Measuring Contagion Effects in the Swedish Banking Sector using Round by Round Simulation

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Örebro University School of Business Master in Economics and Econometrics Supervisor: Daniela Andrén

Examiner: Patrik Karpaty Spring Semester/2013

Measuring Contagion Effects in the

Swedish Banking Sector using Round by

Round Simulation

Tobias Killmann Date of birth: 1988/02/21

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Abstract

Banks play a central role in the Swedish financial markets by covering over 50% of total assets and providing essential intermediary services. The financing opportunities over the interbank market are highly important for a well performing financial system and consequently for the whole economy. Fragilities in the structure of the interbank market present a serious danger to the health of the economy, as they could induce domino effects that have the potential to let the whole banking system fail within a short period of time. The purpose of this thesis is to use round by round simulations with five of the main banks in Sweden in order to identify possible fragilities in the interbank market that could lead to substantial social costs in a financial crisis. The results suggest that contagion is a danger to the Swedish interbank market with the potential to destroy vast amounts of asset value after an instantaneous default of a market participant.

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Table of Content

1. Introduction ... 1

2. Institutional Background ... 4

3. Theoretical Background ... 7

3.1. Interbank Matrix Estimation and Market Structure ... 7

3.2. Data Availability and Market Structure ... 7

3.3. Maximizing Entropy ... 8

4. Simulation Methodology ... 9

5. Data ... 11

6. Empirical Model ... 13

6.1. The Interbank Matrix ... 14

6.2. Losses and Loss Rate ... 15

7. Findings ... 16

7.1. Average Risk Weights, Interbank Loans ... 17

7.2. Average Risk Weights, Interbank Loans+Derivatives ... 19

7.3. Average vs. Adjusted Risk Weights ... 21

7.4. Discussion and further Research ... 23

7.4.1. Is there Potential for Contagion in the Swedish Banking Market? .. 23

7.4.2. Limitations of the Simulation Models ... 24

7.4.3. Further Research ... 24

8. Conclusions ... 25

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1. Introduction

The academic interest in the reasons and consequences of a failing interbank-market due to systemic risk has received increasing attention after the financial-market crisis in 2007 and the following largest recession since the 1930’s. Failures of systemically important banks occur due to fragilities in the interbank-market. Mishkin (1999) points out: “…a financial crisis occurs when shocks to the financial system interfere with information flows so that the financial system can no longer do its job of channelling funds to those with productive investment opportunities.” Bandt & Hartmann (2000) use a more narrow definition of financial distress and define systemic risk as the probability of experiencing a systemic event that leads to the failure of ex ante healthy financial institutions. The authors differentiate between systemic events in the wide and narrow sense, which either affect the entire system indiscriminately or a selective group of financial institutes. Systemic events in the wide sense include macroeconomic shocks such as business cycle fluctuations, devaluation of currencies or a sudden increase of inflation. The systemic event in the narrow sense is driven by contagion effects which propagate shocks through physical exposures or information effects. Contagion effects describe how losses spread through interbank linkages. Bandt & Hartmann (2000) regard contagion effects through physical exposures as the driving force behind systemic risk. Another strand of literature deals with non-physical exposures. Fernando et al. (2012) identify contagion effects through stock prices after the collapse of Lehman Brothers in 2007. Clients whom Lehman offered equity underwritings to suffered adverse effects of minus 5%. In a related paper Dumontaux & Pop (2012) find that the Lehman collapse triggered a market reaction that was informed and selective, rather than random and indiscriminate, thus observing contagion effects in the narrow, rather than wide sense. Contagion effects through non-physical exposures will not be covered in this thesis. They are certainly of great importance when discussing potential risks in the financial system, but focusing on one channel of contagion will lead to more clear-cut results.

Physical exposure contagion analysis has the advantage of delivering estimates for shock propagation after assuming the failure of a market participant. This strand of literature, started by Furfine (1999), is limited by data unavailability issues since the exact size and structure of bilateral interbank exposures are unknown. The standard approach to solve this

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2 issue is to spread the exposures on the other market participants in relation to their size1. The mathematical term of this maximization problem of the interbank-exposure matrix X is called maximizing entropy (e.g. Degryse & Nguyen, 2007; Elsinger, et al. 2006; Sheldon & Maurer, 1998; Upper & Worms, 2004; van Lelyveld & Liedorp, 2006; Rajkamal & Peydró, 2010). Only few papers such as Blåvarg & Nimander (2002) and Mistrulli (2011) use actual interbank exposure data, as this sort of data is usually highly restricted and can only be accessed by regulatory bodies. Hałaj & Kok (2013) use link prediction algorithms to generate random networks of interbank exposures. By simulating a large number of networks the model becomes more dynamic compared to the static maximizing entropy approach, which may reflect the volatile structure of interbank exposures more realistically.

Upper & Worms (2004) produce results where about three quaters of the German banking systems assets will be lost after the failure of one systemically important bank. But this result represents an unrealistic scenario without considering Germanys banking safety net, which would reduce the asset losses to a maximum of 15%. Similary to Upper & Worms (2004) did van Lelyveld & Liedorp (2006) predict a loss of three quaters of the banking systems assets in the Netherlands. This scenario is also considered extremly unrealistic with the assumption of the whole European banking system failing at once. Degryse & Nguyen (2007) finds 20% of the banks assets lost for Belgium, Mistrulli (2011) and Wells (2002) predict a loss of 16% for Italy and the UK respectivly.

This thesis will more or less follow the approach developed by Furfine (1999) that represents a simple but effective way of measuring contagion risk in interbank markets. The analysis is split into two sequential parts. In a first step the market structure of the interbank market is determined, by taking the size of interbank exposures and linkages between them into account (e.g., Upper, 2007, Allen & Gale, 2000). This information is summarized in an interbank matrix of size NxN, where N equals the number of banks. In a second step a simulation model is constructed, which either assumes an idiosyncratic or systemic shock in the banking system. It is generally assumed that contagion is more strongly connected to idiosyncratic shocks and to my knowledge only Elsinger et al. (2006) considered systemic shocks.

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3 The goal of this thesis is to use a round by round simulation model to identify possible structural weaknesses in the Swedish interbank system. Since the interbank crisis in Sweden of the early 1990s the Banking Law Commission has been established to oversee the reformation of the banking sector to minimize systemic risk (Blåvarg & Nimander, 2002). The Swedish interbank market is fairly concentrated with 4 banks holding 75% of total assets. A high concentration of assets will increase the risk for financial contagion, which makes the Swedish interbank market highly interesting to investigate.

The interbank exposure matrix X will be filled with balance sheet data on interbank exposures for five Swedish banks by using the maximizing entropy approach, i.e. spreading the interbank exposures in relation to the size of the banks. In addition, actual interbank exposures by one medium sized financial intermediary will increase the accuracy of the interbank matrix estimation. After determining the structure of the interbank matrix, an idiosyncratic shock is assumed by letting one bank in the system fail, followed by the calculation of losses, depending on the exogenous loss rate θ, . If a bank’s losses exceed its Tier 1 capital2 or its Tier 1 capital ratio falls below a predetermined regulatory threshold it is assumed to be failing and the whole process starts over again until a natural stopping point without further bank failures is reached. The base model runs simulations using average risk weights and data on interbank loans only, while more advanced simulations explore the effects of adjusted risk weights of failing assets and including derivatives to interbank exposures. The different simulation models will additionally shed more light on the discussion about increasing the regulatory Tier 1 ratio above Basel 3s 6% to 10% in Sweden. A thorough assessment of the effects resulting from a change in the regulatory Tier 1 ratio threshold would need to predict the reaction by banks concerning the capital base, i.e. banks would need to hold more equity to assure a large enough buffer for the higher equity requirements. Such an analysis would deserve a master’s thesis on its own and will not be included in this analysis due to time resource limitations. The model in this thesis will therefore focus on the effects of a changing Tier 1 ratio with status quo capital endowments. Findings separate banks into groups of contagious and non-contagious banks that can or cannot trigger domino effects which have the potential to crash the whole interbank system.

