HE RELATIONSHIP OF CAPITAL REQUIREMENTS WITH THE DETERMINANTS OF CAPITAL AND RISK T

T

HE RELATIONSHIP OF CAPITAL

REQUIREMENTS WITH THE

DETERMINANTS OF CAPITAL AND RISK

EVIDENCE FROM NON

-

LIFE

,

INSURANCE FIRMS

UNDER SOLVENCY

I

AND

II

REGULATION

By

Daniil Jakovlev [s2770067] MSc. Finance Thesis

Business economics

University of Groningen

Department of Economics, Econometrics and Finance June 2018

Word count: 12139

* I would like to thank all who supported me in providing structure, linguistic and contextual recommendations.

A

BSTRACT

The purpose of thesis is to investigate the effectiveness of regulatory capital requirements of Solvency I and II European regulation on capital and underwriting risk levels of non-life insurance firms, under supervision of the Dutch Central Bank (DNB). The determinants for capital and underwriting Risk in this study are: profitability, premium growth, underwriting risk and capital. The empirical study uses four multiple linear regressions, where the results are presented in three models by using a ‘moderator dummy’ and interaction terms. The key finding in this thesis is that effectiveness of capital regulation is confirmed through the effects of the several determinants on capital and underwriting risk. Especially, undercapitalized firms tend to increase capital and face decreasing underwriting risk more than adequately capitalized firms. However, results indicate undercapitalized firms hold higher capital levels and seem to have lower risk levels. Robustness test with accumulation of capital and risk, show similar results as capital and risk levels. Moreover, the sub-sample with only Solvency II data (i.e. in the year 2016) shows similar results to the main sample.

Author: Daniil Jakovlev Date: June 7, 2018

Key words: Non-life insurance firms, DNB, Solvency I, Solvency II

Research theme: Effectiveness of capital regulation on determinants of capital and underwriting risk levels

1.

I

NTRODUCTION

The purpose of this thesis is to investigate the effectiveness of regulatory capital requirements of Solvency I and II European regulation on determinants of capital and underwriting risk levels of non-life insurance firms, under supervision of the Dutch Central Bank (DNB). The differences in determinants of capital and underwriting risk levels between adequately and undercapitalized firms suggest the effectiveness of the capital requirements.

The contribution of this paper to prior research of capital and risks levels of non-life insurance firms under capital regulation will be in five areas. Firstly, the focus will be on non-life insurance firms, specifically under supervision of DNB, where prior studies analyze US non-life insurance firms. Particular interest comes from the fact that DNB points out that Dutch insurance firms make no or little use of transitional measures to Solvency II, which may be applied in the next 16 years. Secondly, this paper focuses on Solvency I and II regulation, where prior research studies the insurance industry under the Risk Based Capital (RBC) system regulation or solely Solvency I. Thirdly, a debate on capital regulation comes, among others, from Moosa (2010) who studies regulation in the banking industry. There the author suggests disregarding harmonization and unification of banking regulation because it is not effective in its current form. This debate on effectiveness of regulation can be extended to the insurance industry and this thesis contributes as one of the first starting points. The fourth area of contribution is stemming from the dataset of this thesis. The insurance firms in the dataset used in this thesis operate in various sectors in contrast to the datasets used in prior research where the dataset consists of insurance firms of one sector (e.g. property-liability). Finally, contribution to the theory of this thesis lays in studying the non-life insurance firms instead of life insurance firms. The reason for studying non-life insurance firms is because this sector is more dynamic than of life-insurance firms. The latter have more long-term obligations and a different investment behavior. Consequently, I expect a more short-term response at non-life insurers than with life insurers.

This thesis will consider risk as underwriting risk, calculated per insurance firm. Underwriting risk (Risk) refers to the potential loss to an insurer arising from faulty funding and is intrinsic to future cash flows. This variable relates to the research topic as Browne and Hoyt (1995) came to the conclusion, that the underwriting risk is positively related to the insolvency risk.

Separating the results for under- and adequately capitalized firms shows differences in effectiveness of capital regulation on the determinants of capital and risk levels. Since prior

researches indicate insurers avoid regulatory costs (e.g. Shim, 2010), being an

undercapitalized insurance firm will most likely lead to these additional costs (DNB, 2015). This is because overcapitalized insurers will not face intervention costs while

undercapitalized insurers will. To find the effects of regulatory pressure I use a dummy variable and construct three models with interaction variables and a ‘moderator dummy’. The dummy variable indicates if an insurer is sufficiently or undercapitalized according to the Solvency regulation standards. Shim (2010) and Mankaï and Belgacem (2016) use the same method to compose a dummy based on capital requirements from the Risk Based Capital (RBC) regulation and construct models with interaction terms.

In general, there are a few studies that examine regulation, especially Solvency

regulation, and its relationship with determinants of capital or risk of non-life insurance firms. This observation is confirmed by Gaganis et all. (2015) where the authors conclude that the relationship between profitability and regulation is under-researched in existing literature. Shim (2010) and Mankaï and Belgacem (2016) study the same subjects except for US insurance firms under RBC. These studies are the main background papers upon which this thesis builds on. In their papers they investigate how determinants of capital and risk fluctuate under regulatory pressure and how capital and risk levels are related. Since these studies confirm a positive relationship between capital and risk for US insurance firms, I expect that Solvency capital requirements will have significant impact on the capital and risk levels of non-life insurers under Solvency I and II.

In summary, this thesis will try to find an answer to the following research questions. I. Is there a difference in increase of capital levels for undercapitalized firms

compared to adequately capitalized firms under capital regulation?

II. Is there a difference in increase of risk levels for undercapitalized firms compared to adequately capitalized firms under capital regulation?

The source of the dataset for the empirical analysis is the database from the Dutch Central bank (further as: DNB). The database of DNB provides yearly balance sheets, P&L1 -accounts and other financial statements of non-life insurance firms under its supervision. Depending on the year in the studied period, the dataset for the regressions consists of 102-175 non-life insurance companies between 2011 and 2016 structured in an unbalanced panel. It is important to highlight that Dutch insurance companies do not make use of the

implementation of transitional measures to Solvency II. Hence, their solvency ratios have only been influenced by Solvency I. Therefore, I expect that comparing insurers over several years will give more ‘pure’ results.

For the empirical analysis performed on the sample, I use four multiple regressions using OLS with fixed or random effects. The explanatory variables are: profitability (ROA), growth of premiums, capital2 and underwriting risk3 on the dependent variables capital and underwriting risk.

According to EIOPA4 capital regulations are implemented to protect policyholders (next to other stakeholders) and ensuring financial stability. Capital regulations require insurers to hold an amount of capital to cover extensive amounts of potential risk. Imposing regulation on insurance companies is necessary because insurance firms are accountable for one third of investments made by institutional investors (IMF, 2016). This means that insurance firms could have a severe impact on the overall economy in case of a crisis, as we have seen with AIG in 2008. Moreover, prior reaches suggest that capital regulation

requirements help the financial firms to reduce bankruptcies and their negative externalities on the financial system as a whole (see Dewatripont and Tirole, 1994; Kessler, 2008). In summary, regulation is needed for the financial stability and to protect the consumer, however its effectiveness is the key reason for completing this task successfully.

