THE RELATIONSHIP BETWEEN CAPITAL BUFFER LEVELS AND RISK-TAKING IN EUROPEAN BANKS.

THE RELATIONSHIP BETWEEN CAPITAL BUFFER LEVELS

AND RISK-TAKING IN EUROPEAN BANKS.

Master’s Thesis

Tim Gießler (S3307220)

Institution: University of Groningen

Faculty: Faculty of Economics and Business

Academic Year: 2018-2019

Study Program: MSc International Economics and Business Supervisor: Prof. Dr. Dirk Bezemer

Table of Contents

5. Data and Descriptive Statistics ... 20

Abstract:

1. Introduction

The recent financial and economic crises emphasise the importance of capital regulations for safety and soundness of the financial system. Thereby, it has been widely concluded that the current regulations under Basel II are not sufficient to ensure that the banks’ behaviour concerning capital- and risk adjustment are in line with their regulatory objectives (Anderson, 2011). Tanda (2015) state that “(…) [r]egulation acts as an external force in the capital optimization process as banks set simultaneously the level of capital and the amount of risky assets to hold in order to comply with minimum capital ratio” (p.31). In fact, the banks’ decisions on the coordination of these factors are affected by changes in the regulatory requirements. Banks behave hazardously when they must react to stricter capital requirements to avoid costs associated with the violation of the regulatory guidelines (Stolz and Wedow, 2011). “Understanding the relationship between capital and risk is therefore fundamental in banking and the underlying mechanism should be investigated to adjust regulation and correct any hazardous behaviour” (Tanda, 2015 p.32).

Empirical findings in literature regarding the effect of regulatory interventions on risk and capital state that the effectiveness of the banks’ regulation depends on the business cycle (see Stolz and Wedow, 2011), the regulatory pressure on capital (see Heid et al., 2003) as well as on the country specification (see Guidara et al., 2013).

The impact of regulatory pressure, reflected by the banks’ capitalization degree, has been found to be an important driver in the coordination of the capital (buffer) and the risk. In fact, banks act in line with the capital buffer theory, and, hence, will maintain capital buffer levels above the required minimum to avoid fines and costs related to a violation of the regulatory guidelines (Jokipii and Milne, 2011). Thereby, low-capitalized banks face a higher regulatory pressure and are assumed to adjust risk faster than high-capitalized peers (Milne and Whally, 2002). Furthermore, capital pressure provides a different impact on the coordination of the relationship between risk and capital buffer. Thus, high-capitalized banks maintain their capital buffer levels by increasing their capital levels when the risk is also increasing, and when the risk decreases, banks reduce their capital levels accordingly. In contrast, low-capitalized banks build up capital buffers by increasing capital and reducing risk (Heid et al., 2003).

The adjustment of the capital buffer and risk appears to be sensitive to business cycle movements. The negative co-movement of the banks’ capital buffers and the business cycle is regarded as a factor for the banks’ vulnerability during the recent financial crisis (Huang and Xiong, 2014). This negative co-movement has serious and harmful implications for the macroeconomic stability. Thereby, banks increase risk by expanding their lending activities without a cover of sufficient capital. In downturn periods, banks, which have not built up capital buffers in upturn periods face a high regulatory pressure to meet the required capital levels (Stolz and Wedow, 2011).

requirements on the adjustment of the capital buffer and risk. The underlying assumption is that banks try to avoid the violation of the regulatory minimum when managing the capital buffer and the risk. Thus, the relationship between capital buffers and risk in banks is likely to change with the business cycle and the degree of regulatory pressure.

As a contribution to the existing literature, this thesis extensively investigates the impact of the two determinants (regulatory pressure and the business cycle) on the relationship between the capital buffer and the risk. In this context, most studies focused on the impact of these determinants separately, whereas this thesis combines regulatory pressure and business cycle conditions to investigate their effect on the relationship between the banks’ capital buffer and their risk behaviour. A simultaneous equation model is used to analyse the impact on risk taking on the capital buffer, and vice versa, while examining the impact of both determinants. Using panel data on 45 banks spread over 14 European countries from 2007 to 2015, this thesis intends to answer the following research questions:

1) How sensitive is the relationship between the capital buffer and the risk to regulatory pressures?

2) How do business cycle movements affect the relationship between the banks’ behaviour regarding capital buffer holding and risk taking?

2. Institutional Framework

Traditional theories on bank regulation state that banks which hold more capital can absorb potential losses more easily than those that do not (Lindquist, 2003). Therefore, it is assumed that well-capitalised banks are more likely to survive an outflow on their liquidity. The aspiration of the Basel committee was to create a safe and sound banking system by requiring minimum thresholds for the banks’ capital holdings. Despite this effort, the established requirements were unable to prevent the recent financial crisis, which caused one of worst economic downfalls in history. In the wake of this crisis, the scepticism regarding the quality of Basel II increased, which prompted the Basel Committee on Banking Supervision (BCBS) to introduce a new set of regulatory measures to improve the resistance and robustness of the financial system in September 2010 (Sbârcea, 2014).

Due to the increasing criticism of the first Basel framework, a revised regulatory framework – known as Basel II – was introduced in June 2004 (Drumond, 2009). The EU commission decided that this new regulatory framework must be applied by banks in its member states (EU) (Lin, 2007). The adoption of Basel II was assisted by the new Capital Requirements Directive (CRD), which forced the financial service industry (banks, credit institutions and investment firms) to apply the required regulations (Benford and Nier, 2007). The main objective of Basel II was to better adjust regulatory capital requirements with underlying risks. Furthermore, the new regulatory framework equipped banks and their supervisors with different options to assess the adequate capital level of a special bank (BCBS, 2006). This is different from the first Basel Accord, which comprised only one option for the assessment of the banks’ capital adequacy. Moreover, the Basel II framework intended that the measurement, management and mitigation of risks must be bank-specific, meaning that these activities must vary from bank to bank. Thus, the Basel II framework – implemented in 2008 – comprised “three mutually reinforcing pillars”1: (i) minimum capital requirements (ii) a supervisory review and (iii) a market discipline (BCBS, 2004).

The first pillar of the Basel II framework required banks to hold a defined minimum amount of capital, which equated to at least 8 % of the risk-weighted assets (RWA). The RWA were based on the ratio of different risk weights for credit, market and operational risks to total assets. Therefore, the measurements for the minimum capital standards are essentially the same as those in Basel I.