2_{Tier 1 capital is the standard measure for equity in the Basel 2 accord and consists of (a) Common Tier 1}

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4 The base model experiences its first defaults of banks at a loss rate of 0.2 with the whole system of banks being affected at a loss rate of 0.5. More advanced simulations that include derivatives will experience domino effects already at a loss rate level of 0.4. Changing the regulatory Tier 1 ratio requirement from 6% to 10% will increase the likelihood of default for single banks, but will not endanger the health of the whole system.

Some limitations and restrictions of this analysis will affect the findings of the thesis: The models will assume a closed system of banks, an assumption that is necessary to analyse the Swedish interbank market only. Swedish banks are well established in the European and International financial markets which makes the assumption rather strong. Another limitation arises due to data unavailability on exact interbank exposures between Swedish banks. The maximizing entropy approach, which tackles this issue, may miss out on unknown banking relationships between banks, thus leading to biased estimates for the interbank matrix X.

This thesis is structured in the following way: Part 2 will present the institutional setting of the Swedish banking system and the regulatory framework for banks. In part 3 the theoretical background of contagion analysis is presented including a discussion on the structure of the interbank matrix and the maximizing entropy approach. This is followed by a discussion of the simulation methodology in part 4 and the description of the used datasets in part 5. Part 6 will discuss the specific simulation models of this thesis before presenting the results in part 7. Section 7.4 will summarize and benchmark the results to other research in this field before concluding the thesis in part 8.

2. Institutional Background

Financial intermediaries connect the private and public sector to investment and financing possibilities by accessing the stock and credit market. The clearest example for financial intermediaries are banks, which play a key role in the Swedish financial market by accounting for about 50% of total lending (Sveriges Riksbank, 2012). The Swedish banking market is fairly concentrated with 4 banks holding around 75% of total assets (Sveriges Riksbank, 2012). Figure 1 shows the relationship between the total amount of bank’s

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5 balance sheets and the GDP in selected European Countries. Sweden is with 175% below the average in the EU.

A well-functioning banking market depends to a great deal on refinancing possibilities on the interbank market. Interbank exposures account for about 23% of total bank assets in 2011 (Sveriges Riksbank, 2012). The relatively large size and the importance of liquidity needs through this channel makes the interbank market important for the health of the whole economy.

During the last decades the regulation of the banking sector has been driven forward by the Bank of International Settlements. It’s Basel Committee of Banking Supervision has meanwhile published its third version of regulatory measures in order to ensure the safety of the interbank market, called Basel 3.

Figure 1

Totals of Bank’s Balance Sheets to GDP(in %) for selected European Countries3 Source: ECB (2011)

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Included countries: Austria, Belgium, Bulgaria, Cyprus, Czech Republic, Denmark, Estonia, Greece, Spain, Finland, France, Hungary, Ireland, Italy, Lituania, Luxembourg, Latvia, Malta, Netherlands, Poland, Portugal, Romania, Sweden, Slovenia, Slovakia, United Kingdom, Iceland, Liechtenstein, Norway

AT BE BG CY CZ DE DK EE EL ES FI FR HU IE IT LT LU LV MT NL PL PT RO SE SI SK UK IC LI NO 0 100 200 300 400 500 600 700 800 900

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6 After Basel 2 has been ratified in almost all major economies in the world, Basel 3 is on its way to be implemented into national law as well (Basel Committee of Banking Supervision, 2012). Sweden, as part of the EU but not the EURO area follows the implementation schedule of the EU, which has agreed to the new Basel III accord at the 5th Council of Presidents on May 15th 2012.The most relevant part for contagion analysis in the 3 pillar structure of Basel 3 is the minimum capital requirements section.

The standard measure for solvency of a bank is its Tier 1 capital ratio. The BCBS4 defines Tier 1 capital (going-concern capital) as (a) Common Tier 1 Equity plus (b) additional Tier1 equity. Tier 1 equity includes common shares, stock surpluses, retained earnings as well as disclosed reserves (Basel Committee of Banking Supervision, 2010).

In Basel 3 the minimum requirement of Tier 1 capital is 6% relative to the risk-weighted assets, which used to be 4% under Basel II. Risk weights on assets ensure that banks with higher portfolio risks need to hold larger amounts of Tier 1 capital by getting lower risk weights, thus making the ratio between total assets and risk weighted assets larger. In order to ensure a sound transition to the higher capital requirements, transitional rules have been added, which require a Tier 1 ratio of 4.5% in 2013 and 5.5% in 2014, before reaching 6% in 2015 (Basel Committee of Banking Supervision, 2010). Sweden follows those regulations, but is planning to increase the minimum capital requirements over the 6% of Basel III: “The

Government is to propose higher capital adequacy requirements for systemically important banks in an effort to strengthen the stability of the Swedish banking system and reduce the vulnerability of the Swedish economy…. Therefore the capital adequacy requirements for Swedish banks should be set higher and be introduced earlier than is set out in Basel III”

(http://www.government.se, 2013).The Riksbank has set recommendations on Tier 1 capital requirements of 10% for the beginning of 2013 and 12% for the beginning of 2015. (Sveriges Riksbank, 2012)

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7

3. Theoretical Background

3.1. Interbank Matrix Estimation and Market Structure

The basis of all simulation models dealing with contagion in interbank markets are the linkages between banks. The seemingly most convenient way of illustrating such linkages is in matrix form. Furfine (1999), in his first attempt to analyse contagion in the American banking system, used actual bilateral credit exposures from overnight federal fund transactions. In the case of this thesis we consider 5 Swedish banks, leading to the following 5x5 matrix X. [ ]

Where would for example represent bank 1’s lending towards bank 2 and bank 1’s borrowing from bank 2 and the other way round. The sums of the rows are equal to a bank’s total lending, i.e. ∑ , whereas the sums of the columns represent the total borrowing, i.e. ∑ . Since banks do not borrow or lend to themselves, the diagonal is filled with zeros, i.e. .

3.2. Data Availability and Market Structure

One of the key problems in contagion analysis is the availability of data for the interbank ma-trix X. Even though central banks sometimes have access to bilateral exposures, this kind of data is often highly restricted and not available for outside researchers. Blåvarg & Nimander (2002) explain:” The lack of data is naturally connected to the low interest in this issue in the

regulatory system. If supervisors do not demand the reporting of these exposures, no report-ing data that can be used for research will be available. The banks’ incentives to perform re-search themselves or provide data to outsiders are weak”. However, Upper (2007) points out

that such information is available for a small number of countries including Italy, Hungary and Mexico.

Due to the fact that data on bilateral exposures is not available, researchers rely on strong assumptions concerning the actual market structure. The most commonly used approach

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8 builds upon Allen & Gale (2000) who identify a complete market structure that is theoretically least prone to contagion effects. The authors theoretically analyse interregional contagion effects between banks assuming completely homogenous banks with equal equity ratios and size. Even though Mistrulli (2011) finds specific situations with contradictory results using heterogeneous equity ratios, the assumptions are generally applicable to single region interbank markets. Allen & Gale (2000) identify two main properties of interbank markets, completeness and interconnectedness. A market is considered complete if every bank lends directly to all other banks and perfectly interconnected if all banks are indirectly linked to each other. Interconnectedness is therefore a weaker assumption than completeness. One can consider an example where Bank A has exposures towards all other banks except bank B (CDE). If Bank C has exposures towards bank B and all other banks are interconnected in a similar way the market is perfectly interconnected. It is assumed that the more complete a market is, the less likely, and the more interconnected the market is, the more likely contagion effects are. The reason why complete markets are less prone towards contagion is that higher diversification of exposures leads to a less concentrated banking system, while interconnectedness has a negative influence on market stability because shocks can spread through the whole system without a stopping point. The concept of completeness and interconnectedness are closely related to the concept of direct and indirect contagion presented by Bandt & Hartmann (2000).

