Systemic risk indicators : a review of the Basel 3 additional loss absorbency requirements

Name: Kelsey Mandy Daniëlsson

Student number: 10547150

Study: MSc. Economics

Field: Monetary Policy & Banking

Thesis Supervisor: Dr. Cenkhan Sahin

Systemic risk indicators

A review of the Basel 3 additional loss

absorbency requirements

Danielsson, K.M.

7/15/2018

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Statement of Originality

This document is written by Kelsey Danielsson, who declares to take full responsibility for the content of this document. I declare that the text and work presented in this paper is original and that no sources other than those mentioned in the texts have been used. The Faculty of Economics & Business is solely responsible for the supervision of the completion of the work, not for the content.

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Systemic risk Indicators

A review of the Basel 3 additional loss absorbency

requirements

Kelsey Mandy Dani

ël

sson

15-07-2018

Abstract

This paper examines whether the Basel 3 additional absorbency requirements decreased the systemic risk contribution of G-SIBs using the delta CoVaR approach. This paper also analyzes other main factors behind systemic risk. Namely, the Value-at-Risk ratio of an individual bank, a bank’s leverage ratio, their short-term wholesale funding ratio, their book-based asset size, their market-to-book ratio and the maturity mismatch between a bank’s short-term obligations and available short-term funds. A quantile regression is conducted using panel data from 46 banks over the period 2001-2017. No evidence is found that the Basel 3 additional absorbency requirements reduce the systemic risk contribution of G-SIBs. However, the results of this paper do support the Basel 3 rules to treat G-SIBs differently than non G-SIBs, in terms of financial regulation. There is no evidence found that the leverage ratio of a bank and their book-based size are contributing factors to systemic risk. In contrast, this study did find evidence that that the following variables contribute to systemic risk: the Value-at-Risk ratio of a bank, their short-term wholesale funding ratio, their market-to-book ratio and the maturity mismatch between a bank’s short-term obligations and available short-term. Consequently, the advisement of this paper is that regulators should focus more on these variables if they assess the systemic risk contribution of banks.

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Table of Contents

Chapter 1: Introduction ... 5

Chapter 2: An illustrative framework ... 6

2.1 Basel 3 ... 6

2.2 Global Systemically Important Institutions (GSIFIs) ... 8

2.2.1 Policy measures ... 8

2.2.2 Regulatory methodology systemic importance ... 9

2.3 Systemic risk ... 9

2.4 Modelling systemic risk ... 11

2.4.1 The marginal expected shortfall (MES) ... 11

2.4.2 Delta Conditional Value at Risk (∆CoVaR) ... 12

Chapter 3: Methodology ... 14

3.1 Descriptive statistics and dataset ... 14

3.2 Quantile regression ... 15

3.3 The empirical regression model ... 16

Chapter 4: Empirical regression results... 18

Chapter 5: Sensitivity analysis ... 19

5.1 Robustness ... 19

5.2 Standard errors ... 20

Chapter 6: Discussion ... 21

Chapter 7: Conclusion ... 22

Bibliography ... 23

Tables ... 25

Table (1): sample list ... 25

Table (2): Regulatory methodology to systemic importance ... 26

Table (3): 2012 G-SIB buckets ... 27

Table (4): Timeline G-SIB status ... 28

Table (5): summary statistics of the regression variables ... 29

Table (6): regression results ... 30

Table (7): Robustness regression, 5% quantile ... 31

Table (8A): North America vs. Europe regression ... 32

Table (8B): North America vs. Europe regression ... 33

Graphs ... 34

Graph (1): median delta CoVaR (2001-2017) ... 34

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Chapter 1: Introduction

Before the recent financial crisis financial regulation was mainly focused on micro-prudential objectives. Regulators did not focus on the macro-prudential objectives of systemic risk. Assessing risk was mostly based on the risk incentives of a single financial institution, without taking into consideration the risks that come with the interconnectedness of financial institutions (Oordt & Zhou, 2015). Several financial institutions were exposed to the same risks as other banks. Banks lend money to each other or had invested in the same tranche of assets. This makes banks highly interconnected. Therefore, in addition to banks that were considered “too big to fail” (TBTF), there was also a high risk that certain institutions were “too systemic to fail” (TSTF).

During the past financial crisis, the interconnectedness between institutions led to negative spillover effects from banks with solvency and/or liquidity problems to the real economy and other institutions. In many developed countries, governments were forced to use public funds to help distressed financial institutions. Those governments helped those institutions to such a degree that it endangered the stability of sovereign finance. After those bail-outs, it has become a common opinion among researchers, that regulators should be equipped with the right tools to reduce systemic risk and the allocation of the costs of resolving those financial institutions’ difficulties. Those tools should be developed in such a way that it avoids moral hazard incentives (Bogini, Nieri & Pelagatti, 2015). In order to solve the moral hazard problem for macro-prudential regulators and not let the taxpayer pay the burden, the Basel Committee on Banking Supervision (BCBS) revised the Basel Accords (BCBS, 2011) 1_{. In 2011, the}

BCBS and FSB introduced the successor of Basel 2, Basel 3. Besides the revised risk-weighted assets capital ratios, the BCBS introduced the first Systemically Important Institutions (G-SIFIs) list as well. They introduced the list in cooperation with the Financial Stability Board (FSB) (BCBS, 2011). The first G-SIFI list is containing a set of 29 banks (G-SIBs) which are all too systemically important to fail. To decrease their influence on the overall systemic risk the 29 G-SIBs, additional measures on top of the regular Basel 3 capital requirements must be taken. The most important requirement those banks must comply with is the newly introduced additional loss absorbency requirement. Alongside the Basel 3 capital requirements, G-SIFIs must hold on to an additional Common Equity Tier 1 (CET1) capital ratio, ranging from 1% to 3.5% of the total risk-weighted assets on their book-based balance-sheet. A second macro-prudential policy measure is more intensive and effective supervision on G-SIFIs. Additionally, in case of failure G-SIBs must have a pre-planned recovery and resolution plan. The objective of these requirements is to guard the financial system against several spillover risks of G-SIBs and the negative externalities it has on the real economy (BCSB, 2011b).

Seven years after the introduction of the G-SIFI list, the question remains if the additional macro-prudential policies have met their objectives regarding systemic risk? In other words, this paper evaluates the effectiveness of the framework and asks:

Did the introduction of the Basel 3 additional loss absorbency requirements decrease the systemic risk contribution of Global Systemically Important Banks?

In order to give an answer on this research question, this paper makes use of the conditional value at risk model (CoVaR), established by Tobias Adrian and Markus K. Brunnermeier (2011). The ∆𝐶𝑜𝑉𝑎𝑅 identifies the risk to

1 _{A moral hazard problem exists, because banks know they are too systemic or big to fail, and therefore anticipate a bail out}

during a financial crisis. Consequently, in order to maximize their profits, it can lead to excessive risk-taking behavior. Therefore, without intervention the likelihood of a next financial crisis becomes higher.

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the system by individual financial institutions. Those financial institutions are large and interconnected, whereby the possibility develops that they can cause negative spillover effects on others and on the financial system as a whole. Technically, the risk to the system is identified by estimating the difference between the ∆𝐶𝑜𝑉𝑎𝑅 of the financial system as a whole when an individual institution is in distress and when it is in its median state. To test the ∆𝐶𝑜𝑉𝑎𝑅 model a quantile regression is conducted using panel data from 46 banks over the period 2001-2017. To give an answer on the research question several regulatory requirement (dummy) variables are added to the regression. Thereafter, in order to give a possible recommendation for an extension of the regulatory requirements several other variables are added to the regression as well. The main findings reveal that G-SIBs do have a larger systemic risk contribution to the financial system as a whole, than non G-SIBs. However, the results do not give enough explanatory power to show that the additional loss absorbency requirements do indeed decrease a G-SIB’s systemic risk contribution. Therefore, a conclusion on that cannot be made. Furthermore, the Value-at-Risk ratio of an individual bank, a bank’s short-term wholesale funding ratio, their market-to-book-ratio and the maturity mismatch between a bank’s short-term obligations and available short-term funds have a significant contribution to systemic risk as well. That is why this paper advisement to regulators is to focus more on these four variables when they assess the systemic risk contributions of banks.

