Analysis of systemic risk in the European insurance sector

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Analysis of Systemic Risk in the

European Insurance Sector

Shivam Hardwarsing

Master’s Thesis to obtain the degree in Actuarial Science and Mathematical Finance University of Amsterdam

Faculty of Economics and Business Amsterdam School of Economics

Author: Shivam Hardwarsing

Student nr: 10014306

Email: shivamhardwarsing@gmail.com

Date: August 15, 2018

Supervisor: Dr. S.U. Can

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Systemic Risk in the European Insurance Sector — S.R. Hardwarsing iii

Statement of Originality

This document is written by Student Shivam R`ahat Hardwarsing who declares to take full responsibility for the contents of this document. I declare that the text and the work presented in this document are original and that no sources other than those mentioned in the text and its references have been used in creating it.

The Faculty of Economics and Business is responsible solely for the supervision of completion of the work, not for the contents.

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Abstract

This thesis aims to assess the systemic relevance of the European insur-ance sector in comparison to the banking and other financial services sectors. To this end, the three systemic risk measures MES, SRISK and ∆CoVaR are implemented. We find that the insurance sector is sys-temically relevant but on a lower level than the banking sector. There are, however, certain insurers whose systemic relevance are comparable to that of the banks. To identify these insurers, systemic risk measures can be used. We examine whether the systemic risk measures identify the same insurers, with the highest systemic importance. According to our results, this is not the case. Lastly, we verified that the reason the systemic risk measures identify different systemically important insur-ers, is because the systemic risk measures have different determinants.

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The completion of this master’s thesis brings an end to my event-ful student life. This thesis was written to satisfy the last graduation requirement of my master’s program in Actuarial Science and Mathe-matical Finance at the University of Amsterdam. I am very happy to finally see the fruit of my labor and thankful to everyone who provided me with any form of support throughout my time at the university. I would like to take this opportunity to especially express my grati-tude to those people without whom it would not have been possible to successfully complete my thesis.

First and foremost, I owe a lot of gratitude to Dr. Sami Umut Can for his wonderful guidance and support during the writing process. Whenever I had any doubts, I always felt free to approach him and he would each time steer me in the right direction.

Furthermore, I would like to thank my close friends for their words of advice and for sharing their own thesis writing experience with me to help me pass this final hurdle. A special word of thanks goes to my girlfriend, Susila, for making this lonely process that a thesis can often be, a little less lonely whenever required.

Finally, I must express my deep gratitude to my family, especially my parents and my sister Divya. Even though they are almost 8000 kilometers away, they are always in my thoughts. I am forever indebted to my parents for all the sacrifices they made to fulfill my dream of studying abroad. This accomplishment would not have been possible without them.

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Chapter 1

Introduction

The global financial crisis is a clear example of how dangerous systemic risk can be to the financial industry. The crisis emerged from the bursting of the housing bubble, which led to deep declines in the value of securities connected to real estate. Financial institutions holding these securities or backing them through credit default swaps (CDSs) faced a liquidity crisis and reported significant losses even leading to a collapse in the cases of Lehman Brothers, Bear Sterns and others. Stock markets worldwide suffered as a result of low confidence in the financial system and unprecedented losses spread to many sectors and parts of the global economy. American International Group (AIG), an insurance company, was one of the most heavily affected by the financial crisis. The company suffered a near-collapse and had to be bailed out by the U.S. Federal Reserve as it was believed to be too big to fail, meaning that its failure would result in negative consequences for other firms and the broader economy. The insurance industry makes up a significant part of the financial sector but was not seen as systemically important before the crisis due to having longer-term liabilities, being less interconnected with the rest of the financial system, and having a diversified portfolio. The financial crisis and the major role AIG played in it also reignited the interest in systemic risk in general and made some stakeholders aware of the possibility of this risk arising from the insurance sector. Recent empirical evidence suggests that the insurance industry does indeed pose significant systemic risk. As the next source of this risk will probably be different from the past, it is important to consider emerging risks from all possible sectors.

Regulatory authorities work to prevent the occurrence of a financial crisis, since it has a devastating impact on not only the real economy but also on the social well-being of people. Systemic risk is a concept that comprises of many different features with its source not having to be limited to a financial institution. Nonetheless, these institutions are viewed as being the main perpetrators and identifying those contributing to systemic risk is deemed essential. Once identified, these institutions get labeled systemically im-portant financial institutions (SIFIs) and have to follow stronger regulation aimed at reducing the probability and impact of their collapse. This process started in 2009 when the Financial Stability Board (FSB) was asked by the G20 leaders to recommend pol-icy measures that tackle the systemic and moral hazard risks associated with SIFIs. In response, the FSB recommended a policy framework in 2010 and determined the global SIFIs (G-SIFIs) to whom it should apply the year after. G-SIFIs are defined by the

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FSB as institutions of such size, market importance, and global interconnectedness that their distress or failure would cause significant dislocation in the global financial system and adverse economic consequences across a range of countries. The banking sector was given priority and initially only global systemically important banks (G-SIBs) were iden-tified using an assessment methodology developed by the Basel Committee on Banking Supervision (BCBS). Nevertheless, the intention to include insurance companies was there from the start and from 2013 onwards the insurance sector was also covered. The International Association of Insurance Supervisors (IAIS) proposed the methodology to determine the global systemically important insurers (G-SIIs).1 So, G-SIBs and G-SIIs are the two classes of G-SIFIs. The list of G-SIFIs gets updated and published annually. Three main criteria have been put forward by the FSB to determine the systemic im-portance of a financial institution, namely size, interconnectedness and substitutability. In addition to these three, the IAIS initially identified global activity and non-traditional non-insurance (NTNI) activities as indicators of the systemic relevance of an insurer. The size of an institution is an indicator of systemic relevance because the more fi-nancial products and services it provides, the more vital it is for the economy. Thus, size determines whether an institution can be considered too big to fail. For insurance firms, however, size can be a too simple measure of risk. Since larger insurers are of-ten well diversified, implying the opposite, namely a lower systemic relevance. On the other hand, the importance of interconnectedness to the systemic contribution of an insurance firm cannot be disputed. The failure of any financial firm can only lead to distress in the system if it has significant interconnections through which systemic risk can be transmitted. The third criteria suggested by the FSB and endorsed by the IAIS is lack of substitutability. An insurance firm’s failure can have a bigger impact on the economy when it specializes in a specific line of business. In such a case, there might not be any other insurer to take over the failed firms business or none might have enough capacity to do so. Potentially leading some economic activities to come to a standstill. Global activity is considered an indicator of systemic importance because an insurer that’s active in multiple international markets can cause negative externalities internationally. The last category of systemic risk indicators is NTNI activities. Insur-ers can be involved in NTNI activities that carry a greater potential to pose systemic risk. This greater potential comes as a result of these activities being more exposed to liquidity, credit and market risk. Section 2.3 discusses NTNI activities in more detail. In their initial assessment methodology the IAIS understandably gave more weighting to the categories interconnectedness and NTNI activities. The methodology, however, gets reviewed every three years and the NTNI activities category has been discontinued in the last update due to overlaps with the interconnectedness category. Additionally, stakeholders also found the concept confusing. The indicators included under NTNI ac-tivities have been redistributed under the interconnectedness category and a new asset liquidation category. This new category aims to estimate the likelihood of a fire sale of assets that could possibly lead to financial distress.