3.3. Maximizing Entropy

By arguing that banks seek to minimize the risk for contagion through spreading their exposures evenly on all banks in the market, researchers use the concept of maximizing entropy which assumes a perfectly complete market structure (e.g., Degryse & Nguyen, 2007; Elsinger, et al. 2006 ; Sheldon & Maurer, 1998; Upper & Worms, 2004; van Lelyveld & Liedorp, 2006). The basic idea is to distribute the exposures relative to the size of the other banks. In mathematical terms this maximization problem of the interbank matrix X is called maximizing entropy which has the problem that the values for are not equal to zero. The adapted version by Upper & Worms (2004) and Elsinger et al. (2006) gets rid of this problem by introducing new restrictions on X and solving the now more tedious maximization problem numerically with the help of the RAS-algorithm, a matrix maximization algorithm which has mostly been used to calculate input-output tables.

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9 Another advantage of this adapted method is the ability to include observed data and using the RAS-algorithm to solve for the unknowns in the interbank matrix (Upper, 2007). Since the calculation in this thesis only includes five banks, the interbank matrix will be solved by hand, the more efficient solution in this case.

4. Simulation Methodology

After determining the structure of the interbank matrix, an idiosyncratic shock is assumed by letting one bank in the system fail. The reason why a bank fails is exogenous to the model and will not influence the contagion analysis. This means that a failure due to mismanagement is treated the same way as a failure due to a macroeconomic downturn or a collapsing housing market. It is additionally assumed that the shock occurs instantaneous for several reasons. One, it is necessary to assume that banks in the system are not prepared for a failure of neighbouring institutions, since they could otherwise withdraw funds in advance which would make it considerably more difficult to single out the contagion effect itself. Two, major failures such as the crash of Lehman Brothers in 2007 seemed to be a surprise to other market participants which supports this assumption. Point three is dealing with the time horizons of a bank failure. As Upper & Worms (2004) point out in an example of a German bank failure in the 1970’s, it can take years, or even decades until the total losses of a bank failure are known. Introducing a time variable would be a hopeless task. In addition it is generally assumed that contagion is stronger connected to idiosyncratic shocks.

After letting a bank fail, the effects on other banks are calculated. The size of the effect depends on the size of the gross exposures between the banks represented by the value and the loss-rate θ, . The loss rate determines how much of the interbank exposures will be lost in case of a default. A value for θ of 0.5 would mean that 50% of the interbank exposures will be lost at a default. Determining the value for θ is one of the main problems in this modelling process. There is little literature on historical loss rates like James (1991), who identifies an average loss rate of 30% at bank failures in the 1980’s for the United States. Values of less than 5 and greater than 90% have been observed. Most authors that are following the Furfine (1999) approach therefore use the full range of loss-rates between 0 and 1 and compare the differing results. A small strand of literature endogenizes loss-rates

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10 (e.g. Elsinger et al. 2006). Those approaches have to deal with a large set of problems like determining administrative costs of bankruptcy, the availability of collateral, that is whether securities on the lost asset were issued, or the seniority of claims (Upper, 2007). As Mistrulli (2011) mentions, including endogenous loss-rates might create more complicated problems than it solves.

One of the reasons for the large variation in observed loss rates is certainly the complex process of bank defaults. Psychological factors like adverse selection or moral hazard are difficult to quantify and might affect the loss-rate to a great deal. But when doing this kind of analysis one has to bear in mind what the main purpose is: Whether or not contagion is a present danger to the system and at which loss rates.

The next step in the model after determining the size of the losses for all banks is to check whether or not domino effects occur. There are two points of view in the literature concerning bank defaults. One, a bank is considered as failing if the losses exceed the absolute amount of Tier 1 capital, that is .5

This approach stands against the assumption of a bank’s failure when it’s Tier 1 capital ratio falls below the regulatory limit. Researchers in favour of the first approach argue that even if it might be regulatory practice to close banks below the regulatory threshold, this process is unrealistic since regulatory bodies will not be able to act in such a short time span (Upper & Worms, 2004). It seems reasonable to assume that action cannot be taken in this short time horizon, but a predefined threshold has the advantage of being fixed, whereas equalling losses to the absolute Tier 1 holdings seems to be a more arbitrary threshold for bankruptcy. The reasoning behind the absolute Tier 1 threshold builds upon the assumption that banks will cover their losses mainly with equity. Another advantage of using the absolute Tier 1 capital as a measure of failure lies in the drawbacks of the relative Tier 1 threshold approach. Since interbank asset holdings are relatively small, only minor changes in the Tier 1 ratio occur, even though losses might be several times larger than the total Tier 1 capital. By using the total Tier 1 amount as failure threshold one avoids dealing with risk weights of lost assets, which are unknown. Estimation is difficult, since the investment structure of assets between banks are only available on an aggregate level.

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5. Data

Two sorts of data were used in this analysis of the Swedish interbank market. The first dataset contains panel data that summarizes the balance sheet information on interbank lending and deposits for four of the five banks in the time period between 2004 and 2012, quarterly data. This data was provided by Sveriges Riksbanken and covers 75% of the total assets on the Swedish banking market, thus allowing for a detailed and accurate analysis. This data is presented in figure 2 and 3. Even though the model is static in the sense that data of only one period of time is included in the model, this dataset provides a good overview of the Swedish interbank exposures and its lending and borrowing patterns. Interbank deposits are generally on a higher level than lending, which is contradictory to the assumption in this thesis of a closed interbank market, where deposits and lending should be balanced. The interbank market in Europe is well connected, nonetheless is the assumption of a closed system theoretically necessary, in order to analyse the Swedish banking market only. There is furthermore a considerably large variance in both lending and borrowing and a common decrease of lending and borrowing in 2009.

Figure 2

Interbank Lending for the four largest banks in Sweden, quarterly Data

Source: Sveriges Riksbank

04:1 05:1 06:1 07:1 08:1 09:1 10:1 11:1 12:1 0 100000 200000 300000 400000 500000 m SE K

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12 The five banks balance sheets provide the analysis with data on derivative holdings and can be found in the respective annual reports. The banks names will be kept anonymous in order to protect the interests of the analysed banks6.

Figure 3

Interbank Deposits for the four largest banks in Sweden, quarterly Data Source: Sveriges Riksbank

The reason for including data on derivatives is that they usually account for a large part of interbank exposures. The total sum of derivatives over all five banks accounts with 715.068mSEK for about one third (31%) of the total exposures which equal 2.282.503mSEK. This advanced model will assume a closed system of banks, which might be a looser assumption than for interbank loans, since the derivative markets are assumed to be even more internationally connected

Key figures of the five banks can be found in table 1 below. The ratio between Tier 1 capital and RWA7 defines the Tier 1 capital ratio, the most important measure of solvency for banks. The transition from Basel 2 to Basel 3 does not affect the Tier 1 capital itself, but the risk weights of assets, and through this channel the Tier1 capital ratio.

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This thesis focuses on the structural stability of the entire banking system, rather than the stability of individual banks

7_{RWA= Risk Weighted Assets}

04:1 05:1 06:1 07:1 08:1 09:1 10:1 11:1 12:1 0 100000 200000 300000 400000 500000 600000 700000 m SE K

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13 Most banks have information about the transitional RWA on their balance sheet summaries which will be used as the up to date information source for Tier 1 capital. The differences between the Basel 2 Tier 1 ratio and the Tier 1 ratio with transitional rules are in some cases extremely large. The Tier 1 ratio of bank 4 is decreasing over 50% from 21% to 10.17% by including the transitional rules for risk weighted assets. The balance sheet totals range from 283.283mSEK for bank 1 to 5.814.499mSEK for bank 5 with an average of 2.557.207mSEK. The transitional Tier 1 capital ratio is highest for bank 1 with 30.40%8 and lowest for bank 4 with 10.17%, average being 15.29%. Bank 1’s average risk weights are with 98,89% significantly higher than the ones from the other 4 banks that range from around 75 to 79%, showing that bank 1 has assets of lower risk in its portfolio, resulting in a large Tier 1 equity ratio of 30.40%.