This thesis studies the impact of regulation in terms of systemic risk and not a bank’s risk in isolation. This is a relatively new topic, as before the financial crisis most banks neglected their perspective on excessive risk-taking behavior from the systemic perspective. Thus, to the best of my knowledge, this paper contributes to the existing literature because there is little empirical evidence on the regulation of prudential supervision on systemic risk contributions of G-SIBs. Furthermore, this topic is important for regulators, since it is important to balance the benefits of regulation and simultaneously mitigating their unintended side effects (IMF, 2014).

The remainder of this paper starts with an illustrative framework of systemic risk in chapter 2. This chapter provides an explanation of the rules of Basel 3 and the additional requirements G-SIBs must require. Furthermore, it gives a brief explanation on the CoVaR model as well. Chapter 3 gives a description of the methodology of the empirical analysis of this paper. Thereafter, chapter 4 gives an explanation on the results of the empirical analyses. Chapter 5 provides an overview of the sensitivity analysis of the regressions based on their robustness and standard errors. Chapter 6 gives a discussion on the shortcomings and limitations of this research. In chapter 7, a conclusion is provided.

Chapter 2: An illustrative framework

2.1 Basel 3

During the Great Moderation, the financial sector underwent a period of financial liberalization. Regulation became less strict and competitive pressures within the financial market increased. It served as an opportunity for more cost-effective funding channels. It led also to lower lending rates and increased technological innovation and productivity growth (Cetorelli, 2001). However, it led to a more complex and opaque structure of the financial system as well. Therefore, to get a grip on the risks of this period of financial liberalization, governments introduced the Basel Committee on Banking Supervision (BCBS/BIS, 1974). The BCBS introduced several new policies, among which are the Basel Accords. In 1988, the first Basel accord was introduced. The purpose of Basel 1 was to improve financial market discipline and enhance financial stability. They did that by enforcing banks to hold on to a minimum of capital requirements, for the reason of guarding against losses during financial downswings. It enforced the rules to the participating countries, as its requirements were obligated by the national law of those countries (BCBS,

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2001). However, even though the capital requirements were a good start to hedge against capital risks, a shortcoming of Basel 1 was the “one-size-fits-all’” capital requirements (Vlahu, 2018).

To rectify this shortcoming the Basel accords are being continuously improved. Under Basel 1 the capital requirements were virtually the same for all banks, no matter the bank’s actual risk level and activities. Consequently, it did not fully reflect the true credit risk exposure of a bank. Subsequently, Basel 2 introduced the internal-rating-based (IRB) approach of capital requirements. The IRB approach provides banks the opportunity to set risk-weighted asset capital ratios based on a bank’s internal assessment model. Furthermore, the regular minimum capital requirements were revised as well. It became part of a so-called three-pillar framework:

• Pillar 1: Minimum Capital Requirements • Pillar 2: Supervisory Review

• Pillar 3: Market Discipline

The first pillar contains the rules of the minimum capital requirements a bank should hold on their book-based balance-sheet. Its purpose is to increase risk sensitivity by better refined risk weights. The second pillar sets out the supervisory review process, whereby the BIS, together with national regulators, review the IRB approaches of banks and encourage financial institutions to develop better risk management techniques. The last pillar is established to encourage market discipline. The BIS does this by forcing banks to disclose information on their capital ratio, risk management and risk exposure (Decamps, Rochet & Roger, 2002).

Basel 3 (2011) was introduced as a reaction to the financial crisis in 2008. An important modification of Basel 2 were the changes made regarding the first pillar risk-weighted assets capital requirements. The total risk-weighted asset capital did not change after the introduction of Basel 3. However, on the one hand, the composition of the ratio did. To make banks more resilient against capital risks, the Common Tier 1 capital ratio increased from 2% to 4.5%. The additional Tier 1 capital ratio increased as well, from 1.5% to 2%. On the other hand, the required Tier 2 capital ratio decreased from 4% to 2%. In total, banks should have a total capital ratio of at least 8%. Along with the changes of the standard capital ratios, the BIS introduced three new segments of pillar one as well (BCBS, 2011).

The first new component of pillar one is the Capital Conservation Buffer. The buffer is introduced in order to force banks to build up capital buffers in economic booms, so it can be used during economic downswings. Its purpose is to strengthen a bank’s ability to withstand adverse economic periods. The risk-weighted ratio should be at least 2.5% and comes on top of the regular 8% total capital RWA ratio (BCBS, 2011). The second addition to the pillar one capital requirements is the Countercyclical Buffer. The purpose of holding this buffer is to ensure the macro-financial environment, in which a bank operates, is taken into account while determining the height of the capital ratios (BCBS, 2011). The risk-weighted ratio of the Countercyclical Buffer ranges from 0% to 2.5% The magnitude of this ratio is based on the aggregate credit growth of a country, which is monitored and determined by the national authorities. It provides banks the opportunity to lean against excessive excess aggregate credit growth. Currently, during the writing of this paper, only Sweden and the Czech Republic have a Countercyclical Buffer higher than 0% (Perotti, 2018). The third new capital requirement is known as the Systemic Buffer and applies to Global Systemically Important Banks and because of the scope of this paper, it explained in more detail in paragraph 2.2. The newly introduced capital requirements aim to reduce capital risks; however, it does not take into account the liquidity risk. A strong liquidity base is of equal importance to the BIS and, therefore they introduced the Liquidity Coverage Ratio (LCR) and the Net Stable Funding Ratio (NSFR). The former is introduced to promote resilience in case of a thirty-day period of potential liquidity disruptions. In theory, the LCR ensures the market that banks

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have enough high-quality liquid assets during an acute short-term stress scenario (BCBS, 2013). The regulatory standard of a LCR is that it should have a stock of high-quality assets to total net cash outflow ratio above the 100% over a period of thirty calendar days. To continue, to promote a more medium- or long-term funding of assets the BIS introduced the Net Stable Funding Ratio. The NSFR is a ratio whereby banks must have a minimum of stable sources of funding, relative to a bank’s liquidity profile of assets and its off-balance sheet activities (BCBS, 2014). A disruption of a bank’s regular sources of funding can possibly erode a bank’s liquidity position and increase systemic risk and the likelihood of failure and the introduction of the NSFR tries to reduce these risks.

2.2 Global Systemically Important Institutions (GSIFIs)

After 1990, banks have significantly grown in size and moved from traditional bank-based activities to more innovative market-based activities. There are many benefits related to the transition to market-based operating banks. However, a disadvantage of a large bank is that it may operate at a size that can be too large from a social welfare perspective. The shortcomings of the right corporate governance and the “too-big-to-fail” subsidies make it difficult to regulate (IMF, 2014). Therefore, the Basel Committee on Banking Supervision (BCBS) and the Financial Stability (FSB) introduced several macro-prudential policies to address these issues. One of those policies is the introduction of the Global Systemically Important Institutions (G-SIFIs) list. The first list was introduced in 2011 and focused solely on banks. Therefore, it also goes by as the Global Systemically Important Banks (G-SIBs) list. From 2013 and on worth, the FSB published a Global Systemically Important Insurers (G-SIIs) list as well. However, the focus of this research lies on banks, and therefore it will not go further into detail about the G-SII list. The G-SIB list gives an overview of a set of 29 banks which are considered by the FSB and BCBS too systemically important to fail. Therefore, banks on this list must fulfill additional requirements on top of the Basel 3 rules. The purpose of these additional requirements is to reduce the influence of these banks on systemic risk. Every year the list changes if there is a decline or increase in the global systemic importance of a bank. An overview of the banks which are determined as G-SIBs through the years is given in table (3A) in the appendix.