The second pillar contained “(…) the key principles of supervisory review, risk management guidance and supervisory transparency and accountability produced by the Committee with respect to banking risks” (BCBS 2006, p. 204). Following the BCBS (2006), this pillar had the function to detect and to shape the relationship between the banks’ capital holdings and the risk. In more detail, the objective is to improve the connection between the risk profile, the risk mitigation as well as the risk management systems of institutions and their capital holdings (EBA 2018). The main areas in pillar 2 were the handling of risks observed under the first pillar, but not fully considered by its process as well as the treatment of external factors, especially business cycles effects, which influence bank operations. Following the BCBS (2006), “(…) the assessment of compliance with the minimum standards and

disclosure requirements of the more advanced methods in Pillar 1 (…)” (p.204) was another crucial point of pillar 2. The precise period of the business cycle in which the bank operated determined the management of the bank in assessing its capital adequacy. Therefore, stress tests were applied to detect changes in the market or possible events that could adversely affect the banks’ businesses (BCBS 2006). The second pillar acted as a supervisory review process and control mechanism for the capital requirements set up under the first pillar. Thus, pillar 2 controlled if banks held adequate capital levels to back up the underlying risk in their business. Furthermore, this supervisory review process was intended to help and assist banks in developing as well as using improved techniques in monitoring and managing their risks (BCBS 2006).

Pillar 3 of Basel II intended to improve the market discipline through a reinforced disclosure of the banks’ capital and the risk levels to market participants. The improved disclosure enabled them to have a precise view of the adequacy of banks’ capital and risk levels (BIS 2001). The objective of the mandatory disclosure was to provide key information about the adequacy of the banks’ capital levels and their risk profiles to enhance the financial transparency of the banks (BCBS, 2006).

Following a variety of research,2 the new capital requirements of Basel II – which were more sensitive to the risk-taking of the banks’ business operations than those of Basel I – strengthened the concerns that this regulatory framework might lead to a reinforcement of pro-cyclical effects of bank behaviour (Andersen, 2011). In this context, the pro-cyclicality phenomenon stated that bank loans have the tendency “(…) to follow the same cyclical pattern as that of the real economy, i.e. strong growth in an economic upturn and slow growth or even contraction in an economic downturn” (ECB, 2005 p.56). Moreover, Basel II’s risk-sensitive capital requirements had pro-cyclical effects, especially on under-capitalised banks. Thus, the degree of Basel II’s pro-cyclicality was based on the level of the banking sector’s under-capitalisation (ECB, 2009).

Consequently, in times of economic upturns, in which the banking sector is well-capitalised, Basel II requirements have a benign effect on the banks’ business cyclical behaviour, whereas in times of recessions, this effect is considered to be more harmful. The recent financial crisis has proved the negative (pro-cyclical) effects of the framework’s risk-sensitive capital requirements in a recession period (ECB, 2009). During this crisis, banks were forced by market pressure to increase their capital levels, while at the same time losses and write-offs lowered their capital positions. Consequently, banks had to tighten their credit standards, which reinforced the economic downturn (Anderson 2011). As a result, the Basel committee worked on a new capital buffer which must be built up in economic good times. This counter-cyclical capital buffer – which is complementary to the conservation capital buffer – should mitigate the pro-cyclical effect of the previous capital requirements under Basel II (BCBS, 2010). The revised regulation – which aims at improving the ability of banks to absorb losses as well as to overcome the issue of pro-cyclicality – was published by the BCBS under the name Basel III in September 2010 (Sbârcea, 2014).

The new framework required banks to hold more capital in relation to the degree of the banks’ risk exposure to ensure their soundness and economic stability (BCBS, 2011). Besides the new minimum capital requirements,3 Basel III additionally created a conservation capital buffer (BCBS, 2011). The objective of this new buffer was to prevent losses from banks in times of financial and economic downturns. The first stage of the implementation process started in January 2016. As a response to the weaknesses of the previous Basel Accords, the BCBS (2010) introduced a counter-cyclical buffer (complementary to the conservation buffer) to mitigate or eliminate the banks’ pro-cyclical behaviour. In economic good times, banks must load the buffer, meaning that banks are obliged to increase their capital holding to ensure that these banks can release the capital holding of the buffer during times of recession or crisis (BCBS 2010).

Figure 1: Total capital and Tier 1 evolution for European Banks

3. Literature Review

This thesis builds on the main theories regarding the relationship between the banks’ capital and the risk-taking levels. For this reason, it is necessary to outline these theories and their implications, which are: the moral hazard theory, the charter value theory as well as the capital buffer theory. The capital buffer theory and its application under business cycle fluctuation will be discussed in more detail. Finally, some key takeaway points are concluded from the analysed literature and are used to provide a motivation for the underlying hypotheses in this paper.

3.1 Theory

The assumption of the banks’ moral hazard behaviour is commonly used to reason the implementation of capital regulations (Heid et al., 2003). The moral hazard theory describes that the relationship between the required capital holdings and the risk-taking behaviour of banks is influenced by an asymmetrically distributed information and deposit insurance, which protects banks from disciplining controls of their depositors (Jokipii and Milne, 2011). Following Merton (1977), this relationship is explained from a shareholder value maximisation perspective, which causes banks to have an excessive risk appetite while reducing capital levels. The moral hazard theory predicts that banks with low capital levels often take more risks in their portfolios.

In general, it is assumed that managers act in the best interest of the shareholders. Thus, managers must be monitored or controlled by debt holders to stop them from excessive risk-taking (Park, 1997). Due to deposit insurance, monitoring incentives of depositors (major debt holders) are reduced or removed. Consequently, the government must take responsibility for bank monitoring because depositors lack a monitoring incentive (Park, 1997). The intervention of the government by setting restrictions on the banks’ capital levels and the composition of their portfolios regarding riskiness lead to a changing prediction of the moral-hazard framework. By applying these restrictions, the relationship between the banks’ capital levels and the risk of their asset portfolios is positive. For instance, Sharpe (1978) stated that requirements on risk-based capital levels can fully remove moral hazard incentives, whereas Furling and Keely (1989) argued that due to the banks’ capital amount, which is held to balance (cover) credit risk, not dependent on the quality of the assets, these initiatives can only be reduced and not eliminated. As a result, the Basel Accords were developed along with the regulations of adequate capital holdings to reduce shareholder maximisation incentives. In a strategy to avoid regulatory pressure regarding the capital level and the risk of the asset portfolio, banks will set their internal capital levels above the required ones (Park, 1997). The charter value theory provides a much broader view on the relationship between the banks’ capital level and their risk-taking behaviour than the moral hazard theory. The charter value4 of a bank determines its business behaviour and is considered an influencing factor of the previously mentioned relationship. The bank charter value is defined as the present value of the future profits that a bank earns (Demsetz et al., 1996). The theory states that banks

behave more risk-averse for protecting their charter values (Keeley, 1990; Park and Peristiani, 2007). Therefore, the charter value hypothesis predicts that banks are less risky if having a high charter value. Following the theory, banks with a large charter value have little or no incentive to take an excessive risk because possible profits earned with a risk-taking strategy are outweighed by possible losses of the charter value (Park and Peristiani, 2007).

