## Abstract

The European insurance industry is awaiting the new EU-wide harmonised Solvency II framework. Before its introduction, it is important to find out which incentive effects can arise from it. Practitioners predict a trend towards consolidation in the insurance sector due to recognition of geographic diversification effects in Solvency II’s standard formula. This paper studies whether the new European regulation standards will constitute a driver for mergers and acquisitions in the non-life insurance sector. We identify situations in which consolidation becomes profitable. Our results indicate that the Solvency II framework may lead to an enhanced geographic restructuring wave. However, the profitability of this restructuring depends strongly on the correct estimation of costs and the characteristics of the consolidation partner chosen.

## Introduction

Owing to the increased competitiveness of the financial market, insurers, as important participants in this market, are looking for different opportunities to improve their productivity and efficiency and to enhance growth and gains. In addition, the insurance industry has faced constant modifications of its regulatory environment in many countries, especially in the course of the current financial crisis. Risk-based capital requirements now make up the basis of modern insurance regulation in almost all developed countries.^{Footnote 1} At the dawn of Solvency II, the insurance industry is awaiting the new EU-wide harmonised regulatory requirements and is preparing for their introduction. For instance, insurers are looking for an alternative allocation of risk and capital in order to adopt an optimal company-wide risk profile and lower the costs of their business. A prominent example of a regulatorily driven market restructuring occurred in the 1990s. In the course of the harmonisation of the economic landscape in Europe, the deregulation of the European insurance market and the implementation of the Economic and Monetary Union, a wave of intra-European consolidation activities took place which was stronger in the insurance sector than in other financial sectors.^{Footnote 2}

In the light of the upcoming changes in the insurance regulatory environment of the European Union, the focus of business decisions and academic analyses is moving towards the potential implications of Solvency II for different companies’ strategies and possibilities for development. Now, with respect to the introduction of Solvency II and group-wide regulation and supervision, practitioners predict an increase of mergers and acquisitions (M&A) in the insurance sector. On the one hand, many small and medium-sized insurers are more likely to have problems coping with the new regulatory standards and are therefore expected to be involved in M&As. On the other hand, practitioners expect additional positive effects of such consolidation activities, such as diversification and an improved risk profile, and thus enhanced performance.^{Footnote 3} The academic literature on M&As is extensive but also very contradictory on the consequences and effects of consolidation activities. Prior studies in the insurance sector exhibit evidence concerning two controversial hypotheses—the strategic focus hypothesis predicts a negative diversification–performance relation^{Footnote 4} and the conglomeration hypothesis predicts a positive diversification–performance relation.^{Footnote 5}

In this paper, we look at one specific incentive for M&As as a strategic instrument driven by the changes in the regulatory environment in Europe. We seek to provide evidence on whether the quantitative requirements of Solvency II constitute a driver for insurers’ cross-border consolidation as an instrument for achieving cost-efficiency in the sense of lower capital requirements and shareholder benefits. In an empirically calibrated theoretical model, we tackle the problem by constructing the consolidation of two non-life insurers. We test the influence of the implementation of an internal model vs the calibration of the Solvency II standard formula. Our results indicate that the Solvency II framework may lead to an enhanced geographic restructuring wave in the insurance sector. However, the profitability of this restructuring depends strongly on the correct estimation of costs and the characteristics of the consolidation partner chosen.

The remainder of the paper is organised as follows. The next section provides an extensive literature review on the topic of M&As, regulatory changes and geographic diversification. The subsequent section gives an overview of the discussed regulatory calculation of solvency capital requirements according to the standard formula of Solvency II. We then present the non-life module in detail. This section introduces the methodology and the procedure used to compare the results of the different outcomes of this paper. To illustrate our theoretical outcome, a simulation analysis is conducted in the section that follows. The penultimate section relates our theoretical and numerical findings to other recent empirical research. The final section concludes.

## Literature review

The literature on M&As concentrates mainly on the empirical analysis of the motives and drivers for M&As, the financial characteristics of acquirers and targets, the determinants of the deals, the financial performance and other post-consolidation effects. There are two main strands of literature that examine the controversial consequences of consolidation activities: the conglomeration hypothesis and the strategic focus hypothesis.

In the financial sector, the proponents of the conglomeration hypothesis argue that conglomeration may enhance firm value due to positive post-consolidation effects on firms’ characteristics, operations and strategies. For example, conglomeration can add value by taking advantage of scale and scope of economies and synergies through improved allocation of resources, by means of, for example, information technology, common databases, managerial expertise, compound marketing strategies and brand names.^{Footnote 6} Conglomeration may also improve financial efficiency and serve as an instrument in the case of financial distress by creating internal capital markets.^{Footnote 7} Contrary to the conglomeration hypothesis, the proponents of the strategic focus hypothesis argue that firms can maximise value by focusing on their main businesses and core competencies.^{Footnote 8} Agency theory explains M&A activities through managerial incentives, for example “empire building”.^{Footnote 9} Many authors argue that conglomeration may reflect agency problems and asymmetric information and thus reduce firm value. For example, conglomeration may intensify the agency problem through cross-subsidisation between strong and weak subsidiaries.^{Footnote 10}

Many studies provide evidence for both theories described above, depending on specific characteristics of the conglomeration deals. Berger *et al.*
^{Footnote 11} show that the conglomeration hypothesis can be substantiated for large personal lines insurers, while the strategic focus hypothesis is more applicable for small insurers that emphasise commercial lines.^{Footnote 12} In a theoretical work, Schlütter and Gründl^{Footnote 13} find that the consolidation may become beneficial for shareholders as well as for policyholders if the post-consolidation frictional costs of capital do not change. However, in the case of dead-weight costs, for example due to complexity, monitoring costs, etc., insurer default risk and premiums increase and could have severe consequences for both stakeholder groups.