Regulation in banking and insurance industry goes far back in history. In 1988 the ratification of the Basel Accord marked the first step towards transferring the obligation of protecting financial stability in the banking industry, from national to international level (Maurice, 2004). Where banks are under unified regulation of Basel requirements, insurance firms are required to meet requirements of the Solvency regulation. The first solvency margin requirements are established in 1973 for non-life insurers and 1979 for life insurers. These were the first building blocks for an internationally harmonized regulation to protect the financial stability of the insurance industry and its stakeholders. However, the capital requirements did not account properly for the specific risk that each firm faces, which

decreased the incentive for effective risk management. Eventually the financial crisis of 2008 exposed these flaws in the regulation confirming that a new regulation was needed. European regulators started developing this new risk framework in 2009 and it should have been

2 _{Only in the regression on Risk.} 3 _{Only in the regression on Capital.}

implemented in 2012. After the delayed implementation in 2016, part of Solvency I regulation still remains applicable to companies to which Solvency II does not apply.

Solvency II, the new regulation, consists of three pillars. Pillar I contains quantitative requirements, including mark-to-market balance sheet valuation and quantification of market risks and insurance technical risks. Pillar II of the framework sets out the principles and methods of supervision on the one hand and the qualitative requirements for engaging in insurance activities on the other. Pillar III deals with market discipline, transparency and disclosure obligations along with reporting to the supervisory authorities.

Importance of Pillar I in terms of the capital requirements is a distinction made between minimum capital and solvency capital, where the minimum capital represents the absolute floor. The Minimum Capital Requirement (MCR) is the level of own funds below which the consumers are at serious risk if the insurance firms were to continue its business activities. It represents the final supervisory intervention threshold before the any strict sanctions are implemented. The Solvency Capital Requirement (SCR) has to be covered by eligible own funds of the same amount, which enable insurers to absorb high levels

of unexpected losses and give reasonable assurance to policyholders and beneficiaries that payments will be made as they fall due. If the eligible own funds fall below the SCR firms are expected, as a first regulatory consequence, to hand in a ‘recovering plan’ to fulfill to the obligations.

Since 2016 insurance firms are obliged to follow Solvency II requirements. As the regulation is new, to my knowledge the effectiveness of this regulation has not been

thoroughly studied yet. With first financial facts becoming available this thesis contributes to future research on the effectiveness of the regulation.

The remainder of this paper will be as follows. Section two will discuss and reflect on prior research. In section three, I will describe the research methodology and explain the hypotheses. Then, section four describes the data and summary statistics are provided. Next, section five presents the results of the various statistical tests in tables. Thereafter, I perform several robustness checks. The conclusion follows in section seven with a recommendation for future research.

2.

B

ACKGROUND AND LITERATURE REVIEW

In this part I review a number of prior studies on the relationship between the

insurance industry and capital regulation. I consider the used approaches and methods of prior research to apply in my study. The results and findings of prior research should provide expectations for the results and findings in this thesis. Due to limited amount of research related effects of regulation on insurance companies, literature research in this thesis is extended to some key papers investigating the topic in the banking sector. Banking sector, being seen as the closest to insurance sector, is looked at to find similarities or contradictions with the studies on the insurance industry and to explain my results.

2.1

R

I

Prior research and the intent of Solvency I and II show capital and risk levels are related to capital requirements. However, prior studies find a weak relationship between Solvency I and the company’s risk levels. Under Solvency I insurers had a small incentive for risk management. Although my study includes Solvency I data the research period is much closer to the implementation of Solvency II, a more strict capital regulation. This is supported by EIOPA that state the preparatory phase began in 2013, see appendix A figure A.1.

De Haan and Kakes (2010) find a positive relationship between the firm’s risk characteristics and the actual solvency margin however not between the firm’s risk characteristics and the required solvency margin. This means that firms do not react to regulatory pressure and hold higher capital margins than the regulatory minimum. However, they are basing conclusions on data provided by DNB according to Solvency I requirements in the period 1995-2005. With Solvency II, insurance firms are obliged to provide more risk-based information and the capital requirements incorporate more risk factors (DNB, 2015). Furthermore, their paper suggests that undercapitalized insurers increase capital ratios faster than adequately capitalized insurers. In addition, their finding is in line with capital buffer theory that argues that firms have an incentive for holding capital in excess of regulatory minimum.

Another study that shows results in line with capital buffer theory is that of Cummins and Sommer (1996), who investigate the capital and portfolio risk decisions of property-liability insurance firms. Their results suggest a positive relationship between capital and risk. However, their findings lead to the conclusion that regulatory costs do not play a significant

role in determining the insurers capital and risk levels during the research period. De Haan and Kakes (2010) could provide an explanation to this result. The authors state regulatory pressure has little influence on capital and risk decisions because regulation is not enough risk-based.

2.2

R

S

II

To my knowledge this thesis is the first study that will give an insight in the early stage relationship of Solvency II capital requirements on capital and Risk levels. Although prior studies look forward to the Solvency II regulation and expect it to have a positive effect on risk management (e.g. Bijlsma and Vermeulen, 2017; de Haan and Kakes, 2010) Solvency II effectiveness still has to be proven. Taken into account the magnitude of capital invested by insurers, the analyses in this thesis will be relevant for studying the effectiveness of capital regulation in the non-life insurance industry.

One of the factors that can lead to ineffectiveness of Solvency II can be found in Solvency II EC Directive 2009 article 77, which points out that financial instruments can replicate future cash flow obligations. If the market value is reliable, the value of the

replicating portfolio should be equal to the total amount of technical provisions. However this brings additional risks, as insurance firms are not obliged to determine a best estimate and risk margin. For example it gives way of using illiquid assets for the replicating portfolio and additionally correcting value with a liquidity premium. A premium is justified because additional risk is taken. This complex operational procedure of matching a replicating

portfolio with technical provisions lacks scientific support (see Laeven, 2011) and is even not possible according to Danielsson, et all. (2012).

To summarize, prior studies see Solvency II as an improvement, which would lead to stronger relationship between capital regulation and capital and risk levels. Therefore the early-stage analysis of this paper is relevant as a contribution to monitoring the effectiveness of the regulation.

2.3

R

RBC-

This thesis solely focuses on the relationship between capital and risk levels under Solvency I and II regulation, which is applicable for European insurance firms. Other studies that focus on the relationship between capital and risk levels, however under the RBC-system, are important for understanding the methods and models used in this thesis.

This relationship of risk and capital is studied extensively in Cummins and Sommer (1996) and Mankaï and Belgacem (2016), where they focus on this relationship for property-liability insurers and the latter adds reinsurance into their study. Their key findings are that undercapitalized insurers adjust capital and risk more extensively. Mankaï and Belgacem (2016) add to this by concluding that sufficiently capitalized insurance firms maintain their capital levels and increase risk while undercapitalized insurance firms raise capital or by reducing risk. The limitations of their conclusions for my study are related to the fact that they incorporate reinsurance into the study.

Another study that has a more broad set up with macro and micro data is from

Srivastava and Ray (2013). Their paper sets up a framework for predicting insolvency risks of general insurers and suggest the variables incurred claims and premium growth rate

significantly affect the financial health of general insurers. In my regression I incorporate these to variables in the calculation of the variable underwriting risk and as a separate variable growth. Although their sample is very small and consists of eight Indian insurers their regressions have yielded statistically significant results.

To summarize, literature on the insurance industry mostly investigates the relationship between capital and risk under non-European capital regulation including the separation of undercapitalized and sufficiently capitalized insurers. Almost all studies find a positive

relationship between capital and risk, which is in line with the intent of capital regulations that require increase in capital for increase in risk.