2.2.1 Policy measures

The first requirement a G-SIB must have is a resolvability assessment plan. In case a G-SIB goes bankrupt they must have a pre-planned recovery and resolution plan available. The purpose of this plan is to create transparency between financial institutions and the authorities. Therewith, the plan must also be approved by those authorities (FSB, 2011). It should improve the cooperation between G-SIBs and local authorities and by this, it better the local authorities in case of financial crisis. Before the resolvability assessment plan is approved, it should contain a plan of recovery without exposing the burden on to the local taxpayers. At the same time, it should take into account maintaining the continuity of vital economic functions. Furthermore, during the liquidation period, the resolvability of a GSIB must absorb losses of outstanding claims in a manner that respect the hierarchy of the claims (FSB, 2011). Another macro-prudential policy for G-SIBs is the increased supervision of financial authorities, whereby the focus lies on the risk of management functions, risk governance, data aggregation capabilities and internal controls (FSB, 2012). Increased supervision on G-SIBs helps financial supervisors create a better understanding of the underlying risks of financial institutions. The most important and significant policy to answer the research question of this paper is the introduction of the additional absorbency requirements. In addition to the Basel 3 capital ratios, GSIBs must hold on to a systemic buffer ratio. Based on a G-SIB systemic importance the risk-weighted asset ratios vary between the 1% and 3.5%. The ratios are divided between four buckets, whereby the largest contributor to systemic risk must hold a systemic buffer of at least 2.5% and the smallest contributor must have a buffer of at least 1%. To avoid the incentive for G-SIBs to become more systemically important an additional

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systemic buffer of 3.5% is added on top of the highest populated bucket. If in the future the 3.5% bucket becomes populated, a new empty bucket with a higher additional loss absorbency requirement is added to the list of buckets (BCBS, 2011). An example of the FSB representation of the bucket list is given in table (3). Just like the G-SIB list, the bucket list varies every year as well if there is a decline or increase in the global systemic importance of a bank. An overview of which G-SIB must have which systemic buffer can be found in table (4).

2.2.2 Regulatory methodology systemic importance

The Financial Stability Board (FSB) identify G-SIBs based on an indicator measurement approach, which shows to which extent banks are involved in certain activities. The first G-SIB list contains an overview of 29 banks which were chosen from a sample of 73 banks. The sample is based on a bank’s total size and the supervisory judgment of BIS member authorities. After that, the FSB established 12 G-SIB indicators, which are divided into five categories (Oordt & Zhou, 2015).

Table (2) shows the five categories and twelve indicators. The first category represents the size of banks. According to the FSB, it is more likely that the potential damage a bank in distress causes to the real economy is bigger for big banks in distress than small banks in distress. A possible reason for this is, that compared to small banks, big banks have a larger share of global activities (BCBS, 2011). Therefore, the size of a bank is positively correlated with systemic importance. Secondly, the lack of readily available substitutes for services a bank can provide is the second category in table (2). The lower the substitutability of services, the larger the disruption to the real economy will be. Thus, lower substitutability of services means higher systemic risk. In addition, the degree of global

(cross-jurisdictional) activities is a regulatory G-SIB category as well. Internationally active banks are more arduous to

save if they are in distress, as they must comply with every national jurisdiction of the countries where they have branches. The more countries a bank is active in, the more difficult it becomes to divide outstanding claims in case of distress. For the reason, that sometimes different jurisdictions have different views on the hierarchy of outstanding claims, which makes it more complex to divide those claims in case of distress. That is why the degree of a bank’s global activities is positively correlated with systemic risk. The fourth systemic importance category is the structural, business and operational complexity of a bank. If the complexity of banks increases, the more time and financial assistance it needs in case of financial disturbance. Consequently, the complexity of a bank positively influences systemic importance. Finally, the last category is the interconnectedness between banks. Liquidity or solvency problems of a bank can increase the likelihood of negative spillover effects on other financial institutions. Many banks have outstanding loans to each other and given the contractual obligations these banks have to each other, they are vulnerable to systemic risk. Therefore, if more banks invest in the same tranche of assets, the higher systemic risk will be. The explanation of the five categories of systemic importance is based on the principles of systemic importance by the IMF, BIS and FSB (2009).

2.3 Systemic risk

There is no uniform consensus regarding the concept of systemic risk. There are several definitions (Oordt & Zhou, 2015. The European Central Bank defines it as “the risk that financial instability significantly impairs the provision

of necessary financial products and services by the financial system to the point where economic growth and welfare may be materially affected” (ECB, 2016). Bernanke (2009) defines it as the externalities of a bank in distress onto the real economy or financial system. The Financial Stability Board, IMF and the BIS define systemic risk in a broader scope: a risk of disruption to financial services, which is harmed by an impairment of all/ parts of the

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financial sector. This risk of disruption has the possibility to create serious negative consequences on the real economy, because of the interconnectedness between firms and households, which can lead to negative spillover effects (FSB, IMF & BCBS, 2009).

Apparently, there is no uniform consensus regarding systemic risk. Also, there is no uniform consensus about the different types of systemic risk either. Allen & Carletti (2011) classify systemic risk into six different groups. In random order: 1. common exposure to asset price bubbles, 2. multiple equilibria and panics, 3. mispricing of assets and liquidity provision, 4, contagion, 5. currency mismatches in the banking system and 6. sovereign default. The disadvantage is that the different systemic risk groups are usually identified ex-post. Therefore, it is difficult to make a tailor-made prevention system for each group. According to Nier (2009), systemic risk can be divided into a macroeconomic group and microeconomic group as well. Microeconomic systemic risk arises when the failure of a financial institution has an adverse impact on the whole financial system. For example, the default of a G-SIB. Macroeconomic systemic risk appears when the financial system as a whole is exposed to aggregate risk. For example, the growth of correlated exposure to certain assets (Nier, 2009). Furthermore, Bancarewicz (2005) characterize systemic risk into three groups. Namely, failure chains, macro shocks and reassessment failures. Failure chains refer to the spreading of risk, whereby the losses are incurred by one bank and will eventually lead to losses for other banks as well. The second type refers to the external disturbances, which prevent the financial system from fulfilling its function correctly. Differently, the last type refers to the increase of information asymmetry of correlated institution risk exposures and the limited possibilities to differentiate between those exposures. According to Brunnermeier and Sannikov (2011) systemic risk exists out of two important components. First, during credit booms systemic risk is build up in the background, since contemporaneously measured risk is low. Therefore, the risks shown on the surface are low during credit booms and results in a “volatility paradox”. This anomaly is created because low exogenous risk can potentially lead to extreme volatility of risk during a crisis regime. This happens because when fundamental risk factors show no signs of distress, it can lead to a higher leverage equilibrium. The second component of systemic risk are the spillover effects that amplify initial adverse shocks during a financial crisis. Financial frictions can have large effects on the real economy, seeing that the friction’s amplification goes through two different channels. The leverage channel and the price channel. A direct effect of the deterioration of leverage has an indirect effect on prices. A decline in leverage has a negative effect on the net worth of leveraged agents and, therefore the assets owned by those agents decline in value and price (Brunnermeier & Sannikov, 2011).

For macro-prudential policy it is very important to have the right tools to assess systemic risk. According to Laeyen, Ratnovski & Tong (2014), this has two different reasons. First, joint distress may increase the risk of asset sales sold at fire-sale prices. If a bank does not have enough short-terms available for the payments of their short-term obligations, they will sell their long-term assets in order to raise their cash funds. These assets will be sold before their maturity date and are thus sold for a lower price than they are actually worth. This drives down the market price of these assets with subsequent investments of companies with similar assets results in losses as well. This grades into a contagiousness effect, which eventually results in losses on the real economy. Furthermore, there are other reasons for macro-prudential policy to have the right tools to limit systemic risk. Firstly, it reduces the ability of firms to effectively raise capital. Secondly, it reduces the ability for firms to effectively raise capital. During financial booms, a distressed bank can raise new capital or be acquired by other banks. If there are multiple banks in distress, the options to raise capital or be acquired becomes limited. This increases the risk of a domino effect on bank bankruptcies, which eventually leads into a generalized bank panic.

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2.4 Modelling systemic risk

Before the financial crisis (2008) the Value-at-risk (VaR) approach was a very common methodology used to quantify a firm’s risk exposure. This method is a statistical technique to quantify the financial risk of an investment portfolio from a stand-alone firm.