Another literature strand relevant for our research question deals with geographic diversification. The pro-conglomeration arguments suggest that the increased geographical diversification implies an improved spread of risk and therefore allows for more cost-efficient protection against financial distress.^{Footnote 14} On the other hand, geographic diversification may lead to firm value reduction and other inefficiencies. Owing to group complexity, costly monitoring and increased managerial difficulties, operational efficiency is reduced.^{Footnote 15} In the insurance sector, Cummins *et al.*
^{Footnote 16} empirically scrutinise 317 insurers that were involved in a consolidation in the period 1989–1994. They find that geographically diversified companies experience higher total operational productivity than more concentrated firms.^{Footnote 17} However, using data for the period 1994–2002, Elango *et al.*
^{Footnote 18} analyse product and geographic diversification simultaneously. Their results show that the effects of geographic diversification also depend on product diversification. By combining product and geographic diversification, the authors derive three-dimensional diversification–performance profiles. For example, the benefits of high geographic diversification are stronger when product diversification is moderate. Moreover, high levels of both product and geographic diversification result in lower performance levels. Pottier and Sommer^{Footnote 19} link the level of diversification to insurers’ opaqueness. Their results indicate that geographically diversified insurers are more difficult to assess in terms of financial strength.

Analysing the drivers of consolidation activities, the literature also provides empirical evidence that external environmental changes such as technical progress, but also the introduction of new regulatory systems, may incite financial institutions to consolidate. Pasiouras *et al.*
^{Footnote 20}
^{,}
^{Footnote 21} show empirically that the regulatory environment is important for conglomeration decisions of Asian and European banks. They find that banks operating in countries with higher capital standards are more likely to be involved in consolidation activities, both as targets and as acquirers. There are different reasons for M&As driven by regulatory changes. In assessing the impact of Basel II on bank M&As, Hannan and Pilloff^{Footnote 22} develop two hypotheses on how regulatory capital can affect consolidation activities. Although they find no evidence to support these hypotheses, Valkanov and Kleimeier,^{Footnote 23} in an event study, find support for the excess regulatory capital hypothesis, according to which consolidation activities increase due to the creation of excess regulatory capital.^{Footnote 24}
^{,}
^{Footnote 25} Valkanov and Kleimeier^{23} provide evidence that mergers with high excess capital targets generate higher value for shareholders, because the acquiring bank’s shareholders gain profit from the diminishing of the excess capital of the acquired institution and obtain the resulting increase in returns. Conning and Company^{Footnote 26} study another incentive for increased M&As due to regulatory changes. They show empirically for the insurance sector that the adoption of the risk-based capital standards in the U.S. in 1994, as a major change in the regulatory environment, motivated several M&A deals, since weak insurers, limited in their ability to raise additional capital, were forced to consolidate in order to resolve financial distress and avoid significant consequential regulatory costs.^{Footnote 27} Furthermore, recent practitioners’ predictions foresee a spike in M&A activities as a strategic reaction of insurers to the future introduction of Solvency II.^{Footnote 28} The emergence of two strategies is expected: (1) enhancement of capital efficiency through the choice of a consolidation partner or (2) concentration on distinctive value chain aspects, such as distribution, IT, manufacturing or capital provision.^{Footnote 29} The introduction of the Dodd–Frank Act, the Volcker Rule and Basel III in the banking sector is also reported to have impacted M&A activities. Although an increase in the deals volume is predicted, deal values are expected to decrease. The reasoning behind this is that, in the short term, mainly small and mid-cap banks may consider M&As as measures to mitigate difficulties in complying with the regulation and to increase shareholder value under the new rules.^{Footnote 30}

Though the literature on M&As is vast, there is a literature gap, to our knowledge, in analysing, simultaneously in a theoretical approach, the specific effects of regulatory changes, geographic diversification and consolidation activities. Our study contributes to the literature on geographic diversification and M&A activities by analysing the effects of conglomeration in a setting that concentrates on the influence of changes in the regulatory environment. We focus on the new European regulatory framework Solvency II and analyse its expected impact on M&A decisions. By constructing a theoretical model, we are able to indicate under which regulatory cases and exogenous circumstances a consolidation would be beneficial for shareholders. Furthermore, we answer the question of whether policyholders are better off or suffer any negative consequences.

## SCR for the non-life module of the standard formula

The instructions on the construction of the calculation principles for assessing the necessary capital requirements are provided in the first pillar of the Solvency II framework. The most recent version of the proposed calculation procedures is described in the latest impact study on “long-term guarantee assessment”, conducted from 28 January to 31 March 2013. The proposed standard method^{Footnote 31} for determining the solvency capital requirements (*SCR*) is divided into six modules,^{Footnote 32} comprising modules for market risk, counterparty default risk, life, health and non-life underwriting risks, and intangible assets risk. Conducted in 2010, the fifth Quantitative Impact Study (QIS5) indicated that for non-life insurers, the most important module is the non-life risk module.^{Footnote 33} Furthermore, it was shown that in the non-life module of the standard formula, the calculated target regulatory capital can be reduced by 20 per cent on average through the consideration of diversification effects between lines of business (LoBs) and different geographical regions.^{Footnote 34} This effect results mainly from the assumed correlation coefficients between different lines of business and additional terms in the formula allowing for geographical diversification. The CEIOPS report on QIS4 provides detailed information on the geographic diversification effects. The capital charge reduction rises by up to 15 per cent on the solo level and 22 per cent on the group level depending on the line of business. On average, the reduction of the capital charge for non-life premiums and reserves amounts to 11 per cent on the group level.^{Footnote 35} Since we are interested in analysing the geographic diversification as an accelerator for M&As, a closer look at the non-life module will provide an insight into the calculation specifications of the capital requirements for risks in the non-life business.