2.4

F

The method used for analysis in this thesis follows the framework built in the study of Shim (2010). In particular, the models of the empirical analysis show coefficients of

interaction terms and a ‘moderator dummy’. The coefficient of the moderator dummy and the interaction terms should show the differences in effectiveness of determinants on capital and risk levels between adequately and under-capitalized firms, similarly to the study of the main background papers. As in this thesis, Shim (2010) uses separate models that show results with and without a dummy variable and interaction terms to indicate the differences between adequately and undercapitalized firms. Following this model they came to conclusive findings, that undercapitalized insurers increase capital to avoid regulatory interventions / costs and take more risks to generate higher returns.

variables I chose the explanatory variables due to high statistical significance in the studies of Mankaï and Belgacem (2016) and Shim (2010). Moreover, these studies provide a clear justification of the influence of determinants on capital and risk levels. The empirical analyses in their studies test hypotheses that are based on capital structure theory, which will be

reflected in this thesis when I introduce the hypotheses and explain the empirical results. In my study I use four multiple linear regressions as this method is widely used in financial analysis (Brooks, 2014). Important studies use different approaches. In the paper of Cummins and Sommer (1996) the study is done by means of a theoretical model based on option pricing theory. For their empirical analysis they use a simultaneous equation model, which is also used in Shim (2010) and Mankaï and Belgacem (2016). In many areas of applied economics the partial adjustment model has been used as a description of optimal behavior in the face of adjustment costs (Kennan, 1979). This type of model allows analyzing effects caused by exogenous factors while in my analysis I aim to give a more general

conclusion of the relationship between the dependent and endogenous independent variables in the short run.

2.5

L

It is interesting to find contradictory conclusions in studies of the banking industry, which mention that regulations can increase risky investments, and default probability (Kim and Santomero, 1988) on the one hand and decrease risk by increasing capital, on the other hand (Furlong and Keeley, 1989). Studies of the impact of regulatory capital requirements on the bank’s capital and risk adjustments can be found in a large amount (e.g. Jacques and Nigro, 1997 and Rime, 2001). Most studies find a positive relationship between capital and risk adjustments. Mailath and Mester (1994), for example, study the effect of regulatory consequences on risky behavior. In their study they take the perspective of the regulator by investigating its incentives in two different cases of agency problems. Furthermore, they investigate a powerful control tool of the regulator, namely bank closure. The insurance firms in my dataset are under supervision of DNB, which may appoint a secret receiver, impose a production stop or revoke the insurer’s authorization (DNB, 2015).

High risk-levels can lead to defaults, as studies on the banking sector show. Jacques and Nigro (1997) mention that the number of bank failures has risen in the 1980s as a result of new regulations. This could either be the case for insurance firms although they can rely moderately on reinsurance (Mankaï and Belgacem, 2016). According to Alfriend (1988) the increase in bank failures is due the fact that early capital regulations failed to incorporate risk.

Notice that we have seen this conclusion in studies relating to Solvency I (De Haan and Kakes, 2010). Despite that capital and risk are positively related, the adjustment of capital was apparently not enough to cover a rise in risk levels.

My study is not focused on banks. However, due to similar results of studies in the insurance industry I expect to find the same relationship between capital and Risk under Solvency capital regulation. Especially Jacques and Nigro (1997) show similarities with my study namely, since both studies investigate the impacts of risk-based capital regulation on capital and risk in the first year. Their empirical analysis differs from the one in this thesis as they use a three stage least squares (3SLS) model. The finding in their paper is that

undercapitalized banks do not adjust risk and capital as extensively as adequately capitalized banks do. Similar to their paper I will investigate the adjustments of capital and risk for sufficiently and under-capitalized firms separately and jointly. The difference between effects of the variables of sufficiently and under-capitalized insurance firms should shed light on the impact of capital regulations.

In summary, literature on the banking industry show similar results in comparison to studies on the insurance industry. Studies on banks similarly find a positive relationship between risk and capital under a regulatory regime. Moreover, there is a difference in capital adjustment between undercapitalized and sufficiently capitalized banks.

3.

METHODOLOGY AND HYPOTHESES

In this chapter I will explain the empirical model that I use and the hypotheses I test to answer my research questions. In addition, Shim (2010) and Mankaï and Belgacem (2016) specify determinants of risk and capital that I select for the capital and Risk regression.

3.1

H

In this thesis I want to find an answer to the research question: Is there a difference in increase of capital levels for undercapitalized firms compared to adequately capitalized firms under capital regulation? Linked to this, Shim (2010) who suggests that profitability and capital levels are positively related. To proof or disproof that finding and answer my research question I hypothesize as follows:

H1: Profitability and capital ratios are more positively related for undercapitalized insurers than for adequately capitalized insurers.

Accepting this hypothesis suggests that regulatory pressure forces inadequately capitalized firms to increase more capital in order to avoid regulatory intervention, when additional cash flow is available. Additionally, in that case there is evidence for capital structuring by following pecking order theory.

According to Mankaï and Belgacem (2016) this hypothesis is important as it gives one of the reasons that the effectiveness of regulation is growing. Hence, by testing this

hypothesis I am testing the effectiveness of Solvency I and II regulation.

The relationship of capital and risk is positive as prior research indicates, which leads to the second research question of this thesis: Is there a difference in increase of risk levels for undercapitalized firms compared to adequately capitalized firms under capital regulation? A key study on capital regulation (Cummins and Danzon, 1997) suggests capital levels need to be increased when risk increases to avoid default and regulatory intervention. Moreover, the intent of the capital requirements of the new Solvency regulation is to cover a large

magnitude of losses with an increase in capital. Consequently I hypothesize as follows: H2: Undercapitalized firms hold higher capital levels as a result of risk than adequately capitalized firms.

This hypothesis is similar to the hypothesis from Shim (2010) where the author suggests that capital and risk levels are chosen jointly as a function of regulatory capital requirements. Notice that in this thesis I am trying to observe this relationship, not predict it. Rejecting this hypothesis means that the capital requirements are not effective enough when firms are considered undercapitalized. Moreover, rejecting the hypothesis suggests that firms in the used dataset behave differently from firms in the dataset of prior studies, where prior studies find that undercapitalized firms accumulate capital faster and reduces risk more than adequately capitalized firms (Mankaï and Belgacem, 2016; De Haan and Kakes 2010).

3.2

T

In the empirical analysis I will use three models: Model one (I), with exclusively the determinants, which shows their overall relationship with capital and risk levels. The second model (II) includes only the ‘moderator dummy’ next to the determinants. The ‘moderator dummy’ will indicate the average difference of capital and risk levels between well- and undercapitalized firms. The third model (III) includes determinants, the ‘moderator dummy’

and the interaction terms. The interaction terms show the specific difference per determinant among the different ‘groups’ of firms.

The empirical analysis is done by using four multiple linear regressions (see equation 1, 2, 3, and 4) and applying the Ordinary Least Squares (OLS) method with a selection of determinants (as independent variables) of capital and risk levels (the dependent variables) performed on an unbalanced panel. According to Brooks (2014) OLS is a commonly used method in econometric model estimation and which enables me to produce high quality results.