Thus, banks with a high charter value are motivated to protect this value by applying safer strategies, and, hence, select less risky assets and hold more capital (Demsetz et al., 1996). The latter can be realised by building up the current capital levels, and, hence, increase the size of the capital buffer. Thus, as the banks’ charter value begins to increase (due to their high degree of capital), banks take fewer risks to protect their charter. Consequently, similar to capital regulations, the banks’ charter value has a significant impact to mitigate the banks’ moral hazard behaviour driven by the state provision of deposit insurance and safety nets (Demssetz et al., 1996; Park and Peristiani, 2007). Therefore, the depositors’ insurance provides less incentive for depositors when banks act in a riskier manner to withdraw their deposits or ask for a higher interest rate, which corresponds with the banks’ risk (Demssetz et al., 1996). For banks with a lower charter value, the incentives increase to apply higher risks in the business by holding less capital (Jones et al., 2011). Following Jokipii (2009), when the banks’ charter value is below a certain threshold, the behaviour is determined by the moral hazard, implying that banks take riskier businesses and are not motivated to build up a buffer due to fewer losses in the case of insolvency. The potential loss of the banks’ charter value when getting involved in risky businesses can be considered as potential bankruptcy costs. These arising costs affect banks to either increase the amount of capital or to reduce the risk in their businesses (Jokipii and Milne, 2011).

Within the charter value literature, the capital buffer theory has attracted growing attention in recent times. Following Jokipii and Milne (2011), “(…) the buffer theory predicts that banks will maintain a level of capital above the required minimum (a buffer of capital)” (p.166). A lot of literature deals with the question of why banks hold capital buffers. The capital level5 exceeding the required minimum capital standards is known as a capital buffer (Jokipii and Milne, 2011). Following the Basel Accord, regulatory pressure forces banks to hold capital buffers. The motivation of banks to hold capital buffers is to insure them against a breach of the regulatory minimum capital requirement. This motivation is reinforced by a higher probability of violating the regulatory minimum requirements, and, thus, by more volatile capital levels (Milne and Whalley, 2002). However, regulatory interferences that require banks to alter their capital levels are costly for banks (Peuro and Keppo, 2006). Thus, being driven by the motivation to avoid fines and costs and preventing default, the capital buffer theory suggests that “(…) [b]anks with low capital buffers adjust capital (risk) faster than banks with low capital buffers” (Heid et al., 2003 p.6). Banks with low capital buffers are unable to absorb losses for longer times. Thus, these banks must adjust faster to avoid an increasing risk of default. The optimal capital buffer level is determined by the trade-off between the costly raising of capital and the comparatively less costly raising of insured deposits (Milne and Whally, 2002).

Moreover, the capital buffer theory enables to differentiate between the long- and short-term relationship between the banks’ capital levels and their degree of risk-taking (Jokipii and Milne, 2011). The long-term relationship between the capital level and risk-taking is likely to be the same as that of the charter value theory (it can be either positive or negative). On the other hand, the short-term relationship depends on the level of the banks’ capitalisation. The theory predicts that banks with high capital buffers maintain their buffer by increasing capital levels in the case of increased risk, and, when the risk declines, the banks will reduce their capital levels respectively. By contrast, banks with low capital buffers try to build up sufficient buffers by increasing the capital and to reduce risk at the same time. Thus, banks with a high capital buffer exhibit a positive relationship between capital and risk, whereas it is negative for banks with low capital buffers (Heid et al., 2003).

Several empirical studies examined the relationship between the banks’ capital levels and their risk-taking considering the capital requirements based on Shrieves and Dahl’s (1992) approach. The paper by Shrieves and Dahl (1992) considers US commercial banks and stresses that the changes in the banks’ capital levels and their risk in a bank’s asset portfolio are significantly positively related, causing a simultaneous movement of these two variables. The study comprises the time-period between 1984 and 1986. Furthermore, the authors examined high and low bank capitalisation effects and found that the relationship between capital and risk is positive for both, meaning that an increase in risk leads to a simultaneous increase in capital levels. Based on these results, there is evidence that instead of only considering regulatory pressure, other factors like the managers’ private incentives or the managerial risk aversion can also explain this positive relationship (Shrieves and Dahl, 1992). Similarly, Rime (2001) also finds a positive relationship between the banks’ capital level and asset risks, although it is also not entirely affected by regulatory pressure, but rather shows the private incentive of managers.

Jacques and Nigro (1997) investigated US FDIC-insured commercial banks in the years 1990 and 1991 by adopting the model of Shrieves and Dahl (1992). In contrast to the two previous studies, they found a negative relationship between the adjustments in the banks’ capital holdings and their risk levels for well-capitalised banks. Thus, these findings underline that the implementation of risk-based capital standards leads to an increase in the banks’ capital levels, and, at the same time, a decrease in the (asset) portfolio risk.

The previously discussed studies presume that capital levels and risk-taking are related and determined, showing different results concerning whether the relationship between changes in the banks’ capital level and that their risk behaviour is positive or negative. Following Heid et al. (2003), these ambiguous findings occur because the studies “(…) did not control for the size of the capital buffer”(p.6).

buffers) maintain their buffer by increasing capital levels in case of an increased risk, and when the risk declines, banks will reduce their capital levels respectively. On the other hand, poorly capitalised banks (small capital buffers) build up sufficient buffers by reducing the risk and raising capital at the same time. Therefore, the relationship between changes in the capital buffer and the risk levels for well-capitalised banks is positive, and, in contrast, for poorly capitalised banks, the relationship is negative. The findings in the paper of Heid et al. (2003) provide evidence in favour of the capital buffer theory. However, by considering the adjustment speed in capital and risk, the authors found that low capital buffer banks adjust risk and capital faster than their well-capitalised peers, whereas in a model where the regulatory variable (above or below the median capital buffer) is interacted with the adjustment term, there is no significant difference in the adjustment speed of capital for low or high buffer banks. Mixed results are found for small as well as large capital buffer banks, whereby the regulatory pressure is stated as a reason for this.

Jokipii and Milne (2011), who used US commercial banks’ data in the period from 1986 to 2008, showed that adjustments in capital buffers and the bank risk-taking behaviour are positively related over time. Just like Heid et al. (2003), they also examined different degrees of bank capitalisation (size of the capital buffer). The results indicate a positive relationship when banks are well-capitalised, and a negative relationship for under-capitalised banks. Banks with larger (smaller) than average capital buffers are considered as well- (under-) capitalised. The reasoning for this is the same as in Heid et al. (2003). The authors showed that the degree of capitalisation, meaning the capital buffer size, influences the adjustment speed towards the target levels. Their results are in line with the theory and indicate that banks with a smaller buffer adjust faster than those with large buffers.

3.2 Business Cycle Theory

It has been noticed from different literature and shown in figure x that most banks do not hold capital levels equal to the required levels; instead, they keep a capital buffer at a quite significant level. The counter-cyclical movement of capital buffers is regarded as one major factor for the vulnerability of banks during the recent financial crisis (Huang and Xiong, 2014). Thus, the behaviour of the banks’ capital buffer in relation to the business cycle holds major interest to evaluate current and future regulations (frameworks) as well as to provide information on the relationship between the banks’ capital buffers and their risk-taking over time (Ayuso et al., 2002).