The non-life underwriting module is divided into three further submodules to cover different risk categories connected to the non-life underwriting business: the catastrophe risk submodule, the lapse risk submodule and the premium and reserve risk submodule.^{Footnote 36} The catastrophe risk submodule covers “[…] the risk of loss, or of adverse change in the value of insurance liabilities, resulting from significant uncertainty of pricing and provisioning assumptions related to extreme or exceptional events”^{Footnote 37} and makes up 42 per cent of the risk charge for the non-life module. Its calculation as proposed in QIS5 was criticised for its complexity, the effort it required and missing data. The lapse risk submodule covers risk that arises from policyholders’ influence on claim obligations through exercising specific product options, such as earlier termination of contract or renewal to previously agreed conditions.^{Footnote 38} The QIS5 report states that the lapse risk is perceived by non-life firms as almost “immaterial or irrelevant”.^{Footnote 39} It makes up less than 1 per cent of the target capital of the non-life module on the solo and group levels. The premium and reserve risk sub-module handles two main risk sources. It covers risk resulting “[…] from fluctuation in the timing, frequency and severity of insured events” and “[…] from fluctuation in the timing and amount of claim settlements”. It also includes the risk arising from the volatility of expense payments. This submodule amounts to 58 per cent of the whole non-life module. In the calculation of the premium and reserve risk submodule, the standard formula allows explicitly for geographic diversification effects, which places this submodule at the centre of this paper. The catastrophe risk submodule, which is subject to a great number of assumptions, and the lapse risk submodule, the materiality and relevance of which was reported to be negligible, will not be considered in further analyses in this paper.

A glance at the formula for calculating the risk charge for the premium and reserve risk *SCR*
_{
pr
} shows that the capital exposed to those risks, volume measure *V*, and the combined standard deviation *σ*
_{
pr
} of the assumed distribution are the key figures necessary for the calculation.^{Footnote 40}
^{,}
^{Footnote 41}

The aggregated standard *σ*
_{
pr
} deviation is to be estimated considering the standard deviation in the individual lines of business and the defined correlation coefficients between them.

The overall volume measure *V* is determined as the sum of the geographically diversified volume measures for each line of business *V*
_{
s
} calculated as in Eq. (2). For the calculation of the volume measure for reserve risk *V*
_{(res, s)}, the outstanding claims (*PCO*
_{
s
}) should be estimated. The volume measure for premium risk *V*
_{(prem, s)} is the sum of the earned premiums for the following and previous period *P*
_{
s
}, *P*
_{(last, s)}, the expected net premiums of existing contracts (*FP*
_{(exisiting, s)}) and those of expected future contracts^{Footnote 42} (*FP*
_{(future, s)}).^{Footnote 43}

where

where *j* denotes different geographical regions and *s* denotes the different lines of business.

Special attention is drawn to the term *DIV*
_{
s
}, which captures the diversification effects due to geographically spread business.^{Footnote 44} Here, the Herfindahl index (also known as the Herfindahl-Hirschman index, HHI) is used to estimate geographical concentration. It measures the relation of the sum of the squares of the volume measures for premium and reserve risk to the squared sum of both. The minimum value of the Herfindahl index is 0, implying full diversification, that is, no concentration. The technical specifications so far allow a maximum diversification benefit of 25 per cent that equals the assumption of a moderate correlation of around 50 per cent between different regions.^{Footnote 45}

However, there are critics of the accuracy of the assumptions and restrictions of the standard formula. Further suggestions for different distribution assumptions or economic models are considered. Therefore, the Solvency II framework allows for implementing company-specific parameters and flexible internal models.^{Footnote 46} In the following section, we will illustrate how we employ the Solvency II standards (the standard formula and an internal model) in a theoretical consolidation model.

## Model

We consider two solo non-life stock insurers (*j=*1*,*2) operating in the future Solvency II regulatory environment in two different geographic regions of the European Union in a one-period model.^{Footnote 47} Insurers have the possibility to merge into a single company operating in the two regions as an integrated insurer, that is, a single legal entity. Furthermore, the insurers can implement either the Solvency II standard approach or an internal model in order to determine the regulatory solvency capital requirements, *SCR*. Both insurers operate in the same non-life line of business, selling the same product on their national markets. We concentrate on the same product line in order to focus on the geographic diversification effects and to exclude any product diversification effects. The insurers’ premium income is constant and not exposed to fluctuation. However, the insurers are exposed to underwriting risk through their liabilities. The insurers’ decision problem is twofold: whether to merge or not and which *SCR* calculation method to use after the merger. They decide on a shareholder value basis.

### Solo insurers

For constructing the insurers’ Solvency II-consistent balance sheets, we determine insurer’s technical provisions, *TP*
_{0, j
}, as the risk-free discounted value of the expected liabilities. This kind of calculation is, on the one hand, in line with the proposed regulatory requirements^{Footnote 48}; on the other hand, it is also consistent with capital market theory, where in a capital asset pricing model context, no risk adjustment is necessary if the liabilities are uncorrelated with the asset prices on the capital market. For each insurer *j*, we assume lognormally distributed liabilities with mean *μ*
_{
j
} and standard deviation *σ*
_{
j
}. The available own funds *OF*
_{0,j
} which are eligible to cover the target capital required by the regulator are set to meet exactly the solvency capital requirements (*SCR*) as calculated according to the standard formula.

