Measurement of systemic risk for regulatory purposes : an analysis of the European financial sector

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Master’s Thesis

Measurement of systemic risk

for regulatory purposes

An analysis of the European financial sector

Bas Koolstra

Student number: 6054579

Date of current version: August 16, 2015

Master’s programme: Econometrics

Specialisation: Financial Econometrics

Supervisor: Prof. dr. H. P. Boswijk

Second reader: Dr. N.P.A. van Giersbergen

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Abstract

The recent financial crisis has shown that systemic risk can be a great danger to the entire financial sector. As financial firms still have incentives to take on systemic risk at the expense of society as a whole, regulation or taxation is needed to control this risk. We study and compare three popular measures of systemic risk that are based on publicly available market data. We compare those risk measures (∆ CoVar, MES and SRISK) and argue that SRISK includes the major characteristics of systemic risk and therefore forms a good foundation for a tax framework that aims to internalise the negative externalities that systemic risk exposes to financial stability. We introduce a tax framework for regulatory purposes and investigate the impact by studying the banking and insurance sector in Europe between 2002 and 2013. We propose a tax on systemic risk exposure with a two year payment period, based on SRISK as systemic risk measure.

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Introduction

The recent global financial crisis, which peaked in 2008, was one with severe consequences. This crisis is by many economists considered to be the worst and most impactful worldwide crisis since the Great Depression of the 1930s. The global financial crisis showed the danger of the highly interconnected financial sector, as a meltdown of the entire financial system was only just prevented. To keep the system running, governments all over the world had to invest incredible amounts of money to purchase assets of banks and insurance companies to provide liquidity and recapitalize financial institutions. The decision of the US government not to bail-out Lehman Brothers, one of the systemically most important banking institutions in 2008, dramatically spread the shock to the entire financial system.

Because of the crisis and the great dangers of the highly interconnected financial sector it exposed, additional regulation for financial institutions has become a subject of rising interest. In particular regulation for systemic risk has attracted attention since this risk type and its effects have been underestimated for a very long time. As the world is slowly recovering from the crisis, policy makers put systemic risk high on their agendas, which has resulted into the desire to incorporate the management of systemic risk into the root of banking and insurance regulation.

The lack of interest in and focus on systemic risk in the past is also reflected by the absence of an unambiguous and generally accepted definition of systemic risk. A report of the International Monetary Fund (2009) defines systemic risk as: “a risk of disruption to financial services that is caused by an impairment of all or parts of the financial system and that has the potential to cause serious negative consequences for the real economy.” However, analysing the academic literature learns us that definitions vary greatly. Despite differences in definitions, the academic literature is concordant that systemic risk is a serious problem to financial stability.

Key to the problem of dealing with systemic risk is that there are incentives for individual financial institutions to increase risk. This is because the potential benefits (higher profits) are gained by the individual firm. However, in case of extreme negative returns, the losses are socialized with money from tax payers, as a result of bailouts of financial firms that are considered ’too big to fail’.

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Furthermore, it is problematic that there is no straightforward and easy way to quantify and measure systemic risk and especially the contribution of individual institutions to systemic risk. This makes it harder to regulate or tax this risk in a fair and balanced way. Therefore, it is important to find good and consistent measures of systemic risk contribution and then adapt regulation or taxation to handle the risk. In other words, we want to study what market intervention is necessary to manage and control systemic risk.

This thesis adds to the discussion by focusing on possible measures of systemic risk, propos-ing solutions to the problem of systemic risk and presentpropos-ing a guideline for governments and financial supervisors to manage systemic risk in a better way. This is supposed to lead to a more stable financial system and a more fair division of the costs of risk. It also adds to the literature by evaluating the comparability of different risk measures and an extensive sensitivity analysis of these measures.

This thesis follows the approach of Acharya et al. (2010a) to use Marginal Expected Shortfall (MES) and Systemic Risk Measure (SRISK) as measures of systemic risk and the approach of Brunnermeier et al. (2011) to use Delta Conditional Value at Risk (∆CoVar) as a systemic risk measure. These risk measures are based on market data and multivariate volatility and correlation models. The results of the systemic risk calculations are incorporated into a model based on risk premiums to set a framework for rules on systemic risk. This paper makes use of data on the European financial sector (European Union + Switzerland). The data set contains a total of 188 banks and insurance companies and ranges from January 2002 up to and including December 2013. This is a period of special interest as it contains the Global Financial Crisis, as well as the period before and after the peak of the crisis.

The remainder of this thesis is organized as follows. Chapter 2 contains a literature review on the definitions of systemic risk, an overview of possible measurements of systemic risk and an analysis of the presence of systemic risk in the banking sector and the insurance sector. Chapter 3 contains a theoretical explanation of the three risk measures that are studied in this thesis. It also outlines our unified framework of forecasting returns, volatility and correlations. Chapter 4 focusses on the selection of data and contains a short data description. Chapter 5 ranks and quantifies systemic risk contributions of European financial institutions throughout the period of interest, this Chapter also includes an overview of sector effects and a sensitivity analysis. In Chapter 6 the systemic risk measurements are incorporated into a system of taxing for regulatory purposes. Subsequently, Chapter 7 discusses shortcomings and potential improvements of the proposed regulation measures. Lastly, Chapter 8 concludes.

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Chapter 2

Literature Review

In this literature review we first investigate the definitions of systemic risk in the academic literature. Subsequently, we analyse studies focussing on potential methods to measure systemic risk. Then, we distinguish between systemic risk contribution in the banking sector and in the insurance sector and we explain the concept of systemically important financial institutions. Lastly, we study the literature on regulation and taxation to manage and control systemic risk.

2.1 Defining systemic risk

As already mentioned in the introduction, systemic risk is not uniquely defined, but in general is associated with the risk of a global financial meltdown. The Great Depression of the 1930s and the recent financial crisis in 2008 are the most well-known examples of such a global financial meltdown. Eling and Pankoke (2014) summarise 43 theoretical and empirical research papers on systemic risk, also focussing on the chosen definitions, to come up with a generalisation of the concept systemic risk. They identify three common elements in the definitions of most papers: risk, impact and causation of an event.

• Risk of an event: The event that can occur, for example default of a financial institution, shock to the economy, etc. For the recent financial crisis the lack of financial services like interbank-lending and credit availability can be seen as such an event.

• Impact of an event: The consequences of the event that occurs, usually the effects on the real economy. For the 2008 crisis the impact was a huge negative effect on real economies worldwide.

• Causation of an event: Some definitions require a causation of the event, usually related to financial services. The recent financial crisis was triggered by falling prices in the U.S. subprime mortgage market, which quickly spread through the whole system due to interconnectedness.

Furthermore, it is important to acknowledge that systemic risk can roughly be divided into two main concepts. Prokopczuk (2009) refers to them as systemic risk in the narrow and in the

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broad sense. Systemic risk in the narrow sense is the risk of an individual shock to a particular financial firm in the system which spreads to other firms; in literature this event is often referred to as contagion. There are multiple ways through which the individual shock of one firm can spread to other firms. First of all, there is the channel of economic exposure between the firms. This is especially relevant for the financial sector, as exposure between banks through the interbank lending market can be huge. A second way in which an individual shock can spread from one company to another is by means of information. Bad news for one company can cause investors, creditors, and other agents to update their beliefs about other companies in the same sector. This potentially leads to a shock for them as well. Obviously, the shock does not have to stop after one transmission and can lead to a chain reaction.