Including the insurance sector in identifying G-SIFIs shows that economists and regulators do recognize the possibility for systemic risk to emerge from the sector. This

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Systemic Risk in the European Insurance Sector — S.R. Hardwarsing 3

is in contrast with the time before the global financial crisis when this possibility was ignored. Still, academic studies do not manage to find a clear answer whether insurance companies are indeed systemically relevant. For example, Billio et al. (2012) empirically measure the interconnectedness between financial institutions and find that the insur-ance sector has significant interlinkages to transmit shocks, and is thus a major source of systemic risk. On the other hand, Chen et al. (2014) also examine the interrelations be-tween banks and insurers, but the authors only find evidence that suggests that insurers are more the victims than the cause of systemic risk. Most concern indeed arises from banks, which have conventionally had not much in common with insurance companies. Both are financial intermediaries but play different roles within the financial system. Contrary to insurers, banks are highly involved in the crucial financial payment system and interact a great deal with each other and the rest of the market. While insurers tend to match their assets to their liabilities, banks face an asset-liability mismatch and can run into trouble in the case of a bank run. This is part of the reasoning why, at least traditional insurance, is regarded as posing a lower level of systemic risk compared to banking. Insurers have, however, perhaps to increase profits expanded into system-ically relevant NTNI activities, such as CDS trading and securities lending. Moreover, common exposures across firms within and outside the insurance sector are growing according to the International Monetary Fund (IMF, 2016). Likely raising the systemic risk contribution of insurers and creating the potential for a systemic event to originate in the sector.

The aim of this thesis is to make a contribution in the debate around the systemic importance of insurance companies, which as pointed out above, is far from being set-tled. This is attempted to be done by calculating three different quantitative measures of systemic risk and analyzing the rankings produced by them. A quantitative systemic risk measure seeks to determine the risk on the system by individual financial institu-tions. The inspiration for this thesis is a study done by Benoit et al. (2013). In their study they theoretically and empirically compare prominent systemic risk measures that measure the relative contribution to systemic risk of top U.S. financial institutions by assessing market data. The approach employed is market based, where the assumption is made that all the relative information of a company is reflected by the market. There are several risk measures and models available in academic literature that utilize this approach, but there exists no single model that can be considered the most effective. It is worth noting, however, that improved results can be attained from models that use proprietary data. Unfortunately this data is commonly only available to regulators and not to academics. Benoit et al. (2013) examine the marginal expected shortfall (MES), systemic risk measure (SRISK) and delta conditional value at risk (∆CoVaR). The au-thors motivate their choice for these three risk indicators by remarking that they have been discussed and tested in many papers. Furthermore, they are also implemented by central banks and regulators to track SIFIs.

For this thesis, the same three systemic risk measures are utilized as Benoit et al. (2013). To assess the systemic relevance of the insurance sector, we first calculate the measures for three different groups in the European financial system: insurers, banks and other financial services. Thereafter, similar to Berdin and Sottocornola (2015) rankings

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are produced and the insurance sector’s weight in the rankings are examined. Berdin and Sottocornola (2015) choose to focus on the top 10 financial institutions with the highest systemic risk contributions but don’t give an explanation for this. In the latest assessment by the FSB, 19 G-SIFIs have been identified from Europe (14 G-SIBs and 5 G-SIIs). This number has roughly remained the same for the past couple of years. Therefore, we consider a ranking with a size close to 19, namely a top 20. Additionally, the insurance system alone is taken into consideration to see if the systemic risk measures identify the same G-SIIs. The analysis done by Benoit et al. (2013) shows that this is not the case. Lastly, we look at the factors that drive the insurers systemic risk rankings. As one would expect, a top 5 ranking is analyzed for the insurance system.

The remainder of this thesis is structured as follows. In chapter 2 a literature review of some of the main aspects of the phenomenon systemic risk in the insurance sector is provided. Chapter 3 presents the methodology and estimation methods of the systemic risk measures. Moreover, chapter 3 also describes the data that is used. The results of the empirical analysis are presented in chapters 4 and 5. Finally, chapter 6 contains some concluding comments.

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Chapter 2

Literature Review

Following the global financial crisis, the interest around systemic risk increased and a lot more empirical and theoretical research started to emerge on the topic. While reading through this literature, it can quickly be concluded that there is no common understanding on several aspects. In this literature review these aspects concerning systemic risk are discussed. First, the many existing definitions of systemic risk are reviewed. Followed by a discussion of the methods and models that researchers have developed to measure a financial firm’s contribution to systemic risk. Lastly, we weigh upon the ambiguous position of academia and regulators on the systemic relevance of the insurance sector.

2.1 Defining Systemic Risk

Systemic risk is often misunderstood because there is no universal definition of it. Policy-makers, regulatory bodies and scholars each tend to use different definitions, which is not useful for the measurement and analysis of this risk. There are, however, some elements common to most of the definitions. They describe the (i) risk of a particular event occurring, (ii) the impact the occurrence of this event can have on the financial sector and (iii) the causation of the event. Making a distinction between the event, the cause and the impact is where the difficulty seems to lie. In the following paragraphs, we give some definitions of systemic risk.

Huang et al. (2009) very simply refer to systemic risk as “multiple simultaneous defaults of financial institutions.” Adrian and Brunnermeier (2016) put the emphasis on the negative effect on the real economy and define systemic risk as “the risk that the capacity of the entire financial system is impaired, with potentially adverse conse-quences for the real economy.” Billio et al. (2010) view systemic risk as “the probability that a series of correlated defaults among financial institutions, occurring over a short time span, will trigger a withdrawal of liquidity and widespread loss of confidence in the financial system as a whole.” Smaga (2014) reviews systemic risk definitions and proposes his own combining the most significant features from his analysis (contagion, connectedness etc.): “the risk that a shock will result in such a significant materializa-tion of imbalances that it will spread on the scale impairing the funcmaterializa-tioning of financial system and to the extent that it adversely affects the real economy.”

There is slightly less disagreement between regulators. The European Central Bank 5

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(ECB, 2017) gives the following noteworthy definition of systemic risk in their latest Financial Stability Review: “the risk that the provision of necessary financial products and services by the financial system will be impaired to a point where economic growth and welfare may be materially affected.” A definition that focuses more on the aspect of spillover effects to the real economy is proposed by the Group of Ten (2001). They offer systemic risk to be “the risk that an event will trigger a loss of economic value or confidence in, and attendant increases in uncertainly about, a substantial portion of the financial system that is serious enough to quite probably have significant adverse effects on the real economy.” The Committee on Capital Markets Regulation (2009) gives a rather broad definition which can be abbreviated to: “Systemic risk is the risk that the failure of one significant financial institution can cause or significantly contribute to the failure of other significant financial institutions as a result of their linkages to each other.”

The definition that is most frequently used and referenced by regulatory bodies is the one which was developed by the FSB (2009) together with the IMF and Bank of International Settlements (BIS). They propose systemic risk to be: “a risk of disruption to the flow of financial services that is caused by an impairment of all or parts of the financial system and has the potential to have serious negative consequences for the real economy.” A disruption to the flow of financial services happens in situations where these services are temporary unavailable or where the cost of these services show a sharp increase. Furthermore, for an event to be labeled as systemic it is required that there be a negative spillover effect to the real economy. This could take place either through the supply or demand side of other goods and services. The European Insurance and Occupational Pensions Authority (EIOPA) and the IAIS have adopted this definition and the latter implements it when identifying G-SIIs.