Table 1: Balance Sheet Summaries and adjusted Risk Weights

Source: Balance sheets

Another source of data includes detailed information about asset holdings of one Swedish bank. This actual observed data helps to achieve more precise results of the simulations and is included the adapted version of the interbank matrix.

6. Empirical Model

This thesis follows more or less the approach by Furfine (1999), by using an interbank matrix X to model interbank relations and using this information to analyse contagion after assuming an instantaneous idiosyncratic shock. The following part splits the contagion

8_{The transitional Tier1 Ratio equals the Basel II Tier1 Ratio, since no Data for transitional Rules is available}

Bank1 Bank2 Bank3 Bank4 Bank5

Total Assets 283.283 2.453.456 1.846.941 2.387.858 5.814.499 m SEK RWA 3.134 585.839 464.339 487.300 1.441.067 m SEK RWA trans. 3.134 879.237 769.117 1.006.219 1.589.627 m SEK Total Tier1 953 102.393 86.967 102.333 205.596 m SEK Tier1 Ratio Basel II 30.40% 17.48% 18.73% 21.00% 14.27%

Tier1 ratio-Transitional Rules 30.40% 11.65% 11.31% 10.17% 12.93% Average Risk Weights 98.89% 76.12% 74.86% 79.59% 75.22% Adjusted Risk Weights 50.00% 50.00% 50.00% 50.00% 50.00%

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14 analysis into its various steps and describes the different assumption of the simulation model.

6.1. The Interbank Matrix

The standard approach to fill the interbank matrix is to take aggregate lending or deposits data by banks and redistributing the totals on the matrix relative to the size of the banks. This is called maximizing entropy and has mainly been used due to data unavailability concerning interbank asset holdings (e.g., Degryse & Nguyen, 2007; Elsinger, et al. 2006; Sheldon & Maurer, 1998; Upper & Worms, 2004; van Lelyveld & Liedorp, 2006). There are certain obstacles to overcome when using this method. One concern deals with the assumption of a closed interbank market. As mentioned in the part about the institutional setting, the assumption of a closed interbank market requires that lending equals borrowing. In our data this is not the case, but the differences are within an acceptable limit. This gives rise to the question which data to use, lending or borrowing. The deposits are in general larger in this data set which would lead to stronger contagion effects due to higher interbank exposures. The differences in results are not noteworthy such that only the lending based model will be presented.

Another issue dealing the maximizing entropy approach is dealing with the weighting relative to the size of banks, which can either be measured by the balance sheet totals, or the amounts of interbank exposures. One could think that the amount of total assets might be appropriate, but Swedish banks are not only active on the Swedish financial market. A good example is bank 5 which has only about 25% of its operations in Sweden. This suggests that the amounts of interbank lending will represent the relative size on the Swedish interbank market more precisely. The results for the maximizing entropy weighting are represented in table 2. The method of maximizing entropy is easiest to use by including all five banks under consideration and their balance sheet information. This research has furthermore access to actual interbank holdings by one bank, which are included in the adjusted interbank matrix X.

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Table 2: Interbank Loans+Derivatives, Maximizing Entropy Weighting Table

Source: Balance sheets and own calculations

By combining this data with the maximizing entropy approach, the lending relationships between banks are being modelled in more detail, leading to more precise results.

6.2. Losses and Loss Rate

This analysis assumes an idiosyncratic and instantaneous shock within the interbank market. This means the simulation model will let one bank fail at a time before calculating the losses, depending on the interbank exposures and the loss rate θ. As discussed above, loss rates vary a lot historically and attempts to endogenize them have run into many obstacles (see Elsinger, et al., 2006; Mistrulli, 2011). This thesis will therefore use varying rates for θ . The model then checks if the losses result in the default of one or several banks. The standard approach in the literature is to assume a failure if the losses exceed a bank’s total Tier 1 capital (e.g. Degryse & Nguyen, 2007; Furfine, 2003; Mistrulli, 2011; Sheldon & Maurer, 1998; Upper & Worms, 2004). This approach will be implemented into the model and compared to the relative Tier 1 threshold failure scenario, where banks are assumed to be failing when reaching a Tier 1 ratio lower than 6%.

Because the Tier 1 ratio is the quotient of Tier 1 capital and the RWA, it is of importance to choose whether losses are included in full scale or in a weighted way. In our data, average risk weights range from 74.86% to 98.89% with an average of 80.94%. The large variation of risk weights between banks represents the different investment strategies. It seems reasonable to assume that lost assets have higher risk weights than the average exposures in

Bank1 Bank2 Bank3 Bank4 Bank5

Interbank Loans 10.193 200.189 350.439 422.897 583.716 mSEK

Derivatives Parent 62 426.326 125.926 112.525 50.229 mSEK

Loans+Derivatives 10.255 626.515 476.365 535.422 633.945 mSEK Cummulative Lending 10.193 210.382 560.821 983.718 1.567.434 mSEK

Weights by Loans 0.65% 12.77% 22.36% 26.98% 37.24% Weighting Matrix Bank1 0.000000 0.128554 0.225038 0.271568 0.374840 Bank2 0.007455 0.000000 0.256310 0.309306 0.426929 Bank3 0.008376 0.164495 0.000000 0.347493 0.479637 Bank4 0.008906 0.174908 0.306184 0.000000 0.510002 Bank5 0.010362 0.203502 0.356239 0.429897 0.000000

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16 a bank’s portfolio. The argument behind this is simply that government bonds with very high risk weights are less likely to cause a bank failure, than lower rated corporate exposures or derivatives. That is why a second approach of setting risk weights to 50% for lost assets is included in this thesis. The problems of choosing this uniform risk weight are at least twofold. One, since no detailed data including credit ratings is available, it is impossible to make exact estimates for the risk weights. Two, there are large variations across banks concerning risk weights. Choosing one fixed value will overestimate the contagion risk for banks with higher risk weights. While using average risk weights will certainly underestimate the risk for contagion, choosing no risk weights will overestimate the risk for contagion. Using the 50% will therefore be more likely to be an appropriate estimation. The findings will show that the difference between using average values to the 50% approach are rather small, and do not affect the Tier 1 ratios to a great deal.

7. Findings

The following paragraphs will summarize the findings of the various simulation models. The second row of figure 5 shows the different models used in the analysis which can be differentiated on three main dimensions. The hierarchically higher dimension splits the analysis into models with average risk weights and adjusted risk weights as discussed in part 6.2. The models can furthermore be separated whether data on interbank loans or total interbank exposures including derivatives is used. The two models to the far right of figure 5 incorporate a failure threshold of 10%, as proposed by the Swedish regulatory bodies (Sveriges Riksbank, 2012).

average RW

Interbank Lending _{Lending+Derivatives}Interbank

adjusted RW

Interbank Lending _{Lending+Derivatives}Interbank Interbank Lending 10%

Interbank Lending+Derivatives

10%

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17 The presentation of findings will be structured as follows: Section 7.1 will present the results of the base model assuming average risk weights and interbank loans only. Section 7.2 will focus on the comparison between the base model and the model including derivatives. Section 7.3 will first investigate what effect the change in risk weights will have on the likelihood of contagion followed by an increase of the regulatory capital threshold to 10% and its effects on the stability of the interbank system. Section 7.4 will discuss the results and suggest further research on this matter. The full results for individual banks are attached in the appendix.