𝑃𝑟(𝐿 > 𝑉𝑎𝑅(𝛼)) ≤ 1 − 𝛼 (1)

In equation (1) L stands for loss and 𝛼 represents the confidence level. Given this, equation (1) shows the probability of the loss of a portfolio in isolation in a worst-case scenario (Jorion, 2007). After the financial crisis, models based on this equation received severe criticism, because it does not take into account systemic risk. Therefore, to include the systemic nature of risk, several researchers developed alternative models in order to solve this problem.

In practice, there are two ways to quantify the systemic risk contribution of a given financial institution. The first approach is the regulatory approach, which is explained in chapter 2.2.2. This approach relies heavily on confidential information about an institution’s risk exposure. Banks are obligated by their national law to provide such information to the right authorities. The dependency on confidential information complicates the assessment of another institution’s systemic risk exposure. That is why the second approach is largely based on publicly available data. Most of the models within this category rely generally on individual balance sheet data, stock returns option prices, or CDS spreads (Benoit et al., 2013). There are two prominent systemic risk models within this category which are highly recommended by the existing economic literature: The Marginal Expected Shortfall (MES) and the Delta Conditional Value-at-Risk model (∆𝐶𝑜𝑉𝑎𝑅).

2.4.1 The marginal expected shortfall (MES)

The first model discussed in this paper is the Marginal Expected Shortfall (MES). The MES is originally proposed by Acharya, Pedersen, Philippon and Richardson (2010). The model quantifies a firm expected equity loss, conditional on the market taking a loss greater than the Value-at-Risk (𝛼). The model starts with the intuition behind the Expected Shortfall (ES). The ES represents the expected loss of a bank, conditional on the loss being greater than the VaR(𝛼).

𝐸𝑆(∝) = −𝐸[𝑅|𝑅 ≤ −𝑉𝑎𝑅(∝)]

(2)

Equation (2) shows the equation of the Expected Shortfall, given the average return of an investment portfolio at its exceeding 𝑉𝑎𝑅(𝛼). Most of the time the total investment portfolio of a company exists out of different tranches of investments, risks, maturity and liquidity. Therefore, the returns on those investments are different as well. Hence, 𝑅 = ∑ 𝑦𝑖𝑡 𝑖𝑡𝑟𝑡𝑖 and from that definition equation (2) becomes:

𝐸𝑆(∝) = − ∑ 𝑦

𝑖 𝑖,𝑡

𝐸[𝑟

𝑖,𝑡

|𝑅 ≤ −𝑉𝑎𝑅(∝)] (3)

Thereafter, the marginal effect of equation (3) is calculated by taking the first difference of the equation, w.r.t 𝑦𝑖,𝑡:

𝜕𝐸𝑆(𝛼)_𝜕𝑦

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Equation (4) shows how much the risk of a specific tranche of an investment portfolio adds to the overall systemic risk exposure of an institution. There are several extensions of equation (4). One of these extensions is the Systemic Expected Shortfall (SES). In case of a systemic crisis, the SES shows how much an institution’s equity drops below its target level. In theory, a crisis is systemic if the aggregate capital is less than k times the aggregate assets (Beniot et al., 2013).

𝑆𝐸𝑆𝑖𝑡

𝑊𝑖𝑡

= 𝑘𝐿

𝑖𝑡

− 1 − 𝐸(𝑟

𝑖

| ∑

𝑊

𝑖𝑡

𝑁

𝑖=1

< 𝑘 ∑

𝑁𝑖=1

𝐴

𝑖𝑡

)

(5)

𝐿𝑖𝑡 represents the total leverage of a firm, 𝐴𝑖𝑡 total assets and 𝑊𝑖𝑡 the total market capitalization. Following, equation

(5) can be expressed as a linear function of the MES. This is done by substituting equation (4) into (5) and thereafter, placing 𝑊𝑖𝑡 to the right-hand side of the equation:

𝑆𝐸𝑆

𝑖𝑡

= (𝑘𝐿

𝑖𝑡

− 1 + 𝛿𝑀𝐸𝑆

𝑖𝑡

+ 𝜃

𝑖

)𝑊

𝑖𝑡 (6)

𝛿 and 𝜃𝑖 are constant. A benefit of the SES is that it is relatively easy to use, compared to the regulatory approach.

2.4.2 Delta Conditional Value at Risk (∆CoVaR)

Another widely used systemic risk model is the delta CoVaR, designed by Adrian and Brunnermeier (2011). The prefix “Co,” stands for comovement, conditional or contagion. The ∆CoVaR captures the tail-dependency between financial institutions and the market in which they operate. A benefit of this model is that it makes use of a variety of individual balance sheet data. That is why it can give a broader explanation of a firm’s systemic risk exposure than the MES. According to Lopez-Espinosa and Moreno (2012), the ∆CoVaR allows for the characterization of contagions under balance sheet deleveraging. This an important aspect for this paper, as it is a key driver of the regulatory framework of the Basel Accords. Another benefit of the ∆𝐶𝑜𝑉𝑎𝑅 is that it can easily detect non-linear patterns within the given data because it can give information about different quantiles of a distribution. Based on the benefits of the ∆𝐶𝑜𝑉𝑎𝑅 and because it is a relatively new model, this paper does an empirical research on systemic risk factors using the ∆𝐶𝑜𝑉𝑎𝑅, instead of the MES.

Adrian and Brunnermeier (2011) base the ∆𝐶𝑜𝑉𝑎𝑅 model on a VaR approach. The model starts with the calculation of the growth rate of the market-value of the total assets of a bank. The setup of the ∆𝐶𝑜𝑉𝑎𝑅 start with the following equation:

𝑋

_𝑡𝑖

₌

𝑀𝐸𝑡𝑖∗𝐿𝐸𝑉𝑡𝑖−𝑀𝐸𝑡−1𝑖 ∗𝐿𝐸𝑉𝑡−1𝑖

𝑀𝐸_𝑡−1𝑖 ∗𝐿𝐸𝑉_𝑡−1𝑖

=

𝐴_𝑡𝑖−𝐴𝑖_𝑡−1

𝐴_𝑡−1𝑖

(7)

Where 𝐴𝑖𝑡= 𝑀𝐸𝑡𝑖∗ 𝐿𝐸𝑉𝑡𝑖. The left-hand side of equation (7) shows the growth rate of the market-valued total assets

of a firm. 𝑀𝐸𝑡𝑖 stands for the market-valued total equity and 𝐿𝐸𝑉𝑡𝑖 for the ratio of total assets to book equity. There

are several approaches to calculate the growth rate of market valued assets. However, according to Adrian and Brunnermeier (2011), this approach is closely related to the supply of credit to the real economy. It can be based on publicly available data however, regulators can use the model based on a broader definition of total assets. The authorities can capture exposures from derivative contracts, off-balance-sheet assets and other claims which is not captured by the IFRS accounting standards. This can potentially improve the accuracy of the systemic risk exposure of a bank. Accordingly, equation (7) shows the growth rate of assets of an individual. However, to shows its systemic risk contribution to the financial system as a whole, the aggregate growth rate of total assets of the whole financial system must be calculated as well:

13

X

_tsystem

= ∑

Ati_A−At−1i t−1 i n i=0

(8)

One of the benefits of the ∆𝐶𝑜𝑉𝑎𝑅 is that one can look at different quantiles of a distribution. Therefore, based on this benefit and the explanation in chapter 3.2 this paper makes use of a quantile regression. Henceforward, a 𝑞𝑡ℎ_{− 𝑞𝑢𝑎𝑛𝑡𝑖𝑙𝑒 of the financial sector ( 𝑋}

𝑞𝑠𝑦𝑠𝑡𝑒𝑚,𝑖̂ ) asset growth rate, conditional on a particular institution, looks as

follow:

𝑋

_𝑞𝑠𝑦𝑠𝑡𝑒𝑚

̂ = ∝̂

_𝑞

+ 𝛽

̂𝑋

_𝑞 𝑖

₍₉₎

The conditional Value-at-Risk measures the risk when an institution is in distress, that is why this paper makes use of the 0.50𝑡ℎ_{− 𝑞𝑢𝑎𝑛𝑡𝑖𝑙𝑒 and the 0.01}𝑡ℎ_{− 𝑞𝑢𝑎𝑛𝑡𝑖𝑙𝑒. The former denotes the median, which measures systemic risk}

during the normal state of the economy and the latter denotes the left-tail distribution under extreme distress. From the definition of 𝑉𝑎𝑅(𝛼), given in chapter 2.4, it follows that the 𝑉𝑎𝑅𝑞𝑠𝑦𝑠𝑡𝑒𝑚,𝑖

= 𝑋̂

𝑞𝑠𝑦𝑠𝑡𝑒𝑚,𝑖

and the 𝑉𝑎𝑅

𝑞𝑖

= 𝑋

𝑞𝑖

.