2.2 Systemic Risk Measures

The many definitions that exist for systemic risk are proof of it being a complex concept with many different aspects, which is not surprising as it concerns the failure of the increasingly complex financial system. Accordingly, there are many different measures of systemic risk that each focus and capture only one aspect or facet of it. No risk measure captures systemic risk in its entirety. The ∆CoVaR measures the VaR of the whole financial system to look at the impact of a firm in distress. Thus, ∆CoVaR focuses on the interconnectedness between firms in the system and captures the contagion effects, which can potentially occur in times of a financial crisis. The MES and SRISK, on the contrary, focus on the shortfall of a firm during a financial crisis as they respectively measure the expected loss in equity value and expected capital shortfall of a firm when the system is in distress.

Bisias et al. (2012) describe how systemic risk measures can be classified. One way of doing this is by organizing them from the perspective of a supervisor into two cate-gories: macroprudential measures and microprudential measures. Macroprudential mea-sures monitor the increase of systemic risk at the level of the whole financial system, while microprudential measures aim to estimate the systemic contribution of individual

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financial firms. The microprudential category is better represented in studies, since rec-ognizing firms that contribute highly to systemic risk (SIFIs) is deemed important by regulatory authorities.

Another way Bisias et al. (2012) order the risk measures, is by considering the timing of the systemic event. The three categories that then emerge are: ex-ante, contempo-raneous and ex-post systemic risk measures. Ex-ante or pre-event risk measures are predictive in nature and try to track and predict the evolution of various threats to the stability of the financial system. Most ex-ante risk measures belong to the macropruden-tial category discussed above. Another form of an ex-ante risk measure is stress testing. Contemporaneous risk measures can be updated frequently to observe the system in real time. Hence they are able to detect a crisis in its early stages, where a regulator would still be able to intervene and limit some of the damage. Lastly, ex-post risk measures assess the financial system after the systemic event took place. This is still very useful as bringing clarity into what exactly transpired is important for policy-makers, regulators and market participants. The three systemic risk measures MES, SRISK and ∆CoVaR applied in this study are microprudential and contemporaneous.

Benoit et al. (2013) first theoretically compare the systemic risk measures MES, SRISK and ∆CoVaR. From this comparison they learn that, under some assumptions, these systemic risk measures can be rewritten as transformations of the market risk measures beta, expected shortfall (ES) and value at risk (VaR). Afterwards, Benoit et al. (2013) also empirically compare the three systemic risk measures for a sample of financial institutions in the U.S. and rank them by systemic contribution per risk mea-sure. According to their findings, the systemic risk measures lead to different rankings but these rankings are each similar to rankings that follow from market risk measures or institution’s characteristics. So, ranking firms on the basis of their MES produces a similar result as ranking them on their firm beta. Likewise, the SRISK rankings are almost identical to the rankings obtained from ordering the institutions on their liabil-ities. Lastly, they discover that, for a given financial firm, the ∆CoVaR and VaR are strongly correlated. For these reasons, Benoit et al. (2013) conclude that the systemic risk measures are not more useful than traditional market risk measures.

2.3 Systemic Relevance of the Insurance Industry

The systemic relevance of the insurance industry is disagreed upon by academics. There are academics who view the industry as an important source of systemic risk (Billio et al., 2012), others get contrary findings and assume that the industry is not system-ically relevant (Geneva Association, 2010). Still many fall somewhere in between and claim that insurance companies can be systemically relevant if they indulge in non-traditional or non-core activities (Cummins and Weiss, 2014; Baluch et al., 2011). Most authors who consider the insurance industry in detail fall in the last group. According to the IAIS (2011), a distinction between insurance activities can be made in two different manners. First, they can be allocated as being connected to one of the two functions of an insurance company: the underwriting function or the investments and funding func-tion. Secondly, insurance activities can be categorized into traditional or non-traditional

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lines of business. Lastly, the IAIS makes note of non-insurance activities which insurers can partake in. These activities include credit default swap (CDS) underwriting and “shadow” banking. Eling and Pankoke (2016) define the underwriting function as: “all activity that has as its purpose the transfer of a risk to the insurer from a third party in exchange for a fee.”1 Defined as such it incorporates the non-insurance activity of CDS underwriting.

The distinction between traditional and non-traditional insurance activities is dif-ficult to make. Traditional insurance activities have risks associated that are generally idiosyncratic, uncorrelated with each other and independent of the economic business cycle (IAIS, 2012). Underwriting life and non-life (liability, legal, property etc.) risks falls under traditional underwriting activities. Traditional life and non-life insurance is not perceived as systemically relevant because of among other reasons low interconnect-edness between non-life insurers, life insurers and banks.2 _{The failure of a traditional}

insurer would therefore not have much of an impact on banks and other financial in-stitutions. Also, if an insurance company were to fail the wind-up takes place in a well ordered procedure and over a long period of time according to the Geneva Association (2010). Consequently, lowering the systemic contribution of the failure. Furthermore, the claims to a non-life insurer are only reported and paid out when the policyholder suffers a covered loss. Thus, a “run” by policyholders on a non-life insurer is not imagin-able. A run on the liabilities of a life insurer is possible on paper but will rarely actually take place due to policyholders often being protected by guarantees, and having to pay surrender charges and tax penalties when canceling the contract.

Doubts have, however, arisen about some of the points raised above. Billio et al. (2012) empirically examine the interconnectedness of insurers with banks and other financial firms by looking at their monthly stock market return data. Their results show increasing linkages between financial firms. The European Systemic Risk Board (ESRB) (2015) point out that a significant proportion of the liabilities of European life insurers can be surrendered with no or a very low penalty. Paulson et al. (2014) show that life insurers have become more prone to withdrawals in some countries. Studies and reports that calculate systemic risk measures for the insurance industry, such as Berdin and Sottocornola (2015) and IMF (2016), have also found empirical evidence for significant systemic risk contribution from the industry.

Eling and Pankoke (2016) allocate annuities for which the insurer assumes the invest-ment risk and guarantees a minimum interest rate under non-traditional underwriting activities in the life sector. In the non-life sector financial guarantees, financial deriva-tives and credit insurance form part of this group. Acharya and Richardson (2014) are of the opinion that annuities with embedded guarantees have become more common. These annuities expose insurers to investment markets and might lead them to large losses in the event of a market decline. The current low interest rate environment in the EU might also make these life insurers go on a “search for a yield” if they are un-able to deliver the promised return (IMF, 2016). So, guaranteed annuities might make

1_{See Eling and Pankoke (2016) for an extensive review of the literature on systemic risk in the}

insurance industry.

2

See Cummins and Weiss (2014) and the Geneva Association (2010) for this conclusion and following supporting arguments.