The value of the assets of the insurers is calculated as the sum of the technical provisions and the own funds in Eq. (4). The assets are invested at a risk-free rate *r*
_{
f
}.^{Footnote 49}

The sum of the insurers’ technical provisions is constant at *TP*
_{0,G
}. To analyse relative size effects, we allow for a variation of the individual technical provisions.

where *α* ∈[0, 0.5]

Since shareholders possess limited liability, there is a divergence between the fair valuation of the shareholders’ position *E*
_{0, j
} and the value of the own funds *OF*
_{0, j
}, which makes up the insurer’s net present value.

The future cash flow to the shareholders is given by:

Its present value amounts to:

Assuming no correlation between the insurers’ liabilities and capital market developments, the present value of claims *PV*[*L*
_{1, j
}] equals the value of technical provisions *TP*
_{0, j
}. The net present value of a solo insurer *NPV*
_{
j
} is the difference between the value of the equity holder’s position *PV*[*E*
_{1, j
}] and the invested equity capital *OF*
_{0 ,j
}. Combining Eqs (4) and (7), we obtain:

The net present value equals the shareholders’ default put option value, *DPO*
_{0, j
}, which is the value of the unpaid outstanding claims in the case of insolvency.

Since the standard formula was implemented before the consolidation decision, there are no additional costs incurred from using the standard formula further on. Given that there are no other adjunct costs in the case of solo operations, the combined net present value of the solo operation is given by the sum of the value of the default put option of both insurers (Eq. 9).

The chosen model framework implies a positive net present value for the solo alternative, *NPV*
_{
solo
}. The reason behind this lies in the calculation of the insurers’ technical provisions, which does not consider any default risk.

### Consolidated model

Now, the two solo insurers merge into a single legal entity with full consolidation of capital and risk. The consolidated values of assets, technical provisions and own funds are modelled as the sum of the respective values from the solo Solvency II balance sheets. The integrated insurer can choose between two methods for calculating its consolidated solvency capital requirements *SCR*
_{0, G
}
^{k}: the Solvency II standard approach (*k*=*STD*) and an internal model (*k*=*INT*).

The calculation using the standard formula recognises geographic and product diversification effects up to a certain level that is predefined by the calculation procedures and the correlation coefficients given by the regulator. When implementing an internal model for calculating solvency capital charges, the insurer aims for full reflection of its risk situation. Consequently, all diversification effects are captured by the insurer’s liability distribution. Owing to the recognition of diversification effects in both cases, the consolidated solvency capital requirements *SCR*
_{0, G
}
^{k} are lower compared with the sum of the solo target capital ∑_{
j=1, 2}
*SCR*
_{0, j
}. Since the sum of the solo *SCRs* equals the available own funds of the integrated insurer, we calculate the excess regulatory capital, Δ^{k}, as the difference between the actual available capital and the required solvency capital *SCR*
_{0, G
}
^{k}.^{Footnote 50}

The excess regulatory capital, on the one hand, can serve as an additional capital buffer to improve the safety level. On the other hand, it can be used for share repurchasing without deteriorating the solvency situation. In order to exclude any additional demand effects,^{Footnote 51} we assume that the capital reduction is carried out such that the own funds of the integrated insurer are lowered to the level of its solvency capital requirements, *OF*
_{0, G
}
^{k}=*SCR*
_{0, G
}
^{k}.

The value of the shareholders’ payoff is given by the present value of the available assets minus the realised claim payments, taking the limited liability into account.

Rewriting Eq. (11), we obtain the default put option value of the integrated insurer, which now depends on the sum of the lognormally distributed liabilities of both insurers.

Following the transaction cost economics proposed by Coase^{Footnote 52} and Williamson,^{Footnote 53} we introduce consolidation costs covering transaction and integration expenses related to the merging deal. The merger activity comes at a cost rate *τ*
^{MA}, measured as a percentage of the sum of the technical provisions. Choosing technical provisions as a cost driver is reasonable, since the volume of the technical provisions can serve as a proxy for the scope and complexity of the integration process of the existing insurance portfolios. In addition, the implementation of an internal model brings about increased complexity and extra workload compared with the standard formula in use. Therefore, we add extra costs amounting to *τ*
^{INT}·*TP*
_{0, j
}. These extra costs occur if the insurer decides to use an internal model after the merger. If the insurer decides to use the standard formula further on, no extra costs will be incurred.^{Footnote 54}

The net present value of the consolidation alternatives is given by the sum of the excess regulatory capital Δ^{k} and the value of the default put option, , minus the decision-relevant costs: *τ*
^{MA}·*TP*
_{0, G
} or respectively (*τ*
^{MA}+*τ*
^{INT})·*TP*
_{0, G
}.

Merger alternative using the standard formula:

Merger alternative using an internal model:

To analyse the merger effects on policyholders, we calculate the actual default probability of the integrated insurer, that is, the probability that the nominal liabilities in *t*=1 are higher than the available assets, *P*
_{
G
}
^{u}=Pr[*L*
_{1, G
}
^{k}⩾*A*
_{1, G
}
^{k}].