7.1. Average Risk Weights, Interbank Loans

This model represents the simplest version of the simulation model by using average risk weights, calculated as the ratio between banks RWA and total assets, while using data on interbank loans only9. A bank is assumed to be failing if the losses exceed its Tier 1 capital, denoted as “Fail abs. Tier 1” in table 3, or the Tier1 ratio falls below 6%.

Table 3: Average Risk Weights, Interbank Loans, 6% Failure Threshold

Source: Own calculations

The tables in each subsection of the findings show the results for the different simulation models as shown in figure 5 at the loss rate θ ranging from 0.1 to 1. Only the summarizing

9_{For detailed calculations see Appendix: i: Average Risk Weights, Interbank Loans, 6% Failure Threshold} Total

θ avg% max% min% avg% max% min% avg% max% min% avg max min avg max min 0.1 11.83 23.67 4.46 15.27 30.38 10.15 -0.03 -0.04 -0.01 0 0 0 1 1 1 0.2 21.49 47.34 5.70 15.25 30.36 10.14 -0.05 -0.07 -0.01 0 1 0 1 2 1 0.3 32.24 71.00 8.55 15.23 30.33 10.12 -0.07 -0.11 -0.02 0 1 0 1 2 1 0.4 42.98 94.67 11.40 15.21 30.31 10.10 -0.09 -0.15 -0.03 0 1 0 1 2 1 0.5 71.17 138.61 30.98 15.14 30.27 10.06 -0.17 -0.24 -0.09 1 5 0 2 3 1 0.6 81.03 164.51 33.45 15.07 30.18 9.99 -0.24 -0.33 -0.13 1 5 0 1 2 1 0.7 91.81 191.93 32.49 15.04 30.16 9.97 -0.26 -0.37 -0.12 1 5 0 2 2 1 0.8 210.04 448.81 101.44 14.80 29.89 9.76 -0.49 -0.61 -0.33 3 5 0 2 3 1 0.9 183.84 383.03 90.81 14.86 29.97 9.82 -0.54 -0.67 -0.37 3 5 0 2 2 1 1.0 249.40 546.01 117.60 14.75 29.81 9.71 -0.54 -0.68 -0.36 3 5 0 2 2 1 Losses/Tier1 Tier1 Ratio ΔTier1 Ratio Fail abs. Tier1 Rounds

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18 tables, denoted as “Total”, are shown in the text10, displaying the average (avg%), maximum (max%) and minimum (min%) of the five simulations, run for every individual model. “Losses/Tier 1” represents the ratio between occurred losses and the bank’s Tier 1 capital. If this ratio exceeds 100%, a bank is assumed to be failing according to the absolute Tier 1 failure criteria (“Fail abs. Tier 1”). The Tier 1 ratios at the end of the simulations are denoted as “Tier 1 Ratio” while the “Δ Tier 1 Ratio” shows the difference between before and after the bank default. The figures in each subsection support the displaying of results by showing the relationship between the loss rate and the amount of failing banks after letting each bank fail at a time.

The results for the first simulation model with average risk weights and interbank loans only do not deliver failures according to the relative Tier 1 threshold of 6%, since Tier 1 ratios only change marginal. The absolute Tier 1 threshold on the other hand produces its first bank failure already at a loss rate of 0.2 and a full breakdown of the system at a loss rate of 0.5, as shown in table 3. Those results are not universally true for all banks in the system as there seem to be major differences concerning further contagion between banks. Figure 6 shows that a failure of Bank 1 will not lead to contagion at the full range of θ.

Figure 5

Loss Rate and failed Banks, Average Risk Weights, Interbank Loans, 6% Failure Threshold Source: Own calculations

10_{The simulation results for each individual bank can be found in the apendix. Each row of a simulation table}

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19 Bank 5 on the other hand will have one bank fail at loss rates between 0.2 to 0.4 and the whole system at a loss rate from 0.5. It is specifically noteworthy that there seems to be high potential for a complete breakdown of the system if certain key-banks fail. This is indicated by the fact that either only one or the whole system crash at a time. Figure 5 displays bank 4 as an extreme example for this behaviour, as there is no failure until a loss rate of 0.7 and a complete breakdown in three11 rounds at a loss rate of 0.8. Banks 1 and 2 are on the other hand not nearly as contagious, as their default cannot enable a chain reaction that affects the whole system.

7.2. Average Risk Weights, Interbank Loans+Derivatives

As discussed in part 5, does including derivatives violate the closed market assumption to a larger extent than using interbank loans only. This could lead to an overestimation of contagion, relative to the base model. While acknowledging this problem, it is nonetheless interesting to analyse an increase in volume in interbank exposures concerning the relative and absolute Tier 1 threshold.

Table 4: Average Risk Weights, Interbank Loans+Derivatives, 6% Failure Threshold

The general expectation when adding data on derivatives is that the increase in volume of interbank exposures will lead to an increase in risk for contagion, as exposures increase

11_{For detailed Data for each Bank see Appendix} Total

θ avg% max% min% avg% max% min% avg% max% min% avg max min avg max min 0.1 15.34 24.88 9.35 15.26 30.38 10.15 -0.04 -0.05 -0.02 0 0 0 1 1 1 0.2 27.95 49.76 8.37 15.23 30.36 10.13 -0.07 -0.09 -0.02 0 1 0 1 2 1 0.3 41.92 74.64 12.55 15.21 30.33 10.10 -0.10 -0.13 -0.02 0 1 0 1 2 1 0.4 81.79 134.32 41.15 15.11 30.28 10.04 -0.20 -0.26 -0.12 1 5 0 1 2 1 0.5 100.12 167.90 45.62 15.07 30.25 10.01 -0.24 -0.32 -0.13 1 5 0 1 2 1 0.6 142.71 230.83 81.32 14.97 30.17 9.92 -0.33 -0.46 -0.20 2 5 0 2 2 1 0.7 191.84 307.76 115.39 14.85 30.09 9.85 -0.44 -0.62 -0.27 3 5 0 2 2 1 0.8 265.07 454.36 140.42 14.71 29.95 9.73 -0.58 -0.80 -0.40 3 5 0 2 2 1 0.9 298.21 511.16 157.97 14.64 29.89 9.68 -0.65 -0.88 -0.44 3 5 0 2 2 1 1.0 388.63 696.25 185.92 14.48 29.71 9.53 -0.81 -1.08 -0.60 3 5 0 2 2 1

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20 relative to the Tier 1 capital. Table 4 shows that this hypothesis is true on average, as the first breakdown of the system occurs at a loss rate of 0.4, as opposed to 0.5 of the base model. When looking at the banks individually, one can distinguish two groups. Figure 6 shows that bank 1 and bank 2 are again not contagious and fail at the same levels as before. Contagious banks on the other hand fail at earlier levels, as expected.

Figure 6:

Loss Rate and failed Banks,average Risk Weights, Interbank Loans+Derivatives, 6% Failure Threshold Source: Own Calculations

Following a failure of bank 3 affects now the whole system at a loss rate of 0.7, in contrast to the base model where only one bank failed at this loss rate. A failure of bank 4 will now affect the whole system at a loss rate of 0.5 instead of 0.7, and a failure of bank 5 will affect the whole system at a loss rate of 0.4. To summarize: Previously non contagious banks will not be affected by including derivatives, while the group of contagious banks have lowered the loss rate necessary to induce a breakdown of the system. The effect that a crash of one contagious bank will induce a domino reaction that lets the whole system fail is still present for including derivatives.

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21

7.3. Average vs. Adjusted Risk Weights

Using average risk weights in the simulations might underestimate contagion if the lost assets are classified as more risky than the average asset. This is, as discussed in part 6.2, a plausible assumption, even though it is impossible to know ex ante which assets will cause a default. Using a uniform risk weight of 50% is therefore a rather rough estimate, but will only affect the relative Tier 1 threshold, as the ratio between losses and total Tier 1 capital will not change.