Thereafter, based on this explanation, the 𝐶𝑜𝑉𝑎𝑅𝑞 is given by:

𝐶𝑜𝑉𝑎𝑅

_𝑞(

𝑠𝑦𝑠𝑡𝑒𝑚

|

𝑋

𝑖

= 𝑉𝑎𝑅

𝑞𝑖 )

: = 𝑉𝑎𝑅

_𝑞𝑠𝑦𝑠𝑡𝑒𝑚

|𝑉𝑎𝑅

_𝑞𝑖

_=∝

_̂

𝑞

+ 𝛽

̂𝑉𝑎𝑅

𝑞𝑖 𝑞𝑖

(10)

T

he final step for computing the ∆𝐶𝑜𝑉𝑎𝑅𝑞 is simply calculating the first difference of equation (10):

∆𝐶𝑜𝑉𝑎𝑅

_𝑞(

𝑠𝑦𝑠𝑡𝑒𝑚

|

𝑋

𝑖

_{= 𝑖}

₎

= 𝛽

̂(𝑉𝑎𝑅

𝑞𝑖 𝑞𝑖

− 𝑉𝑎𝑅

50%𝑖

) (11)

Equation (11) presents the final formula of ∆𝐶𝑜𝑉𝑎𝑅𝑞 that is constant over time.

According to FSB (2012), the Basel 3 capital ratios and the additional absorbency requirements have a significant contribution to systemic risk. However, there are also other factors which contribute to systemic risk. According to Lopez-Espinosa, Morena, Rubia and Valderrama (2012), the short-term wholesale funding ratio is a key contributor to systemic risk. They concluded that the short-term wholesale funding ratio has a positive effect on systemic risk. In other words, an increase in this ratio leads to an increase in systemic risk. A reason for this is, that it is strongly related to the liquidity risk and interconnectedness exposure of a bank. In addition, the maturity mismatch between short-term liabilities and cash or cash equivalents of a firm is an important characteristic as well. If a bank Is not able to pay off its short-term obligations, it exposes themselves to substantial systemic risks (Farhi & Tirole, 2012). Reasoning that a significant maturity mismatch can lead to a liquidity problem. This forces banks to “fire sale” their assets. If this happens, securities are traded below their intrinsic value, which negatively affects the market price of these securities. Institutions which hold these securities will, therefore lose on their investments as well. It creates a contagiousness effect (Bleakley & Cowan, 2012). The market-to-book ratio has a contribution to the ∆𝐶𝑜𝑉𝑎𝑅 as in individual variable as well. Lopez-Espinosa et al. (2012) report that it is a proxy for growth opportunities of a bank and due to the expected market value realignments, it can also capture systemic risk. Furthermore, the representation of the total assets to equity ratio (leverage) has an important influence on systemic risk as well (Lopez-Espinosa et al., 2012). The ratio is a proxy for the solvency of an institution. Insolvency problems can possibly lead to a bank run, which can trigger market panic within the financial system. Eventually, this affects other banks as well. Therefore, if a bank cannot meet its long-term obligations, systemic risk increases. Another key contributor to systemic risk is the size of a bank. Laeven, Ratnivski and Tong (2014) say that large banks are riskier and therefore create more systemic risk. The failure of a large bank is more disruptive to the financial sector than

14

the failure of a small bank. The activities of large banks usually rely on economies of scale, which cannot simply be replaced by small banks, in case of a failure.

Chapter 3: Methodology

3.1 Descriptive statistics and dataset

Every November The Basel Committee on Banking Supervision and the Financial Stability Board present an updated version of the G-SIB list. Updating the list is required, as every year the systemic importance of a bank changes. The decision on whether the list should be updated is based on a methodology composed by committee members of the BCBS and FSB (BCBS, 2011). Part of this methodology is explained in chapter 2.2. Another part of the methodology is simply not enclosed by the BCBS and FSB. This part is about the decision which banks should be in the sample of the methodology assessment of the G-SIB list. The only thing that is known, is that they use a sample of 73 individual banks. For the reason that an overview of this sample is not publicly known, this paper makes use of the sample list by Bogini, Nieri & Pelagatti (2015). Their research makes use of a sample of 70 individual banks. These banks are picked based on the following three requirements.

• The banks in the sample have all a total asset value exceeding the $200 million.  The banks are enlisted during the entire testing period of the research.

 The headquarters of the banks are all located in the following regions: North-America, South-America, Central-America, Western-Europe, Scandinavia, Far East Asia or Central Asia.

In total, this paper uses 46 banks on that list. 16 North-American banks and 30 European banks. An overview of these 46 banks can be found in table (1). The systemic risk contributions of these banks are analyzed within the period of 2001 till 2017. This timeframe is chosen, because Basel 2 was implemented in 2004 and Basel 3 in 2011, this period gives a good representation of the years prior to and after the introduction of Basel 2 and 3. The regressions of this research are based on a strongly balanced panel dataset, whereby quarterly data is used. Table (5) provides a general overview of this data. First, the table shows that the median of the conditional value at risk is equal to -0.0022652. This means that the median of the worst return of the financial sector as a whole is equal to -0.0022652. The ∆𝐶𝑜𝑉𝑎𝑅𝑖,𝑡(1%) and the 𝑉𝑎𝑅𝑖,𝑡(1%) are composed based on the calculations of the 𝐶𝑜𝑉𝑎𝑅𝑖,𝑡,

explained in chapter 2.4.2. The data that used for the determination of these two variables is based on market- and book- based individual bank balance sheet data. The market-based individual bank balance sheet data is obtained from DataStream and the book-based individual bank balance sheet data is obtained from the CAPITALIQ database and the CRSP database. The base variables 𝐿𝑒𝑣𝑒𝑟𝑎𝑔𝑒𝑖,𝑡 (total asset to equity ratio), 𝑊𝑆𝐹𝑖,𝑡 (short-term

wholesale funding ratio), 𝑆𝑖𝑧𝑒𝑖,𝑡 (total book-based asset value), 𝑀𝑇𝐵𝑖,𝑡 (market-to-book ratio), and the 𝑀𝑀𝑀𝑖,𝑡

(maturity mismatch) are obtained from those three databases as well. Furthermore, 𝐺𝑆𝐼𝐵𝑖,𝑡 represents a dummy

variable. If this dummy variable is equal to zero it means that the bank is not a G-SIB and if it is equal to one the bank is a G-SIB. An overview of whether a bank qualifies as a G-SIB or not can be found in table (4). This table shows that not every year the same banks are enlisted as G-SIBs, during the time period 2011-2017. For example, Dexia and Lloyds Banking Group were only considered G-SIBs in 2011. After this year, they lost their G-SIB status because of their decrease in systemic importance. Instead, the Royal Bank of Canada just recently qualifies as a G-SIB (2017). The 𝐵𝑢𝑐𝑘𝑒𝑡𝑖,𝑡 variable represents another dummy variable group. The values one to four indicates

the level of additional loss absorbency requirement in ascending order. The zero indicates that the bank is not a G-SIB and therefore, does not have an additional loss absorbency requirement ratio. The values one till four

15

indicates the systemic importance of a bank in ascending order. Hence, one represents the banks which need an additional loss absorbency requirement ratio of 1% and four represents the banks which need an additional loss absorbency requirement ratio of 2.5%. Just as the G-SIB dummy, the bucket dummies do not have a constant value through the years of this sample. For instance, Citigroup was considered a bucket 4 bank in 2012, while in 2013 they were considered a bucket 3 bank. The FSB and BCBS changed Citigroup’s G-SIB status because their systemic importance changed. An overview of the ranking of systemic importance of G-SIBs can be found in table (4). Following, the regulatory capital regulatory capital requirement ratios: 𝑡𝑖𝑒𝑟1𝑟𝑎𝑡𝑖𝑜𝑖,𝑡, 𝑡𝑜𝑡𝑐𝑎𝑝𝑟𝑎𝑡𝑖𝑜𝑖,𝑡 and

𝑡𝑖𝑒𝑟1𝑙𝑒𝑣𝑟𝑎𝑡𝑖𝑜𝑖,𝑡. Respectively, the tier 1 RWA capital ratio, the total RWA capital ratio and the tier 1 RWA leverage

ratio. These ratios are chosen in particular, because they are important systemic risk contribution factors and must be obtained by non G-SIBs as well. The data on these ratios is retrieved from the CAPITALIQ database and the Orbis Bankfocus database.