## Numerical analysis

Since a derivation of closed-form solutions is not possible,^{Footnote 55} we conduct a numerical calibration of the theoretical model to obtain insight into the incentive for M&A under Solvency II. We adopt Solvency II-consistent parameters for the distribution and the volatility of liabilities and for the risk-free interest rate (compare Table 1).

When considering the merging costs, we use a broad definition. Merging costs include transaction costs as well as integration costs after the consolidation. The theoretical and empirical literature provides different parameter estimations for the level of the merging costs.^{Footnote 56} According to Altman Weil,^{Footnote 57} the transaction costs range from 6 to 8 per cent of gross revenue of the organisation. A closer study of two specific merger deals provides an estimation of the overall one-time merger costs as between 2 and 7 per cent of the deal value.^{Footnote 58} In our model, we relate the cost factor to the technical provisions, which equal the discounted expected claims. Since they represent only a part of the insurers’ revenues, we set *τ*
^{MA} to be 5 per cent of the technical provisions. In a sensitivity analysis, we will test different parameterisations of the merging costs to assess their influence on the merging decision.

Since Solvency II is still not in force, the calibration of the implementing costs of an internal model is based on practitioners’ judgments. In a survey, Accenture^{Footnote 59} asked individual German insurance companies about their overall estimated expenses on the implementation of Solvency II. We set the reported absolute costs in proportion to the average premium income per insurer. Since there is no detailed information on the implementation costs of an internal model separately, we assume the costs for an internal model to be half of the overall Solvency II implementation costs and calculate a cost ratio of 3 per cent of the technical provisions.

Since we implement a linear cost function, the assumptions concerning the cost rates are not crucial for our results. In the sensitivity analysis section, we show that the cost parameterisation leads to a certain net present value of the merger decision which can be interpreted as the value of additional costs that can be incurred before the merger becomes disadvantageous. Therefore, it would even have been an alternative to assume a zero cost rate that results in a net present value showing the maximum acceptable transaction costs.

### Two solo entities alternative

By implementing the input parameters from Table 1 and calculating the solvency capital charges for premium and reserve risk according to the standard formula, we attain the solo Solvency II balance sheets as a starting point for our analysis shown in Table 2. The aggregation of the different positions for insurers 1 and 2 is also reported in Table 2.

If the insurance companies operate separately, they can achieve a net present value of 0.0847, which is the sum of the default put option values (Table 3).

### Merger and use of the standard formula

According to the standard formula, as described in the section “SCR for the non-life module of the standard formula”, specific distribution parameters and for the compound liabilities must be applied and diversification effects must be considered. However, as for the *SCR*, the integrated insurer cannot map its real risk situation, even if its combined liability distribution deviates from the assumed regulatory distribution. Hence, the calculated consolidated solvency capital requirements, *SCR*
_{0, G
}
^{STD}, amount to 95.7. The *SCR* reduction due to recognition of geographic diversification effects is 12 per cent and the excess capital, Δ^{STD}, equals 13.05. After the share repurchase, the own funds of the integrated insurer are reduced to the level of the consolidated solvency capital requirements. The calculated merging costs add up to 12.5. Table 4 summarises the results.

For the calculation of the *NPV* of the merger alternative, we need to estimate the default put option value of the integrated insurer, which is presented in Table 5. The net present value of the merger alternative using the standard formula is mainly driven by the excess capital and the incurred costs (Table 4). The value of the default put option has negligible impact. However, it is an indicator for the insurer’s default risk, which depends on the correlation between the liability portfolios of the solo insurers.

As Figure 1 shows, the results imply that the actual default probability remains in the admissible regulatory range for correlation coefficients lower than around 50 per cent.^{Footnote 60}

In this range, the insurer is overcapitalised and policyholders are sufficiently protected. However, the merger becomes harmful for policyholders when the liability dependence increases extremely. This could be the case when the two solo insurers operate on the border between two geographic regions and are exposed to almost the same risk.

### Merger and use of an internal model

Since there are no regulatory constraints on the implementation of specific model assumptions, the integrated insurer using an internal model is able to reflect all dependencies and diversification effects between its liabilities. Therefore, in its *SCR* calculation, the real correlation between the liabilities of insurers 1 and 2 is considered in the estimation of the consolidated solvency capital requirements, *SCR*
_{0, G
}
^{INT}. Unsurprisingly, for higher correlation coefficients between the liabilities, the volatility of their sum increases and the solvency capital requirements surge. Table 6 summarises the results for different correlation coefficients. It also includes estimation of the excess capital, the value of the default put option and the net present value of the investment.

A closer look at the development of the default put option value reveals a special feature of the compound liability distribution. Though the default probability is constant at 0.5 per cent, the skewness of the distribution amplifies with the correlation, that is, the absolute value of the claims exposed to the default risk increases.

However, the impact of the default put option on the consolidation decision is unimportant, since the excess capital represents the main cash inflow, which is used to cover the merging and implementation costs of 20. The development of the net present value indicates that the merger alternative using an internal model is not always profitable, since the overall costs exceed the benefits of the capital reduction for high correlation coefficients.

A comparison of the net present value of the three alternatives provides an additional understanding of the effects of firm consolidation. The results are summarised in Figure 2. The dotted line represents the resulting *NPV* of the solo alternative for different correlation coefficients between the liabilities of insurers 1 and 2. This alternative is slightly dominated by the merger alternative under the Solvency II standard approach, shown by the solid line in the figure. The merger alternative, using an internal model, dominates the first two alternatives only for negative or slightly positive correlated liabilities.