I am following the main background papers by using the determinants profitability, underwriting risk, capital and growth opportunities as explanatory variables. Further in this thesis I will provide specific reasons for using these variables. The analysis in this thesis is limited to only explanatory variables that are related to the performance of the firm. This means that any exogenous (macroeconomic) variables that can have an influence on capital and/or risk levels will not be taken into the regressions. This is different to other studies that are more extensive with variables such as: exposure to extreme risk and reinsurance (Mankaï and Belgacem, 2016; Shim, 2010).

Following Mankaï and Belgacem (2016) and Shim (2010) where they measure speed of adjustment, I study not only the levels of capital and risk but also the accumulation of it (see equation 2 and 4) and use it as a robustness check. By analyzing the impact of

determinants on percentage change in capital and risk I gain more insight in the behavior of firms affected by being classified as adequately capitalized or undercapitalized under capital-based regulation.

𝐶𝐴𝑃!,! = 𝛼!+ 𝛼!𝑅𝐼𝑆𝐾!,! + 𝛼! 𝑅𝑂𝐴!,! + 𝛼! 𝐺𝑅𝑂𝑊𝑇𝐻!,!+ 𝑢!,! (1)

𝛥𝐶𝐴𝑃!,! = 𝛽!+ 𝛽!𝑅𝐼𝑆𝐾!,!+ 𝛽! 𝑅𝑂𝐴!,!+ 𝛽! 𝐺𝑅𝑂𝑊𝑇𝐻!,!+ 𝑢!,! (2)

𝑅𝐼𝑆𝐾_!,! = ϒ_!+ ϒ_! 𝐶𝐴𝑃_!,! + ϒ_! 𝑅𝑂𝐴_!,!+ ϒ_! 𝐺𝑅𝑂𝑊𝑇𝐻_!,!+ 𝑢_!,! (3) 𝛥𝑅𝐼𝑆𝐾_!,! = 𝜃_!+ 𝜃_! 𝐶𝐴𝑃_!,! + 𝜃_! 𝑅𝑂𝐴_!,! + 𝜃_! 𝐺𝑅𝑂𝑊𝑇𝐻_!,!+ 𝑢_!,! (4)

where 𝐶𝐴𝑃_!,! is the capital level of an insurer i on time t, 𝐺𝑅𝑂𝑊𝑇𝐻 is the yearly percentage growth of premiums, 𝑅𝐼𝑆𝐾 is underwriting risk measured as the variance of the

loss ratio, 𝑅𝑂𝐴 represents the profitability as return on assets of an insurer, 𝑢_!,! is the error term, 𝛥 represents the percentage change of the dependent variable per year and the Greek letters in front of independent variables represent the coefficients of the independent variables. Note that all variables are cross sectional and time variant. Moreover, equation 2 and 4 are used to test the results and conclusions from equations 1 and 3 on robustness.

Equation 1 and 3 will additionally be used to perform a cross section5 linear regression on a sub-sample consisting only of Solvency II data i.e. data from 2016. This robustness check will test the findings of the whole sample by using time-series instead of panel data. If the results of this sub-sample analysis are close to the results of the main sample, this implies of strong estimates in the main analysis.

3.3

R

In this paper I distinguish between adequately capitalized and undercapitalized insurance firms by using a ‘moderator dummy’ variable and interaction terms. To determine the value of the dummy variable, in line with De Haan and Kakes (2007), I use a threshold for the actual to required solvency margin ratio of 150%. The value of the threshold is larger than the required solvency margin ratio under Solvency I. The reason why this value is larger is because in practice there is a low amount of undercapitalized firms since firms hold higher solvency margins than required by Solvency I (De Haan and Kakes, 2010). This leads to high solvency margin ratios. Under the Solvency I regulation firms have to reach a ratio of

available solvency margin (i.e. actual solvency margin) to required solvency margin of at least 1 (i.e. 100%). However, this regulation did not sufficiently include risk in the capital requirements, as mentioned in the literature review. Since the firms in this study are not categorized by size and group affiliation, I find it inappropriate to use the median of solvency margin as a threshold for regulatory pressure.

I determine the value of the dummy variable under Solvency II regulation according to the requirements without a mark-up. For solvency II the ratio of total eligible own funds to SCR has to be higher than one, otherwise the likelihood of regulatory intervention is high and the dummy variable gets the value one.

A prior study on other regulations (Shim, 2010) similarly assumes a threshold larger than the solvency margin to indicate supervisory attention and consequently regulatory

5 _{Meaning that the variables will only differ in cross section and not in time. Therefore, the}

pressure. Not reaching this threshold means that regulatory intervention and costs will most likely occur, as is supported by DNB (2015) for Solvency I and II. Following these studies the expected coefficient values in the regression on capital levels of undercapitalized firms will be higher than the coefficient values of adequately capitalized firms, since they will

accumulate more capital to avoid regulatory costs. In addition, the expected coefficient values in the regression on risk levels can be higher or lower since firms can rely on reinsurance (see Minkaï and Belgacem, 2016) or have higher risk levels due to various reasons such as high amounts of unresolved claims.

3.4

P

(ROA)

According to Fama and French (2002), return on assets (ROA) is a proxy for

profitability. In this thesis, earnings before interest and taxes are scaled by admitted assets to result in ROA. The more profitable a firm is, the more retained earnings it can accumulate that can be transformed into capital (Park and Pincus, 2001). For this reason the expected sign on this variable is positive if the pecking order theory and negative if the trade-off theory holds for the insurer’s capital decision. For the impact on underwriting risk the expected sign is negative since more profitable firms are able to cover more insurance obligations. Also a positive effect of this variable is expected on the change of capital.

3.5

G

Firms with high capital have the means to grow during a certain period i.e. firms can have more obligations towards policyholders. In order to come up with this Growth variable I follow Carayannopoulus and Kelly (2004) by calculating the percentage change of premiums in the past five years. The expected sign of this variable is positive on capital levels and change in capital, which is a result of capital regulation (Kim et al., 1995). On risk levels and its change this determinant can have a positive effect since the firm will also grow in

insurance obligations and it can have a negative impact since this means reinsurance possibilities will grow too.

3.6

C

In the risk equations (3 and 4) the capital variable will be the explanatory variable and in the capital equation (1 and 2) the risk variable will be the explanatory variable. Then, I can compare the results that will show the difference in magnitude of the impact on each

dependent variable. Moreover, this way the findings of the analysis in this paper can be compared to the existing literature.

Following Shim (2010), CAPITAL will be defined as the ratio of capital (surplus) to total admitted assets. Where capital (surplus) is the total capital and reserves including cash and equivalents.

To my knowledge this paper is the first that studies the relationship between underwriting risk and capital requirements. In line with Lamm-tennant and Starks (1993) RISK will be defined as the variance in loss ratio of claims to premiums written over the last five years. In the mentioned paper they need a risk proxy that is applicable for different kind of organization forms, lines of business and geographical areas. Moreover, the risk proxy is normalized for the size of business. Similar to their dataset, the companies in my dataset are different in size and lines of business. Therefore I find this risk proxy applicable for my analysis. Underwriting risk is the risk inherent to future cash flows and therefore positively related to insolvency risk. Moreover, premium charged by the insurer must incorporate the risk premium that covers not only the claims but also the capital requirements. However a company cannot increase risk premiums without taking into account competitiveness and other exogenous factors. On the other hand, in the event that the matching is not done in a pragmatic manner, the underwriting risk arises.