Systemic risk can also be regarded in the broad sense. In that case a systemic shock hits multiple firms at the same time, leading to problems and defaults for some of the firms. In practice it’s very difficult to distinguish between these two concepts of systemic risk and they usually occur in a combination. The macroeconomic situation (like a sovereign debt crisis for example) can lead to a system wide shock, weakening financial firms and destabilizing the system. At that moment an individual shock can easily spread from firm to firm, leading the weakened system to totally collapse.

Figure 2.1: Two concepts of systemic risk

For the remainder of this thesis we follow the systemic risk definition of the Financial Stability Board (FSB). This international organisation was founded by the G20 in 2009 to monitor and advise on the global financial system. We choose the definition proposed by the FSB since it is the one agreed upon by financial regulators worldwide. The Financial Stability Board (2009) define systemic risk as the risk of disruption to financial services that is (i) caused by an impairment of all or parts of the financial system and (ii) has the potential to have serious negative consequences for the real economy. It is important that this definition focusses on the effects on the real economy, this is necessary to be labelled systemic.

Systemic risk has proven to pose serious threats to financial stability worldwide. In terms of economic theory it can best be seen as a negative externality. The benefits and profits of taking additional risks that contribute to systemic risk are for individual financial institution,

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but the negative effects and costs (e.g. a bailout) are for society as a whole. According to e.g. Acharya et al. (2010a), this gives financial institutions the incentive to take on too much risk. They take actions to prevent their own collapse, but not to prevent the system as a whole to collapse. In this way the financial institutions’ risk is a negative externality on the system. Hellwig (2009) describe the cause of the recent subprime-mortgage financial crisis as an example of this negative externality. Financial institutions heavily traded in portfolios of mortgages which faced relatively low idiosyncratic risk, but high amounts of system-wide risk.

2.2 Measuring contribution to systemic risk

In the process of identifying, assessing and managing risk it is crucial to be able to understand what causes the risk, and it is essential to be able to measure the risk and to quantify it. Systemic risk is a threat to a complete sector or system, meaning that to manage the risks a regulator or policy maker needs to determine in what way individual firms should contribute to the process of systemic risk management. For this purpose it is useful to have risk measures that quantify the contribution of a single firm to the total systemic risk. However, the complexity of systemic risk is already noted by the absence of a single general definition. The complexity also makes it difficult to propose a single measurement or criterion of systemic risk. There are several approaches in literature, all having their advantages and drawbacks. A common problem is the availability of data, especially for non-publicly traded financial institutions and information on the interbank-lending market. Despite those challenges, the literature on systematic risk has grown enormously over recent years.

In order to study the contribution of a specific financial institution to the overall systemic risk, two main classes can be distinguished, one focussing on market data and one focussing on balance-sheet and regulatory data. Recently, Acharya et al. (2012) introduced a third class, combining market data and balance-sheet data.

The first class has a large focus on publicly available market data, mainly on stock prices and Credit Default Swap (CDS) information. In this class, Adrian and Brunnermeier (2011) introduce ∆CoVar as a measure for systemic risk. It is an extension of the traditional Value at Risk (VaR) measure. The prefix Co is not uniquely defined, but can stand for conditional, contagion or co-movement Using a quantile regression method, they compare the Conditional Value at Risk (CoVar) of a firm in its ’normal’ (median) state to the CoVar of a firm suffering an individual shock (stressed state). The difference between those values is considered a proxy for systemic risk contribution of an individual firm. CoVar, in contrast to most measurements for systemic risk, is not based on the dependence structure between the equity values of the firms. Extensions of the model have been introduced, for example by adding bivariate copulas (Hakwa et al. (2012)). As another extension of ∆CoVar, Chan-Lau (2010) proposes the Conditional Risk Co-dependence measure (CRC), which captures in what way the default risk of a financial firm changes as a reaction to changes in the risk of another institution while controlling for common risk factors.

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Acharya et al. (2010a) introduce Marginal Expected Shortfall (MES) and Systemic Expected Shortfall (SES) as new measures of systemic risk. MES focusses on the marginal contribution of a financial institution. The MES of an institution can be defined as its expected equity loss when the market returns are at their 5% or 1% lowest quantile. SES reflects the undercapitalisation of a financial institution in case of a systemic crisis, which occurs when the system as a whole is undercapitalised. Acharya et al. (2012) combine MES, market capitalization and balance sheet data on liabilities to compute SRISK. SRISK can be interpreted as the amount of capital that needs to be injected into a financial firm to restore the minimal capital requirement. This latter risk measure is mostly based on market data (class 1), but also uses some balance sheet data (class 2) and therefore forms a new class of systemic risk measures in terms of data that is used. Although ∆CoVaR, MES and SRISK are usually considered most important in the recent debate on systemic risk, other market data related approaches are also worth mentioning. A different stream of research of systemic risk focusses on Credit Default Swap (CDS) data, because Credit Default Swaps played a vital role in the recent crisis. Markose et al. (2010) study CDS data of major US banks and provide a Systemic Risk Ratio as a measure of systemic risk. Huang et al. (2009) introduce the Distress Insurance Premium (DIP) index as a systemic risk measurement based on CDS data. The systemic risk is measured by the price of an insurance against financial distress, the calculations are based on credit default swap (CDS) spreads of individual banks and the co-movements in banks equity returns. Their results suggest that US banks needed a total insurance premium of $110 billion in March 2008 and had a projected maximum of $250 billion in July 2008. Huang et al. (2012) extend this approach and have a deeper focus on the risk contributions of individual firms. Inspired by the idea of Tarashev et al. (2009) they make use of the game theory concept ’Shapley Value’. This approach leads them to the conclusion that some financial institutions are correctly considered ’too big to fail’. Giglio (2011) uses a similar approach, using information in bond and credit default swap prices, he measures the joint default risk of large financial institutions.

Another way to go is to use measurements of interconnectedness and spillover effects in a network topology framework to quantify systemic risk. Billio et al. (2012) use monthly stock returns and Granger-causality tests to asses the level of systemic risk in the finance and insur-ance industry over time. Diebold and Yılmaz (2014) also present several interconnectedness measures which use variance decompositions based on the volatility of stock returns of financial institutions.

Systemic risk measures classified in the second class are based on balance sheet data and regulatory data. Indicators of counterparty exposure, liquidity and interconnectedness are pop-ular indicators of fragility and contribution to systemic risk. Cont et al. (2010) use a Brazilian database of mutual exposures and capital levels of financial institutions and conclude that ex-posure positions have a greater impact on systemic risk contribution than size. The focus on liquidity leads Brunnermeier et al. (2011) to a Liquidity Mismatch Index (LMI), which proved itself to be a good indicator for the systemic importance of a financial firm. Greenwood et al.

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(2014) model the build-up of systemic risk based on the distribution of leverage and risk expo-sures, they use data published by the European Banking Authority on the banks exposures to the European sovereign debt.