It becomes unprofitable for correlation coefficients higher than 37 per cent. The reason for the advantage of the standard formula for higher correlation is that the *SCR* calculated with it leads to an insolvency probability that is higher than the *SCR* under the internal model (0.5 per cent). Therefore, an unjustified amount of own funds is extracted under the standard model. If this becomes visible, especially in the context of the “own risk and solvency assessment” of Solvency II’s Pillar 2, the supervisor might forbid the share repurchase and thereby destroy shareholder value.

### Sensitivity analysis

To check their robustness, we test our results under different input parameters. We check for size and cost effects, that is, changes in the size parameter *α* and variations of merging costs *τ*
^{MA}, and the costs for implementing an *SCR* calculation method *τ*
^{INT}. In addition, we investigate the impact of the riskiness of the business line.

#### Size effect

The highest diversification effect is attained when the merging insurers are of the same size. For the size factor *α*=0.5, the diversification term in the *SCR* formula arrives at its lowest value of 0.5 and allows for a maximum risk reduction under the standard formula. The maximum solvency capital reduction is 12.5 per cent compared with the sum of the solo solvency target capital. The implementation of an internal model is also more profitable when the merging insurers are of equal size, since they exhibit greater diversification potential. For low size factors (*α*<0.4 for the standard formula and *α*<0.2 for the internal model), the geographic diversification effects of a merger will always be disadvantageous. These results contradict the findings of Hawawini and Swary,^{Footnote 61} who provide evidence that M&A transactions are more successful when the target is relatively small compared with the acquirer. Our results concur with the empirical findings of Müller,^{Footnote 62} who studies cross-border M&As in emerging market economies and argues in favour of the hypothesis that larger targets provide larger synergy effects, thus enhancing the success of the M&A.

#### Cost effect

We use a linear cost function in our model. This implies a parallel shifting of the *NPV* curves in Figure 2 when the cost factors change. On the one hand, a positive change of the merging cost factor *τ*
^{MA} leads to a parallel downside movement of both *NPV* curves, *NPV*
_{
G
}
^{STD} and *NPV*
_{
G
}
^{INT}. Since the absolute change of the costs is equal for both consolidation alternatives, the dominance of the internal model over the standard formula remains constant for low to moderate correlations. However, the higher the cost rates are, the less the gains accrued from the merger. For merging costs higher than 5 per cent of the technical provisions, a merger using the standard formula is unprofitable.

On the other hand, an increase in the implementation cost rate *τ*
^{INT} leads to a downside shift of only the *NPV*
_{
G
}
^{INT} curve of the merger alternative using an internal model, the dashed line in Figure 2. Hence, the internal model becomes less attractive and dominated by the standard formula in more cases. For example, if the implementation cost factor increases to 8 per cent, the merger alternative using an internal model is unprofitable for any positive correlation between the liabilities of the insurers, *ρ*(*L*
_{0, 1}; *L*
_{0, 2})>0. For *τ*
^{INT}=0, the critical correlation coefficient coincides with the correlation coefficient in Figure 1 that leads to the actual default probability of 0.5 per cent. For higher correlation coefficients, the standard model becomes advantageous for shareholders, because the insurer is undercapitalised with respect to the default risk targeted by the regulator.

We can conclude that the cost effect has a crucial influence on the insurers’ decision on whether to consolidate and which calculation method to use for determining the consolidated solvency capital requirements.

#### Riskiness of business line

Another interesting effect comes from the riskiness of the initial liabilities, that is, the riskiness of the product segment in which the two insurers operate. Since the absolute magnitude of the diversification effects depends on the riskiness of the liabilities, less risky insurers derive lower benefits from a merger than their risky competitors and are therefore less likely to be involved in a merger deal.

According to the technical specifications for the long-term guarantee assessment, there are nine separate segments (LoBs) within the non-life insurance sector. The standard deviation for reserve risk for each segment varies between 9 per cent for motor vehicle liability insurance and 20 per cent for assistance insurance, indicating the riskiness of the different lines of business.^{Footnote 63} Therefore, insurers selling credit or assistance insurance would derive greater benefits from a consolidation with a competitor, whereas insurers operating in the motor vehicle liability insurance business would generate lower benefits.

#### Interest rate effects

Considering the recent low-interest environment, we also tested for interest rate effects. For the calibration of the interest rate, we chose a very low interest rate of 1.21 per cent, as proposed in the latest technical specifications for the “long-term guarantee assessment”. By changing the interest rate, we did not observe systematic changes of our results. The main explanation for this is the non-life-specific time horizon chosen of one year which makes time effects almost negligible. However, an analysis of the interest rate sensitivity in a multi-period context would be an interesting extension of this paper.

## Discussion

Studies that analyse the effects of regulatory changes and geographic diversification on merger activities provide heterogeneous results: On the one hand, risk diversification between a group’s entities can reduce the consolidated required capital compared with the sum of the *SCR*.^{Footnote 64} Shareholders benefit from the reduction of the regulatory excess capital.23 On the other hand, there are several arguments suggesting that a consolidation may be disadvantageous and inefficient. The disadvantages result from a reduction in the consolidated cash flow volatility which reduces the shareholder value, and from related costs due to transaction expenses, higher complexity and asymmetric information.^{Footnote 65}