3.7

C

Capital structure theory has the purpose in this thesis to help understand the results. When firms need capital for investments or paying off obligations they do have a preferable order of consuming this capital. This is explained by so-called pecking order theory; firms will first consume from retained earnings and secondly issue debt, since internal funds are less costly. Furthermore Myers (2001) suggest that more profitable firms have less debt as they have more internal funds. In contrast to pecking order theory there is tradeoff theory. This theory states that firms try to maintain a target (optimal) debt ratio by balancing the corporate tax advantages of additional debt financing against costs of possible financial distress. Although this sounds as if insurance companies structure capital according to this theory, prior studies found that insurers adjust capital levels according pecking order theory.

4.

D

ATA

Included in this section are the descriptive statistics of the used data in the analyses and an explanation of the calculations I performed. Moreover, I explain what (type of) data is provided by the source and how I selected data for the research dataset.

4.1

D

DNB provides annual statements and other (non-) financial data of individual, non-life insurance companies per year. These companies are all under supervision of, and are obliged to report to, this supervisory authority. In this study I use the financial and other reported statements from the end of 2011 until the end of 2016. The statements include: Balance sheets, P&L accounts and Solvability ratios, which are calculated and registered according to Solvency I and II requirements.

After restructuring and eliminating non-useful data, depending on the year of the studied period, the dataset for the regression consist of 102 to 175 subsidiaries and holdings. This dataset further consists of firms that started and ceased to exist during the research period. All included insurers in this research are shown in appendix B table B.1.

I remove firms that have missing data for calculating critical financial ratios such as the capital and risk levels. P&L-accounts from 2016 are those of life and non-life insurance firms and I filter the insurance firms that are not non-life out of the total. As a last step I gather all calculated variables in one unbalanced panel and remove the outliers in the 0.1st and 99.9th percentile so that these extreme values will not influence my regression analysis.

Furthermore, the database of DNB provides a file where it registers the actual and required solvency margin per firm. With this file I calculate the solvency ratio per firm and compare it against the threshold of 150% for Solvency I. I calculate the dummy variable to identify undercapitalized firms resulting from Solvency II in the balance sheets, where the ratio of eligible own funds to SCR is given.

As a summary of the dataset, table 2 shows the descriptive statistics of the total sample and tables A.4 and A.5 in the appendix show the descriptive statistics of the sample with respectively only adequately or undercapitalized firms.

4.2

L

DNB provides extensive datasets in terms of amounts of years and firms. However, there are still some limitations that obstruct me from performing a proper regression analysis.

Firstly, I compose the variables used in the regression by hand because the provided financial statements from DNB show no financial ratios. Secondly, the names of the firms differ between Solvency I and II statements. Therefore, to create consistency in the insurers’ names I rename all deviating insurance firms from the Solvency II to the names from Solvency I statements.

Table 1

Correlation matrix of explanatory variables used in the regressions.

CAPITAL ΔCAPITAL ΔRISK GROWTH RISK ROA

CAPITAL 1.000 0.428 -0.041 -0.067 -0.014 0.282 ΔCAPITAL 0.428 1.000 -0.079 -0.089 -0.029 0.218 ΔRISK -0.041 -0.079 1.000 -0.048 0.027 -0.042 GROWTH -0.067 -0.089 -0.048 1.000 -0.158 0.027 RISK -0.014 -0.029 0.027 -0.158 1.000 -0.082 ROA 0.282 0.218 -0.042 0.027 -0.082 1.000

Before performing the regression I have to reassure there is no perfect

multicollinearity. Table 1 shows the correlations among variables used in the regressions. ROA has a high correlation with CAPITAL and ΔCAPITAL this is because they all three represent nearly the same financial fact. In addition, CAPITAL and ΔCAPITAL have a high correlation meaning the percentage change of capital increases with nearly half of the value of increase in capital ratio. Various financial items drive the increase of capital, such as: assets. The percentage change is just driven on the change in capital ratio from time t to time t+1.

Table 2

Descriptive statistics of the variables used in the multiple regressions for all firms.

CAPITAL ΔCAPITAL ΔRISK GROWTH RISK ROA

Mean 0.438 -0.033 0.228 0.030 0.038 0.033 Median 0.407 0.017 -0.115 0.018 0.003 0.028 Max. 0.993 1.568 4.511 3.124 1.930 0.518 Min. -0.000 -1.000 -1.000 -2.839 0.000 -0.314 Std. Dev. 0.264 0.329 0.792 0.302 0.174 0.056 Skewness 0.155 -1.101 2.006 1.191 8.005 0.460 Kurtosis 1.930 6.317 7.633 35.935 74.738 10.936 Jarque-Bera 43.79*** 416.96*** 607.40*** 38,254.07*** 150.598.70*** 2,252.34*** P-value 0.000 0.000 0.000 0.000 0.000 0.000 N 847 631 388 842 669 847

Note: the table reports the mean, median, maximum, minimum, standard deviation, skewness, kurtosis, Jarque-Bera test statistic and observations (N) of all variables individually therefore the amount of observations differs per variable. The sample consists of all non-life insurance firms under supervision of DNB between the year 2011 and 2016. *** Significant at 1% level,

** _{significant at 5% level and} *_{significant at 10% level.}

It is surprising to see in table 2, B.2 and B.3 that the mean of the ΔCapital is negative. Hence, firms decrease capital on average more than they increase the capital level. Contrarily, ΔRISK is positive indicating that insurance firms cope with more Risk. This appears to

indicate regulation has little to no influence on capital accumulation and/or reduction of risk. The Jarque-Bera test hypothesis is that the data is normally distributed. According to the larger Jarque-Bera test statistic and its significance, several variables have a non-normal distribution. However, I employ an estimation method, which assumes normality. Therefore, I appeal to the central limit theorem, which states that the test statistics will asymptotically follow the appropriate distribution even in the absence of normality (Brooks, 2014). Overall risk is most positively skewed of the variables, meaning there is more risk than capital.

4.3

P

For this analysis I assume each firm has its own intercept, hence there is heterogeneity in the data. This assumption is based on the facts that the firms in the dataset operate in different lines of business and are different in size. For this reason I will explicitly not use the pooled OLS model (as used in Cummins and Sommer (1996)) and allow for fixed or random

fixed effects for all firms. They do this to capture systematic events and high losses as a result of manmade and natural disasters.

To determine if it is appropriate to correct for fixed or random effects, I will perform a Hausman specification test that detects endogenous regression variables in the regression model. Since one of the assumptions of OLS is that there is no correlation between an

independent variable and the error term, this Hausman test is necessary to perform in order to assure the reliability of the regression coefficients. Specifically the Hausman test is used to test the following hypothesis.

H0: Cov (ut,vt) = 0

Where Cov is the covariance of the error terms, ut is the error term on time t and vt is

the explanatory variable on time t. By accepting the null hypothesis the random effects model is appropriate and the regression variables will be quasi-demeaned. This is a benefit since time-invariant variables will not be cancelled out. On the other hand I have to assume that unobserved individual effects in the error term are not correlated with independent variables, which is rarely the case. If the hypothesis is rejected part of the error term is than correlated with the explanatory variables and the fixed effects model should be used. Then, I determine for which fixed effects I have to allow by performing a redundant fixed effects test. In this test every found fixed effect is accompanied with a dummy variable that has the value of 1 for the matching entity of the order of the dummy variable. For example, D2i is the dummy variable

for the second firm and takes the value of 1 for all the observations of that entity. The redundant fixed effects test is then applied on the following hypothesis:

H0: µ2 = µ3 =...= µN = 0

using an F-test, where µN is the cross section fixed effect. If I reject the null

hypothesis, than the entity fixed effects model is necessary. The same test can be performed to determine time fixed effects (i.e. µt).