2.3 Regulation of systemic risk

Banks and insurance companies are subject to regulatory supervision, on a national and on a European level. In Europe Basel III for banks and Solvency II for insurance companies are the most important regulatory guidelines. Both regulatory frameworks mainly focus on risk, leverage and capital requirements of individual financial institutions. No explicit systemic risk measures and restrictions are included. With the growing interest in systemic risk and its negative consequences, it is an important idea to incorporate systemic risk regulation into a new version of the regulatory requirements.

Anabtawi and Schwarcz (2011) propose several key points supervisors needs to take into account to regulate systemic risk. Their strongest opinion is that regulation should aim at decorrelating the financial system, to realise a smaller effect of shocks. Korinek (2011) focusses on the pro-cyclical character of the financial sector. In good times asset prices rise and con-straints decrease, in bad times the opposite is the case. This leads to amplification effects. Korinek’s model demonstrates that these amplification effects lead to a socially inefficient al-location of risk. Bankers tend to undervalue the importance of liquidity in times of crisis and do not internalize those fire sales during crises decrease asset prices, which trigger amplification effects that hurt others in the economy. One possible solution to this problem is to impose a tax on these negative externalities, also known as Pigouvian tax (Pigou, 1920).

Acharya et al. (2010a) think that a tax per institution is needed to address the negative externalities, similar to the manner in which companies are charged for CO2 emission and

pollution (Rubio and Escriche, 2001). Acharya et al. (2010b) propose two different ways of taxation. The first option is a periodically contribution to a special governmental fund that is used for bailouts and financial aid in times of crises. However, Acharya et al. (2010b) prefer a public-private plan, in which financial institutions are by law required to buy insurance against its own systemic risk losses in a scenario of economic downturn.

2.4 Systemic risk in the banking sector

It is generally accepted that the banking sector is more vulnerable than other sectors. Gavin and Hausmann (1996) outline some reasons why the banking sector is more fragile than regular industries. First of all, banks are extremely leveraged, their ratios between liabilities and assets are very high compared to other sectors. The value of a bank’s equity is typically equal to about 10 % of its debt. This causes small shocks to have very large impacts, potentially leading to insolvency and bankruptcy. Furthermore, banks have a tendency to be illiquid as their investment portfolios have a longer time horizon than their liabilities. Usually this is not too

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much of a problem, as customers normally do not withdraw their money all at the same time. However, in times of uncertainty and bank runs this is problematic to the bank and leads to illiquidity.

Because of the extreme fragility of the banking sector, most literature on systemic risk primarily focusses on banks and in the second place on other financial institutions. There is hardly any literature that questions whether banks contribute to systemic risk; it is generally accepted to be true. However, there is quite some literature that shows that banks have larger systemic risk impact than firms in other (financial) sectors. Bijlsma and Muns (2011) use stock market data of the 20 largest U.S. firms in four different sectors to investigate systemic risk. They conclude that systemic risk is significantly larger in the banking sector than in the other sectors. Billio et al. (2012) find that banks have a more important role in transmitting shocks than other financial institutions and therefore they are expected to have larger systemic risk contributions. Chen et al. (2014) conclude that the impact of banks on insurers is stronger and of longer duration than the impact of insurers on banks. This is a strong indicator that banks create significantly more systemic risk for insurance companies than insurance companies create systemic risk for banks. Trichet (2005) also explicitly acknowledges the special role of banks in the financial system, leading to potentially high degrees of systemic risk. He mainly points out the threats of the balance sheet composition of banks and the interconnectedness through the interbank lending market.

2.5 Systemic risk in the insurance sector

In contrast to the banking sector, the significance of systemic risk in the insurance sector is subject to debate. There is agreement that insurance companies are less important in systemic risk than banks (among others Billio et al. (2012) and Bijlsma and Muns (2011)), but there is disagreement about the exact impact of insurance companies. Considering that in 2008, insurer American International Group (AIG) was one of the first companies that needed financial support from the government to prevent its insolvency, it is reasonable to explore to what extent insurance companies are dealing with systemic risk. Based on a study of 43 papers, Eling and Pankoke (2014) research systemic risk in the insurance sector. Their most noteworthy observation is that there is a big difference between the traditional business activities and non-traditional business activities of insurers. Underwriting life, health, legal and all other kind of common insurances are considered traditional, as well as funding through premiums, hedging and asset liability management. The non-traditional business activities are for example annuities with guarantees, CDSs and reinsurance activities like catastrophic bonds and industry-loss warranties. On the funding side of the balance sheet securization of future cash flows or profits and short-term funding are seen as non-traditional.

For underwriting traditional business activities the contribution systemic risk is considered to be very low, this has multiple reasons. First of all interconnectedness of these activities is considered to be low, this is for example mentioned by Trichet (2005), Rauch et al. (2014) and

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Kessler (2014). Secondly, claims depend on loss events and therefore an ’insurance run’ is not possible (Cummins and Weiss, 2014 and Kessler, 2014) and cash outflows in case of a loss event are rather slow (Cummins and Weiss, 2014 and Jobst, 2012) so liquidity issues as a result of a systemic event is low. Furtheremore, several studies (e.g. Van Lelyveld et al., 2011 and Park and Xie, 2014) show that bankruptcies of re-insurers would not lead to market failure. All in all, it is concluded that insurers only underwriting traditional business activities do not (or hardly) contribute to systemic risk.

Funding of traditional business activities is also considered to have very low contribution to systemic risk as premiums are paid upfront (e.g. Trichet, 2005 and Kessler, 2014) and fire sale of assets in case of insolvency is prohibited (Cummins and Weiss, 2014).

However, non-traditional business activities have grown over recent years and pose a greater threat of systemic risk. Most studies agree that underwriting non-traditional insurance prod-ucts leads to a medium systemic risk contribution. Prodprod-ucts with financial guarantees impose market risk on insurance companies and can have a direct liquidity effect, therefore increasing vulnerability to a broader financial crisis. (e.g. Geneva Association, 2010 and Cummins and Weiss, 2014). The most important reason is the effects of Credit Default Swaps. They have direct liquidity impact and make a selling party vulnerable to systemic crises. (e.g. Geneva Association, 2010; Baluch et al., 2011 and Cummins and Weiss, 2014).

Non-traditional funding and investments activities for insurance companies are in general accepted to increase vulnerability, but there is uncertainty about the systemic risk contribution. Eling and Pankoke (2014) classify it as a medium contributor to systemic risk.

All in all, we can conclude that there is no consensus on the exact impact of insurance companies on systemic risk. Nevertheless, we can conclude that banks have a greater impact than insurance companies, but that especially the growing share of non-traditional insurance business activities makes insurance companies as a whole play a significant role in systemic risk. Therefore, we decide to also take insurance companies into account in our research.

2.6 Systemically important financial institutions

As soon as the effects of the recent crisis became visible, regulators and policy makers from all over the world came to an agreement to identify financial institutions with global importance and limit the effects of failure of one of these institutions. Banks, insurance companies and other financial institutions whose default is expected to trigger a financial crisis are named systemically important financial institutions (SIFIs). In November 2011, the Financial Stability Board published their first list of global systemically important financial institutions (GSIFIs). The list is updated on a yearly basis. Currently 25 European financial institutions are considered to be GSIFIs, 19 of them are banks (including ING Bank, Barclays, UBS, etc.) and 5 are insurance companies (including Allianz, Prudential and Generalli). This underlines our previous conclusions that banks are higher contributors to systemic risk than insurance companies.

