls in the light grey area, as banks generally hold an excess capital buffer on top of the minimum capital requirements. The actual level of capital held by each bank i determines the failure event.

STEP 4: Aggregate distribution of losses for the whole system.

Aggregate losses are obtained by summing losses in excess of capital plus potential recapitalization needs of all distressed banks in the system (i.e. both failed and undercapitalised banks) in each simulation run.

Annex 2: Additional results.

The tables reported here show the details of the distributions of financing needs for the years 2007, 2009 and 2012 for the

the bank specific shock, while fi is a common component. The parameter p controls the degree of commonality in the shocks of two different banks.

ARTICLE IN PRESS

P. Benczur et al. / Journal of Financial Stability xxx (2016) xxx-xxx

correlation matrix E1, and for the year 2012 for correlation matrices E2, E3 and E4 (results for 2007 and 2009 are available upon request). Results are expressed as a share of EU GDP. Notes for the tables:

counterparties resident in other countries (called "Consolidated banking statistics" in the BIS database). In order to obtain a correlation matrix starting from these data, the following steps have been implemented.

• Scenario 1 financing needs after capital are identical to baseline financing needs after capital, since there is no change in banks' capitalization.

• LAC: loss absorbing capacity, SRF: Single Resolution Fund, NRF: National Resolution Fund, FN: Financing Needs.

See Tables A2.1-A2.5.

Annex 3: Steps to build a correlation matrix using cross-country exposures.

This approach makes use of information on cross-country exposures published by the Bank for International Settlements (BIS, http://www.bis.org/statistics/consstats.htm), in order to build a correlation matrix which allows some differentiation in the degree of co-movement of banking shocks in different countries.

The BIS publishes, on a quarterly basis, banking data which capture the consolidated positions of banks with respect to

1. Quarterly data are averaged over the four quarters to get a single matrix of cross-border exposures for a given year. Data are also rescaled over the home country amount of total assets. We denote this as EXC.,Cj., where Ci is the home country and the counterparties are resident in country Cj.

2. The matrix EX is in general not symmetric. For this reason we transform it into a new symmetric matrix EX*, defined as the average of the exposure of country Ci on country Cj, and of country Cj on country Ci:

C C-4>Ci

[EX4Qic( = [EX*]C с =

3. We split country pairs into low, medium and high exposure groups according to their EX* values. Near half of the pairs have a value less than 0.5%, and are assigned to the low exposure group. There is a second, though smaller group between 0.5%

Table A2.1

2007 EU distributions of financing needs for all the scenarios, correlation matrix E1, share of GDP.

Percentiles Baseline: no new legislation Scenario! bail-in Scenario2: bail-in, Basel III, RF

Initial = FN Initial = FN Final = FN Initial = FN Intermediate» FN FinalA=FN FinalB = FN

after capital after capital after LAC after capital after LAC after SRF after NRF

80 0% 0% 0% 0% 0.0% 0.0% 0.0%

82 1.5% 1.5% 0.2% 0.0% 0.0% 0.0% 0.0%

84 1.7% 1.7% 0.3% 0.0% 0.0% 0.0% 0.0%

86 1.8% 1.8% 0.3% 0.0% 0.0% 0.0% 0.0%

88 2.0% 2.0% 0.4% 0.1% 0.0% 0.0% 0.0%

90 2.1% 2.1% 0.4% 0.1% 0.0% 0.0% 0.0%

95 2.6% 2.6% 0.6% 0.2% 0.1% 0.0% 0.0%

97.5 3.1% 3.1% 0.8% 0.4% 0.1% 0.0% 0.0%

99 3.9% 3.9% 1.1% 0.8% 0.2% 0.0% 0.1%

99.5 4.6% 4.6% 1.4% 1.3% 0.4% 0.1% 0.2%

99.9 6.6% 6.6% 2.4% 2.7% 1.0% 0.5% 0.7%

99.95 7.5% 7.5% 2.9% 3.5% 1.2% 0.8% 0.9%

99.99 10.0% 10.0% 4.3% 5.7% 2.2% 1.8% 1.9%

99.995 11.2% 11.2% 5.0% 6.9% 2.8% 2.4% 2.4%

99.999 13.4% 13.4% 6.9% 9.8% 4.3% 3.9% 3.9%

99.9999 17.7% 17.7% 7.8% 11.2% 5.0% 4.6% 4.6%

100 18.1% 18.1% 8.0% 11.5% 5.2% 4.8% 4.8%

Table A2.2

2009 EU distributions of financing needs for all the scenarios, correlation matrix E1, share of GDP.

Percentiles Baseline: no new legislation Scenario1: bail-in Scenario2: bail-in, Basel III, RF