Through consolidation, independently of the *SCR* calculation method selected, the consolidated regulatory target capital is reduced. This reduction represents the main source for post-merger shareholders’ gain. It occurs because the calculation methods include risk diversification effects. This result provides theoretical support for the excess regulatory capital hypothesis, similar to the empirical results of Valkanov and Kleimeier23 for the banking sector. They show that acquiring banks benefit from consolidation with high excess capital targets and generate higher value for shareholders of the acquiring bank through the reduction of the excess capital of the target bank. In the context of our paper, we look at the post-merger excess capitalisation, which we define as the additional capital endowment above the consolidated solvency capital requirements. The value of the excess capitalisation depends on the selected calculation method for the capital threshold. Using the Solvency II standard formula, the consolidated insurer is not able to consider all risk and geographic diversification effects beyond the admissible regulatory level. Therefore the excess capital is lower compared with the implementation of an internal model, where the solvency capital requirements can attain their minimum and the insurer achieves maximum excess capitalisation. However, the value of the excess capital decreases with the increase of the actual compound liability risk, since the consolidated solvency requirements rise. The insurers’ strategy would be to find the best consolidation partner to generate maximum post-merger excess capital.

Our results also provide support for both the conglomeration and the strategic focus hypotheses. Our findings primarily support the conglomeration hypothesis, but we show examples for which the strategic focus hypothesis holds. The main characteristic that plays an essential role concerning whether a consolidation is beneficial or not is the cost associated with it. If the merging and implementation costs exceed the benefits of the excess capital reduction and the value of the default put option, a consolidation may be detrimental for shareholders. Our results are consistent with a recent theoretical work by Schlütter and Gründl.13 They find that a consolidation may become profitable for shareholders as well as for policyholders if the post-merger frictional costs of capital remain constant. However, in case of additional costs, insurer default risk and premiums increase, and could have severe consequences for both stakeholder groups.

The “Own Risk and Solvency Assessment” (ORSA) of the second pillar of Solvency II may have an impact on our results. According to the Solvency II Directive,^{Footnote 66} insurers have to assess their own specific risk profile and must report significant deviations from the assumptions underlying the standard formula. Therefore, a significantly unjustified (compared to the true risk situation) reduction of the target regulatory capital due to geographic diversification in the standard formula would have to be reported. However, since ORSA “shall not serve to calculate capital requirements” (Art. 45 [7]), the capital requirements as calculated under Pillar I would not change. In principle, therefore, the resulting advantage or disadvantage of a merger would persist. Nevertheless, the ORSA rules require insurers to implement risk management processes to cope with significant deviations from the underlying assumptions, especially for avoiding existential risks. If such risk management processes became necessary, their extra costs would decrease merger benefits. Therefore, these possible extra costs due to the ORSA must be considered in the insurer’s calculations.

Finally, our contribution makes it clear that more research is necessary to identify and predict the parameters of the cost functions. We have shown that shareholders’ merger incentives depend mainly on the associated costs. Moreover, in order to focus on the geographic diversification, we excluded from the analysis all other risks, such as market, reputational and contagion risk that might have an impact on the results and might be an interesting topic for future research. Directions of further research could include synergy effects, such as reputation effects, better relations with regulators and increased market power. Policy issues, such as the “too-big-to-fail” topic or companies’ influence on shaping regulation or the competitive order, might also be further research questions.

## Conclusion

This article investigates whether the introduction of regulatory solvency standards has an influence on insurers’ cross-border merging decisions and what consequences arise for policyholders. To this end, we have employed a model in which two insurers consider the decision to merge in order to take advantage of geographic diversification effects. In addition, they have to choose whether to implement an internal model or to apply the Solvency II standard formula for calculating the consolidated solvency capital requirements. The influence on policyholders is analysed by observing the actual insurer default probability. To evaluate the impact of Solvency II on merger decisions, we compare the shareholders’ net present value of cash flow for the three alternatives: (1) two solo entities, (2) merger and usage of the standard formula, and (3) merger and usage of an internal model.

In their shareholder value calculus, the insurers mainly concentrate on the reduction of the solvency capital load. Therefore, conditions that increase the recognised diversification effects drive insurers’ integration. One of these conditions is the riskiness of the underwriting business. Whereas low-risk insurers do not profit much from merging, insurers involved in risky business derive greater gains from diversification and hence lower their solvency capital requirements. Similarly, the relative size of the merging companies is important, since it enhances or diminishes the diversification benefits. The choice of the *SCR* calculation method also impacts the profitability of the integration. For example, merging insurers should choose to use an internal model for *SCR* calculation if their liabilities are negatively or slightly positively correlated and should choose the standard formula if the liabilities’ dependence is high. Under the standard formula, policyholders are not always sufficiently protected since the distributional assumptions for calculating the default probability and *SCR* are not tailor-made and the actual insolvency risk can deviate from the regulatorily admissible risk.

Our findings suggest that Solvency II as a regulatory environment may serve as a driver for M&As. However, insurance companies should correctly predict the associated costs. Policymakers and supervisors should take into account Solvency II-inherent merger incentives and must attempt to assess possible macroprudential consequences of the Solvency II rules.

## Notes

- 1.
- 2.
- 3.
- 4.
- 5.
- 6.
- 7.
- 8.
- 9.
- 10.
Empirical studies by Berger and Ofek (1995) show a reduction in firm value after consolidation of 13–15 per cent for the U.S. market due to cross-subsidisation and managerial overestimation. For overestimation as a reason for value-reducing effects, see also Roll (1986); Rau and Vermaelen (1998). Empirical studies by Shim (2011); Cummins et al. (2010); Cummins and Nini (2002); Liebenberg and Sommer (2008) provide further evidence of the applicability of the strategic focus hypothesis in the insurance sector.