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Weistroffer et al. (2011) also emphasise that, although banks are considered important fac-tors in systemic risk, non-bank financials should not be forgotten. Investment funds, insurance companies and other providers of financial services also play a role in serving the financial needs of the real economy. Therefore all these companies can become systemically important if certain criteria are met. Elliott and Litan (2011) provide several examples of how non-bank financials contribute to systemic risk. The criteria for classification of G-SIFIs can roughly be split into five categories:

• Size: Obviously size plays an important role in determining global significance. A larger financial institution has higher exposures and therefore failure has a larger impact. Size is usually measured in market capitalization or the value of total assets on the balance sheet.

• Interconnectedness: A higher degree of interconnectedness means that more exposure to counterparties is present, which increases the risk of spreading a shock to the rest of the system. Interconnectedness is often measured by trading volumes of transactions between financial institutions.

• Global activity: Financial institutions that are active on a global scale have liabilities all over the world. This means that a shock as result of failure quickly spreads across national borders. The more global activities, the wider shocks spread over the world. Global activity can be measured by looking at the value of claims and liabilities with counterparties from other countries.

• Substitutability: The extent to which financial institutions are replaceable by other players in the market. This factor is very hard to measure numerically. An analysis of possible consequences of a default might be the best way to rate this factor.

• Complexity: The main idea behind this factor is that more complex financial institutions lead to more difficult solutions in case of failure. Complexity is related to the structure of an institution and its assets. More complex assets like OTC derivatives add to the complexity of the financial institutions. Measurement can for example be based on the amount of complicated financial products on the balance sheet.

Although all criteria are clear on first sight, it is not always true that larger values for these criteria means higher risk. Cih´ak et al. (2011) find that for banking sectors that are not very connected to a global network of banks, increases in interconnectedness lead to a reduced probability of a banking crisis. Once interconnectedness reaches a certain value, further increases in interconnectedness can increase the probability of a banking crisis. This shows that several causes makes it difficult to unambiguously determine if a financial institution is a SIFI.

Now the question remains why it is important for regulators and financial institutions to identify SIFIs and what the market effects of ’too-big-to-fail’ financial companies are. Due to regulation policies (mainly Basel III and Solvency II) banks and insurance companies pay a

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premium for their own risk of default. However, there is no premium for the risk that their own failure causes additional problems to the rest of the financial system. As mentioned before (G-)SIFIs cannot disappear from the market without having major effects on the rest of the financial system. This potentially leads to moral hazard problems. (G-)SIFIs can be expected to be bailed-out by the government, as we have often seen during the recent crisis. This means that creditors of those institutions have an incentive to prefer debt financing over equity financing. This potentially leads to unfair competition, the incentive to increase leverage and to maintain or raise levels of systemic relevance. Those things are likely to contribute to more instability in the financial system.

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Chapter 3

Systemic Risk Measures

As discussed in Chapter 2 there are multiple ways of measuring systemic risk. In this research we focus on ∆CoVar, MES and SRISK, because they are based on publicly available data and have an intuitive economic meaning. This chapter focusses on the three risk measures in more detail and provides a theoretical comparison.

3.1 ∆CoVar

As mentioned in the literature review, ∆CoVar is a systemic risk measure proposed by Adrian and Brunnermeier (2011). It is a risk measure that heavily relies on the concept of Value at Risk, which is the maximum loss within the α% -confidence interval (Jorion, 1997). A financial institution’s ∆CoVar is defined as the difference between the VaR of the market conditional on financial firm i being in financial distress and the VaR of the market conditional on financial firm i being in its median state. Financial firm i is considered to be in financial distress at times when the loss is equal to its α%-VaR. Adrian and Brunnermeier (2011) use a quantile regression approach to estimate:

∆CoVari,t(α) = CoVart(α)m|ri,t=VaRi,t(α)− CoVart(α)m|ri,t=Med(ri,t)

In this equation ri,t denotes the daily log-return of the stock of financial firm i at time t. Girardi

and Erg¨un (2013) extend the ∆CoVar to a more general approach by defining financial distress as a period in which the loss of financial firm i exceeds its α%-VaR. This leads to a slightly different expression:

∆CoVari,t(α) = CoVart(α)m|ri,t≤VaRi,t(α)− CoVart(α)m|ri,t=Med(ri,t)

For this thesis we follow a multivariate GARCH approach, which we specify later in this chapter. As economic interpretation ∆CoVar can be seen as an estimation how much the system’s (or market’s) loss increases because of financial institution i being in distress.

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3.2 MES

Marginal Expected Shortfall (MES) is a measurement of the sensitivity of a financial firm to systemic risk. MES is defined as the expected change in equity of financial firm i, conditional on a loss of the market that is larger than its α% Value-at-Risk. Therefore we define MES as:

MESi,t(C) = −Et[ri,t:t+1|rm,t:t+1< C]

in which ri,t denotes the daily log-return of the stock of financial firm i at time t, rm,t the daily

log-return of the complete market and C is defined as tail risk in the market, based on the α% Value-at-Risk choice.

The MES of a firm can be interpreted as a reflection of its participation in total systemic risk. A higher MES value means a higher contribution to systemic risk. However, be aware that it is not based on a percentage scale. In times of distress total MES is higher than in normal periods. Acharya et al. (2010a) claim that MES would have been able to predict the cross section of losses incurred by financial firms in the United States during the crisis. However, Idier et al. (2014) find that a combination of simple balance-sheet ratios were better able to predict equity losses during the crisis than MES.

3.3 SRISK

Now let us incorporate MES as a risk measure into a framework of capital buffers and expected shortfall of capital. For every individual financial firm i we denote Di,t as the book value of its

liabilities (deposits, borrowings etc.) and M Vi,t as the market value of its equity. A simplified

balance sheet of a financial institution consists of total assets (securities, loans, cash etc.) on one side and total liabilities (equity and debt) on the other side. Due to regulation policies of Central Banks there is a restriction on the ratio between equity and assets. This fraction λ, as we define it, is regulated for prudence reasons and is for example defined for banks in Basel III and in Solvency II for insurance companies. If during a crisis λ falls underneath the required value a financial institution is at serious risk of default and needs to raise equity. In a normal situation the financial institution would be able to raise equity capital with the help of other financial institutions, but as markets tend to stop working properly during a crisis the financial institution might not be able to refinance itself and hence default. It is at this point that governments and central banks need to decide whether to intervene or not by the use of a bail-out. For such moments it is useful to have a measure of potential under-capitalization that a financial institution would face in a crisis. This leads to the expression for the capital buffer of a financial institution at time t as

CBi,t= M Vi,t− λ(M Vi,t+ Di,t)

= (1 − λ)M Vi,t− λDi,t

A positive capital buffer means that the financial firm is functioning properly, but a negative capital buffer is a sign that the firm is experiencing capital shortages. In periods of economic

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prosperity this will not be a big threat to the system because other financial firms are very likely to be able to cope with some potential losses. However, in times of economic downturns and periods of distress a capital shortage of an individual firm will generate negative externalities to the rest of the economy. Therefore, to quantify and asses systemic risk it is important to calculate expected capital shortage in times of economic distress. This economic distress is defined as a drop of the market index below treshold C, over a time period h and is denoted by rm,t:t+h< C. Therefore the expected capital shortage of an individual financial firm in times of

marketwide economic distress is defined as follows

CS_i,t+h|t= Et[−CBi,t+h|rm,t:t+h< C]