Initial»FN Initial» FN Final = FN Initial» FN Intermediate Final A: FN Final B = FN

after capital after capital after LAC after capital FN after LAC after SRF after NRF

80 0% 0% 0% 0% 0.0% 0.0% 0.0%

82 0% 0% 0% 0% 0.0% 0.0% 0.0%

84 0.4% 0.4% 0.0% 0.0% 0.0% 0% 0%

86 0.7% 0.7% 0.1% 0.0% 0.0% 0.0% 0.0%

88 0.8% 0.8% 0.1% 0.0% 0.0% 0.0% 0.0%

90 0.9% 0.9% 0.2% 0.1% 0.0% 0.0% 0.0%

95 1.3% 1.3% 0.3% 0.2% 0.1% 0.0% 0.0%

97.5 1.8% 1.8% 0.4% 0.4% 0.1% 0.0% 0.0%

99 2.4% 2.4% 0.7% 0.7% 0.2% 0.0% 0.1%

99.5 3.0% 3.0% 0.9% 1.1% 0.3% 0.0% 0.1%

99.9 4.8% 4.8% 1.6% 2.4% 0.8% 0.3% 0.4%

99.95 5.7% 5.7% 2.0% 3.3% 1.1% 0.5% 0.7%

99.99 8.0% 8.0% 3.3% 5.4% 2.1% 1.5% 1.5%

99.995 9.1% 9.1% 3.9% 6.3% 2.6% 2.0% 2.0%

99.999 10.9% 10.9% 5.5% 9.0% 3.9% 3.2% 3.3%

99.9999 14.8% 14.8% 6.7% 10.7% 5.0% 4.3% 4.3%

100 16.6% 16.6% 6.9% 11.1% 5.2% 4.4% 4.5%

ARTICLE IN PRESS

14 P. Benczur et al. / Journal of Financial Stability xxx (2016) xxx-xxx

Table A2.3

2012 EU distributions of financing needs for all the scenarios, correlation matrix S2, share of EU GDP.

Percentiles Baseline: no new legislation Scenario1: bail-in Scenario2: bail-in, Basel III, RF

Initial = FN Initial = FN Final = FN Initial = FN Intermediate: Final A = FN Final B = FN

after capital after capital after LAC after capital FN after LAC after SRF after NRF

80 0.26% 0.26% 0.04% 0.03% 0.01% 0.00% 0.00%

82 0.27% 0.27% 0.04% 0.03% 0.01% 0.00% 0.00%

84 0.29% 0.29% 0.05% 0.04% 0.01% 0.00% 0.00%

86 0.31% 0.31% 0.06% 0.04% 0.01% 0.00% 0.00%

88 0.33% 0.33% 0.06% 0.05% 0.02% 0.00% 0.00%

90 0.35% 0.35% 0.07% 0.06% 0.02% 0.00% 0.00%

95 0.45% 0.45% 0.12% 0.11% 0.03% 0.00% 0.01%

97.5 0.56% 0.56% 0.17% 0.18% 0.06% 0.00% 0.02%

99 0.73% 0.73% 0.23% 0.32% 0.11% 0.01% 0.05%

99.5 0.87% 0.87% 0.29% 0.46% 0.15% 0.02% 0.08%

99.9 1.31% 1.31% 0.42% 0.86% 0.28% 0.06% 0.17%

99.95 1.51% 1.51% 0.46% 1.08% 0.34% 0.12% 0.22%

99.99 2.00% 2.00% 0.58% 1.61% 0.46% 0.19% 0.33%

99.995 2.25% 2.25% 0.83% 1.90% 0.69% 0.38% 0.56%

99.999 2.73% 2.73% 1.29% 2.33% 1.11% 0.75% 0.98%

99.9999 3.19% 3.19% 1.40% 2.45% 1.22% 0.86% 1.08%

100 3.25% 3.25% 1.46% 2.50% 1.28% 0.91% 1.14%

Table A2.4

2012 EU distributions of financing needs for all the scenarios, correlation matrix S3, share of EU GDP.

Percentiles Baseline: no new legislation Scenario!: bail-in Scenario2: bail-in, Basel III, RF