Hsiao (2007) mentions several reasons as benefits of using panel data. One of these reasons is that unobservable effects (of human behavior) are also analyzed. Obviously humans lead firms and therefore this type of data is suitable for the analysis.

4.4

R

The importance of the chosen research period is because the purpose was to start with the implementation of Solvency II in 20136. Therefore I expect firms (especially large firms) were preparing their risk management to meet the requirements before that year.

Moreover, DNB requested the insurers to submit Solvency II figures in a so-called ‘dry-run’, before the implementation in 2016. Due to this preparation phase I expect to have made the best tradeoff in capturing as much as possible years and having Solvency II ‘ready’ observations. The data from 2016 is compiled based on the Solvency II template, which is more structured and detailed.

To summarize, the total dataset used for the estimations consists of 847 observations of which 102 to 175 non-life insurance firms depending on the year. This dataset consist of firms that started and ceased to exist within the research period. Furthermore, the research period captures as much as possible implementation of the new Solvency II regulations.

5.

R

ESULTS

In this section I will show the results from the multiple regression and explain the economic meaning of them. In addition, I will compare my results with relevant studies mentioned in the literature review. Furthermore, I will explain how the results answer the research questions and proof or disproof the hypotheses.

For every regression I perform the Hausman test to determine if the random or fixed effects model is appropriate to use. Then, when fixed effects are detected, I perform the redundant fixed effects test. The tables in this section include the outcomes of these tests.

5.1

Table 3

Results from the multiple linear regression with dependent variable CAPITAL performed on all firms. I II III Intercept 0.4042*** (0.0000) 0.3997*** (0.0000) 0.4013*** (0.0000) RISK 0.1493*** (0.0024) 0.1434*** (0.0033) 0.1670*** (0.0007) ROA 0.6041*** (0.0000) 0.6330*** (0.0000) 0.5520*** (0.0000) GROWTH -0.0542** (0.0180) -0.0531** (0.0196) -0.0625*** (0.0065) REG 0.1054** (0.0141) 0.1455** (0.0022) RISK*REG -0.1146 (0.7164) ROA*REG 0.9255** (0.0276) GROWTH*REG 0.2092 (0.2839) Adjusted R2 0.8262 0.8283 0.8312

Fixed effects Cross section and time

Cross section and time

Cross section and time

Random effects None None None

N 668 658 658

𝐶𝐴𝑃_!,! = 𝛼_!+ 𝛼_!𝑅𝐼𝑆𝐾_!,! + 𝛼_!𝑅𝑂𝐴_!,! + 𝛼_!𝐺𝑅𝑂𝑊𝑇𝐻_!,!+ 𝑢_!,! Model I shows the overall effect of determinants on capital levels. Model II includes the ‘moderator dummy’ variable REG to measure the average difference between adequately capitalized and undercapitalized firms. Model III includes the dummy variable regulatory pressure and interaction terms with the determinants. The interaction terms show the differences between adequately firms and undercapitalized firms per determinant of capital. *** _{Significant at 1% level,} ** _{significant at}

5.1.1OVERALL AND PROFITABILITY

On average, as seen by the statistically significant ‘moderator dummy’ in model II (III) of table 3, the undercapitalized firms have 10.54% (14.55%) higher capital levels than adequately capitalized firms do. Having a higher capital level is still not a sufficient condition to be categorized as an adequately capitalized firm. Clearly, capital levels are not sufficient to cover potential risk according to Solvency regulation. The biggest difference in increase in capital among the ‘group’ of firms occurs due to profitability (0.9255), as is seen by the statistically significant interaction term ROA*REG in model III of table 3. Due to this result I cannot reject the first hypothesis “Profitability and capital ratios are more positively related for undercapitalized insurers than for adequately capitalized insurers”. This result is in line with Shim (2010) as they find undercapitalized insurers increase capital to avoid regulatory and bankruptcy costs. In fact, undercapitalized firms are pushed to increase capital when additional funds are available suggesting an effective regulation where undercapitalized firms avoid regulatory consequences.

5.1.2GROWTH

The negative statistically significant coefficients of GROWTH (-0.0542; -0.0531 and -0.0625) show a decrease in capital levels when adequately capitalized firms face a growth in premiums. The result of the growth coefficient is both in line and contradicts the studies of respectively Mankaï and Belgacem (2016) and Shim (2010). Moreover, this result contradicts the paper of Feldblum (1996), which shows a positive effect of growth on capital implies that fast growing insurers have larger reserve deficiencies and therefore should hold more capital to stay solvent. On the one hand this result is odd since more premiums means more

obligations and, due to regulatory requirements, firms should hold more capital (see Kim et al. 1995). On the other hand, agency theory predicts that firms with high growth opportunities have more agency problems between shareholders and debt-holders (Shim, 2010). Agency problems arise due to amounts of free cash flows consequently, this result might indicate insurance companies reduce capital levels to reduce agency problems. The difference in signs between the coefficients GROWTH*REG (0.2092) and GROWTH (-0.0625) in model III supports this theory, suggesting that undercapitalized firms have no agency problems. Hence, undercapitalized firms seem to increase capital when premiums grow however there is not enough statistical evidence to support this conclusion.

5.1.3RISK

The RISK coefficients are positive and significant (0.1493; 0.1434 and 0.1670 in respectively model I, II and III) and are in line with Cummins and Danzon (1997), where they find insurers increase capital as a result of increase in risk and external pressure for financial quality. This result further confirms the capital buffer hypothesis and shows, as in Jokipii and Milne (2011), adequately capitalized firms increase capital levels to withstand unanticipated extreme losses. Again, these results suggest an effective capital regulation since the intent of capital regulation is to hold more capital when Risk increases.

On the other hand, the negative, insignificant coefficient RISK*REG suggest undercapitalized firms have decreasing amounts of capital for an increase in Risk. An essential study on banks (Jacques and Nigro, 1997) states a possible explanation for this result. Capital from external sources may be too costly for firms with already low capital levels and therefore are not able to accumulate capital to cover losses.

Due to the insignificance of this coefficient, the model (III) cannot reject nor accept the second hypothesis: “Undercapitalized firms hold higher capital levels as a result of risk than adequately capitalized firms.”

To summarize, the ‘moderator dummy’ shows a statistically significant, positive coefficient, meaning undercapitalized firms have on average higher capital levels. Variables that influence capital levels positively are ROA and RISK and negatively by the variable GROWTH. The interaction term ROA*REG is positive and significant which gives an positive answer to the first research question, namely: “Are capital levels increased when an insurance firm is undercapitalized according to capital regulation?”. Overall these models have a good fit with an adjusted R-squared going from 0.8262 to 0.8312.