Now plugging in the equation for the capital buffer leads to

CSi,t+h|t= Et[−(1 − λ)M Vi,t+h+ λDi,t+h|rm,t:t+h< C]

Now let us have a closer look at the first part of this formula, we rewrite the expression of the change in market value conditional on a crisis as:

Et[M Vi,t+h|rm,t:t+h< C] = (1 − LRMESi,t:t+h)M Vi,t

with LRMES as an extension of the earlier defined MES, leading to a long-term marginal expected shortfall for times of financial distress. LRMES is defined as:

LRMESi,t:t+h= −Et[

M Vi,t+h

M Vi,t

− 1|rm,t:t+h< C]

Now incorporating this into the formula of Capital Shortfall that we have already seen we can simplify the equation to:

CSi,t+h|t = −(1 − λ)(1 − LRMESi,t:t+h)M Vi,t+ λEt[Di,t+h|rm,t:t+h< C]

To further simplify this expression we assume debt to be non-renegotiable in times of economic distress, leading to the expected capital shortage expression

CSi,t+h|t= −(1 − λ)(1 − LRMESi,t:t+h)M Vi,t+ λDi,t+h

Now we define the systemic risk index as

SRISKi,t,h = max(0, CSi,t+h|t)

We note that the individual systemic risk amount does not only depend on the firm itself and the current time, but also on the chosen time period h and the benchmark for the market. Furthermore, we note that in case of an expected positive capital buffer in times of economic distress, a firm will have an SRISK value of 0. The total systemic risk for the economy/sector is easily computed as the sum of the individual risk contributions:

SRISKt,h = N

X

i=1

SRISKi,t,h

and the relative contribution of one firm is defined as: SRISK%i,t,h=

SRISKi,t,h

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3.4 LRMES

We have seen that LRMES plays an important role in the computation of SRISK and therefore it requires some more explanation on the computation and assumptions that we use for LRMES. The expected shortfall in capital depends on the expected change in the market value of the financial institution in case of a financial crisis. We define a financial crisis and a period of financial distress as a huge decline on the stock markets in a relatively short period of time. We follow the definition of a financial crisis as a 40% market decline within a period of six months, this is a common definition in literature on systemic risk measures. Using h = 6 months (approximately equal to 126 trading days) we have this expression for LRMES:

LRMESi,t:t+h= −Et[Ri,t:t+h|Rm,t:t+h< −40%]

Where Ri,t:t+h = exp( h

P

k=1

ri,t+k) − 1 and Rm,t:t+h= exp( h

P

k=1

rm,t+k) − 1 denote the cumulative

returns.

A market decline of 40% within half a year is a very rare event in mature markets. In recent history it only took place three times. In 1929 there was a serious crash, also known as the start of the Great Depression. The second time was in 2000, when the internet bubble burst heavily. The third time was in 2008, often seen as starting point for the recent financial crisis. This scarcity of severe market drops make it more difficult to estimate LRMES consistently. Brownlees and Engle (2012) propose two methods to estimate LRMES. The first manner relies on simulations. Using the framework of returns, volatility and correlations that is discussed in the next section the 6 months returns of the market and the individual firm are simulated to approximate the amount of 6 month returns lower than -40%. This approach provides accurate estimates of the true expectation as long as the number of simulations is large enough. The second approach is proposed by Acharya et al. (2012) and is based on an extrapolation of a MES decline of 2% per day. Using extrapolation, calibration and some extra assumptions LRMES can be approximated as:

LRMESi,t:t+h= 1 − exp(p M ESi,t:t+1)

This approximation represents the expected loss per euro over the next six months, conditional a market drop of the market by 40% or more over the next months. p is estimated using Extreme Value Theory and for this specific market equal to 18 for a period of half a year. As we believe the market tails to be relatively comparable based on maturity and diversity of the market we use this approximation in our LRMES calculations for the remainder of this thesis.

3.5 Unified framework of returns, volatility and correlations

The three chosen risk measures are based on market data on stock prices and also market value and total liabilities for the SRISK measure. To compute the risk measures assumptions need to be made on returns, volatility and correlation structures. This section motivates our

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choices of econometric processes for forecasting purposes. We are inspired by the approaches of Brownlees and Engle (2012) and Benoit et al. (2013) to make one unified framework of a multivariate GARCH-DCC model, that is applicable to all the risk measures mentioned in this Chapter. We estimate the model in two steps, using Quasi Maximum Likelihood. First of all we use univariate GARCH models to obtain conditional volatility and standardised residuals of the market and of the financial institution of interest. Then, we use a DCC model to obtain conditional correlations to relate the two to each other. Lastly, the different risk measures are calculated. In the remainder of this section we explain our choices on return, volatility and correlation modelling.

Returns

For returns we distinguish between the log-return of an individual firm, ri,t, and the log-return

of the total market, denoted as rm,t. In this approach we model the market return as:

rm,t= σm,tεm,t

in which σm,t denotes the conditional standard deviation of the market portfolio at time t and

error term εm,t is IID with mean zero, variance one and covariances zero. The firm specific

return is modelled as:

ri,t = ρi,tσi,tεm,t+

q

1 − ρ2_i,tσi,tεi,t

in which σi,t is the conditional standard deviation of the firm, ρi,t is the conditional correlation

between market and firm and error term εi,tis IID with mean zero, variance one and covariances

zero. We assume error terms εm,t and εi,t to be uncorrelated at time t. More details on the

derivation of the equations mentioned above can be found in Appendix A.

Volatility

For volatility modelling there are many specifications to choose from. In this paper we focus on the TGARCH(1,1) model, because of two main reasons. First of all, including one lag for σi,t

and one lag for ri,t in general is sufficient for most time series on stock returns. Furthermore,

TGARCH(1,1) takes the leverage effect (negative shocks have a larger effect on volatility than positive shocks) into account whereas GARCH(1,1) does not. Another option would have been to choose for a EGARCH(1,1), but in practice it is expected to perform quite similar to the TGARCH(1,1). The TGARCH(1,1) is specified as follows:

σm,t= α0,m+ (α1,m+ γ1,mI[rm,t−1<0])r

2

m,t−1+ β1,mσm,t−12

σi,t = α0,i+ (α1,i+ γ1,iI[ri,t−1<0])r

2

i,t−1+ β1,iσi,t−12

Correlations

Another important aspect is the correlation between returns of the stocks. We choose to use the Dynamic Conditional Correlation (DCC) model, because it satisfies most desirable prop-erties of a multivariate GARCH model. A strong characteristic of this model is that it allows

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for correlations to change over time. To estimate this model univariate volatility models are estimated for all assets. Then, the standardized residuals are constructed and those results are used to estimate correlations. The conditional covariance matrix is given by:

Ht= DtPtDt

With Dt being a diagonal matrix with the square root of the estimated univariate GARCH

variances on the diagonal. The correlation matrix is given by: Pt= Diag(Qt)−1/2QtDiag(Qt)−1/2

Qt is calculated by:

Qt= (1 − α − β)Q + αt−10t−1+ βQt−1

Engle and Sheppard (2002) find that for most data sets a DCC(1,1) model is adequate, so in this research DCC(1,1) is used as a starting point.