Table 5: Adjusted Risk Weights, Interbank Loans, 6% Failure Threshold

The results in table 5 show that there is still no default when using the 6% failure threshold, as the minimum Tier 1 value of 8.7%12 is still well above the 6% minimum capital requirement. The effects on the Tier 1 ratio are larger in this simulation compared to the base model. The average decrease of Tier 1 capital in this model of -3.15%, is 6 times larger than the 0.54% of the base model. It is surprising that such large changes in the Tier 1 ratio can still not achieve the default of any bank.

The last model presented discusses an increase of the relative Tier 1 failure threshold to 10%, as proposed by the Swedish regulatory bodies, and uses adjusted risk weights equal to 50%. The findings of this model are unique, in the sense that they show bank defaults for the

12

See Appendix: iii: Adjusted Risk Weights, Interbank Loans 6% Failure Threshold

Total

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22 relative Tier 1 threshold. The occurring defaults are different to the failures of the previous models, as there are no contagion effects at all. As shown in table 6 and figure 7 does the simulation model stop after two rounds with a maximum of two banks failing due to the 10% Tier 1 threshold.

Table 6: Adjusted Risk Weights, Interbank Loans, 10% Failure Threshold

Source: Own Calculations

Figure 7

Loss Rate and failed Banks, average Risk Weights, Interbank Loans, 10% Failure Threshold

Source: Own Calculations

The results suggest that banks with low Tier1 ratios are more likely to fail when considering the relative Tier 1 threshold, but will not trigger contagion that could endanger the whole system of banks.

Total

θ avg% max% min% avg% max% min% avg% max% min% avg max min avg max min avg max min avg max min 0.1 11.83 23.67 4.46 15.07 29.48 10.13 -0.27 -0.93 -0.03 0 0 0 1 1 1 0 0 0 1 2 1 0.2 21.49 47.34 5.70 14.88 28.66 10.09 -0.46 -1.74 -0.05 0 1 0 1 2 1 0 1 0 1 2 1 0.3 32.24 71.00 8.55 14.70 27.93 10.04 -0.66 -2.47 -0.07 0 1 0 1 2 1 0 1 0 1 2 1 0.4 42.98 94.67 11.40 14.53 27.28 10.00 -0.85 -3.13 -0.09 0 1 0 1 2 1 0 1 0 1 2 1 0.5 58.82 121.36 20.83 14.33 26.62 9.96 -1.02 -3.79 -0.17 1 5 0 2 3 1 1 1 0 1 2 1 0.6 81.03 164.51 33.45 14.08 25.76 9.85 -1.28 -4.64 -0.24 1 5 0 2 2 1 1 1 0 1 2 1 0.7 91.81 191.93 32.49 13.93 25.25 9.80 -1.39 -5.16 -0.23 1 5 0 2 2 1 1 2 0 1 2 1 0.8 168.83 346.48 84.50 13.56 24.70 9.49 -1.74 -5.89 -0.44 3 5 0 2 3 1 1 2 0 1 2 1 0.9 183.84 383.03 90.81 12.81 21.19 9.44 -2.48 -9.22 -0.55 3 5 0 2 2 1 1 2 0 1 2 1 1.0 249.40 546.01 117.60 12.14 18.60 9.19 -3.15 -11.80 -0.72 3 5 0 2 2 1 1 2 0 1 2 1 Fail rel. Tier1 Rounds Losses/Tier1 Tier1 Ratio ΔTier1 Ratio Fail abs. Tier1 Rounds

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23

7.4. Discussion and further Research

When discussing the findings two questions need to be asked: First, is there considerable danger for contagion in the Swedish interbank system? And second, how accurate do the different models represent contagion effects? The answer of those questions and suggestions for further research will be subject of the following paragraphs.

7.4.1. Is there Potential for Contagion in the Swedish

Banking Market?

The findings of all models separate banks into contagious and non-contagious banks. While non-contagious banks cannot trigger domino effects that will endanger the whole system, are contagious banks able to induce a breakdown of the system at varying loss rates. In the base model the first bank already fails at a loss rate of 0.2(0.1)13 and the whole system at a loss rate of 0.5 (0.4)14. Such loss rates are definitely within a plausible range of scenarios when looking back in history, as has been pointed out in part 4. Another aspect which would suggest danger for contagion in the Swedish interbank system is the fact that there is either no breakdown of contagious banks, or a default of the whole system in two or three rounds. This suggests a highly unstable structure of the interbank system.

The findings of the relative Tier 1 threshold suggest less severe consequences for the Swedish interbank system as was found by (Blåvarg & Nimander, 2002) for similar loss rates. Two banks will fail at a loss rate of 70% with the regulatory threshold being 10% in this simulation model, whereas 2 banks will fail at a loss rate of 75% for Blåvarg & Nimander (2002) at a regulatory threshold of 4 %. Since the authors only use the relative Tier 1 threshold the results suggest that contagion will not take place in the Swedish interbank system. As discussed in part 4 the relative Tier 1 threshold will underestimate the risk for contagion compared to the absolute Tier 1 threshold.

Upper & Worms (2004) and van Lelyveld & Liedorp (2006) produce similar results to this analysis, with contagion effects destroying about three quaters of the German and Dutch banking sectors assets. Both are worst case scenarios and are not considered likely by the authors.

13_{Interbank Loans+Derivatives Model} 14_{Interbank Loans+Derivatives Model}

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24

7.4.2. Limitations of the Simulation Models

Counterfactual simulation models of the interbank system are dealing with a number of issues concerning data availability and uncertainty about bank-failure scenarios. This makes this kind of research rely on strong assumptions which will affect the accuracy of the results. Starting with the estimation of the interbank matrix, by using maximizing entropy could underestimate the danger of contagion since no lending relationships are assumed. By including the actual exposures of one market participant, the analysis has reduced this bias. Including derivatives in the first advancement step of the model might overestimate the danger for contagion, since derivatives are assumed to violate the assumption of a closed banking system to a greater deal than interbank loans. Furthermore might the changing to adjusted risk weights not improve the precision of the model as the risk weights of lost assets are ex ante unknown. While the uncertainty about possible loss rates might look like a disadvantage of this research, it will actually improve the dynamics of the model by adding more possible failure scenarios, thus identifying possible weaknesses in the interbank market more accurately.

Another limitation deals with the regulatory framework of the banking sector. The possible extremely high socio-economic costs of a banking crisis had governments agree on safety nets which will keep systemically important banks from failing. For Sweden, the law 2008:814 will allow the Swedish government to assist failing banks with capital injections, guarantees or other actions (Swedish Government, 2013). Upper & Worms(2004) analyse the German interbank market with considerations of safety nets and find that institutional guarantees will reduce but not eliminate the danger for contagion.

7.4.3. Further Research

There is certainly room for further research in this field of stress testing. One of the shortcomings of this model is its static approach, which might not account for differences in the risk for contagion across time. This research would probably have to deal with data accessibility issues and the changes in banking regulations over time. The high level of confidentiality in the banking sector makes researchers rely on strong assumption concerning the structure of the interbank exposures. Regulatory bodies could more easily access such data and use contagion risk analysis models to increase the accuracy of results.

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25 Including collateral and regulatory agreements on institutional guarantees would bring this model a step closer to reality of the financial markets.

8. Conclusions

This thesis uses round by round simulations to investigate whether financial contagion is a present danger to the Swedish banking system. A shock in a fragile structured interbank market has the potential to induce domino effects which could endanger the entire financial system and consequently the whole economy.

The contributions of this thesis to the existing literature are at least twofold. First, it provides an up to date analysis of the Swedish banking sector using a simulation model, based on an interbank matrix, estimated by the maximizing entropy approach. The maximizing entropy estimation is improved by adding actual interbank data for one of the five banks, thus improving the accuracy of the interbank structure estimates. The thesis further differentiates the results into simulations run with average and adjusted risk weights while using either data on loans or loans and derivatives. Second, the thesis analysis the effect of an increase of the regulatory Tier 1 threshold from 6% to 10%, as suggested by the Swedish regulatory bodies.