5.2

Table 4

Results from the multiple linear regression with dependent variable RISK performed on all firms. I II III Intercept 0.0214 (0.1595) 0.0211 (0.1736) 0.0146 (0.3494) CAPITAL 0.0595* (0.0934) 0.0580 (0.1121) 0.0649* (0.0791) ROA -0.2461** (0.0181) -0.2377** (0.0250) -0.2220** (0.0415) GROWTH -0.0086 (0.6907) -0.0085 (0.6951) 0.0099*** (0.0000) REG 0.0218 (0.5992) -0.0227 (0.7649) CAPITAL*REG 0.0942 (0.5301) ROA*REG -0.3474 (0.3957) GROWTH*REG -0.4944*** (0.000) Adjusted R2 0.7475 0.7474 0.6496

Fixed effects Cross section Cross section Cross section

Random effects None None None

N 668 658 658

𝑅𝐼𝑆𝐾!,! = ϒ!+ ϒ!𝐶𝐴𝑃!,! + ϒ! 𝑅𝑂𝐴!,!+ ϒ! 𝐺𝑅𝑂𝑊𝑇𝐻!,! + 𝑢!,! Model I shows the overall

effect of determinants on risk levels. Model II includes the ‘moderator dummy’ variable REG to measure the average difference between adequately capitalized and undercapitalized firms. Model III includes the dummy variable regulatory pressure and interaction terms with the determinants. The interaction terms show the differences between adequately firms and undercapitalized firms per determinant of risk. *** Significant at 1% level, ** significant at 5% level and *_{significant at 10%level. In parentheses are the p-values.}

5.2.1OVERALL

The coefficient of the ‘moderator dummy’ (0.0218) in model II of table 4 is positive, suggesting that undercapitalized firms have higher underwriting risk levels. However, this result cannot be supported by the data, as the coefficient is statistically insignificant. Model III, where the ‘moderator dummy’ is conditional to the interaction terms, seems to contradict this result since the coefficient (-0.0227) is negative yet insignificant. That is, from the data it is not clear whether risk levels are higher when a firm is undercapitalized according to

Solvency regulation.

5.2.2GROWTH

According to the only significant interaction term GROWTH*REG undercapitalized firms have lower risk levels when premiums increase. This result seems to contradict Kim et al. (1995) where they find that a rapid growth in premiums for property-liability insurers is one of the causal factors of insolvency risk. Comparing results of table 3 and 4, as a result of increase in premium growth, Risk decreases and capital increases for undercapitalized firms. However there is no statistical evidence for increase in capital (see table 3). In contrast, premium growth increases Risk and decreases capital for adequately capitalized firms. This might indicate that capital regulation is effective since undercapitalized firms show results following the intent of the regulation.

In this thesis underwriting risk is the proxy for risk and this type of risk occurs when premiums are not well matched with liabilities. The result of the growth coefficients for both under- and adequately capitalized firms suggests that non-life insurance firms match

premiums well against liabilities. Kim et al. (1995) does not incorporate a growth variable to their analysis to back this result.

5.2.3CAPITAL

Table 4 model III shows a positive and insignificant coefficient of the interaction term CAPITAL*REG. This result, although not supported by the data, suggests undercapitalized firms face increasing Risk levels when capital levels increase. This result seems to confirm the positive relationship between capital and risk, as concluded in prior research.

There is a positive relationship of capital and underwriting risk, according to the positive and significant CAPITAL coefficient in model I and III (respectively 0.0595 and

0.0649). This result extends existing research (Mankaï and Belgacem, 2016; Shim 2010; Cummins and Danzon, 1997) where the authors consider other risks. The aim of capital regulation is to have higher capital than risk levels, to finance severe losses (DNB, 2015). In table 3 the coefficients of RISK (0.1493 and 0.1670) show capital levels increase as a result of increase in risk, more than Risk increases as a result of increase in capital (0.0595 and

0.0649), as shown in table 4. These results suggest a one-way relationship of capital and risk levels.

5.2.4ROA

A negative and significant coefficient for profitability (-0.2220) suggests an effective regulation, since profitability is likely to be transferred into capital according to pecking order theory (Park and Pincus, 2001). Despite the insignificance, the coefficient of the interaction term ROA*REG (-0.3474) seems to be in line with the conclusion from Mankaï and

Belgacem (2016). They conclude that undercapitalized insurance firms having decreasing risk levels as a result of increase in profitability. In addition, in their study they find that

undercapitalized insurers adjust capital and reinsurance more extensively than adequately capitalized insurance firms, leading to lower risk levels.

To summarize, results from the regression show that risk is diminished by

profitability, capital and growth in premiums for adequately capitalized firms. Furthermore, the results in the models answer the second research question “Is there a difference in increase of risk levels for undercapitalized firms compared to adequately capitalized firms under capital regulation?” not as expected since the expectation is Risk would increase due to increase in the determinants of capital (used in equation 3) and capital levels. The

‘moderator dummy’ conditional to interaction terms (model III) seems to suggest that undercapitalized firms have on average lower risk levels than adequately capitalized firms, although the data used in the model cannot confirm this statistically. As for adequately capitalized firms, undercapitalized firms face lower Risk levels when premiums grow. These results indicate an effective regulation since risk is mitigated due to profitability and premium growth as intended by capital regulation. Overall these models have a good fit with an

6.

R

In this chapter I will test the results shown in the previous chapters on robustness to test my conclusions. I will do this by substituting the dependent variable Capital and Risk, with respectively ΔCapital and ΔRisk. These analyses are comparable with the main background papers of this thesis since these papers measure adjustments in capital and risk levels. The results in the following tables will have to lead to the same conclusion in order for the previously mentioned conclusion to be robust.

6.1

F

Table 5

Results from the multiple regression with dependent variable ΔCAPITAL performed on all firms. I II III Intercept -0.0572*** (0.0000) -0.0543*** (0.0000) -0.0523*** (0.000) RISK 0.0328 (0.5403) 0.0333 (0.5360) 0.0449 (0.4119) ROA 0.6839*** (0.0001) 0.6799*** (0.0001) 0.6291*** (0.0006) GROWTH -0.0596* (0.0921) -0.0626* (0.0804) -0.0814** (0.0377) REG -0.0311 (0.5568) -0.0208 (0.7209) RISK*REG -0.1182 (0.8341) ROA*REG 0.4348 (0.5113) GROWTH*REG 0.0720 (0.6937) Adjusted R2 0.4937 0.4860 0.4853

Fixed effects Time Time Time

Random effects None None None

N 620 612 612

𝛥𝐶𝐴𝑃_!,! = 𝛽_!+ 𝛽_! 𝑅𝐼𝑆𝐾_!,!+ 𝛽_! 𝑅𝑂𝐴_!,!+ 𝛽_!𝐺𝑅𝑂𝑊𝑇𝐻_!,!+ 𝑢_!,! Model I shows the overall effect of determinants on capital levels. Model II includes the ‘moderator dummy’ variable REG to measure the average difference between adequately capitalized and undercapitalized firms. Model III includes the dummy variable regulatory pressure and interaction terms with the determinants. The interaction terms show the differences between adequately firms and undercapitalized firms per determinant of change in capital. *** Significant at 1% level, ** significant at 5% level and *significant at 10%level. In parentheses are the p-values.

6.1.1OVERALL

Moreover, according to table 3, B.2 and B.3 the mean of ΔCAPITAL is negative for all firms, indicating more capital is decreased than increased, supported by the negative and significant intercepts in table 5.