Initial = FN after capital Initial = FN after capital Final = FN after LAC Initial = FN after capital Intermediate» FN Final A= FN after LAC after SRF Final B = FN after NRF

80 0.2% 0.2% 0.0% 0.0% 0.0% 0.0% 0.0%

82 0.3% 0.3% 0.0% 0.0% 0.0% 0.0% 0.0%

84 0.3% 0.3% 0.0% 0.0% 0.0% 0.0% 0.0%

86 0.3% 0.3% 0.1% 0.0% 0.0% 0.0% 0.0%

88 0.3% 0.3% 0.1% 0.0% 0.0% 0.0% 0.0%

90 0.4% 0.4% 0.1% 0.1% 0.0% 0.0% 0.0%

95 0.6% 0.6% 0.2% 0.1% 0.0% 0.0% 0.0%

97.5 0.8% 0.8% 0.2% 0.3% 0.1% 0.0% 0.0%

99 1.1% 1.1% 0.3% 0.5% 0.2% 0.0% 0.1%

99.5 1.4% 1.4% 0.4% 0.7% 0.2% 0.0% 0.1%

99.9 2.2% 2.2% 0.8% 1.4% 0.5% 0.1% 0.3%

99.95 2.6% 2.6% 0.9% 1.8% 0.6% 0.2% 0.4%

99.99 3.7% 3.7% 1.4% 2.8% 1.1% 0.6% 0.8%

99.995 4.2% 4.2% 1.7% 3.2% 1.3% 0.8% 0.9%

99.999 5.3% 5.3% 2.4% 4.9% 1.9% 1.4% 1.5%

99.9999 6.2% 6.2% 2.7% 5.7% 2.2% 1.7% 1.8%

100 11.1% 11.1% 2.8% 5.9% 2.2% 1.7% 1.8%

Table A2.5

2012 EU distributions of financing needs for all the scenarios, correlation matrix S4, share of EU GDP.

Percentiles Baseline: no new legislation Scenario1: bail-in Scenario2: bail-in, Basel III, RF

Initial = FN after capital Initial = FN after capital Final = FN after LAC Initial = FN after capital Intermediate» FN Final A= FN after LAC after SRF Final B = FN after NRF