Graph (1) shows the median movements of the ∆𝐶𝑜𝑉𝑎𝑅𝑖,𝑡 between the period 2001 and 2017. The graph shows

that the volatility of the variable increased during the financial crisis of 2008 and 2012. The downturns in the graph indicate a drop in returns, conditional on the institution’s lowest percentile returns. A drop in returns indicates an increase in systemic risk. Thereafter, the graph complies with the theory that systemic risk increased during the 2008 and 2012 financial crisis. The period between the two vertical blue dashed lines shows the movements of the ∆𝐶𝑜𝑉𝑎𝑅𝑖,𝑡 after the introduction of the FSB G-SIB list. The black line indicates the median movements of the

∆𝐶𝑜𝑉𝑎𝑅𝑖,𝑡 of non G-SIBs and the red line indicates the median movements of the ∆𝐶𝑜𝑉𝑎𝑅𝑖,𝑡 of G-SIBs. The lines

show that the ∆𝐶𝑜𝑉𝑎𝑅𝑖,𝑡 of G-SIBs is more volatile than that of non G-SIBs. This backs the idea that G-SIBs have

a larger contribution to systemic risk than non G-SIBs. Graph (2) presents the mean development of the 𝑇𝑖𝑒𝑟1𝑟𝑎𝑡𝑖𝑜𝑖,𝑡 variable. The graph shows a clear upward trend in the tier 1 RWA capital ratio. A reason for this

increasing trend is the Basel accords. According to Basel 2, banks needed a 4.5% tier 1 RWA capital ratio. After Basel 3, this ratio increased with 2% to 6.5%. However, the graph shows a higher value than the two Basel ratios. A possible reason for this is that banks want to have a buffer ratio, in order to withstand against possible drawbacks. If their ratios fall below the legally required ratio it will possibly create market panic. If this happens, investors signal the solvency issues of a bank, which can possibly result in a bank run. The period between the two vertical blue dashed lines shows the mean movements of the 𝑇𝑖𝑒𝑟1𝑟𝑎𝑡𝑖𝑜𝑖,𝑡 after the introduction of the FSB G-SIB list. The black

line shows the tier 1 ratio of non G-SIBs and the red line shows the tier 1 ratio of G-SIBs. The two lines show that non G-SIBs have a larger tier 1 ratio than G-SIBs. A probable reason for this is that G-SIBs makes more profits than non SIBs and therefore, can have a lower tier 1 ratio. They make more profits because most of the time G-SIBs have more funds available to invest in a diverse set of investments (Laeven, Ratnovski & Tong, 2014).

3.2 Quantile regression

A standard OLS regression shows the average relationship between the outcome variable and a set of individual variables. Conditional on the mean distribution function 𝐸(𝑦|𝑥) (Stock & Watson, 2015). However, sometimes it is also interesting to show the results of the relationship at different points of the conditional distribution of 𝐸(𝑦|𝑥). Especially, if the data does not have a normal distribution. A quantile regression includes this option (Rodriguez & Yao, 2017).

𝑄

_𝑞

(𝑦

_𝑖

) = 𝛽

₀

(𝑞) + 𝛽

₁

(𝑞)𝑥

_𝑖1

+. . + 𝛽

_𝑝

(𝑞)𝑥

_𝑖𝑝

𝑖 = 1, … . . , 𝑛 (15

)

Equation (15) shows the basic theoretical formula of a quantile regression. The q stands for the quantile level. According to Koenker & Bassett (1978), a quantile regression has several advantages over a linear OLS regression.

16

First, it does not need the requirement of a normal distribution, as it looks at the different quantiles of the distributions. Secondly, it shows robustness in handling outliers. It is also insensitive to monotonic transformations of the dependent variable. Finally, it gives a more “complete” overview of the relationship between the dependent variables and its covariates. As a result of these advantages, this research makes use of a quantile regression, since it gives the opportunity to study which bank contributes the most to the systemic risk of the financial system as a whole.

3.3 The empirical regression model

This research paper examines the theoretical relevant systemic risk factors for a sample of 46 banks, for the period 2001-2017. An overview of the 46 participating banks is given in table (1).

The baseline of this model is based on the IMF research paper of Lopez-Espinosa, Moreno, Rubia and Valderrama (2012). This regression test the significance of independent variables other than the regulatory Basel 3 requirement variables.

• Regression (1): baseline regression

∆𝐶𝑜𝑉𝑎𝑅

𝑡𝑖

(𝑞): 𝛽̂

𝑠𝑦𝑠𝑡𝑒𝑚|𝑖

(𝑉𝑎𝑅

𝑡𝑖

(𝑞) − 𝑉𝑎𝑅

𝑡𝑖

(50%)) = 𝛽

0

+ 𝛽

1

∆𝐶𝑜𝑉𝑎𝑅

𝑖,𝑡−1

+ 𝛽

2

𝑉𝑎𝑅

𝑖,𝑡

+

𝛽

3

𝐿𝑒𝑣𝑒𝑟𝑎𝑔𝑒

𝑖,𝑡

+ 𝛽

4

𝑊𝑆𝐹

𝑖,𝑡

+ 𝛽

5

𝑆𝑖𝑧𝑒

𝑖,𝑡

+ 𝛽

6

𝑀𝑇𝐵

𝑖,𝑡

+ 𝛽

7

𝑀𝑀𝑀

𝑖,𝑡

+ 𝜀

𝑖,𝑡

First, the dependent variable of regression (1) is based on the ∆CoVaR explanation in paragraph 2.4.2. Secondly, the independent variable ∆𝐶𝑜𝑉𝑎𝑅𝑖,𝑡−1 . represent the first lag of the delta conditional value at risk. It tests if the

dependent variable is partly determined by its past levels. Moreover, the 𝑉𝑎𝑅𝑖,𝑡 represents the Value at Risk of

each individual bank. According to Adrian & Brunnermeier (2012), the variable has a low correlation with the ∆𝐶𝑜𝑉𝑎𝑅 in the cross-sectional dimension, but a strong relationship within the time dimension. The expectation of this variable is that it shows a negative sign, as it seems logical that individual risk contributes to systemic risk as well, because of the interconnectedness of banks.

The variable 𝐿𝑒𝑣𝑒𝑟𝑎𝑔𝑒𝑖,𝑡 represents the total assets to equity ratio. The expectation is that has a negative effect on

∆𝐶𝑜𝑉𝑎𝑅

𝑡𝑖

(𝑞). The same counts for the 𝑊𝑆𝐹

𝑖𝑡−1, 𝑆𝑖𝑧𝑒𝑖𝑡−1, 𝑀𝑀𝑀𝑖𝑡−1 and 𝑀𝑇𝐵𝑖𝑡−1, respectively, the short-term

wholesale funding ratio, the total book valued assets, market-to-book ratio and the maturity mismatch. All those variables are expected to negatively influence the dependent variable. The expectations of the independent variable are based on the expectations of the paper by Lopez-Espinosa, Morena, Rubia and Valderrama (2012). A short explanation of these variables’ expectations is given in chapter 2.