Overall, the coefficients of the ‘moderator dummy’ (-0.0311 and -0.0208 in model II and III respectively) show an insignificant difference between adequately and

undercapitalized firms. This difference seems to indicate that undercapitalized firms have (more) decreasing capital levels. As shown in table 3 and possibly explained by theory (Jacques and Nigro, 1997) this result can be explained by the suggestion that Risks diminish capital levels. Despite that the statistical evidence for the coefficient of the ‘moderator dummy’ is weak, in my opinion this finding is interesting to study further in future research.

6.1.2DETERMINANTS

There is not enough statistical evidence to support the coefficients of the interaction terms. Therefore it is inconclusive if there is a difference in fluctuations in capital levels as a result of an increase in underwriting risk, profitability or premium growth with significant difference between adequately and undercapitalized firms. Due to these results the model cannot confirm the robustness of the previous results for the difference among the ‘groups’ of firms.

All RISK coefficients are not statistically significant indicating that the robustness of the capital and underwriting risk relationship cannot be confirmed by the data. However, the positive coefficients suggest again a positive relationship and capital buffer theory might be confirmed. The highly significant coefficients for ROA (0.6839; 0.6799 and 0.6291 in model I, II and III respectively) show that an increase in capital arises mostly due to profitability, which confirms the positive relationship of capital levels and profitability in table 3 and the first hypothesis. As is presented earlier, in table 3, results indicate that capital levels decrease by growth in premiums. In table 5 the results indicate the same effect of capital decrease by an increase in growth in premiums according to significant, negative GROWTH variables (-0.0596; -0.0626 and -0.0814 in respectively model I, II and III), supporting the robustness of results in table 3.

In summary, the results that show the difference between adequately capitalized and undercapitalized firms are not supported by statistical evidence of the interaction terms. Despite the weak statistical evidence the value of the coefficients still show similarities with prior research and the results mentioned in chapter 5. Most of the capital accumulation

increases due to increase in profitability as is shown before, confirming pecking order theory, results in table 3 and the first hypothesis. Furthermore, the model can confirm the robustness of the effect of growth mentioned before. The insignificant yet positive coefficient of RISK could confirm capital buffer theory, as firms seem to increase capital with increase of risk. However, together with the positive relationship of Risk and capital levels, this theory cannot be confirmed due to absence of statistical evidence.

6.2

F

R

Table 6

Results from the multiple regression with dependent variable ΔRISKperformed on all firms.

I II III Intercept 0.2989*** (0.0003) 0.3033*** (0.0002) -0.3103*** (0.0002) CAPITAL -0.1135 (0.5011) -0.1086 (0.5239) -0.1202 (0.4887) ROA -0.4260 (0.6032) -0.4890 (0.5563) -0.5419 (0.5306) GROWTH -0.1529 (0.3325) -0.1535 (0.3308) -0.1577 (0.3233) REG -0.2046 (0.4896) -0.4936 (0.4581) CAPITAL*REG 0.4387 (0.6590) ROA*REG 0.4850 (0.8846) GROWTH*REG 0.4111 (0.7341) Adjusted R2 -0.0025 -0.0070 -0.0105

Fixed effects None None None

Random effects Cross section Cross section Cross section

N 387 384 384

Dependent variable: ΔRISK. Model I shows the overall effect of determinants on capital levels. Model II includes the ‘moderator dummy’ variable REG to measure the average difference between adequately capitalized and undercapitalized firms. Model III includes the dummy variable regulatory pressure and interaction terms with the determinants. The

interaction terms show the differences between adequately firms and undercapitalized firms per determinant of change in risk. *** Significant at 1% level, ** significant at 5% level and

*_{significant at 10%level. In parentheses are the p-values.}

Table 6 shows different results of the Hausmann test indicating that I have to use the random effects model. This is because I cannot reject the hypothesis of correlated errors with the explanatory variables. For all models, both the significant intercept and the insignificant

independent variables show that the change in Risk level is not supported by the used data and that other variables should be included to analyze relationship with change in Risk.

The ‘moderator dummies’ in model II and III show negative, insignificant coefficients suggesting that undercapitalized firms have decreasing risk levels more than adequately capitalized firms, which implies the answer on the second research question. Despite the lack of statistical evidence the interaction terms show positive values suggesting that

undercapitalized firms face an increase in risk instead of a decrease. This might provide an explanation why the ‘moderator dummy’ in table 3 is positive and firms are still marked as undercapitalized. The table further shows results that are in line with the intent of capital regulation, because most coefficients of the determinants are negative which might indicate that firms tend to decrease risk in general.

6.3

R

In the panel data stationarity can mean that the covariance among the dependent variable values only depends on the length of time concerning those values. A panel unit root test ensures that the data is not influenced by linear trends. This implies there are no periodic fluctuations, such as seasonality, and the data has a constant autocorrelation structure.

To test for stationarity I perform an augmented Dickey-Fuller test which has a null-hypothesis of: H0: the data consist a unit root. Table B.4 in the appendix summarizes the results, as indicated by the p-values the null hypothesis is rejected for all explanatory

variables. This means that all explanatory variables I use in the regressions are stationary and the assumption of stationary data is satisfied.

6.4

S

-

In this sub-section I will analyze the relationship of the independent with dependent variables used before, with the variation of the sample consisting of only Solvency II data. One of the robustness checks in Shim (2010) is an analysis where the main sample is divided by the median of total net premiums written into two sub-samples. The robustness test in this thesis will consider only one sub-sample that is a cross-sectional time series consisting of exclusively Solvency II data from 2016. The tables with results are split into model I and II, where model I is without and model II is with a ‘moderator dummy’. I was not able to construct model III since than it will be a near singular matrix even when I remove the

The results in this section are only from the regressions on CAPITAL and RISK. The regressions on the dependent variables ΔCAPITAL and ΔRISK will use a mix of Solvency I and Solvency II data and reduce the effectiveness of the robustness test.

6.4.1REGRESSION SET-UP

Before I can discuss the results from the regression I need to reassure that the regression coefficients are not influenced by heteroskedasticity and autocorrelation. The results of the tests explained below are placed in table B.8 in the appendix B. First, I performed a White’s heteroskedasticity test. This test tests on the following hypothesis H0: the error term is homoscedastic. From the result of the test I cannot reject the null hypothesis of variance of the residuals being explained by the regression coefficients and the error term is therefor not constant. Because H0 is not rejected I do not have to apply robust White standard deviation correction.

Furthermore, by eyeballing the correlogram and considering the related P-values there is no autocorrelation up to 32 lags. In addition, the Durbin Watson test statistic does not exceed the critical value in any of the regressions and therefore it is inconclusive whether there is autocorrelation according to this test.

Next, the Dickey-Fuller test should show if the residuals are stationary. For this test due to a very significant residuals regression, I reject the null hypothesis therefor the residuals have a unit root. This means that when shocks occur the effects of that shock will stay in the process infinitely. In my opinion regulations cannot be seen as shock as they are implemented in a long run. However hypothetically, if the regulation would be undone firms will probably keep the capital levels steady in order to stay solvent for the long-term. The results of the cross section regression are shown in tables B.7 and B.8 in appendix B.

To conclude, the dataset for the cross section regression consists of financial ratios exclusively after the implementation of Solvency II regulation. In this section I reassure that the data is homoscedastic and has no autocorrelation. Moreover, there is a unit root in the residuals, which means that any shocks will have a permanent effect in the data.

6.4.2RESULTS

After the implementation of Solvency II insurance the results show slightly different values for coefficients than before the implementation. The ‘moderator dummy’ in model II