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life insurers systemically relevant. The Geneva Association (2010) argues that credit insurance is not systemically relevant because of the small scale and the low level of interconnectedness with the rest of the financial sector. On the other hand, providing financial guarantees on debt securities is widely agreed to potentially make a firm con-tribute to systemic risk.3 The links can be strong between this type of activity and the real economy when major financial firms are exposed to the guaranteed debt securities. Additionally, a rating downgrade of a financial guarantee insurer can lead to contract cancellations, calls for collateral, as well as losses on the guaranteed securities, which can transfer fast due to their mark-to-market valuation. A somewhat similar reasoning follows for writing CDSs. This activity also has strong linkages with banks and imposes considerable counterparty risk, since the CDS selling firm might not be able to meet its obligation in case the debt issuer referred to in the contract defaults. Furthermore, CDSs are also valued mark-to-market. A CDS contract can be seen as a form of credit insurance with the big difference being that no insurable interest is required on the side of the buyer. This makes it susceptible to use by speculators. The exposure of insurers to the CDS market, $270 billion in 2010, is large compared to the industry capitalization (Cummins and Weiss, 2014). In sum, the high level of interconnectedness, large size of the exposures and quick transfer of losses are reasons why studies agree that CDS trading can be a source of systemic risk.4

Activities that can be classified as traditional funding and investing activities are: As-set liability management (ALM), liquidity management, premium funding and insurance-linked securities (ILS). Eling and Pankoke (2016) do not find any substantial contribu-tion to systemic risk from this group of activities. The business model of receiving funding up-front in the form of premiums and matching the maturities of assets and liabilities, mitigates systemic risk. Insurance-linked securities, of which cat bonds are the most well-known, are not systemically relevant because insurers only have a small exposure towards them (IAIS, 2011). So, losses on cat bonds will never be significant enough to lead to the default of an insurer.

Short-term funding through securities lending, issuing commercial papers and credit rating utilization are considered non-traditional funding and investing activities by Eling and Pankoke (2016). Although unlikely, all these three activities could lead to a fire sale of assets when practiced on a very large scale, and thus potentially contribute to systemic risk. In the case of securities lending, the lender receives a fee and collateral from the borrower. The lending insurance firm can invest the collateral in risky or illiquid assets to earn an extra profit but as a result it will also increase its liquidity risk. When this liquidity risk is not managed very well the insurer might be unable to meet its obligations towards the borrowers and be forced to start selling assets. The same possibility arises with credit rating utilization and issuing commercial papers, where the insurer effectively takes out a short term loan and has the obligation to repay it.

3

See Chen et al. (2013) and the Geneva Association (2010).

4

See for example Baluch et al. (2011), Chen et al. (2013), IAIS (2011) and the Geneva Association (2010).

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Methodology

In this chapter, we present the methodology used to assess the systemic relevance of the insurance sector as compared with the banking and other financial services sector. The definitions of the three quantitative systemic risk measures that will be implemented on the three groups are provided. Additionally, the data set collected for our empirical analysis and the estimation techniques used are described.

3.1 MES

First proposed by Acharya et al. (2010), the marginal expected shortfall (MES) is a systemic risk measure that is adapted from the expected shortfall (ES). The MES is defined as the expected drop in equity value of a financial institution conditional on the market being in distress. This is considered to be the case when the market as a whole incurs a loss greater than its Value at Risk (VaR) at α%. Since the ES takes losses in the worst α% cases into account, the MES measures the marginal systemic risk contribution of a financial firm by taking into account the ES of the whole market or system. Let rmt and rit respectively denote the market return and the return of

firm i at time t. The market return rmt is the value-weighted average of all the firm

returns, rmt=PNi=1witrit, where witis the relative weight of firm i in the total market

capitalization. Then the ES of the system with N financial firms at time t is defined as:

ESmt(C) = Et−1(rmt| rmt< C) = N

X

i=1

witEt−1(rit| rmt < C). (3.1)

Here a general form of ES is given, where not the VaR but C is the constant threshold the market return has to exceed. The MES of a financial institution then equals the partial derivative of the system’s ES to the institution’s market share wit. This is where

marginal in the name of the MES risk measure derives from. It is clear to see from the expression below that MES measures the increase in systemic risk resulting from a marginal increase in the weight of a firm i in the system.

MESit(C) =

δESmt(C)

δwit = Et−1

(rit| rmt< C). (3.2)

Acharya et al. (2010) make a further contribution and present an extension to the MES risk measure, called systemic expected shortfall (SES).The SES combines a

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cial firm’s MES and leverage to measure its expected capital shortage in case a financial crisis happens and the system ends up undercapitalized, meaning that the aggregate capital is less than k times aggregate assets. The expected capital shortage of a firm is defined as the amount its equity drops below the target level, a fraction k of its assets. However, the SES risk measure is similar to SRISK, which is presented in the next section. For this reason we omit SES from this analysis.

3.2 SRISK

Brownlees and Engle (2012) and Acharya et al. (2012) introduce the risk measure SRISK, which is an extended concept of the MES that additionally considers a financial institution’s size and leverage.1 SRISK estimates the expected capital shortfall of an individual institution, conditional on a systemic event occurring. A systemic event is defined by Brownlees and Engle (2012) as a ’substantial market decline over a given time horizon.’ The authors consider SRISK as an alternative to the regular stress tests performed on financial firms by regulators, since both aim to determine the expected capital shortage in times of distress. The higher the SRISK of a firm, the higher its potential shortfall and the more systemically important a firm is. Moreover, the aggre-gate of SRISKs of all the firms in a system amounts to the potential capital shortfall a government may need to recapitalize in a crisis. SRISK depends on the MES, leverage and size of a firm. Since a negative SRISK means that the firm has a capital buffer large enough to remain unaffected by a crisis, we only look at positive SRISK values. Acharya et al. (2012) define SRISK as follows:

SRISKit= max[0, Et−1(Capital Shortfalli| Crisis)] (3.3)

= max[0, E(k (Dit+ Eit) − Eit| Crisis] (3.4)

= max[0, k Dit− (1 − k) (1 − LRMESit) Eit]. (3.5)

Here k stands for the prudential capital ratio, Dit for the book value of total liabilities

and Eit for the market value of equity. Benoit et al. (2013) show how SRISK can be

rewritten as a function of leverage, when leverage is defined as the quasi leverage ratio, Lit= (Dit_E+E_it it):

SRISKit = max[0, (k Lit− 1 + (1 − k) LRMESit) Eit]. (3.6)

From equations (3.4) to (3.6) it is clear to see that SRISK increases with debt, quasi value of total assets (Dit + Eit), quasi leverage and LRMES. LRMES stands

for long-run marginal expected shortfall and equals the expected loss in equity value a firm would suffer if the market were to fall by more than a given threshold over the next six months. Brownlees and Engle (2012) state that the LRMES can roughly be approximated as 1 − exp(log(1 − 40%) × βit), with βit being the time-varying firm beta

and 40% being the threshold the market drops by over the next 6-month period. The

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SRISK can then be calculated by assuming that the book value of debt remains about the same during the six-month period the equity drops by LRMES.