80 0.1% 0.1% 0.0% 0.0% 0.0% 0.0% 0.0%

82 0.2% 0.2% 0.0% 0.0% 0.0% 0.0% 0.0%

84 0.2% 0.2% 0.0% 0.0% 0.0% 0.0% 0.0%

86 0.3% 0.3% 0.0% 0.0% 0.0% 0.0% 0.0%

88 0.3% 0.3% 0.1% 0.0% 0.0% 0.0% 0.0%

90 0.4% 0.4% 0.1% 0.0% 0.0% 0.0% 0.0%

95 0.6% 0.6% 0.2% 0.1% 0.0% 0.0% 0.0%

97.5 0.8% 0.8% 0.2% 0.3% 0.1% 0.0% 0.0%

99 1.2% 1.2% 0.4% 0.6% 0.2% 0.0% 0.1%

99.5 1.6% 1.6% 0.5% 0.9% 0.3% 0.0% 0.1%

99.9 2.9% 2.9% 1.0% 2.0% 0.6% 0.2% 0.3%

99.95 3.6% 3.6% 1.3% 2.5% 0.9% 0.4% 0.5%

99.99 5.3% 5.3% 2.1% 4.2% 1.5% 1.0% 1.1%

99.995 6.8% 6.8% 2.6% 5.3% 2.0% 1.5% 1.5%

99.999 9.8% 9.8% 4.8% 9.0% 4.1% 3.5% 3.5%

99.9999 12.4% 12.4% 5.8% 10.5% 5.0% 4.4% 4.4%

100 15.7% 15.7% 6.0% 10.8% 5.2% 4.6% 4.6%

ARTICLE IN PRESS

P. Benczur et al. / Journal of Financial Stability xxx (2016) xxx-xxx

AT BE BG CY CZ DE DK EE ES FI FR GR HU IE IT LT LU LV MT NL PL PT RO SE SI SK UK

Fig. A3.2. Cross-country correlation levels after the correction. Note: white cells correspond to correlation coefficients in the range 25-35%; light grey cells to 35-45%; medium grey cells to 45-55%; dark grey cells to 55-65%; extra-dark grey cells to 65-75%.

and 1%, which is assigned to the medium exposure group.20 The remaining pairs above 1% form the high exposure group.

4. Low exposure is translated into a correlation coefficient of 0.3 (like in E3 - reflecting only the same exposure to common risks), medium exposure into 0.4 and high exposure into 0.5:

[CC]q,Cj =

0.3 0.4 0.5

if[£X*]cjjcJ. < 0.5%

if0.5% < [EX*]CjjC. <1% v [CC]Cj>C. = 0

if[EX*]q,c. 0.65 if C = Cj

-i.^-j > 1%

5. The matrix CC is used to build the banks' correlation matrix E4: the correlation between bank k and bank l is set equal to the correlation level set in matrix CC between their home countries Ci and Cj:

[^4]k,i =

CCc.c . k = l a k e C1 a l e C.

6. As the correlation matrix might not be a proper correlation matrix (i.e. it might not be positive definite), we apply the alternating projection method by Higham (2002). This algorithm, commonly used in this context, computes the nearest symmetric and positive definite correlation matrix.

20 Country pairs with no exposure data were also put into the middle group.

To visualize the outcome of this procedure, and also the effects of this correction on the cross-country correlation coefficients,

ARTICLE IN PRESS

P. Benczur et al. / Journal of Financial Stability xxx (2016) xxx-xxx

Fig. A3.1 present the original cross-country correlation coefficients, while Fig. A3.2 shows the corresponding values after the correction The shading in the two charts reflects similar correlation coefficients. By comparing the two charts, one can notice that crosscountry correlation levels do not change significantly after the correction, only domestic correlations increase for some countries (from 60% to more than 70%).

References

Acharya, V.V., Santos, J.A.C., Yorulmazer, T., 2010. Systemic risk and deposit insurance premiums. Fed. Reserve Bank N. Y. Econ. Policy Rev. 16 (1), 89-99. Alter, A., Schüler, Y., 2012. Credit spread interdependencies of European states and

banks during the financial crisis. J. Bank. Financ. 36,3444-3468. Anginer, D., Demirguc-Kunt, A., Zhu, M., 2014. How does deposit insurance affect

bank risk? Evidence from the recent crisis. J. Bank. Financ. 48,312-321. Avgouleas, E., Goodhart, C., 2015. Critical reflections on bank bail-ins.J. Financ. Regul. 1 (1), 3-29.

Bank of England, 2012. Financial Stability Report, No 27, November.

Basel Committee on Banking Supervision, 2005. An Explanatory Note on the Basel

IIIRB Risk Weight Functions. Basel Committee on Banking Supervision, 2006. International Convergence of Capital Measurement and Capital Standards. Basel Committee on Banking Supervision, 2010 [rev 2011]. A Global Regulatory

Framework for More Resilient Banks and Banking Systems. Basel Committee on Banking Supervision, 2013. Revised Basel III Leverage Ratio

Framework and Disclosure Requirements. Benczur, P., Berti, K., Cariboni, J., Di Girolamo, F.E., Langedijk, S., Pagano, A., Petracco Giudici, M., 2015. Banking Stress Scenarios for Public Debt Projections. European Economy Economic Papers 548. Bennett, R.L., 2002. Evaluating the Adequacy ofthe Deposit Insurance Fund: A Credit