- 11.
- 12.
Meador et al. (2000); Cummins et al. (2003) also present contradictory results.

- 13.
- 14.
Hughes et al. (1996) and Hughes et al. (1999) study the effects of improvement of the risk return profiles of banking organisations. They find that geographically diversified large banking organisations perform more efficiently and tend to be more solvent. The efficiency gains amplify with the number of states of operation.

- 15.
- 16.
- 17.
Cummins and Xie (2008) also provide evidence that geographical diversification is associated with higher revenue efficiency and total factor productivity growth.

- 18.
- 19.
- 20.
- 21.
- 22.
- 23.
- 24.
The excess regulatory capital is defined by Hannan and Pilloff (2004) as the “difference between the actual capital ratios less some critical level based on regulatory requirements or standards”.

- 25.
Under the second hypothesis, the relative capital advantage hypothesis, M&As increase due to the difference in the capital standards applied to bank holding companies using the A-IRB approach and other banking organisations.

- 26.
- 27.
- 28.
- 29.
- 30.
- 31.
We use “standard method” and “standard formula” in this paper as synonyms.

- 32.
EIOPA (2013a, p. 114).

- 33.
The non-life underwriting module makes up as much as 52.4 per cent of the diversified solo Basic Solvency Capital Requirement (BSCR) of non-life insurers EIOPA (2011), p. 67.

- 34.
EIOPA (2011, p. 86).

- 35.
CEIOPS (2008, pp. 241, 351).

- 36.
EIOPA (2013a, p. 224).

- 37.
European Commission (2009, Article 105).

- 38.
European Commission (2010, p. 204).

- 39.
EIOPA (2011, p. 87).

- 40.
For the calculation of the risk charge for the premium and reserve risk, we follow the technical specifications of the recently conducted “long-term guarantee assessment” (LTGA). While valuation aspects of long-term guarantees are still heavily discussed, there is less discussion centred on the non-life module. Therefore, we see a high probability that the calculation procedures proposed so far in the non-life area will be implemented when Solvency II comes into force.

- 41.
For the lognormal distribution, three times the standard deviation provides a good approximation of the 99.5 per cent quantile. See CEIOPS (2009, p. 12); Hürlimann (2009a, Table 2.1, p. 4).

- 42.
The recognition date of the expected future contracts falls into the following 12 months, but the premiums are to be earned during the 12 months after the valuation date.

- 43.
For a detailed calculation, see the Appendix.

- 44.
According to EIOPA (2013b), Annex L, Europe is divided into four geographic regions: northern, western, eastern and southern Europe.

- 45.
- 46.
- 47.
The standard formula for the non-life and health module recognises only geographic effects within the single line of business; therefore, we concentrate in our study on the consolidation of two insurers operating in the same insurance line. For considering a consolidation between insurers operating in different lines of business, we would have to account for risk diversification effects between these lines of business and not for geographic diversification effects.

- 48.
EIOPA (2013a), p. 45 (TP.1.5).

- 49.
As we concentrate on the geographic diversification effects on the liability side, we do not consider the market risk on the asset side.

- 50.
Similar definitions are used by Hannan and Pilloff (2004) and Valkanov and Kleimeier (2007).

- 51.
Insurance demand reacts not only to price, but also to default risk. See Zimmer et al. (2012).

- 52.
- 53.
- 54.
A more detailed cost structure may give additional insights into the resulting cost effects. However, based on the low data availability, further assumptions may distort the explanatory power of the results.

- 55.
The reason for this lies in the fact that there is no closed-form representation for the sum of lognormally distributed variables. The different approximation approaches that can be found in the literature are not exact enough.

- 56.
For example, Zhao (2009) estimates a bound for monopoly merging costs of 13 per cent of premerger profits; Masten et al. (1991) estimate organisational costs in integration to be 14 per cent of total costs.

- 57.
- 58.
We studied the merger between JPMorgan Chase & Co. and Bank One Corporation in 2004 and the merger between AMP Limited and AXA APH in 2011.

- 59.
- 60.
The estimation of the correlation coefficient, which leads exactly to a 0.5 per cent insolvency probability, depends on the approximation of the distribution of insurer’s compound liabilities. Using a simple approximation of volatility and the 99.5 per cent quantile of the sum of lognormally distributed variables, we calculate the respective correlation coefficient of 0.53 per cent (Hürlimann, 2009a and Hürlimann, 2009b).

- 61.
- 62.
- 63.
EIOPA (2013a, pp. 229–230).

- 64.
- 65.
- 66.
Solvency II Framework Directive (2009/138/EC of the European Parliament and the Council of 25 Nov. 2009 on Solvency II [OJ L 335/1 of 17.12.2009]), Art. 45.

- 67.
Assuming a lognormal distribution, 3

*σ*equals a confidence level of 99.5 per cent for a volatility of 14.5 per cent Hürlimann (2009a).

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## Appendix

### Appendix

Solvency II standard formula for calculating the capital charge for the premium and reserve risk submodule

where

where *j* denotes different geographical regions.

In a second step, the standard deviation per line of business and the aggregated standard deviation are to be estimated according to the following formulas:

The overall risk charge for the premium and reserve risk is then calculated as follows^{Footnote 67}:

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Stoyanova, R., Gründl, H. Solvency II: A Driver for Mergers and Acquisitions?.
*Geneva Pap Risk Insur Issues Pract* **39, **417–439 (2014). https://doi.org/10.1057/gpp.2013.32

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### Keywords

- insurance regulation
- Solvency II
- mergers and acqusitions
- capital efficiency
- geographic diversification