The results show that contagion is a potential danger to the Swedish banking market, as a loss rate from 0.5 can trigger the breakdown of the system when using the absolute Tier 1 threshold as measure for bank defaults. The thesis separates banks into groups of contagious and non-contagious banks. The failure of non-contagious banks will not trigger domino-effects that could endanger the whole system. Defaults by contagious banks on the other hand will endanger the whole interbank system.

The differences between the base and the advanced model, including derivatives and adjusted risk weights are very small and do not change the main conclusions. An increase in the regulatory Tier 1 threshold from 6% to 10% leads to an increased chance for banks with low Tier 1 ratios to fail according to the relative Tier 1 threshold failure scenario, without endangering the complete system of banks.

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26

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27 Mishkin, F., 1999. Global financial instability: framework, events, issues. The Journal of Economic

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List of Figures

Figure 1: Total of Bank’s Balance Sheets in GDP(in %) for selected European Countries ... 5

Figure 2: Interbank Lending, quarterly Data ... 11

Figure 3: Interbank Deposits, quarterly Data ... 12

Figure 4: Simulation Models ... 16

Figure 5: Loss Rate and failed Banks, Average Risk Weights, Interbank Loans, 6% Failure Threshold 18 Figure 6: Loss Rate and failed Banks,average Risk Weights, Interbank Loans+Derivatives, 6% Failure Threshold ... 20

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29

List of Tables

Table 1: : Balance Sheet Summaries and adjusted Risk Weights ... 13

Table 2: Interbank Loans+Derivatives, Maximizing Entropy Weighting Table ... 15

Table 3: Average Risk Weights, Interbank Loans, 6% Failure Threshold ... 17

Table 4: Average Risk Weights, Interbank Loans+Derivatives, 6% Failure Threshold ... 19

Table 5: Adjusted Risk Weights, Interbank Loans, 6% Failure Threshold ... 21

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30

Appendix

Simulation Tables

i. Average Risk Weights, Interbank Loans, 6% Failure Threshold

Bank 1

θ avg% max% min% avg% max% min% avg% max% min%

0.1 0.43 0.47 0.32 15.29 30.40 10.17 0.00 0.00 0.00 0 1 0.2 0.85 0.93 0.64 15.29 30.40 10.17 0.00 0.00 0.00 0 1 0.3 1.28 1.40 0.96 15.29 30.40 10.17 0.00 0.00 0.00 0 1 0.4 1.70 1.86 1.28 15.29 30.40 10.17 -0.01 -0.01 0.00 0 1 0.5 2.13 2.33 1.60 15.29 30.40 10.17 -0.01 -0.01 0.00 0 1 0.6 2.55 2.80 1.92 15.29 30.40 10.16 -0.01 -0.01 -0.01 0 1 0.7 2.98 3.26 2.24 15.28 30.40 10.16 -0.01 -0.01 -0.01 0 1 0.8 3.40 3.73 2.56 15.28 30.40 10.16 -0.01 -0.01 -0.01 0 1 0.9 3.83 4.19 2.88 15.28 30.40 10.16 -0.01 -0.01 -0.01 0 1 1.0 4.25 4.66 3.19 15.28 30.40 10.16 -0.01 -0.01 -0.01 0 1

Losses/Tier1 Tier1 Ratio ΔTier1 Ratio Fail abs. Tier1 Rounds

Bank 2

0.1 12.29 24.74 6.27 15.27 30.37 10.15 -0.02 -0.03 -0.02 0 1 0.2 24.59 49.47 12.55 15.25 30.35 10.13 -0.05 -0.06 -0.04 0 1 0.3 36.88 74.21 18.82 15.23 30.32 10.11 -0.07 -0.09 -0.06 0 1 0.4 49.17 98.95 25.10 15.21 30.30 10.09 -0.10 -0.11 -0.08 0 1 0.5 50.87 123.69 2.28 15.19 30.27 10.07 -0.10 -0.15 -0.01 1 2 0.6 61.05 148.42 2.74 15.17 30.25 10.05 -0.12 -0.18 -0.01 1 2 0.7 71.22 173.16 3.19 15.15 30.22 10.03 -0.14 -0.21 -0.01 1 2 0.8 81.40 197.90 3.65 15.13 30.20 10.01 -0.17 -0.24 -0.01 1 2 0.9 91.57 222.63 4.11 15.11 30.17 9.99 -0.19 -0.27 -0.01 1 2 1.0 101.75 247.37 4.56 15.09 30.15 9.97 -0.21 -0.30 -0.01 1 2

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31 Bank 3

0.1 14.60 16.02 10.98 15.26 30.38 10.14 -0.04 -0.05 -0.02 0 1 0.2 29.21 32.04 21.97 15.23 30.37 10.10 -0.07 -0.10 -0.03 0 1 0.3 43.81 48.06 32.95 15.20 30.35 10.07 -0.11 -0.15 -0.05 0 1 0.4 58.42 64.08 43.94 15.18 30.34 10.04 -0.14 -0.20 -0.06 0 1 0.5 73.02 80.10 54.92 15.15 30.32 10.00 -0.18 -0.25 -0.08 0 1 0.6 87.63 96.12 65.91 15.12 30.30 9.97 -0.21 -0.30 -0.10 0 1 0.7 228.95 304.46 179.46 14.72 30.09 9.80 -0.57 -0.84 -0.31 5 2 0.8 261.65 347.95 205.10 14.64 30.05 9.75 -0.65 -0.95 -0.35 5 2 0.9 294.36 391.45 230.74 14.57 30.00 9.71 -0.72 -1.06 -0.40 5 2 1.0 613.52 1,076.40 308.35 14.00 29.34 9.17 -1.29 -1.69 -1.00 5 2

Bank 4

0.1 13.56 19.03 3.03 15.26 30.40 10.17 -0.04 -0.06 0.00 0 1 0.2 27.12 38.07 6.05 15.22 30.39 10.17 -0.09 -0.12 -0.01 0 1 0.3 40.68 57.10 9.08 15.18 30.39 10.17 -0.13 -0.18 -0.01 0 1 0.4 54.24 76.14 12.10 15.15 30.39 10.17 -0.18 -0.24 -0.01 0 1 0.5 67.80 95.17 15.13 15.12 30.38 10.17 -0.22 -0.30 -0.02 0 1 0.6 194.20 260.97 151.03 14.80 30.14 9.86 -0.49 -0.72 -0.26 5 2 0.7 226.57 304.46 176.20 14.73 30.09 9.81 -0.57 -0.83 -0.31 5 2 0.8 488.09 861.12 244.12 14.25 29.54 9.36 -1.05 -1.39 -0.81 5 2 0.9 549.11 968.76 274.64 14.13 29.44 9.27 -1.16 -1.54 -0.90 5 2 1.0 610.12 1,076.40 305.15 14.01 29.34 9.18 -1.28 -1.68 -0.99 5 2

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32

ii. Average Risk Weights, Interbank Loans+Derivatives, 6%

Failure Threshold

Bank 5

0.1 35.81 64.15 26.12 15.23 30.33 10.11 -0.07 -0.08 -0.06 0 1 0.2 57.97 128.29 0.64 15.17 30.27 10.06 -0.12 -0.17 0.00 1 2 0.3 86.96 192.44 0.96 15.12 30.20 10.00 -0.17 -0.25 0.00 1 2 0.4 245.41 430.56 123.34 14.74 29.97 9.75 -0.55 -0.74 -0.42 5 2 0.5 306.76 538.20 154.17 14.61 29.86 9.65 -0.68 -0.91 -0.52 5 2 0.6 368.11 645.84 185.01 14.48 29.75 9.55 -0.81 -1.08 -0.62 5 2 0.7 429.46 753.48 215.84 14.36 29.65 9.45 -0.93 -1.24 -0.72 5 2 0.8 490.81 861.12 246.68 14.24 29.54 9.36 -1.05 -1.40 -0.81 5 2 0.9 552.17 968.76 277.51 14.12 29.44 9.26 -1.17 -1.55 -0.91 5 2 1.0 613.52 1,076.40 308.35 14.00 29.34 9.17 -1.29 -1.69 -1.00 5 2