Risk Modeling Approach. FDIC Working Paper. Beck, T., 2012, October. Banking Union for Europe - Risks and Challenges. Vox eBook. Blanchard, O., 2009. The Crisis: Basic Mechanisms, and Appropriate Policies. Working Paper 09/80, IMF. Bologna, P., Caccavaio, M., Miglietta, A., 2014. EU Bank Deleveraging. Bank of Italy

Occasional Paper, No. 235. Breuss, F., Roeger, W., in't Veld, J., 2015. The Stabilizing Properties of a European Banking Union in Case of Financial Shocks in the Euro Area. European Economy Economic Papers 550. Bridges,J., Gregory, D., Nielsen, M., Pezzini, S., Radia, A., Spaltro, M., 2014. The Impact of Capital Requirements on Bank Lending. Bank of England Working Paper 486. Brunnermeier, M., Garicano, L., Lane, P., van Nieuwerburgh, S., Pagano, M., Reis, R., Santos, T., Vayanos, D., 2011, September. European Safe Bonds: An Executive Summary. The Euro-nomics Group. Campolongo, F., Cariboni, J., Guilleme Moreno, D., 2011. JRC Report under Article 12 of Directive 94/19/EC as amended by Directive 2009/14/EC. JRC Scientific and Technical Report, JRC, 56324. Cannas, G., Cariboni, J., Kazemi Veisari, L., Pagano, A., 2013a. Updated estimates of EU eligible and covered deposits. JRC Scientific and Technical Report, JRC, 87531. Cannas, G., Cariboni, J., Naltsidis, M., Pagano, A., Petracco Giudici, M., 2013b. 2012 EU 27 Banking Sector Database and SYMBOLSimulations Analyses. JRC Scientific and Technical Report, JRC, 86395. Cannas, G., Cariboni, J., Forys, M., Joensson, H., Langedijk, S., Marchesi, M., Nda-cyayisenga, N., Pagano, A., Petracco-Giudici, M., 2013c. Quantitative Estimation of a Part of the Costs and Benefits of Bank Structural Separation. JRC Scientific and Technical Report, JRC, 88531. Cariboni, J., Petracco Giudici, M., Pagano, A., Marchesi, M., Cannas, G., 2012. Costs and Benefits of a New Bank Resolution Framework. European Commission JRC Scientific and Policy Report, JRC, 78882. Cariboni, J., Petracco Giudici, M., Pagano, A., Cannas, G., Di Girolamo, F.E., 2014. JRC Contribution to the Commission Staff Working Document: Economic Review of the Financial Regulation Agenda. European CommissionJRC Scientific and Policy Report, JRC, 90638. Cecchetti, S.G., 2014. The Jury is In. CEPR Policy Insight, No, 76. Claessens, S., Dell'Arriccia, G., Igan, D., Laeven, L., 2010. Lessons and Policy Implications from the Global Financial Crisis. IMF Working Paper 10/44. Committee of European Banking Supervisors, 2010. Results of the Comprehensive Quantitative Impact Study. http://www.eba.europa.eu/documents/10180/ 16145/EU-QIS-report-2.pdf/bef29568-4a54-433d-9f3a-0ba1750a92d4. Cohen, B., Scatigna, M., 2014. Banks and Capital Requirements: Channels of Adjustment. BIS Working Papers, No, 443. Conlon, T., Cotter, J., 2014. Anatomy of bail-in. J. Financ. Stabil. 15, 257-263. Dewatripont, M., 2014. European banking: bailout, bail-in and state aid control. Int.

J. Ind. Organ. 34, 37-43. De Lisa, R., Zedda, S., Vallascas, F., Campolongo, F., Marchesi, M., 2011. Modelling deposit insurance scheme losses in a Basel 2 framework. J. Financ. Serv. Res. 40 (3), 123-141.

Duffie, D., Jarrow, R., Purnanandam, A., Yang, W., 2003. Market pricing of deposit

insurance. J. Financ. Serv. Res. 24,93-119. European Banking Authority, 2013. Basel III Monitoring Exercise Results Based on Data as of 31 December 2012. http://www.eba.europa.eu/documents/10180/ 16145/EU-QIS-report-2.pdf/bef29568-4a54-433d-9f3a-0ba1750a92d4.