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Chapter 4

Data

4.1 Collection and selection

To analyse the systemic risk measures we need a data set to work with. We choose to focus on the European market of banks and insurance companies in the pre-crisis and recent crisis period to identify the behaviour of the risk measures under different circumstances. Daily data on individual stock prices, market indices and market value are gathered for the period 01-01-2002 up to and including 31-12-2013. For the same period we have accounting data on the total liabilities of each company, this data is published on a yearly basis. We make use of linear interpolation to determine the total liabilities on a daily basis. We choose this period, because it starts with the introduction of the Euro and December 31, 2013 is the latest data point that all companies have published their accounting data for.

Datastream is used as our primary source of data. We include bank and insurance companies of all countries in the European Union and Switzerland, we add Switzerland because it plays a very prominent role in the financial sector. Furthermore we exclude firms that have all data available for less than one year and firms with a market value under 200 million Euros.

All data are converted to Euros by using the exchange rates at that point in time, we do this to be able to give a uniform representation of the SRISK measure. This is useful for comparison purposes.

4.2 Data description

The collection and selection process leads to a final data set of the European financial sector for the time period January 1, 2002 up to and including December 31, 2013. This is a 12 year time period, which can roughly be divided into 6 years of pre-crisis and 6 years of crisis. The total data set consists of 188 companies, of which 133 are banks, 39 insurance companies with a main focus on non-life activities and 16 insurance companies with a main focus on life. We note that some financial agglomerates focus on both banking and insurance, we classified them according to their core business.

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We have data on the complete time period of interest for 81 % of our data set. The remaining firms have a complete data set for at least the year 2013, but most of them for a much longer period. Unfortunately, data on financial institutions that existed in 2002, but disappeared sometime before the end of our period of interest was not available. We don’t think that survivorship bias influences the outcomes of our research, because the majority of financial institutions adds to systemic risk. We acknowledge that this data issue makes a comparison of total systemic risk from year to year somewhat more difficult and especially complicates back testing. However, we feel that these issues do not have a big impact on the final results.

Table 4.1: Financial institutions per market and sector Market Banks Insurers Total Switzerland 21 7 28 United Kingdom 8 18 26 Italy 17 5 22 France 11 5 16 Poland 14 1 15 Denmark 10 3 13 Germany 5 6 11 Spain 7 2 9 Greece 7 0 7 Austria 5 1 6 Netherlands 2 2 4 Belgium 3 1 4 Portugal 4 0 4 Sweden 4 0 4 Ireland 2 1 3 Finland 1 1 2 Romania 2 0 2 Cyprus 2 0 2 Bulgaria 2 0 2 Slovenia 0 2 2 Croatia 2 0 2 Slovakia 2 0 2 Luxembourg 1 0 1 Hungary 1 0 1 Total 133 55 188

Table 4.1 gives a complete overview of the banks and insurance companies per country. Indeed, Switzerland turns out to be a very important country in the financial sector. Switzerland has most banks and most total financial institutions in our data set, United Kingdom adds most

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in-surance companies to the data set. It is important to point out that some financial institutions, especially banks, have a system of regional banks that closely work together and therefore use the same name. Examples are Credit Agricole in France and Rabobank in the Netherlands. Juridically these regional banks are considered individual banks, therefore we decide to in-clude all these regional banks separately, provided that they meet the earlier mentioned data requirements.

Another important aspect is the market index, we choose to use the STOXX Europe 600 Index. It is a broad index of 600 large, mid and small capitalization firms from 18 European countries. These 18 European countries very much correspond to the countries that are used in our own data set.

Table 4.2: Pre-crisis and Crisis Descriptive Statistics

Pre-crisis Crisis

Average Std. Dev. Min. Max. Average Std. Dev. Min. Max.

Total portfolio 0,04% 0,70% -3,69% 3,72% -0,05% 1,32% -7,40% 7,88%

Market index 0,01% 1,10% -5,16% 5,64% -0,01% 1,42% -7,93% 9,41%

Banks 0,04% 0,64% -3,78% 3,31% -0,06% 1,38% -7,60% 8,18%

Insurance companies 0,01% 0,95% -4,46% 4,80% 0,00% 1,31% -7,03% 7,86%

Table 4.2 gives an overview of the daily log-returns of the total portfolio, the market index and the sector portfolios before the crisis (2002-2007) and during the crisis (2008-2013). All stocks are equally weighted in this overview. The table clearly shows a difference between the pre-crisis period and the years during the crisis. Average daily log-returns were positive in the first period and negative in the last period. Furthermore, the market was more much volatile during the crisis and experienced both very low and very high daily returns. The days of low returns were the days of dark news about bankruptcies of giant American financial institutions and potential bankruptcy of entire countries. The occasional very high returns were based on unexpected positive news messages in a bearish market; for example on September 19, 2008 when the American government was expected to announce an extensive plan to save the financial sector. It is also important to notice that the chosen market index is more volatile than the data set portfolio, even during the crisis. In comparison to the data set portfolio, the market portfolio has lower returns in the first period and higher returns during the crisis. This implies that the financial sector grew faster than average before the crisis and fell harder during the crisis.

Figure 4.1 gives an overview of the logarithm of the stock prices of the market index, our data set portfolio and the portfolio split into banks and insurers separately. We see that the portfolio more or less moves in a same manner as the reference portfolio of the market. We also see that stock prices of insurance companies rose faster towards the end of the crisis than the stock prices of banks.

Figure 4.2 gives an overview of the development of the market value and liabilities of the average bank and insurance company in our data set. We note that the crisis is very clearly visible and even displays some signs of a double dip around 2011. It is remarkable that the total liabilities of the banks in our data set have grown much faster over the last twelve years than

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Figure 4.1: Stock prices 01/2002 - 12/2013

Figure 4.2: Market values and total liabilities between 01/2002 and 12/2013

the total liabilities of insurance companies. Another important observation is that on average the liabilities are roughly ten times higher than the market value, this is a sign of the high leverage of financial firms.

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Chapter 5

Quantifying and ranking European

systemic risk contributions

This chapter has a primary focus on the results of the empirical study. Firstly, we outline some additional assumptions and subsequently we show the main results. Then, we introduce a system of ranking to compare the outcomes of the three risk measures on an individual level.Based on the results of our empirical study we pick one system risk measure to use in the regulating framework of Chapter 6. That section is followed by a sensitivity analysis to get insights in the effects of different assumptions. We backtest the chosen risk measure by comparing it to the results of Credit Default Swap data and data on bail-outs and capital injections during the crisis. Furthermore, we compare the identification of Systemically Important Financial Institutions in our model to the list of the Financial Stability Board. Lastly, we investigate potential differences between the banking sector and insurance sector in terms of systemic risk.