(downturns), capital buffers enable banks to fulfil capital requirements despite facing losses. Banks with stronger precautionary motives are considered to be forward-looking banks that tend to build up larger capital buffers in periods of economic upturn to cover a credit risk during downturns. This implies that capital buffers move pro-cyclically6 (Huang and Xiong, 2014).

Various empirical studies, like Ayuso et al. (2004), Lindquist (2004), Jopikii and Milne (2008) and Stolz and Wedow (2011), displayed that the capital buffer of western European banks moves counter-cyclically. In these papers, it is concluded that the dependence of the banks’ capital buffers on the business cycle fluctuation is harmful for the macroeconomic stability, which has been recently proven by the last financial crisis. In economic good times, banks act riskier in their business by expanding their lending activities without adequately increasing their capital buffers. This behaviour provides evidence for the banks’ short-sightedness (Stolz and Wedow (2011). Consequently, poorly capitalised banks that did not build up a sufficient buffer face the fear of failing to meet the capital requirements in downturn periods due to arising credit risks. For the avoidance of penalties associated with the default, banks must reduce lending sharply to increase capital buffers or issue new equity. The latter option is less applicable due to high costs and the lack of available capital in recessions. Therefore, the banks’ loan reduction reinforces the extent of the recession (Garcia-Suaza et al., 2011).

Basel II’s new capital requirements, which are more sensitive to the risk-taking of the banks’ business operations than those of its predecessor, have been discovered to even reinforce the pro-cyclicality of the bank behaviour (Kashyap and Stein, 2004; Repullo and Suarez, 2008; Moosa, 2010). In this context, pro-cyclicality is defined as the tendency of bank loans “(…) to follow the same cyclical pattern as that of the real economy”(p.56) by expanding the banks’ lending activity in economic upturns or contracting in downturn periods (ECB, 2005). Thus, during boom times, banks increase their lending without building up a buffer capital to cover the potential credit risk, which is (usually) low during this period. When the cycle is set in a recession, building up external capital for banks is very expensive, and, due to lower returns, there is no longer the option to retain profit, which is a main source for raising capital levels. Hence, capital buffer adjustments behave in a counter-cyclic manner. Consequently, the inability to build up capital levels to comply with the required minimum capital levels (Basel II) leads to restrictions on the issuance of bank loans, mostly followed by a credit crunch (Shim, 2013; Repullo and Suarez, 2009). Researchers agree that the pro-cyclicality caused by the new risk-sensitive capital requirements of the Basel Accords was a major issue in the recent financial and economic crisis.

Several empirical studies investigated the effect of business cycles (macroeconomic developments) on the adjustments in the banks’ capital buffers and risk-taking levels. To research the cyclical behaviour of capital buffers, Guidara et al. (2013) used a sample of the six largest Canadian banks over a period of 28 years (1982 to 2010). The results of this paper, when differentiating between crisis (downturn) and non-crisis (upturn) periods, demonstrate

that the banks’ capital buffer increases in upturns and decreases during downturns. The authors found a counter-cycle effect7 (positive co-movement) between the capital buffer of Canadian banks and the business cycles, indicating that capital has been raised during upturns. This positive co-movement is constantly present over the whole sample period (including both periods of Basel I and Basel II). The authors suggest that this counter-cyclical effect (positive co-movement) was a possible cause why the Canadian banking sector was less affected by the recent financial crisis (Guidara et al., 2013).

In contrast to the findings of Guidara et al. (2013), the studies of Jokipii and Milne (2006), Stolz and Wedow (2011) as well as Shim (2013) documented a negative co-movement between the capital buffer and the business cycle. The research by Jokipii and Milne (2006) examines the relationship between the business cycles and capital buffer of European banks between 1997 and 2004. Part of their research was to distinguish banks by both their type and size (banks total assets). The findings exhibit a counter-cyclical relationship between the business cycle and the capital buffers of larger banks as well as those of commercial and savings banks. On the other hand, the capital buffers of small and commercial banks fluctuate pro-cyclically (Jokipii and Milne, 2006). The authors also examined different groups of countries. The results indicate that the capital behaviour differs between developed and developing countries. In developing countries, the capital buffer demonstrates a positive co-movement, whereas in developed countries the buffer fluctuates negatively with the business cycle.

Similar to Jokipii and Milne (2006), the study of Stolz and Wedow (2011) also looked at how business cycles affect regulatory capital buffers of German banks. The results indicate that the banks’ capital buffers fluctuate counter-cyclically during downturns, whereas the effect of business cycles on capital buffers is insignificant in upturn periods. When separating banks by their level of capitalisation, the findings demonstrate that low-capitalised banks reduce capital buffers, while high-capitalised banks build up a capital buffer in both up- and downturn periods. Therefore, Stolz and Wedow (2011) stressed that low-capitalised banks increase their risk-weighted assets in upturn, leading to a rising credit risk although they neglect to build up capital accordingly.

Shim (2013) examined the effect of macroeconomic developments (business cycle) on US-banks’ capital buffers and their risk levels from 1992 to 2011. He (2013) underlined that capital buffers fluctuate counter-cyclically, meaning that capital buffers increase in periods of economic upturns and decline in downturn periods. This is in line with the findings of Jokipii and Milne (2006). In economic downturns, banks reduce their risk-weighted assets by cutting lending to increase their capital buffers. Moreover, risk (measured as non-performing loans to total loans and credits) exhibits a negative co-movement to the business cycle. The results do not provide evidence for a statistically significant relationship between risk and capital buffer. Shim (2013) replaced non-performing loans to total loans and credits with the z-score as a measure (proxy) for risk, whereby the banks’ risk level fluctuates pro-cyclically, while the

capital buffer still shows pro-cyclical movement. Furthermore, the results indicate a significant positive relationship between the banks’ capital buffer and the risk-taking levels. Taking into account that “a higher (lower) Z-score indicates a lower (higher) probability of bank default”, this finding states that the size of the capital buffer (level) is strongly linked to the banks’ default probability. Therefore, banks with riskier portfolios must hold higher capital buffer levels to reduce the probability of default (Shim 2013).

3.3 Key Takeaways

The review of the relevant literature, discussed and outlined in this chapter, generate a variety of key takeaways, which help to underpin the undertaken research and to motivate the underlying hypotheses of this thesis.

Takeaway 1: Deposit insurance enables banks to undertake moral hazard behaviour when managing capital buffers and risk taking.

The deposit insurance protects banks from discipline controls of their depositors (Jokipii and Milne, 2011). This protection of the depositors8 causes a negative relationship between risk-taking- and capital levels, where shareholders of banks try to maximise the value by taking an excessive risk while decreasing the capital levels (Merton, 1977). The government intervenes by setting up restrictions on the banks’ capital levels as well as on the riskiness of the banks’ portfolios to reduce the impact of moral hazard on the relationship between capital and risk (Park, 1997).