3.3 ∆CoVaR

As the name suggests, ∆CoVaR is a systemic risk measure that is closely related to the popular VaR methodology. Originally proposed by Adrian and Brunnermeier (2016), the ∆CoVaR captures a financial institution’s contribution to systemic risk by calculating the change in the VaR of the financial system resulting from the institution becoming financially distressed. Let Xit and Xmt be the variables of institution i and the system

for which their VaR is defined. The α% VaR for i then is the number that satisfies:

Pr Xit≤ VaRit(α) = α. (3.7)

The CoVaR in its turn is the VaR of the financial system conditional on a specific event C(Xit) occurring at firm i. The “Co” in CoVaR thus stands for conditional. CoVaR can

implicitly be defined by:

P r Xmt| C(Xit) ≤ CoVaR

m|C(Xit)

t = α. (3.8)

The systemic risk contribution of firm i is the difference in CoVaR conditional on the firm being in a distressed state (Xit = VaRit(α)) and CoVaR conditional on the firm

being in its median state (Xit = Median(Xit)), that is:

∆CoVaRit(α) = CoVaRm|Xt it=VaRit(α)− CoVaR

m|Xit=Median(Xit)

t . (3.9)

In earlier versions of their paper, Adrian and Brunnermeier (2016) let the variable Xit

be the growth rate of the institution’s market value of total assets, where they used the market-to-book equity ratio to transform the book value of total assets to the market value of total assets. However, in the latest version they make an alteration and describe Xit as the return losses on market equity, Xit= −∆Nit/Ni,t−1. Here Nit stands for the

institution’s net worth. As a result, we can just use the equity returns rmtand ritdefined

above as Xmt and Xit to estimate ∆CoVaR.

When comparing the formal definitions of the three measures of systemic risk, a clear difference can be noticed. The MES and SRISK aim to estimate the impact of systemic distress on an individual institution, whereas ∆CoVaR does the opposite and determines the impact of distress occurring only at the level of an institution on the whole financial system.

3.4 Data

For the empirical analysis, market and balance sheet data of European financial insti-tutions are used. The dataset spans the time period from January 2, 2006 up to and including December 31, 2015. Thus covering the global financial crisis and the Euro-pean debt crisis. In the first part of the analysis we assess the systemic relevance of the

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insurance sector in comparison with the banking and other financial services sectors. The other financial services sector comprises of non-insurer and non-bank institutions, such as (real estate) holding companies, investment companies and private equity funds. For the systemic relevance analysis we construct three groups by selecting the top 20 institutions from the STOXX Europe 600 Insurance, STOXX Europe 600 Banks and STOXX Europe 600 Financial Services sector indexes. These indexes represent firms from 17 countries in the European region including countries outside the eurozone, such as the United Kingdom and Switzerland. The selection is done on the basis of the yearly average market capitalization. All current and historical constituents of the indexes for our time period are ranked for each year according to their yearly average market capi-talization. The institutions that consistently ranked in the top 20 and were continuously listed over the time window are selected. The full list of selected institutions can be found in Appendix A. It is conform to our expectations but still important to note that all 19 European G-SIFIs identified in 2017 make the list. In the second part of the analysis we focus on the insurance sector and examine whether the systemic risk measures identify the same G-SIIs. For this part of the analysis, only the insurance group containing the top 20 insurance companies is used.

The equity returns and market values of equity were collected at daily frequency for all the 60 firms in the data sample. In addition, the daily value-weighted market index returns and the quarterly firm book values of total liabilities were also obtained. Table 3.1 displays some descriptive statistics of the averaged firm variables we collected, for each financial group. The descriptive statistics are also presented for the G-SII group of insurers, since this group is considered separately from the full insurance group in the next chapter. The table shows that banks have, on average, higher book values of total liabilities, market values of equity and leverage ratios. G-SII insurers are also seen to have, on average, higher values of the three variables presented in the table compared to the full insurance group. Lastly, to estimate the ∆CoVaR systemic risk measure we rely upon data, including the VSTOXX volatility index and German government bond yields. See subsection 3.5.2 on the estimation of ∆CoVaR for the full details. All data were collected from Thomson Reuters Datastream and Worldscope.

3.5 Estimation

3.5.1 MES and SRISK

In computing the MES we follow the method put forward by Brownlees and Engle (2012). Theirs is a dynamic version of the MES that can be estimated on a daily basis. The model is characterized by time-varying correlations, volatilities and tail expecta-tions. The bivariate process that makes up the model is defined as follows:

rmt= σmtmt (3.10)

rit= σitρitmt+ σit

q

1 − ρ2_itξit (3.11)

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Total Liabilities Market Cap Leverage mean 231,424 16,515 16.38 median 230,074 16,448 15.12 Insurance min 192,741 6,344 10.36 max 292,755 26,154 43.88 std dev 23,131 4,189 4.31 mean 996,689 43,431 30.56 median 1,004,315 42,739 27.82 Banks min 771,580 13,813 14.07 max 1,106,715 66,943 110.21 std dev 85,224 11,027 13.74 mean 25,126 6,023 5.37 median 20,910 5,754 5.76

Other Fin. Services min 8,573 2,405 2.30

max 54,544 10,115 9.35

std dev 14,211 1,612 1.77

mean 489,384 30,065 21.19

median 479,501 29,318 19.62

G-SII Insurers min 395,010 9,631 12.94

max 616,407 49,049 56.71

std dev 55,067 9,228 5.95

Table 3.1: Descriptive statistics of different firm variables.

The table reports descriptive statistics of the average quarterly book values of total liabilities and average daily market values of equity, for each financial group considered in this study. In addition, descriptive statics of the average calculated leverage ratios are also shown. Total liabilities and market values of equity are both in EUR million.

where σmt is the conditional standard deviation of the market return, σit is the

condi-tional standard deviation of the financial firm i return, ρit is the conditional correlation

between rmt and rit. Furthermore, mt and ξit are the innovations or shocks. These

in-novations are assumed to be independently and identically distributed with zero mean, unit variance and zero covariance under distribution F that remains unspecified. They are however not considered to be independent from each other, since extreme values of these shocks typically occur simultaneously for the systemically risky firms. Given equations 3.2 and 3.11 the MES can be expressed as a function of firm return volatility, correlation and tail expectations of the standardized innovations :

MESit C = Et−1 rit|rmt< C (3.13) = σitρitEt−1 mt|mt< C σmt + σ_itq1 − ρ2_itEt−1 ξit|mt< C σmt . (3.14) To estimate the MES we implement a multi-step modeling approach that is based on generalized autoregressive conditional heteroskedasticity (GARCH) and dynamic con-ditional correlation (DCC). These models are known to capture stylized facts associated with financial time series. A GARCH model captures leptokurtic returns and volatility clustering, while a DCC model captures correlation clustering. Consequently, the con-ditional volatilities σmt and σit are modeled using a threshold GARCH (or TGARCH)

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increasing volatility more than a large positive shock. The conditional correlations ρitare

modeled according to a DCC model. Both the TGARCH and the DCC model can then be estimated using quasi-maximum likelihood to obtainσ_bmt,bσit andρbit. See Brownlees and Engle (2012) for the full mathematical details of the TGARCH and DCC models.