5.1 Assumptions

Next to the assumptions on the framework of returns, volatilities and correlations as discussed in Chapter 3 we also need to make assumptions on minimal capital ratios and confidence levels for Value at Risk calculations. LRMES and SRISK calculations are based on a capital shortfall in times of crisis and a minimum capital ratio (λ) is necessary for these calculations. In practice this minimum capital ratio can differ between countries and even between firms. For example, in the Basel III framework there are rules that require banks too hold up till 2.5 % extra Common Equity Tier 1 capital if total lending grows faster than national GDP. Furthermore, from 2019 onwards banks need to hold a higher minimum capital ratio if they are identified as systemically relevant. In this thesis we use a standard minimum capital ratio of 8 %, because this is the limit set by the European Central Bank for normal circumstances. However, in their own stress tests they usually use a 5.5 % or 6 % minimum. In the sensitivity analysis we investigate the effects of different minimum capital ratio’s, which are important for interpreting the results.

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conditional market Value at Risk. By definition we need a confidence level α, which we fix at 5% because this is a very common assumption. Furthermore, we would like to emphasize that all amounts are in Euros, unless stated otherwise.

5.2 Results

In this section the results of the empirical study are provided. All three systemic risk measures are discussed separately and afterwards the three measurements are compared. Figure 5.1 shows the levels of ∆CoVar between January 2002 and December 2013. We choose to display the 10th percentile, mean, median and 90th percentile of the 188 financial institutions in our data set. ∆CoVar is a measure of the extra negative impact that firm i has on the market as a whole

Figure 5.1: ∆CoVar 01/2002 - 12/2013

in times of financial distress of firm i. The ∆CoVar levels show a relatively volatile behaviour. There are several peaks, we identify four main moments of sudden increase in systemic risk. The first peak is clearly visible halfway 2002, this is mainly caused by stock market crashes in July and September as a result of the internet bubble bursting. The highest ∆CoVar levels are reached in the second half of 2008, which corresponds with the most turbulent period of the recent financial crisis. The bankruptcy of Lehman Brothers and problems on the inter-banking lending market make this a period with high systemic risk. The third major increase in systemic risk is visible in the first part of 2010. Early 2010 is the first time that the financial market clearly have huge doubts about the sovereign debt risk of Greece. This had a huge effect on the entire Eurozone, because of the interconnectedness between all financial institutions. The fourth peak in ∆CoVar levels is visible by the end of 2011. This period is known for worsening

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of the crisis, extra need for the European Financial Stability Facility and the increasing fear of a default of Greece and as a result an exit of the Eurozone.

The 10th percentile, mean, median and 90th percentile lines have relatively similar patterns. We note that there are some financial institutions that barely add to systemic risk, those are represented by the 10th percentile line. Furthermore, for ∆CoVar the mean and median levels behave very similar. On average the median value is slightly lower, probably caused by the relatively high share of financial institutions that have almost no systemic risk contribution.

Figure 5.2: MES 01/2002 - 12/2013

In Figure 5.2 the levels of MES for the given time period are displayed. MES is defined as the expected change in equity of financial firm i, conditional on a specified large loss of the market. The MES of a firm can be interpreted as a reflection of its participation in total systemic risk. A higher MES value means a higher contribution to systemic risk. We directly notice that the MES pattern throughout the years looks much like Figure 5.1, implying that two different methods produce relatively similar results. In Figure 5.2 the four identified systemic risk peaks are even better visible, because the other peaks are smaller and less frequent than we noticed in the ∆CoVar levels.

Figure 5.3 represents the SRISK values from 2002 up to and including 2013. SRISK needs to be interpreted as the amount of capital that needs to be injected into financial firm to restore the minimal capital requirements for financial institutions. All values on the y-axis are in Euros. It is interesting to see that the 10th percentile, mean, median and 90th percentile follow a different pattern than the levels of ∆CoVar and MES. The 10th percentile is (very close to) zero, meaning that about 10 % of the financial institutions in the data set do not contribute to systemic risk. There is also a big difference between the median and the mean as a result of

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this. Furthermore, we see that there are some very big contributers to systemic risk in the 90th percentile.

Overall we observe that the SRISK level recovers much slower from shocks than the levels of ∆CoVar and MES. This is caused by the longer time horizon of the SRISK measure and the information on market value and liabilities that is taken into account. A shock leads to a weaker position of the financial institution and it costs time to recover from this, especially if another shock occurs after a relatively short time. This is exactly what Europe experienced during the Euro crises over the last years, the systemic risk has been very high between 2008 and early 2012. From 2012 onwards it seems to follow a downward going trend again.

Figure 5.3: SRISK 01/2002 - 12/2013

Table 5.1 and Figure 5.4 show the development of the average level of ∆CoVar, MES and SRISK over the years. Both the table and graph show a massive increase in total systemic risk over the years. ∆CoVar and MES clearly show several shocks to the economy over the years, whereas SRISK has a gradual increase. However, the same shocks are also clearly visible in the development of SRISK. The average systemic risk is highest in the second half of 2008 according to ∆CoVar and MES measurements. SRISK singles out the period between July and December 2011 as the period with highest systemic risk, with the second part of 2008 in a second place. This difference can be explained by considering that the 2008 crisis as a consequence of the default of Lehman Brothers was the first serious shock after a long time of prosperity. The shock in 2011 was a result of the need for new loans to Greece and write-off of Greek debt. However, because this was a new shocks after several in a short time the position of banks and insurance companies had already weakened. SRISK takes this into account by the means of market value and liabilities and therefore shows a more consistent increase in systemic risk over the years.

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Looking at the sector effects in Table 5.1 we see something remarkable. There is a significant difference in measurement of systemic risk per sector between ∆CoVar, MES and SRISK. The first and second measure show very similar movements in systemic risk levels for both the banking sector and insurance sector. The average systemic risk contribution is generally a little bit higher for insurance companies, but this is a result of the presence of more systemically unimportant banks in the data set than systemically unimportant insurance companies. The SRISK measure learns us that systemic risk in the banking sector has increased enormously over the years, whereas the systemic risk contribution of insurers has been relatively stable. Both sectors clearly encounter the same periods of distress.

Table 5.1: Mean of sytemic risk measures 01/2002 - 12/2013

∆CoVar MES SRISK (billions)