Total

θ avg% max% min% avg% max% min% avg% max% min% avg max min avg min 0.1 15.34 24.88 9.35 15.26 30.38 10.15 -0.04 -0.05 -0.02 0 0 0 1 1 0.2 27.95 49.76 8.37 15.23 30.36 10.13 -0.07 -0.09 -0.02 0 1 0 1 1 0.3 41.92 74.64 12.55 15.21 30.33 10.10 -0.10 -0.13 -0.02 0 1 0 1 1 0.4 81.79 134.32 41.15 15.11 30.28 10.04 -0.20 -0.26 -0.12 1 5 0 1 1 0.5 100.12 167.90 45.62 15.07 30.25 10.01 -0.24 -0.32 -0.13 1 5 0 1 1 0.6 142.71 230.83 81.32 14.97 30.17 9.92 -0.33 -0.46 -0.20 2 5 0 2 1 0.7 191.84 307.76 115.39 14.85 30.09 9.85 -0.44 -0.62 -0.27 3 5 0 2 1 0.8 265.07 454.36 140.42 14.71 29.95 9.73 -0.58 -0.80 -0.40 3 5 0 2 1 0.9 298.21 511.16 157.97 14.64 29.89 9.68 -0.65 -0.88 -0.44 3 5 0 2 1 1.0 388.63 696.25 185.92 14.48 29.71 9.53 -0.81 -1.08 -0.60 3 5 0 2 1 Losses/Tier1 Tier1 Ratio ΔTier1 Ratio Fail abs. Tier1 Rounds

Bank 1

0.1 0.43 0.47 0.32 15.29 30.40 10.17 0.00 0.00 0.00 0 1 0.2 0.85 0.93 0.64 15.29 30.40 10.17 0.00 0.00 0.00 0 1 0.3 1.28 1.40 0.96 15.29 30.40 10.17 0.00 0.00 0.00 0 1 0.4 1.70 1.86 1.28 15.29 30.40 10.17 -0.01 -0.01 0.00 0 1 0.5 2.13 2.33 1.60 15.29 30.40 10.17 -0.01 -0.01 0.00 0 1 0.6 2.55 2.80 1.92 15.29 30.40 10.16 -0.01 -0.01 -0.01 0 1 0.7 2.98 3.26 2.24 15.28 30.40 10.16 -0.01 -0.01 -0.01 0 1 0.8 3.40 3.73 2.56 15.28 30.40 10.16 -0.01 -0.01 -0.01 0 1 0.9 3.83 4.19 2.88 15.28 30.40 10.16 -0.01 -0.01 -0.01 0 1 1.0 4.25 4.66 3.19 15.28 30.40 10.16 -0.01 -0.01 -0.01 0 1

(36)

33 Bank 2

0.1 12.29 24.74 6.27 15.27 30.37 10.15 -0.02 -0.03 -0.02 0 1 0.2 24.59 49.47 12.55 15.25 30.35 10.13 -0.05 -0.06 -0.04 0 1 0.3 36.88 74.21 18.82 15.23 30.32 10.11 -0.07 -0.09 -0.06 0 1 0.4 49.17 98.95 25.10 15.21 30.30 10.09 -0.10 -0.11 -0.08 0 1 0.5 50.87 123.69 2.28 15.19 30.27 10.07 -0.10 -0.15 -0.01 1 2 0.6 61.05 148.42 2.74 15.17 30.25 10.05 -0.12 -0.18 -0.01 1 2 0.7 71.22 173.16 3.19 15.15 30.22 10.03 -0.14 -0.21 -0.01 1 2 0.8 81.40 197.90 3.65 15.13 30.20 10.01 -0.17 -0.24 -0.01 1 2 0.9 91.57 222.63 4.11 15.11 30.17 9.99 -0.19 -0.27 -0.01 1 2 1.0 101.75 247.37 4.56 15.09 30.15 9.97 -0.21 -0.30 -0.01 1 2

Bank 3

0.1 14.60 16.02 10.98 15.26 30.38 10.14 -0.04 -0.05 -0.02 0 1 0.2 29.21 32.04 21.97 15.23 30.37 10.10 -0.07 -0.10 -0.03 0 1 0.3 43.81 48.06 32.95 15.20 30.35 10.07 -0.11 -0.15 -0.05 0 1 0.4 58.42 64.08 43.94 15.18 30.34 10.04 -0.14 -0.20 -0.06 0 1 0.5 73.02 80.10 54.92 15.15 30.32 10.00 -0.18 -0.25 -0.08 0 1 0.6 87.63 96.12 65.91 15.12 30.30 9.97 -0.21 -0.30 -0.10 0 1 0.7 228.95 304.46 179.46 14.72 30.09 9.80 -0.57 -0.84 -0.31 5 2 0.8 261.65 347.95 205.10 14.64 30.05 9.75 -0.65 -0.95 -0.35 5 2 0.9 294.36 391.45 230.74 14.57 30.00 9.71 -0.72 -1.06 -0.40 5 2 1.0 613.52 1,076.40 308.35 14.00 29.34 9.17 -1.29 -1.69 -1.00 5 2

Bank 4

0.1 13.56 19.03 3.03 15.26 30.40 10.17 -0.04 -0.06 0.00 0 1 0.2 27.12 38.07 6.05 15.22 30.39 10.17 -0.09 -0.12 -0.01 0 1 0.3 40.68 57.10 9.08 15.18 30.39 10.17 -0.13 -0.18 -0.01 0 1 0.4 54.24 76.14 12.10 15.15 30.39 10.17 -0.18 -0.24 -0.01 0 1 0.5 67.80 95.17 15.13 15.12 30.38 10.17 -0.22 -0.30 -0.02 0 1 0.6 194.20 260.97 151.03 14.80 30.14 9.86 -0.49 -0.72 -0.26 5 2 0.7 226.57 304.46 176.20 14.73 30.09 9.81 -0.57 -0.83 -0.31 5 2 0.8 488.09 861.12 244.12 14.25 29.54 9.36 -1.05 -1.39 -0.81 5 2 0.9 549.11 968.76 274.64 14.13 29.44 9.27 -1.16 -1.54 -0.90 5 2 1.0 610.12 1,076.40 305.15 14.01 29.34 9.18 -1.28 -1.68 -0.99 5 2

(37)

34 Bank 5

0.1 35.81 64.15 26.12 15.23 30.33 10.11 -0.07 -0.08 -0.06 0 1 0.2 57.97 128.29 0.64 15.17 30.27 10.06 -0.12 -0.17 0.00 1 2 0.3 86.96 192.44 0.96 15.12 30.20 10.00 -0.17 -0.25 0.00 1 2 0.4 245.41 430.56 123.34 14.74 29.97 9.75 -0.55 -0.74 -0.42 5 2 0.5 306.76 538.20 154.17 14.61 29.86 9.65 -0.68 -0.91 -0.52 5 2 0.6 368.11 645.84 185.01 14.48 29.75 9.55 -0.81 -1.08 -0.62 5 2 0.7 429.46 753.48 215.84 14.36 29.65 9.45 -0.93 -1.24 -0.72 5 2 0.8 490.81 861.12 246.68 14.24 29.54 9.36 -1.05 -1.40 -0.81 5 2 0.9 552.17 968.76 277.51 14.12 29.44 9.26 -1.17 -1.55 -0.91 5 2 1.0 613.52 1,076.40 308.35 14.00 29.34 9.17 -1.29 -1.69 -1.00 5 2

Total