The final step then consists of estimating the conditional tail expectations. Brownlees and Engle (2012) utilize a nonparametric kernel estimation approach, considering that the distribution F of mt and ξit is not specified. Let

K(x) = Z x/h

−∞

k(u) du, (3.15)

where k(u) is a kernel function and h is a positive bandwidth value. The Gaussian probability distribution function is chosen as the kernel and the bandwidth value is fixed at T−1/5. The estimates of the conditional tail expectations are expressed as:

b Et−1 mt| mt < κ = PT t=1mtK κ−mt h PT t=1K κ−mt h (3.16) b Et−1 ξit| mt < κ = PT t=1ξitK κ−_hmt PT t=1K κ−hmt . (3.17)

Now that all the terms of the MES in equation 3.14 are estimated, we can at last compute this risk measure by using the same equation. For the threshold C, we assume a value equal to the unconditional daily market VaR at 5%. The SRISK risk measure can now be determined as well. First, we compute the LRMES using the approximation given in section 3.2, LRMES ≈ 1 − exp(log(1 − c) × βit), with βit = bρitσbit

b

σmt . Implementing

equation 3.5 then enables us to obtain the SRISK: \

SRISKit= max[0, k Dit− (1 − k) (1 −LRMES\it) Eit]. (3.18)

Here, the prudential capital ratio k is set at 8%. The SRISK represents the expected capital shortfall of a firm in case a financial crisis occurs. This is the reason why we only consider positive values, as mentioned previously in section 3.2. The MES, on the other hand, is typically a negative return on a firm’s equity on a day the market index is below its 5% VaR. To make our analysis more convenient, we change the sign of the MES to make it positive number.

3.5.2 ∆CoVaR

Adrian and Brunnermeier (2016) consider quantile regression to be a convenient method to use for estimating ∆CoVaR. A standard quantile regression of the financial system returns on the returns of an individual institution can be performed to estimate the α%-quantile of the system, conditional on a given value of the return Xi of the institution.

The predicted value of this regression can be denoted as:

b Xm|Xi ₌

b

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Given the definitions of the VaR and the CoVaR, the predicted value of the quantile regression is exactly the VaR of the system conditional on Xi. also known as the CoVaR:

\

CoVaRm|Xi = bXm|Xi _(3.20)

The CoVaRm|Xi _{measure can be obtained by substituting the particular value of X}

i =

VaRi(α) that distinguishes the conditioning event into equation 3.19. The VaR input

values are just the unconditional α%-quantiles of institution i’s returns. Note that the median return of an institution is equal to its VaR at the 50%-quantile Median(Xi) =

VaRi(50%).

\

CoVaRm|Xi=VaRi(α)=µ_b_αi +γ_b_αiVaRi(α) (3.21)

\

CoVaRm|Xi=VaRi(50%)=µ_b_αi +γ_b_αiVaRi(50%) (3.22)

Lastly, the systemic risk contribution of an institution to the system is calculated as follows: ∆ \CoVaRi(α) = \CoVaR m|Xi=VaRi(α) − \CoVaRm|VaRi=(50%) =µ_bi_α+_bγi_αVaRi(α) −µb i α+bγ i αVaRi(50%) =_bγ_αi(VaRi(α) − VaRi(50%) (3.23)

The methodology presented above gives an estimate for the CoVaR and ∆CoVaR measures that is an average and therefore constant over time. To facilitate comparison with the other risk measures during both stable times and times of distress, the estimates need to be made dynamic. This can be achieved by making the returns of individual institutions and the system depend on lagged state variables Mt−1. The estimators of

VaR and CoVaR are then based on the following quantile regressions:

Xit= µiα+ ψiαMt−1+ εit (3.24)

Xmt= µm|iα + γαm|iXit+ ψm|iα Mt−1 (3.25)

The estimated parameters from the quantile regressions are subsequently used to form the VaR of the individual institution and afterwards the CoVaR:

d VaRit(α) =bµ i α+ bψαiMt−1 (3.26) \ CoVaRit(α) =bµ m|i α +bγ m|i α VaRd_it(α) + bψ_αm|iM_t−1 (3.27) Finally, the time-varying ∆CoVaR systemic risk measure can be computed as follows:

∆ \CoVaRit(α) = \CoVaRit(α) − \CoVarit(50%)

=_bγ_αm|i VaRd_it(α) − dVaR_it(50%)

(3.28)

To estimate the ∆CoVaR systemic risk measure, we perform 5%-quantile regressions. For the state variables Mt we should include variables that are deemed to be able to

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capture the time variation in the conditional moments of returns. The following variables are included:

• VSTOXX, the European implied volatility index based on Euro STOXX 50. • A short term liquidity spread, defined as the difference between the 3-month euro

area repo rate and the German 3-month bond yield.

• The first differences of the German 3-month bond yield. This variable seemingly captures the tail variation in financial sector market valued asset returns, according to Adrian and Brunnermeier (2016).

• The yield spread change, defined as the difference between the 10-year German bond rate and the 3-month German bond rate.

• The change in the credit spread, defined as the difference between a 10-year in-vestment grade euro corporate bond rate and the 10-year German bond rate. • The STOXX Euro 600 index returns in excess of the STOXX Euro 600 real estate

returns.

Just like the MES, the ∆CoVaR also gives a negative return. For similar reasons, we also change the sign of the ∆CoVaR.

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Empirical Results: The Systemic

Relevance of the European

Insurance Sector

This chapter presents the results obtained from our analysis on the systemic relevance of the European insurance sector. As mentioned before, the systemic relevance is examined by calculating the systemic risk measures MES, SRISK and ∆CoVaR for insurers, banks and other financial services firms. Figure 4.1 shows the results of these calculations in the form of the average daily values of the three systemic risk measures for the full dataset. We can examine figure 4.1 to verify that the calculations were performed correctly. The systemic risk measures should display their ability to track systemic events or other economic events that threaten the financial stability of the system.

A quick look at the average daily values in figure 4.1 confirms that the three risk measures perform well in tracking systemic risk. There are clear peaks common between the three and their patterns are similar. In addition, the peaks correspond with major economic events during recent times of financial turmoil. Dashed vertical lines have been plotted to illustrate this. With the global financial crisis soon to unfold, all three systemic risk measures rise from the beginning of our sample period. A peak is reached in September 2008 when the collapse of Lehman Brothers and the bailout of AIG occurred. This is the point where the global financial crisis truly escalated. The market stabilized fairly quickly by the end of the first quarter of 2009 due to an agreement reached at the 2009 G20 London summit, to tighten regulation worldwide and establish the FSB; however, the European debt crisis followed soon after. By the beginning of 2010 alarms had been raised about the debt levels of several member states of the eurozone. As a result, the measures of systemic risk increase and reach another common peak in May 2010, when the first bailout for Greece was issued. Europe now found itself in the midst of a debt crisis with speculation of further contagion of the Greek default to other eurozone countries. Improvement only came when measures were taken by the ECB to increase liquidity in the system. For example, the cost of the US dollar currency swaps was lowered in November 2011. A speech given by Mario Draghi, President of the ECB, in which he made clear the ECB’s preparedness to do “whatever it takes to preserve the euro”, further calmed investors. Afterwards, slowly and gradually recovery began until

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Systemic Risk in the European Insurance Sector — S.R. Hardwarsing 19 2007 2008 2009 2010 2011 2012 2013 2014 2015 0 2 4 6 8 10 12 % 5 10 15 20 25 30 35 (1) (2) (3) (4) (5) CoVaR MES SRISK

Figure 4.1: Averages of the systemic risk measures

The figure displays the average daily MES, SRISK and ∆CoVaR of all the institutions in the dataset. The ∆CoVaR and MES are expressed in percentages, while SRISK is expressed in EUR billion. The dashed vertical lines indicate major dates during the global financial crisis and the European debt crisis. (1) September 15-16, 2008: Lehman Brothers collapse and AIG bailout. (2) April 2, 2009: G20 London summit. (3) May 2, 2010: Agreement on a bailout package to rescue Greece. (4) November 30, 2011: The ECB, Federal Reserve and other central banks agreed to lower the pricing of dollar currency swaps. (5) July 26, 2012: Speech by the ECB President, Mario Draghi, in which he pledged to preserve the euro.

the situation in Greece hit a roadblock again near the end of our sample period; as a result of, a newly elected government rejecting existing bailout terms and calling for a referendum.