A helpful method for answering the research question of this paper is to analyze whether the G-SIBs are systemically more important than non G-SIBs. Therefore, a second regression is performed:

• Regression (2): GSIB regression

∆𝐶𝑜𝑉𝑎𝑅

𝑡𝑖

(𝑞) = 𝛽

0

+ 𝛽

1

∆𝐶𝑜𝑉𝑎𝑅

𝑖,𝑡−1

+ 𝛽

2

𝑉𝑎𝑅

𝑖,𝑡

+ 𝛽

3

𝐿𝑒𝑣𝑒𝑟𝑎𝑔𝑒

𝑖,𝑡

+ 𝛽

4

𝑊𝑆𝐹

𝑖,𝑡

+ 𝛽

5

𝑆𝑖𝑧𝑒

𝑖,𝑡

+𝛽

6

𝑀𝑇𝐵

𝑖,𝑡

+ 𝛽

7

𝑀𝑀𝑀

𝑖,𝑡

+ 𝛽

8

𝐺𝑆𝐼𝐵

𝑖,𝑡

+ [

𝛽

9

⋮

𝛽

12

] ∗ [

𝐵𝑢𝑐𝑘𝑒𝑡0

𝑖,𝑡

⋮

𝐵𝑢𝑐𝑘𝑒𝑡3

𝑖,𝑡

] + 𝜀

𝑖,𝑡

17

𝐺𝑆𝐼𝐵𝑖 is a dummy variable and tests whether G-SIBs indeed have a larger contribution to systemic risk than non

G-SIBs. The expectation of this variable is that has a positive sign. It shows that G-SIBs have a larger contribution to systemic risk than non G-SIBs. This theory is based on the theory of the FSB (2011). Furthermore,

[

𝛽

9

⋮

𝛽

12

] ∗ [

𝐵𝑢𝑐𝑘𝑒𝑡0

𝑖,𝑡

⋮

𝐵𝑢𝑐𝑘𝑒𝑡3

𝑖,𝑡

]

test if G-SIBs with a larger additional loss absorbency requirement contribute more to

systemic system than banks in with lower requirement ratios. The banks in 𝐵𝑢𝑐𝑘𝑒𝑡0𝑖,𝑡 represents the banks which

do not have an additional loss absorbency ratio and 𝐵𝑢𝑐𝑘𝑒𝑡4𝑖,𝑡 is used as reference dummy. The expectation is

that all four dummy variables have a negative sign (FSB, 2012). This means that the banks in those buckets are systemically less important than the banks in bucket 4.

Another helpful method for answering the research question is to analyze whether the regular Basel 3 ratios have a significant influence on systemic risk. That is why, a fourth regression is analyzed:

• Regression (3): regulatory capital requirements regression

∆𝐶𝑜𝑉𝑎𝑅

𝑡𝑖

(𝑞) = 𝛽

0

+ 𝛽

1

∆𝐶𝑜𝑉𝑎𝑅

𝑖,𝑡−1

+ 𝛽

2

𝑉𝑎𝑅

𝑖,𝑡

+ 𝛽

3

𝐿𝑒𝑣𝑒𝑟𝑎𝑔𝑒

𝑖,𝑡

+ 𝛽

4

𝑊𝑆𝐹

𝑖,𝑡

+ 𝛽

5

𝑆𝑖𝑧𝑒

𝑖,𝑡

+𝛽

6

𝑀𝑇𝐵

𝑖,𝑡

+ 𝛽

7

𝑀𝑀𝑀

𝑖,𝑡

+ 𝛽

8

𝐺𝑆𝐼𝐵

𝑖,𝑡

+ [

𝛽

9

⋮

𝛽

12

] ∗ [

𝐵𝑢𝑐𝑘𝑒𝑡0

𝑖,𝑡

⋮

𝐵𝑢𝑐𝑘𝑒𝑡3

𝑖,𝑡

] + 𝛽

13

𝑇𝑖𝑒𝑟1𝑟𝑎𝑡𝑖𝑜

𝑖,𝑡

+ 𝛽

14

𝑇𝑜𝑡𝑐𝑎𝑝𝑟𝑎𝑡𝑖𝑜

𝑖,𝑡

+ 𝛽

15

𝑇𝑖𝑒𝑟1𝑙𝑒𝑣𝑟𝑎𝑡𝑖𝑜

𝑖,𝑡

+ 𝜀

𝑖,𝑡

The independent variables 𝑇𝑖𝑒𝑟1𝑟𝑎𝑡𝑖𝑜𝑖,𝑡 and 𝑇𝑜𝑡𝑐𝑎𝑝𝑟𝑎𝑡𝑖𝑜𝑖,𝑡 represents the regular Basel 3 pillar 1 capital

requirements. The expectation is that both variables have a positively effect on

∆𝐶𝑜𝑉𝑎𝑅

_𝑡𝑖

(𝑞).This means that a

higher capital ratio reduces systemic risk. This is in line with the Basel 3 (2011) theory. The

𝑇𝑖𝑒𝑟1𝑙𝑒𝑣𝑟𝑎𝑡𝑖𝑜

𝑖,𝑡

represents the Tier 1 leverage ratio. The expectation is that it has a positive effect on

the dependent variable (Basel, 2013)

In analyzing whether the additional absorbency requirement ratios significantly contribute to systemic risk, a final regression is analyzed:

• Regression (4): additional loss absorbency requirement regression

∆𝐶𝑜𝑉𝑎𝑅

𝑡𝑖

(𝑞) = 𝛽

0

+ 𝛽

1

∆𝐶𝑜𝑉𝑎𝑅

𝑖,𝑡−1

+ 𝛽

2

𝑉𝑎𝑅

𝑖,𝑡−1

+ 𝛽

3

𝐿𝑒𝑣𝑒𝑟𝑎𝑔𝑒 + 𝛽

4

𝑊𝑆𝐹

𝑖,𝑡−1

+ 𝛽

5

𝑆𝑖𝑧𝑒

𝑖,𝑡−1

+𝛽

6

𝑀𝑇𝐵

𝑖,𝑡−1

+ 𝛽

7

𝑀𝑀𝑀

𝑖,𝑡−1

+ 𝛽

8

𝐺𝑆𝐼𝐵

𝑖

+ [

𝛽

9

⋮

𝛽

12

] ∗ [

𝐵𝑢𝑐𝑘𝑒𝑡0

𝑖,𝑡

⋮

𝐵𝑢𝑐𝑘𝑒𝑡3

𝑖,𝑡

] + 𝛽

13

𝑇𝑖𝑒𝑟1𝑟𝑎𝑡𝑖𝑜

𝑖,𝑡

+ 𝛽

14

𝑇𝑜𝑡𝑐𝑎𝑝𝑟𝑎𝑡𝑖𝑜

𝑖,𝑡

+ 𝛽

15

𝑇𝑖𝑒𝑟1𝑙𝑒𝑣𝑟𝑎𝑡𝑖𝑜

𝑖,𝑡

+ [

𝛽

16

⋮

𝛽

19

] ∗ 𝑇𝑖𝑒𝑟1𝑟𝑎𝑡𝑖𝑜

𝑖,𝑡

∗ [

𝐵𝑢𝑐𝑘𝑒𝑡0

𝑖,𝑡

⋮

𝐵𝑢𝑐𝑘𝑒𝑡3

𝑖,𝑡

] + 𝜀

𝑖,𝑡

18

[

𝛽

16

⋮

𝛽

19

] ∗ 𝑇𝑖𝑒𝑟1𝑟𝑎𝑡𝑖𝑜

𝑖,𝑡

∗ [

𝐵𝑢𝑐𝑘𝑒𝑡0

𝑖,𝑡

⋮

𝐵𝑢𝑐𝑘𝑒𝑡3

𝑖,𝑡

] represents the interaction variables between the Basel 3 Tier 1

ratios and the buckets. It is a proxy for the additional absorbency requirement ratios. The expectations

of these variables are that positively influences the delta conditional value at risk, as the ratios are

introduced to reduce systemic risk (FSB, 2012).