European Central Bank, 2014. Banking Structures Report.

European Commission, 2011a. Directorate-Generalfor Economic and Financial Affairs, Public Finances in EMU 2011. http://ec.europa.eu/economy_finance/ publications/european_economy/2011/pdf/ee-2011-3_en.pdf.

European Commission, 2011b. Directorate-General for Internal Market and Services: Commission Staff Working Document - Impact Assessment Accompanying the Proposal for a Directive of the European Parliament and of the Council Establishing a Framework for the Recovery and Resolution, http://ec.europa.eu/internaLmarket/bank/docs/crisis-management/2012_ eu_framework/impact_assessment_final_en.pdf, SWD(2012) 166 final.

European Commission, 2012a. Directorate-General for Economic and Financial Affairs. Fiscal Sustainability Report http://ec.europa.eu/economy_finance/ publications/european_economy/2012/pdf/ee-2012-8_en.pdf.

European Commission, 2012b. Impact Assessment - Accompanying the Document Proposal for a Directive of the European Parliament and of the Council Establishing a Framework for the Recovery and Resolution of Credit Institutions and Investment Firms and Amending Council Directives 77/91/EEC and 82/891/EC, Directives 2001/24/EC, 2002/47/EC, 2004/25/EC, 2005/56/eC, 2007/36/EC and 2011/35/EC and Regulation (EU) No 1093/2010, Annex 13, Appendix 5.

European Commission, 2014a. Directorate-General for Internal Market and Services. In: Commission Staff Working Document - Economic Review ofthe Financial Regulation Agenda. http://ec.europa.eu/internaLmarket/finances/docs/general/ 20140515-erfra-working-document_en.pdf.

European Commission, 2014b. Directorate-General for Competition, "State Aid Scoreboard 2014", http://ec.europa.eu/competition/state_aid/scoreboard/ amounts_used_2008-2013.xls, http://ec.europa.eu/competition/state_aid/ scoreboard/financial_economic_crisis_aid_en.html.

European Council, 2014. Council Implementing Regulation (EU) 2015/81 Specifying Uniform Conditions of Application of Regulation (EU) No 806/2014 of the European Parliament and of the Council with Regard to Ex Ante Contributions to the Single Resolution Fund. http://eur-lex.europa.eu/legal-content/EN/TXT/ PDF/?uri=CELEX:32015R0081&from=EN.

European Parliament and Council, 2013. Directive 2013/36/EU of the 26 June 2013 on Access to the Activity of Credit Institutions and the Prudential Supervision of Credit Institutions and Investment Firms, Amending Directive 2002/87/EC and Repealing Directives 2006/48/EC and 2006/49/EC, 2013. Off. J. Eur. Union L 176/338 http://eur-lex.europa.eu/LexUriServ/LexUriServ. do?uri=0J:L:2013:176:0338:0436:EN:PDF.

European Parliament and Council, 2014. Directive 2014/59/EU of the European Parliament and of the Council of 15 May 2014 Establishing a Framework for the Recovery and Resolution of Credit Institutions and Investment Firms and Amending Council Directive 82/891/EEC, and Directives 2001/24/EC, 2002/47/EC, 2004/25/EC, 2005/56/EC, 2007/36/EC, 2011/35/EU, 2012/30/EU and 2013/36/EU, and Regulations (EU) No 1093/2010 and (EU) No 648/2012, ofthe European Parliament and of the Council, L 173/190. http://eur-lex.europa.eu/ legal-content/EN/TXT/PDF/?uri=CELEX:32014L0059&from=EN.

Financial Stability Board, 2014. Adequacy of Loss-absorbing Capacity of Global Systemically Important Banks in Resolution, Consultative Document. http:// www.financialstabilityboard.org/wp-content/uploads/TLAC-Condoc-6-Nov-2014-FINAL.pdf.

Fontana, A., Langedijk, S., Petracco Giudici, M., 2015a. The bank-sovereign loop and financial stability in the euro area. Eur. Comm. JRC Sci. Policy Rep. (forthcoming).