Takeaway 2: Banks with a low capital buffer must adjust faster than banks with a high buffer due to regulatory pressure.

Low-capital buffer (or low-capitalized) banks have capital levels which are closer to the regulatory minimum. For this reason, regulatory interferences that require banks to alter their capital levels are costlier for low-capitalized banks (Peuro and Keppo, 2006). The banks’ motivation is driven by avoiding fines and preventing defaults (Milne and Whaley, 2002). Due to their nature, low-capitalized banks are unable to absorb significant losses for longer periods. Consequently, they must adjust their capital faster than their high-capitalized peers to prevent violating the regulatory requirements.

Takeaway 3: Regulatory pressure affects the relationship between the banks’ capital buffers and their risk-taking behaviour.

High-capitalized banks are assumed to maintain their capital buffer by increasing capital levels when the risk increases, and a reduction in the risk has the consequence that capital levels also decline. On the other hand, low-capitalized banks increase their capital and reduce risk at the same time when trying to build up their capital buffer levels.

Takeaway 4: The dependence of the banks’ capital buffers on business cycle fluctuations is harmful for the macroeconomic stability as highlighted by the recent financial crisis.

The business cycle affects the capital buffer levels since they react to variations in risk that occur due to changes in the economic environment. Forward-looking banks tend to increase capital buffers in economic good times to prepare for a potential credit risk, which arises in downturn periods (Huang and Xiong, 2014). Bank short-sightedness implies that banks act

8_{Following the European Commission (2007) “(…) deposit guarantee and investor compensation arrangements}

riskier during boom times by expanding their lending activities without adequate increases of the capital buffers. Hence, banks that do not to build up a sufficient buffer face the risk of failing to meet the capital requirements during downturn periods due to increases of a credit risk. Banks driven by the motivation to avoid penalties are more likely to reduce lending to increase the capital buffers than issuing new equity.

The main takeaway is that capital regulations have a major impact on the coordination of the banks’ capital and risk taking. As pointed out in literature, the effectiveness of underlying regulations depends on the banks’ capitalization degree, indicating the exposed regulatory pressure as well as the stage of the business cycle in which the bank acts.

Literature indicates that further promising research potential lies in answering the question of how changing regulatory pressures during different stages of the business cycle affect the relationship between the adjustment in the capital buffer and risk-taking levels. A simultaneous equation approach (see Shrieves and Dahl (1992) as well as Jokipii and Milne (2011)) is applied to investigate the coordination of the variables of interest, which are specified by regulatory pressure as well as their stage in the business cycle.

3.4 Hypotheses

Several empirical studies investigated the relationship between the adjustments in the banks’ capital levels and their risk-taking behaviour based on the three theories described in the previous section (3.1). This thesis seeks to investigate the impact of (i) the capital regulation and the relation of banks capital buffer and risk taking levels, as well as (ii) the impact of changing macroeconomic conditions on the relationship between the banks’ capital buffer and their risk-taking. The following hypotheses are built on the discussed literature, which includes these three theories and their main aspects.

The capital buffer theory is mainly driven by regulatory pressure, which forces banks to hold a capital buffer to avoid fines when breaching the regulatory minimum standards (Milne and Whalley, 2002). The theory suggests that high-capital buffer banks maintain their buffer by building up capital levels when the degree of risk increases, while the low-capital buffer peers create sufficient buffers by reducing risk and build up capital at the same time. Based on previous findings (similar to Jokipii and Milne (2011)), the following hypothesis is proposed: 𝐇𝟏_𝐨: In line with the capital buffer theory, when holding high-capital buffers, European banks indicate a positive relationship between the capital buffer and the risk, whereas low-capital buffer peers exhibit a negative relationship between the two key variables.

(Huang and Xiong, 2014). The negative dependence on the business cycle fluctuation is harmful for the macroeconomic stability. Banks without exhibiting capital buffers in a recession face an increased probability of failing capital requirements due to the increasing credit risk (Garcia-Suaza et al., 2011). Literature has proven the vulnerability of western European banks due to the counter-cyclical movement of their capital buffers, leading to the following hypothesis:

𝐇𝟐_𝐨: EU banks are assumed to act short-sided, meaning that in good times, banks take more risk and have fewer incentives to load capital buffers, whereas in a recession, they reduce risks to build up a buffer. This negative relationship is driven by a counter-cyclical movement of the capital buffer. In recessions, it is assumed that low-capital buffer banks reduce their risk more than banks with high-capital buffers to increase capital levels.

4. Methodology

The literature in the previous section presumes that the banks’ changes in the capital buffer and the risk levels are related. The empirical model testing this relationship must consider that periodic adjustments are caused by exogenously determined components (e.g. shocks) and the banks’ discretionary behaviour (Hart and Jaffee, 1974; Marcus, 1983). To examine possible effects of capital regulation, the charter value and the business cycle on the adjustments of the banks’ capital buffer and the risk-taking levels, the simultaneous equations model used by Shrieves and Dahl (1992) and later applied and extended by Jokipii and Milne (2011), who studied the short-run relationship between the adjustment in the capital buffer and in risk-taking, are adapted and modified in this study. In the model of Jokipii and Milne (2011), observed changes in the banks’ capital buffer and the risk-taking levels are the sum of two components, one of which is internally managed by the bank9 (discretionary component) as well as by an externally-determined factor (exogenous shock). Thus, the model with simultaneously interrelated variables looks as follows:

(1) ∆buf_!" = ∆buf_!"!"#$_{+ ε} !" (2) ∆risk_!" = ∆risk_!"!"#$_{+ µ}

!"

where ∆buf!" and ∆risk!" are the observed changes in the banks’ capital buffer and the

risk-taking levels. ∆buf_!"!"#$ _{and ∆risk} !"

!"#$ _{are the endogenously determined changes in the banks’}

capital buffer and the risk level (∆buf_!" and ∆risk_!" are fully driven by the banks’ impact, including from the market, so no superscript “bank”). Referring to Jaffee (1974) and Marcus (1983), Heid et al. (2003) argued “(…) that the observed changes of capital and risk are not only the result of the discretionary behaviour of banks, but also the result of exogenous shocks”(p.10). ε_!" and µ_!" are random/exogenous shocks for bank i at time t that are externally determined. For instance, unanticipated changes in earnings cause an exogenous shock to the banks’ capital. Unanticipated changes in the economic situation, like changing the loan quality or the demand, lead to exogenous shocks of the banks’ risks (Heid et al., 2003).