Chapter 4: Empirical regression results

Table (6) shows the regression results of the 1% delta conditional value at risk regressions. Column (1) gives the results of the baseline regression. Column (2) explains the results of G-SIB regression. Column (3) describes the results of the regulatory capital requirement regression and column (4) shows the results of the additional absorbency requirement regression.

Starting from column (1) we observe that the 𝑝𝑠𝑒𝑢𝑑𝑜 − 𝑅2 equals 0.3766. This means that the independent variables of regression (1) explain 37.66% of the variation of the ∆𝐶𝑜𝑉𝑎𝑅𝑖,𝑡(1%). The F-statistic (F(7,2134)) equals

1.9e+06, which means that with a 1% significance value the null hypothesis which tells that all independent variables are equal to zero can be rejected. This means that the combination of all the variables results in a good explanation of the values of ∆𝐶𝑜𝑉𝑎𝑅𝑖,𝑡(1%). Taking a closer look at each coefficient of column (1) one can see that

the first lag of the dependent variable is negatively significant at the 1% rejection region. The variable is included in the regression to show the results of the speed of adjustment of the dependent variable. Instead of an abrupt increase or decrease of the ∆𝐶𝑜𝑉𝑎𝑅𝑖,𝑡(1%), the variable gradually adjusts to its new value when one of the

independent variables changes. Furthermore, the value-at-risk is negatively significant at the 1% significance level as well. It means that an isolated individual risk exposure has a negative effect on the delta CoVaR. It is related to the microeconomic system risk factors, and therefore it shows the same results as the theory in chapter 2. Thereafter, we can see that the 𝐿𝑒𝑣𝑒𝑟𝑎𝑔𝑒𝑖,𝑡 variable negatively affects the ∆𝐶𝑜𝑉𝑎𝑅𝑖,𝑡 and therefore, it positively

affects systemic risk. The delta CoVaR shows the worst returns conditional on the bank’s 1% left-tail returns. Therefore, a decrease in ∆𝐶𝑜𝑉𝑎𝑅𝑖,𝑡(1%) represents a decrease in the lowest returns and hence, an increase in

systemic risk. If assets are relatively less funded with capital than with debt, systemic risk increases, according to theory in chapter 2. 𝐿𝑒𝑣𝑒𝑟𝑎𝑔𝑒𝑖,𝑡 shows similar results and therefore, it is in line with the theory. The same goes for

𝑊𝑆𝐹𝑖,𝑡, as an increase in the variable reduces the lowest returns in the 1% left-tail with -0.0772. The short-term

wholesale funding ratio is strongly correlated to the liquidity risk exposure and interconnectedness between banks. The results show similar results as in the paper of Lopez-Espinosa, Moreno, Rubia and Valderrama (2015). Still, the size of a bank is insignificant in this regression. This means that it does have a statistical influence on systemic risk. The market-to-book ratio of a bank’s capital does have a statistical influence on systemic risk, according to table (6). If the market value of capital increases while the book-value stays constant, the ∆𝐶𝑜𝑉𝑎𝑅𝑖,𝑡(1%) decreases

with -0.0282. A possible reason for the positive influence on systemic risk is that the market value of capital is more volatile than its book-value. If the volatility increases uncertainty increases also and therefore, the risks that come with it as well. In addition to 𝑀𝑇𝐵𝑖,𝑡, the maturity mismatch of a bank’s short-term obligation has a negatively

significant effect on ∆𝐶𝑜𝑉𝑎𝑅𝑖,𝑡(1%) as well. If there are not enough short-term funds available to pay the short-term

obligations systemic risk increases. This can possibly lead to the sale of assets at fire-sale prices. Both variables are in line with the theory in chapter 2.

19

Column (2) in table (2) shows the regression results of the G-SIB regression equation. It shows the results of the baseline regression, with an inclusion of the regulatory dummies. One can observe that the regression has a 𝑝𝑠𝑒𝑢𝑑𝑜 − 𝑅2 _{of 0.3769. The F-statistic (F(5,2129)), whereby the null hypothesis states that the regulatory dummies}

are equal to zero is 1.85. This means that the null hypothesis cannot be rejected and that the dummies combined do not significantly contribute to systemic risk. Compared to column (1) the variables 𝐿𝑒𝑣𝑒𝑟𝑎𝑔𝑒𝑖,𝑡 and 𝑀𝑇𝐵𝑖,𝑡 are

insignificant. A possible reason why the t-statistics of these variables are different in column (1) is the occurrence of an omitted variable bias. This happens if the error term is correlated with one or several independent variables. If this is the case, the regression coefficients are meaningless for interpretation (Stock & Watson, 2015).

Additionally, the introduction of a G-SIB dummy shows that a G-SIB significantly influences systemic risk more than non G-SIBs. Statistically, G-SIBs contribute 0.0472 more to ∆𝐶𝑜𝑉𝑎𝑅𝑖,𝑡(1%) than non G-SIBs. Furthermore, with

the introduction of the bucket dummies only the banks in bucket 0 shows significant results. Bucket 4 is used as a reference dummy. At a 5% significance level the banks in bucket 0 influences ∆𝐶𝑜𝑉𝑎𝑅𝑖,𝑡(1%) -0.00657 less than

the banks in bucket 4. For example, this shows that JP Morgan Chase & Co is systemically more important than Erste Group Bank AG. This shows that banks in bucket 0 are less systemically important than banks in bucket 4. This is in line with the theory in table (3A) in the appendix.

In column (3) the regulatory capital requirement ratios are included in the regression. The results in table (6) shows that the regression has a 𝑝𝑠𝑒𝑢𝑑𝑜 − 𝑅2 _{of 0.3770. This means that it only explains 0.01% more of the variation of}

the ∆𝐶𝑜𝑉𝑎𝑅𝑖,𝑡(1%) than regression (2). The F-statistic (F(3,2126)) equals 0.73. This means that the null hypothesis

which states that the regulatory capital requirement ratios are equal to zero cannot be rejected. It shows that the ratios combined do not significantly contribute to systemic risk. Furthermore, at a 10% significance level, the base variable 𝑆𝑖𝑧𝑒𝑖,𝑡 goes from insignificant in column (2) to significant in column (3). If the book-based total assets of a

bank increase with one unit, the ∆𝐶𝑜𝑉𝑎𝑅𝑖,𝑡(1%) increases with 0.0116. This result must be carefully interpreted, as

it in is line with the findings of the in 2014 published IMF paper; “Bank size and Systemic Risk”. Additionally, the base variable 𝑀𝑇𝐵𝑖,𝑡 goes from insignificant in column (2) to significant in column (3). The regulatory capital

requirement ratios 𝑡𝑖𝑒𝑟1𝑟𝑎𝑡𝑖𝑜𝑖,𝑡 , 𝑡𝑜𝑡𝑐𝑎𝑝𝑟𝑎𝑡𝑖𝑜𝑖,𝑡 and 𝑡𝑜𝑡𝑙𝑒𝑣𝑟𝑎𝑡𝑖𝑜𝑖,𝑡 are all insignificant. Therefore, a conclusion

whether they have an influence on systemic risk cannot be drawn, at least not for the dataset of this paper.

Column (4) shows the results of the additional loss absorbency requirement regressions. It shows a 𝑝𝑠𝑒𝑢𝑑𝑜 − 𝑅2

of 0.3771. The F-statistics (F(4,2122)) is equal to 2.48. This means that with a 5% significance level regression (4) gives a better description of systemic risk than regression (3). Therefore, the additional loss absorbency interaction terms give combined a good interpretation of systemic risk. In addition, the G-SIB dummy goes from significant in column (3) to insignificant in column (4). The addition of the interaction variables does not significantly influence systemic risk, individually. Consequently, a conclusion cannot be drawn about the influence of the additional absorbency requirements on systemic risk.

Chapter 5: Sensitivity analysis

5.1 Robustness

To justify the estimation results in table (6), several robustness tests are performed. The first test replaces the dependent variable ∆𝐶𝑜𝑉𝑎𝑅𝑖,𝑡(1%) by the ∆𝐶𝑜𝑉𝑎𝑅𝑖,𝑡(5%). The results are expected to show the same signs as the