Fontana, A., Langedijk, S., Rancan, M., 2015b. Where do the bank bail-in losses go? An analysis of financial contagion risk with euro area sectorial balance sheets. Eur. Comm. JRC Sci. Policy Rep. (forthcoming).

Galliani, C., Zedda, S., 2014. Will the bail-in break the vicious circle between banks and their sovereign? Comput. Econ. 43 (4).

Goyal, R., Brooks, P.K., Pradhan, M., Tressel, T., Dell'Ariccia, G., Pazarbasioglu, C., 2013. A Banking Union forthe Euro Area. IMF Staff Discussion Notes, No. 13/1.

Higham, N., 2002. Computing the nearest correlation matrix—a problem from finance. J. Numer. Anal. 22 (3).

Huertas, T.F., 2010. The Road to Better Resolution: From Bail-Out to Bail-In. LSE Financial Markets Group Paper Series, Special Paper No. 195.

Huertas, T.F., Nieto, M.J., 2012. Banking union and bank resolution: how should the two meet? Vox http://www.voxeu.org/article/banking-union-and-bank-resolution-how-should-two-meet.

Juncker, J.-C., Tusk, D., Dijsselbloem, J., Draghi, M., Schulz, M., 2015. Completing Europe's Economic and Monetary Union. European Commission http://ec. europa.eu/priorities/economic-monetary-union/docs/5-presidents-report_en. pdf.

Kuritzkes, A., Schuermann, T., Weiner, S.M., 2002. Deposit Insurance and Risk Management ofthe US Banking System: How Much? How Safe? Who Pays? Warton School Center for Financial Institutions, University of Pennsylvania, Working Paper No. 02-02 B.

Laeven, L., Valencia, F., 2013. Systemic banking crises database. IMF Econ. Rev. 61, 225-270, http://dx.doi.org/10.1057/imfer.2013.

Maccaferri, S., Cariboni, J., Schoutens, W., 2013. Levy processes and the financial crisis: can we design a more effective deposit protection? Int. J. Financ. Res. 4 (1).

Macroeconomic Assessment Group, 2010, December. Assessing the Macroeconomic Impact of the Transition to Stronger Capital and Liquidity Requirements.

Marchesi, M., Petracco Giudici, M., Cariboni, J., Zedda, S., Campolongo, F., 2012. Macroeconomic Cost-benefit Analysis of Basel III Minimum Capital Requirements and of Introducing Deposit Guarantee Schemes and Resolution Funds. European Commission JRC Scientific and Policy Report, EUR, 24603.

ARTICLE IN PRESS

P. Benczur et al. / Journal of Financial Stability xxx (2016) xxx-xxx 17

Merton, R., 1974. On the pricing of corporate debt: the risk structure of interest rates.

J. Financ. 29 (2), 449-470. Merton, R., 1977. An analytical derivation ofthe cost of deposit insurance and loan guarantees - an application of modern option pricing theory. J. Bank. Financ. 1 (1),3-11.

Miles, D., Yang, J., Marcheggiano, G., 2012. Optimal bank capital. Econ. J. Muresano, R., Pagano, A., 2014. Automatic tuning for a Systemic Model of Banking Originated Losses (SYMBOL) tool on multicore. Int. J. Soc. Manage. Econ. Bus. Eng. 8 (10), 3024-3034.

Schoenmaker, D., Gros, D., 2012, September. A European Deposits Insurance and Resolution Fund - An update. CEPS Policy Briefs.

Schoenmaker, D., Peek, T., 2014. The State of the Banking Sector in Europe. OECD Economics Department Working Papers, No. 1102.

Schoenmaker, D., Siegmann, A., 2013. Winners of a European Banking Union. Duisenberg School of Finance Policy Briefs, No. 23/February 2013.

Sironi, A., Zazzara, C., 2004. Applying credit risk models to deposit insurance pricing: empirical evidence from the Italian banking system. J. Int. Bank. Regul. 6,10-32.

Vasicek, O.A., 2002. Loan portfolio value. Risk.