The framework by Jokipii and Milne (2011) stated that banks will define an optimal capital buffer and a risk-taking level, which is internally determined. These optimal levels vary over time. As stated by Milne and Whalley (2001), the target or optimum capital buffer levels10 of banks are determined by a trade-off between the cost of the holding capital and the cost of failure. For instance, banks would keep a capital buffer in the absence of adjustment costs. In practice, where adjustment costs are present, banks cannot adjust their optimal capital buffer immediately due to adjustment costs and market illiquidity (Shim, 2013). Following Flannery and Rangan (2006), the banks’ target buffer levels are not observable. Literature assumes that this target level depends on the banks’ specific characteristics (Shim, 2013) Therefore, the long-term target capital buffer and the risk levels are estimated by the following equations:

(3) buf_!"∗ _{= ξz}

!"+ η!" (4) risk_!"∗ _{= φz}

!"+ ω!"

9 _{Variables that are internally determined by the banks are labelled with the superscript “bank”.}

Here, z_!" capture all variables (including ∆buf_!" in the risk equation and ∆risk_!" in the buffer capital equation) that determine the banks’ target level of the capital buffer and the risk. ξ and φ are the vectors of the coefficients, which must be estimated. ∆buf!" is included in the target

risk estimation, given that a shift in the banks’ capital level will influence the probability of the banks’ default risk. In the estimation of the target capital buffer, changes in the banks’ risk-taking behaviour (∆risk!") will affect the distance of the banks’ capital from the required

minimum set by regulators.

Due to exogenous factors that move the actual capital and the risk levels towards or away from the target levels, banks need to adjust their capital buffer and risk-taking levels to return to their optimal levels (Jokipii and Milne, 2011). The partial adjustment framework is very common in literature to model the firms’ capital adjustments under a dynamic setting as well as to estimate the speed (or cost) of adjustments with which firms shift towards their internally optimal levels (Shim, 2013). Thus, the banks’ (partial) adjustments are defined as:

(5) ∆buf_!"!"#$ _{= ξ}

!(buf!"∗ − buf!"!!!"#$) (6) ∆risk_!"!"#$ _{= φ}

!(risk!"∗ − risk!"!!!"#$)

Therefore, in the partial adjustment model, the banks’ change in capital buffer (risk-taking behaviour) is proportional to the difference in the banks’ target capital buffer level (risk-taking level) and their capital buffer level (risk-(risk-taking level) in the previous period.

The coefficients ξ_! and φ_! represent the adjustment speed (cost) of the capital buffer and risk, respectively. buf_!"∗ _{and risk}

!"

∗ _{are the target levels of capital buffer and risk; and buf}

!"!! and

risk_!"!! capture the lags of the actual capital buffer capital and risk-taking levels. The actual change between the two periods in the capital buffer and the risk behaviour is represented by buf_!"− buf_!"!! and risk_!"− risk_!"!!, while the desired long-run change between the target and the lagged levels is measured by buf_!"∗ _{− buf}

!"!! and risk!"∗ − risk!"!!.

Subsequently, equations (5) and (6) are substituted into equations (1) and (2), such that changes in the capital buffer and risk-taking level are given by:

(7) ∆buf_!" = ξ_!(buf_!"∗ _{− buf}

!"!!) + κ!" (8) ∆risk_!" = φ_!(risk_!"∗ _{− risk}

!"!!) + ϕ!"

Equations (7) and (8) illustrate that the observed adjustments (changes) in the banks’ capital buffer and the risk-taking levels can be modelled as a function of the difference between the banks’ target capital buffer and the risk-taking levels in period t and their lagged capital buffer and the risk-taking levels, plus any exogenous changes (Jokipii and Milne, 2011). The coefficients ξ_! and φ_! represent the adjustment speed (cost) of the banks’ capital buffer and risk-taking towards their individual target levels. In the case that banks must not incur (pay) adjustment costs, ξ_! and φ_! are both equal to one. Thus, banks can instantaneously adjust their actual level towards their target levels, since buf_!" = buf_!"∗ _{and risk}

!" = risk!"∗. By

the optimal level is not completed immediately, which is caused by costs for raising capital as well as illiquid markets (Shim 2013).

Following Flannery and Rangan (2006), the banks’ target buffer levels are not observable. The same is true for the target levels of the banks’ risk-taking. Thus, to estimate (approximate) these levels, the model uses a set of bank-specific explanatory variables that influence the banks’ capital buffer and the risk-taking levels.

(9) ∆buf_!" = α_!− ξ_!buf_!"!!+ ξ_!Y_!"+ ξ_!∆risk_!"+ κ_!" (10) ∆risk_!" = α_!− φ_!risk_!"!!+ φ_!Z_!"+ φ_!∆buf_!"+ φ_!"

In equation (9) and (10), the vectors Y!" and Z!" account for the bank-specific variables that

proxy the target levels of the capital buffer and the risk-taking behaviour respectively. The variables adopted to measure these target levels are the same as those used by Jokipii and Milne (2011) and are described in section X.

Substituting the vectors Y_!" and Z_!" in equations (9) and (10)11, which are the baseline model for further research through the proxy for banks target levels, the model can be written as follows:

(11) ∆buf_!" = α_!− ξ_!buf_!"!!+ ξ_!liquidity_!"+ ξ_!roa_!"+ ξ_!loanloss_!"+ ξ_!size_!"+ ξ_!q_!"+ ξ!∆risk!"+ κ!"

(12) ∆risk!" = α!− φ!risk!"!!+ φ!liquidity!"+ φ!roa!"+ φ!loanloss!"+ φ!size!"+

φ!q!"+ φ!∆buf!"+ φ!"

The set of bank variables that determines the target level of the capital buffer and the risk-taking includes the bank’s liquidity (liquidity), charter value proxied by Tobin’s q (q), the bank’s return on assets (roa) as a measure of profitability, the bank’s quality of loans proxied by the loans loss reserve (loan loss) and the size of the bank (size). Equation 11 and 12 indicate the baseline model of this research. Further model specification (Table A5) as well as a description of the used variables (Table A3) can be found in the appendix.

In contrast to empirical studies in the past12 (Shrieves and Dahl (1992), Jacques and Nigro (1997), Rime (2001), etc.), as well as Jakopii and Milne (2011), a dynamic panel data technique was conducted to account for possible bank-specific effects in this thesis. The model used to answer the research questions includes lagged endogenous variables (buf_!"!! and risk_!"!!). Therefore, the analysis is based on Bundell and Bond’s (1998) two-step Generalised Method of Moments (GMM) system estimation procedure, with a finite sample correction derived from Windmeijer (2005). Arellano and Bover (1995) were the first to illustrate the system GMM methodology, which was later improved by Bundell and Bond (1998). The two-step GMM approach provides more accurate standard errors and less biased coefficient estimates. Furthermore, this system estimator is employed to account for biases in estimates from unobserved bank heterogeneity (Haq and Henaey, 2012). The change in the capital buffer and the risk as well as the lags of the capital buffer and risk are treated as endogenous variables, whereas the rest of the variables are used as either instruments or

11 _{Specification of this equation 11 and 12, to investigate the stated hypothesis, can be found in the appendix} Table A5.

control variables. The number of lags in this estimation of the instruments is limited to three. This is the maximum number of generated instruments in the GMM system, for which instrument proliferation can be avoided13 (Roodman, 2009). Furthermore, the Hansen J-statistic for over-identifying restrictions checks the validly of instruments. The acceptance of the null-hypothesis indicates that all applied instruments are valid. The finite stand errors by Windmeijer (2005), as stated above, are used to correct the downward biases of the standard errors in the 2SGMM. Therefore, the estimations have robust standard errors.