Period Mean (total) Mean (banks) Mean (insurance) Mean (total) Mean (banks) Mean (insurance) Mean (total) Mean (banks) Mean (insurance) Jan - Jun 2002 0.005 0.005 0.006 0.013 0.012 0.016 2.791 2.973 2.326 Jul - Dec 2002 0.010 0.010 0.012 0.021 0.017 0.029 5.329 5.252 5.529 Jan - Jun 2003 0.009 0.008 0.010 0.018 0.015 0.027 5.317 5.206 5.604 Jul - Dec 2003 0.004 0.004 0.005 0.012 0.011 0.015 4.341 4.313 4.415 Jan - Jun 2004 0.004 0.004 0.005 0.011 0.010 0.014 4.534 4.675 4.173 Jul - Dec 2004 0.004 0.004 0.004 0.010 0.009 0.012 5.414 5.812 4.424 Jan - Jun 2005 0.003 0.003 0.004 0.010 0.009 0.011 5.610 6.148 4.271 Jul - Dec 2005 0.004 0.003 0.004 0.010 0.009 0.012 5.657 6.264 4.153 Jan - Jun 2006 0.005 0.005 0.006 0.013 0.013 0.015 5.917 6.700 4.013 Jul - Dec 2006 0.004 0.004 0.005 0.012 0.011 0.014 6.497 7.587 3.891 Jan - Jun 2007 0.005 0.005 0.006 0.013 0.012 0.014 6.675 8.160 3.090 Jul - Dec 2007 0.008 0.007 0.009 0.017 0.016 0.019 8.650 10.842 3.172 Jan - Jun 2008 0.010 0.009 0.011 0.021 0.020 0.023 10.105 12.653 3.722 Jul - Dec 2008 0.018 0.017 0.020 0.038 0.037 0.040 10.962 13.419 4.908 Jan - Jun 2009 0.011 0.010 0.011 0.034 0.034 0.034 11.150 13.526 5.371 Jul - Dec 2009 0.007 0.007 0.008 0.021 0.021 0.020 9.413 11.436 4.487 Jan - Jun 2010 0.008 0.008 0.009 0.020 0.021 0.019 9.714 11.864 4.530 Jul - Dec 2010 0.006 0.005 0.007 0.016 0.016 0.016 9.648 11.869 4.368 Jan - Jun 2011 0.005 0.004 0.006 0.014 0.013 0.015 9.492 11.708 4.216 Jul - Dec 2011 0.012 0.011 0.014 0.029 0.029 0.028 11.675 14.118 5.765 Jan - Jun 2012 0.006 0.006 0.008 0.020 0.021 0.020 10.618 12.807 5.227 Jul - Dec 2012 0.005 0.005 0.006 0.017 0.017 0.016 9.504 11.460 4.749 Jan - Jun 2013 0.004 0.004 0.005 0.015 0.015 0.014 8.486 10.157 4.445 Jul - Dec 2013 0.004 0.004 0.005 0.014 0.014 0.014 8.055 9.647 4.205

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5.3 Ranking systematics

In the previous section we have seen a comparison of the three risk measures on a macro-level. Average levels and percentiles tell us something about the level and distribution of the risk measures over time, but not so much about systemic risk contributions on an individual scale. As the level of individual contributions certainly plays a major role in a framework of taxing or regulation, it is important to also check whether the three systemic risk measures classify the same financial firms as systemically relevant.

To investigate the similarities in individual contributions we study the ranking of institutions according to our own ranking systematics. We study the systemic risk contributions of all financial firms on July 1, on a yearly basis. Then, we sort the systemic risk contribution from high to low for all the risk measures. We develop our own ranking comparison method, based on a squared penalty factor for a ranking difference of financial institution i for two different risk measures. We choose for a squared penalty factor, because fierce deviation needs a higher penalty. As a result we name our method the Squared Ranking Difference (SRD). We define SRD between systemic risk measure a and b as follows:

SRDa,b=

PN

i=1(Ra,i− Rb,i)2

N (N₂)2

The denominator is introduced to include a correction term for the amount of financial institu-tions in the database at the moment of interest. As we research three systemic risk measure they all need to be compared to each other. To acquire the total SRD we simply take an average:

SRDtotal=

SRDCoV ar,M ES+ SRDM ES,SRISK + SRDCoV ar,SRISK

3

The results of the individual ranking per systemic risk measure are displayed in Table 5.2. We immediately notice that SRD between ∆CoVar and MES is much lower than others. This is not totally unexpected, as we also have seen similar patterns in the average level of ∆CoVar and MES. However, it is remarkable to see that the results are very similar considering that there is an explicit difference between the two in theoretical terms. ∆CoVar measures the effect of financial firm i on the system as a whole, given that the individual firm is in a period of economic distress. On the other hand, MES (and SRISK) focus on the effects of single institutions, given that the system encounters a serious shock.

We also see that the ranking differences between SRISK and the two other measures are relatively similar. This is explainable again by the fact that SRISK is based on more data than the other two. One would maybe expect a higher correlation in ranking between SRISK and MES as they are somehow related in their approach, but apparently the different time horizon and extra information have a big impact on the outcomes of the ranking. Furthermore, we notice that the SRD is fairly stable over the years.

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Table 5.2: Squared Ranking Difference

Year SRDCoVar,MES SRDMES,SRISK SRDCoVar,SRISK SRDtotal

2002 0.07 0.32 0.31 0.23 2003 0.07 0.26 0.26 0.20 2004 0.09 0.35 0.29 0.25 2005 0.11 0.41 0.35 0.29 2006 0.14 0.33 0.26 0.25 2007 0.12 0.31 0.27 0.23 2008 0.19 0.25 0.25 0.23 2009 0.09 0.25 0.23 0.19 2010 0.09 0.25 0.23 0.19 2011 0.12 0.24 0.24 0.20 2012 0.14 0.26 0.30 0.24 2013 0.13 0.29 0.26 0.23 Overall 0.11 0.29 0.27 0.23

5.4 Risk measure for regulation

To implement a framework for regulation and/or taxation of systemic risk it is important to make a choice for a single systemic risk measure to base regulation on. We have seen that total systemic risk and individual contributions perform similar to a certain extent, but also provide difference in results between ∆CoVar, MES and SRISK. In this section we consider theoretical reasons, literature and results from our empirical study to make a choice.

From a theoretical point of view the biggest difference is the extra data on liabilities and market value that SRISK takes into account. Although more data is not automatically better, this extra information is likely to be precious. Based on theoretical and empirical research Benoit et al. (2013) conclude that SRISK is a better choice than ∆CoVar and MES and that SRISK is most likely to act as a leading indicator of financial crises. Our own empirical study also proves that the development of total systemic risk according to SRISK is closest to the situation as Europe has experienced it over the last years. Ongoing problems with weaker countries in Southern Europe have had strong influence on financial stability over the last years. Another advantage of SRISK is the useful economic interpretation, it is expressed in monetary terms and therefore very suitable for comparisons and calculations.

Based on the information above we choose to continue with SRISK as the best measure of systemic risk. Some additional information and tests on the adequacy of SRISK as a systemic risk measure for a regulatory framework are provided in the next sections. Most of this research has also been conducted for the other two systemic risk measures, but SRISK performed best.

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5.5 Sensitivity analysis

This section is devoted to a sensitivity analysis of the SRISK measure.The outcomes of the calculations of systemic risk levels are sensitive to the assumptions that we make. There are several key factors that influence the results of the calculations, but the reference market and the required capital ratio are probably most influential. Using a difference reference market (for example a portfolio/index of financial institutions only) is beyond the scope of this thesis, but would be interesting for further research.

In this paragraph we focus on the effects of different minimum capital ratios. Until now we assumed a minimum capital ratio of 8%. However, the ECB has conducted stress tests with lower ratios (5.5%) so we want to investigate the effects of choosing a lower required capital ratio. On the other hand, regulators started a trend of increasing capital requirements. Therefore, we also look into the effects of higher minimum capital ratio requirements.

Figure 5.5: Sensitivity analysis

Figure 5.5 shows the average SRISK levels for minimal capital ratios of 4.0%, 5.5%, 8.0% and 10.0%. It is clearly visible that the shocks are similar and that all the periods of economic distress correspond, this is exactly as expected. The figure proves that a higher required capital ratio leads to a higher systemic risk exposure. This can easily be explained, because more money is needed to recover financial institutions with problems to the minimal level required.

Another interesting indicator is the percentage of financial institutions that are considered not to be systemically relevant (SRISK level of 0). As an average over the complete time period about 57% of the financial institutions are systemically irrelevant if the required capital ratio is

Measurement of systemic risk for regulatory purposes : an analysis of the European financial sector

Master’s Thesis