Now that we have verified that our calculations are indeed correct, we van move on to the main point of this chapter, which is to assess the relative systemic risk contribution of the three financial groups, for each systemic risk measure. To this end, the weighted average systemic risk contribution of each group is determined using firm market values of equity as weights. The weighted averages are used for the reason that the size of the financial firms differ quite considerably within and between groups. The difference as compared to using the simple average is not much for the MES and ∆CoVaR. However, differences are there for SRISK, since this risk measure takes the total liabilities and market capitalization of the firms into account. This approach is also taken by other research papers. Furthermore, the daily top 20 rankings of the financial institutions are analyzed to find out to what degree insurers are represented in these rankings. To conclude, we end this chapter with a discussion

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2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 0 2 4 6 8 10 12 % Insurers Banks Others (a) 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 0 2 4 6 8 10 12 14 % Non-G-SII G-SII Banks Others (b)

Figure 4.2: Averages of the MES by group

This figure shows the time series evolution of the weighted average of the MES for each financial group. The weighted averages are computed daily but have been retimed to a weekly time series for a clearer plot. This was done by using the median daily value in a week. In (b) the insurers group has been divided into two groups. One group holding the five G-SII insurers and the other group holding the rest of them. The MES is reported in percentages.

4.1 Analysis of the Relative Systemic Risk Contributions

4.1.1 MES

Figure 4.2a plots the average contribution to the risk of the system from insurers, banks and other financial services firms, according to the MES systemic risk measure. The MES corresponds to the expected equity loss if the overall market declines by a certain threshold, which in our case is the unconditional market VaR at 5%. The two peaks close to each other that occur in the midst of the global financial crisis, visually standout in the graph. The highest peak, seen at the end of 2008, is roughly 11% and is reached by

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the banking group. The plot shows, perhaps surprisingly, that in the short run-up to the 2008 financial crisis the other financial services firms contribute the most to systemic risk. These firms come out on top of several of the spikes in that period. Once the crisis is in full swing, however, it is the banks that form the main source of systemic risk, with insurers coming second. The group of banks remain the highest contributors over the insurers once the European debt crisis sets in until the end of our sample period. Therefore, a reasonable deduction to make from figure 4.2a, is that banks in general seem to contribute more to systemic risk, according to the MES systemic risk measure. It would be interesting to discover how G-SII insurers differ from the rest. Or more precisely, find out if they indeed exhibit a greater level of systemic relevance compared to the insurance firms that have not been identified and labeled as G-SII. For this reason, we divide the insurance group into two. One group that includes the G-SII insurers and one group with the rest of them. Figure 4.2b presents the evolution of the MES for the new group arrangement. The graph shows that the MES differentiates significantly between the G-SII group of insurers and the non-G-SII group of insurers. In fact, the G-SII insurers clearly display the highest systemic contribution from the beginning of our sample period until the end of the global financial crisis in early 2009. Afterwards, banks come more into play and start going head-to-head with the G-SII insurers. The two groups then somewhat alternate to be the most systemically relevant. Interestingly, the non-G-SII group of insurers in general seems to have the lowest level of MES. Hence, the extent to which the G-SII insurers make a difference in the systemic relevance of the full insurance group, should be clear. From this analysis, we can conclude that the MES does suggest that there are certain insurers (G-SIIs) that can match the systemic importance of banks.

4.1.2 SRISK

The dynamics of the SRISK measure of systemic risk are displayed in figure 4.3a by financial group. SRISK equals a firm’s expected capital shortfall in case the market index declines by 40% over six months. What is striking about the figure at first instance, is the low level of SRISK of the other financial services group. Up until early 2008 the time series of this group is not even visible on the graph, whereas this was exactly the period where it was often on top for the MES. An explanation for this can be the low leverage of the other financial services firms. Thus, most of these firms do not have a positive expected capital shortfall during stable and even unstable times. The group of insurers display a weighted average SRISK that is not comparable to the one from the banking group but is still substantial. Moreover, the average seems to remain fairly consistent throughout the sample period, fluctuating between 10 and 20 billion euros. Zooming in on the graph, however, does show the spikes characteristic of the two financial crises. They just don’t standout. The SRISK of the banking group, on the other hand, displays significant peaks and moves up considerably from around 20 billion euros in the pre-crisis period to almost 90 billion euros by early 2009. From then onwards, the SRISK of banks never returns to the pre-crisis level. The SRISK of the banking group is at all times significantly higher than the SRISK of the other two groups.

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2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 0 10 20 30 40 50 60 70 80 90 Banks Insurers Others (a) 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 0 10 20 30 40 50 60 70 80 90 % Banks G-SII Non-G-SII Others (b)

Figure 4.3: Averages of the SRISK by group

This figure shows the time series evolution of the weighted average of the SRISK for each financial group. The weighted averages are computed daily but have been retimed to a weekly time series for a clearer plot. This was done by using the median daily value in a week. In (b) the insurers group has been divided into two groups. One group holding the five G-SII insurers and the other group holding the rest of them. The SRISK is reported in EUR billion.

G-SII and non-G-SII insurers. In contrast to the full group of insurers, there are now discernible spikes for the G-SII insurers. At its topmost peak, the G-SII insurance group also achieves an SRISK that is twice the one of the full insurance group in figure 4.3a. The expected capital shortfall for the G-SII insurers mainly fluctuates between 20 and 35 billion euros. The big differences in the levels of SRISK for the financial groups, are mainly due to the differences that also exist in their leverage and liabilities. Banks are on average substantially more leveraged and have higher liabilities than insurers and

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other financial services firms (See table 3.1). Another factor is the LRMES, which is also not alike between the groups. Here banks are ahead as well, similar to figure 4.2a. All in all, the SRISK measure of systemic risk puts the banking sector unquestionably ahead in systemic relevance. The insurers come behind banks but their systemic risk contribution, especially from the G-SII insurers, is still substantial. The other financial services firms have barely any systemic importance, according to SRISK.

4.1.3 ∆CoVaR 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 0.5 1 1.5 2 2.5 3 3.5 4 4.5 % Insurers Banks Others (a) 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 % Non-G-SII G-SII Banks Others (b)

Figure 4.4: Averages of the ∆CoVaR by group

This figure shows the time series evolution of the weighted average of the ∆CoVaR for each financial group. The weighted averages are computed daily but have been retimed to a weekly time series for a clearer plot. This was done by using the median daily value in a week. In (b) the insurers group has been divided into two groups. One group holding the five G-SII insurers and the other group holding the rest of them. The ∆CoVaR is reported in percentages.

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our analysis. The ∆CoVaR measures a financial firm’s contribution to systemic risk as the difference between the CoVaR conditional on the institution being in distress and the CoVaR conditional on the firm being in its median state. The CoVaR is of course the VaR of the system conditional on a firm-specific event. In the first two years of our sample period there seems to be a clear order between the three groups. Similar to the MES, it is the other financial services group that at first exhibits the highest systemic relevance. It is also again the two financial crises that bring a change in the dynamics. The major difference with MES is that now the full insurance group as a whole seems to be able to challenge the banking group with regard to systemic importance. At the climax of both the global financial crisis and the European debt crisis, the contribution of insurers is the highest, reaching a ∆CoVaR of roughly 4 percent in late 2008 and a ∆CoVar of roughly 2.25% in November of 2011.