5. Data and Descriptive Statistics 5.1 Data Sources

This thesis uses annual panel data of listed banks in Europe from 14 countries.14 The dataset is created by building on the sample used in the 2014 EU-wide stress tests. Only for 45 out 123 banks, sufficient data was available to conduct the research. The sample contains data from 2007 until 2015.15 Due to the lagged variables of the capital buffer and the risk, the observation period ranges only from 2008 to 2015. The dataset is unbalanced, as data points of some bank-specific variables are missing. The data for the dependent variables capital buffer and risk are subtracted from SNL Financial. Furthermore, total assets as an indicator of the banks’ size as well as loan loss reserves as a proxy for the loan quality are also provided by the SNL Financial database. The banks’ liquidity, the return on assets and the components for Tobin’s q, which are market capitalisation, book values of assets and liabilities, are collected from Thomson Reuters Datastream. The business cycle is proxied by the Output Gap, which is the annual real GDP growth rate data for the calculation. The World Development Indicators (WDI) database provides the required data.

5.2 Descriptive statistics and correlations:

Table A1 provides summary statistics of the dataset. The average change of the banks’ capital buffer is 0.7694 % with a minimum starting at -16.2433 % and a maximum of 17.3252 %. The largest changes in capital buffers are seen in the years 2009 and 2013. The distribution of the change in the capital buffer is approximately symmetric. The mean of the changes in the (risk) ratio of risk-weight assets to total assets is -1.4742 %, whereas the maximum is 13.1969 and the minimum is -19.8681 %. Looking at the skewness and kurtosis of the risk, the values indicate a relatively normal distribution of this variable. The z-score included in the dataset as an alternative measure for risk ranges between -3.3705 and 2.3991. The distribution of risk is normally distributed around its mean of -0.3123. In the analysed equation, the lags of the endogenous variables capital and risk are used to measure the adjustment speeds towards their target levels. The mean of the capital buffer is 5.8561 %, with a minimum of minimum of -14.102 % and a maximum of 22.280 %. Figure 1 shows the trend of the average capital.

13 _{For estimations including more dummy variables, the maximum number of lags was reduced.}

14 _{Austria, Belgium, Denmark, France, Germany, Greece, Ireland, Italy, Norway, Poland, Portugal, Spain,} Sweden and the United Kingdom.

By the definition of this thesis, the capital buffer is the difference of the total capital ratio and the required minimum ratio. Therefore, the constant increase in the total capital indicates a capital buffer growth over the observation period. Only in 2011, this growth was interrupted, possibly caused by the start of the European debt crisis in 2010. The constant growth towards the end of the period leads to the assumption that prepare themselves for stricter capital requirements under Basel III (implemented in 2019). The average capital buffer per country in Figure A4 shows that Denmark and Sweden hold the largest buffers, whereas the southern European countries (like Greece, Portugal and Italy) exhibit the lowest buffers. The risk proxied by the ratio of risk-weighted assets to the total assets has a mean of 48.039 %, where the minimum is 14.488 % and the maximum is 86.081 %. Revealed by the skewness and kurtosis, the risk is relatively normally distributed. The z-score is normally distributed around its mean of 1.9122. Turning to the control variables, the business cycle movement proxied by the output gap has a mean of -0.3978 and is relatively normally distributed. The real GDP growth rate is slightly negatively skewed. It has a mean of 0.2872, with a maximum of 25.557 and a minimum of -9.132.

Table A2 reports the pairwise correlations of the variables used in the estimations. The dependent variables change in the capital buffer is negatively correlated to the change in risk. Furthermore, it is slightly negatively correlated to the z-score. The depended variable capital buffer change is negatively related to the lagged variable of the capital buffer. The change in risk also appears to be negatively correlated to the lagged variable of risk. The change in the z-score is highly negatively correlated to the lag of the z-score. As expected, the change in the capital buffer is negatively related to the output gap, indicating the capital buffers’ counter-cyclical behaviour. Interestingly, the real GDP growth is slightly positively related to the capital buffer change. The change in risk is positively correlated to the output gap as well as to the real GDP growth, which also proxied the business cycle movements. The bank size is positively correlated to the lag of capital buffer but strongly negative correlated to the lag of the risk.

5.3 Variables description Dependent variables:

Capital buffer (buf!"): Following Jokipii and Milne (2011), the capital buffer is defined as

“(…) the observed change in the amount of actual capital the bank holds in excess of the required minimum capital ratio of 8 %” (for the calculation, see appendix Table A3). After the introduction of the capital requirements under Basel I, which measures the capital as the total capital to the total risk-weighted assets, the total capital ratio (alternative Leverage ratio) is commonly used in literature (Jacques and Nigro (1997), Aggarwal and Jacques (2001), Rime (2001) and Heid et al. (2003)). This thesis uses the total capital ratio, which is the total capital (tier 1 plus tier 2) divided by the risk-weighted assets minus 8 % (required minimum capital ratio) to calculate the banks’ capital buffer.

RWATA are chosen as a risk proxy because the bank risk is determined by “the allocation of banks assets among risk categories” (Heid et al. 2003). A disadvantage of RWATA as a measure for risk is that it only accounts for the credit risk and does not serve to capture the market risk. Therefore, only one part of the actual asset risk is captured (Jokipii and Milne, 2011). In this thesis, risk (risk_!") is calculated similarly to previous studies (Jacques and Nigro (1997); Heid et al. (2003)) as the ratio of risk-weighted assets to the total assets (see appendix Table A3).

The following bank-specific variables, suggested by literature and especially by Jokipii and Milne (2011), are used to proxy the banks’ optimal capital buffer and the risk-taking levels. Explanation variables:

Charter value (q!"): Banks with a higher charter value have greater incentives to reduce

risk-taking in their business (or to cover their risk by building up capital buffers), and, hence, to ensure that the capital buffer level does not fall below the minimum requirement (Demsetz et al., 1996). The charter value can be calculated as the difference between the market value of the assets and the replacement costs of the bank. Hence, it is defined as the net present value of the banks’ future rents (Keeley, 1990; Demsetz et al., 1996). In many empirical studies as well as in this thesis, Tobin’s q is used to calculate the banks’ charter value (see appendix Table A3 for the calculation of Tobin’s q). Tobin’s q, as a market-based measure, is able to reflect the level of market values in both asset- and deposit markets in a single q value (Jokipii and Milne, 2011).