In figure 4.4b, the higher-level systemic importance of the G-SII insurers is easily noticed. They reach a maximum ∆CoVaR of almost 5.5%. In the pre-crisis period, however, it is still the group of other financial firms that are the riskiest. Between the banks and the other financial services firms, it is difficult to say which of them is the second most systemically important.

4.2 Analysis of the Systemic Risk Rankings

In this section, we go further in analyzing the systemic relevance of the insurance sector by considering systemic risk rankings. We form a top 20 ranking by sorting the 60 financial institutions in our data sample according to their systemic risk contributions. If insurers are indeed systemically relevant, they should consistently make up a significant part of the top 20. As stated in the introduction, we specifically examine the top 20 because this is close to the total amount of G-SIFIs in Europe, which is 19. Since 5 of these 19 G-SIFIs are G-SIIs, we would expect roughly this number of insurers to appear in the top 20. To further explain, if for example banks were by far the most systemically relevant, as was once believed, then the top 20 would only consist of banks. So, the more insurers occur in the top 20, the more evidence there is for them being systemically relevant. Table 4.1 shows the ranking for the last day of our sample period, December 31, 2015. The compositions of the three rankings differ quite a bit. In the MES top 20 ranking, there are 5 insurers, 9 banks and 6 other financial services firms. In the top 20 for the SRISK, there are 4 insurers, 15 banks and 1 other financial services firm. Finally, the top 20 for the ∆CoVaR consists of 6 insurers, 6 banks and 8 other financial services firms. So, in two of the three rankings there are at least five insurers. Table 4.1 only presents the systemic risk ranking for one day. To get a better un-derstanding of the insurers’ share in these rankings, we can look at figure 4.5 where the daily percentage of the insurers share in the systemic risk rankings are presented. In case there are 5 insurers in the top 20 on a given day, the daily percentage is 25%. This important percentage is represented by dashed black lines in the figure. On average, the daily percentage of insurers in the top 20 ranking of the MES equals 25.29%. The aver-age for the SRISK is a bit lower, 20.08% to be precise. The highest number of insurers are apparently found in the top 20 of the ∆CoVaR, with an average daily percentage

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Rank MES SRISK ∆CoVaR

1 Old Mutual BNP Paribas Old Mutual

2 Investec Deutsche Bank Investec

3 Banco Santander Credit Agricole Banco Santander

4 Aegon Barclays BBVA

5 Deutsche Bank Soci´et´e Generale Investor

6 Schroders HSBC Standard Chartered

7 BBVA Banco Santander Svenska Handelsbanken

8 Cr´edit Agricole Royal Bank of Scotland Unibail-Rodamco-WFD

9 Soci´et´e Generale UniCredit Groupe Bruxelles

10 Standard Chartered London Stock Exchange Generali

11 London Stock Exchange Lloyds Industriv¨arden

12 Kinnevik ING Schroders

13 BNP Paribas Credit Suisse Deutsche Bank

14 Deutsche B¨orse BBVA Hannover R¨uck

15 Mapfre AXA Munchener R¨uck

16 AXA Standard Chartered Aegon

17 Hannover R¨uck Legal and General HSBC

18 UniCredit Nordea Pargesa

19 Credit Suisse Aegon Allianz

20 Unibail-Rodamco-WFD CNP Assurances Kinnevik

Table 4.1: Systemic risk rankings

This table presents the top 20 rankings of the financial institutions for the systemic risk measures MES, SRISK and ∆CoVaR on December 31, 2015.

of 28.44%. Once again, two of the systemic risk measures do give us the results we are seeking. We further discuss all the results we got till now, in the next section.

MES 2006 2008 2010 2012 2014 2016 0 20 40 60 SRISK 2006 2008 2010 2012 2014 2016 0 20 40 60 CoVaR 2006 2008 2010 2012 2014 2016 0 20 40 60

Figure 4.5: Percentage of insurers in the top 20 rankings

The figure displays the daily percentages of insurers in the top 20 systemic risk rankings for the systemic risk measures MES, SRISK and ∆CoVaR. The dashed black lines represent 25%.

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4.3 Discussion

As seen in the graphs of the section above, the equity-based risk measures MES and ∆CoVaR at times show very small differences between their values for the different groups. To aid us in drawing further conclusions, we decide to calculate some statistics of the weighted average time series of the systemic risk measures. Table 4.2 presents these statistics. For the first part of our analysis here, we leave the G-SII insurers group out. The statistics for the MES and SRISK confirm that the banks are on average systemically the most important compared to the full group of insurers and the group of other financial services. Since, the mean, median and maximum values of these two indicators are higher for the group of banks. The ∆CoVaR, however, does not support this conclusion, but there is little to choose between the three initial groups, as their mean values are very close together for this risk measure. According to the ∆CoVaR, the systemic risk contributions of insurers, banks and other financial services firms are very similar. Somewhat notable from the weighted averages graphs, was that the MES and ∆CoVaR do not agree with the SRISK on the level of contribution to systemic risk of insurers and other financial services firms. The MES and ∆CoVaR at times classify these two groups as the most systemically relevant. The SRISK, on the other hand, consistently identifies banks as the riskiest group. As stated before, the reason behind this is that the SRISK takes into account an institution’s size and leverage. Banks are on average far ahead in these two factors.

Moving on to the other financial services firms. These firms are, on average, behind banks and insurers for the risk measures MES and SRISK. Their expected shortfalls cannot compare with the other two financial groups. It does make us wonder whether the collapse of these firms would significantly affect the system; since, SRISK also signifies the required bailout funds a firm would need in a crisis. Most of these firms have a SRISK of zero and would survive a crisis in any case. The other financial services firms are generally slightly ahead in systemic risk contribution, according to the ∆CoVaR. The ∆CoVaR focuses on the interconnectedness, so the other financial services firms do have the interconnections to transmit losses. The question is then how big those losses can be. Their limited size suggest that those losses would be limited.

According to table 4.2, the insurers seem to be behind banks but ahead of other financial services firms with regard to systemic relevance. The MES and SRISK are, on average, higher for insurers when compared to the other financial services firms. The SRISK for insurers is indeed considerably lower than that of the banks, but consider a scenario where multiple insurers were to fail. The capital shortfall would in that case certainly be a significant amount to recapitalize. Insurers are also well connected to the system, according to the ∆CoVaR. So, their losses would transmit to the rest of the system. Looking at the systemic risk rankings presented in section 4.2, Figure 4.5 shows that insurers do consistently find themselves in the top 20 systemic risk rankings. Certainly for the MES and ∆CoVaR. In the pre-crisis period, insurers had a bigger share in the top 20 systemic risk rankings for the SRISK. This share has gone down since times of distress arrived due to the leverage and liabilities of banks rising more than the leverage and liabilities of insurers. The insurers that feature in the top 20 systemic risk rankings are the G-SII insurers. Table 4.2 and the weighted averages graphs reveal

Analysis of systemic risk in the European insurance sector