Liquidity (liquidity_!"): Banks equipped with a high ratio of liquid assets need less insurance against a possible violation of the minimum capital requirements, given that liquid assets can be converted without any problems into cash if necessary (Jokipii and Milne, 2011). Thus, highly liquid banks can make short-term financial investments without being forced to sell capital investments or fixed assets (Shim, 2013). Following Jokipii and Milne (2011), banks with more liquid assets typically hold smaller capital buffers and possibly behave in a riskier manner. The liquidity is calculated as the ratio of the liquid assets to the total assets.

Bank size (size_!"): is included in the model to account for size effects on the capital buffer and the risk-taking behaviour. Large banks tend to hold a relatively lower capital buffer because they have better access to capital markets compared to smaller banks (Shim, 2013). Smaller banks tend to maintain higher capital levels since their possibility of being liquidated or being a target of unprofitable takeovers is higher during financial distress (Francis and Osborne, 2012). Larger banks are more likely to be affected by the moral hazard problem. Due to their size, larger banks are characterised by the government as “too big to fail”, which can be perceived as an assurance against bankruptcy. Therefore, these banks tend to engage in riskier businesses (Shim, 2013). Like previous studies (Jokipii and Milne, 2011; Shim, 2013), the bank size is measured as the natural log of total assets.

Loan quality (loanloss!"): The loan-loss reserve reflects the amount of a bank’s cash or

Return on assets (roa_!"): The return on assets is included as a proxy for the banks’ profitability because banks may depend on profits (retained earnings) to increase their buffer capital. In case of high earnings, banks can increase their capital buffer easily. On the other hand, when banks are not able to build up their buffer with retained earnings, they must issue equity or costly raise funds from the capital market (Jokipii and Milne, 2011).

Control and dummy variables

Dummy variables Dcap_!"# and Dcap_!"#! are included in the models to investigate if the banks’ capitalization degree (can also be regarded as an indicator for regulatory pressure) has an impact on their capital buffer levels and the risk-taking behaviour. These two dummy variables are created to account for well-capitalised (Dcap!"#!) banks with a capital buffer

above a defined threshold and low capitalised banks (Dcap_!"#), where the capital buffer levels are below a marginal value. The dummy variable Dcap_!"# is one if the bank is in the bottom 25th percentile regarding the capital buffer size in the total bank sample for a respective year, and zero otherwise. Hence, undercapitalised banks have capital buffer levels below 3 %. Dcap_!"#! is a dummy variable for well-capitalized banks, which is one if the banks’ capital buffer ratio is in the top 50th percentile of the total sample in a given year. The knot of the 50th percentile is used as threshold value of the capital buffer, which is 5 %, to separate/isolate well-capitalized banks.16 These dummy variables (Dcap_!"#and Dcap_!"#!) are interacted with the ∆buf!" and ∆risk!" as well as with the buf!"!! and risk!"!! in the capital

buffer and risk equation, respectively.

The output gap (outgap_!"): In a variety of studies, the output gap is used as an indicator for business cycle movements. Following Stolz and Wedow (2011), the output gap is calculated by “(…) subtracting a non-linear trend from real GDP using the Hoddrick-Prescott filter.” (p.101) Alternatively, literature uses the real GDP growth to measure the business cycle fluctuation (later, the real GDP growth will be used to check the robustness of the results under the output gap). The output gap in comparison to the real GDP growth “(…) removes trends from time series variables.” (Guidara et al. 2013, p.3375). Hence, the output gap differentiates between the economy’s actual output and its potential output (indicated by real GDP growth). In this thesis, it is assumed that the majority of bank businesses is undertaken in the (market) country, where the banks’ headquarters are located. Therefore, the output gap for each country, used in the sample, is calculated separately.

16 _{As stated by Stolz and Wedow (2011), the difference in the effect for well- and low-capitalized banks declines} when the threshold rises. For instance, a higher threshold leads to an increasing share of undercapitalized banks with “moderate capital buffer levels” in the undercapitalized group. To diminish this effect and to ensure the sub-division of the two groups, a gap is put in-between to account for the different effects of Dcap_!"!_{and Dcap}

6. Regression Results

This section presents and summarises the empirical results of the research questions. It explains and discusses the main empirical findings regarding the sensitivity of the relationship between the banks’ capital buffer and risk taking with regards to capital regulations (pressure) as well as the business cycle movements. The simultaneous equations are estimated using the 2SGMM (two-stage generalized method of moment) estimation. The estimation results are presented in Tables 1 and 2.

Bank-specific variables are chosen to estimate the banks’ internal target capital buffer and the risk levels. All estimation coefficients besides size are at least once significant in the different specifications of the capital buffer and the risk equations. Interestingly, size was never significant in the buffer equation of Tables 1 and 2. The significance of the variables as well as the (rejection of H0) Hansen J-statistic show that these variables are useful for the estimation of the banks’ optimal capital buffer and risk-taking levels. A more detailed interpretation of theses variable coefficients is not relevant for answering the research questions in this thesis.

6.1 Step 1 - Regulatory pressure

The first specification in Table 1 describes the baseline model of this research, which shows the simultaneous estimation17 of equations 11 and 12. The coefficient change in the capital buffer (∆buf_!") in the risk equation and the coefficient change in risk taking (∆risk_!") in the capital buffer equation are both negative and significant. The fact that both coefficients are significant indicates that the adjustment capital and the risk adjustment are simultaneously negatively related and that the coordination can be done from two sides of the relationship. These findings suggest two possible interpretations: When banks increase their capital buffer, they reduce their risk taking at the same time, whereas when banks increase their risk-taking behaviour, they simultaneously decline their capital buffer. As stated by Jokipii and Milne (2011), the simultaneous interrelation between the change in the capital buffer and the risk levels enables banks to manage their internal optimal default probability. The management of the banks’ capital is driven by the incentive to prevent or to reduce the costs associated with violations of the regulatory requirements (Milne and Whalley, 2002). Therefore, banks would increase their capital and reduce the riskiness in their asset portfolio. This finding is contrary to Jakipii and Milne (2011), who discovered a positive relationship between ∆buf_!" and ∆risk_!" when accounting for the overall effect of low- and high-capitalized banks. Second, banks that aim at reaching the regulatory minimum capital ratios will increase their risk-taking levels to restore their buffer. This behaviour is described by Jokipii and Milne as “(…) gambling for resurrection”(p.166), which could cause their capital buffer to temporarily decline even more. The coefficients of buf_!"!! and risk_!"!! indicate the adjustment speed18

17 _{The simultaneous equation method provides causality to the interpretation of the relationship between ∆buf}

!"

and ∆risk_!". Thereby, the two-equation set up enables to show from which side the possible relation is coordinated, and, thus, distinguishes between a one-way and a two-way coordination of the relationship (see for instance Heid et al. (2003) and Jokipii and Milne (2011)).