solvency ii: an internal opportunity to manage the ......solvency ii: an internal opportunity to...

Solvency II: An Internal Opportunity to Manage the

Performance of Insurance Companies

July 2009

An EDHEC Financial Analysis and Accounting Research Centre Publication

with the support of

Solvency II: An Internal Opportunity to Manage the Performance of Insurance Companies — July 2009

Table of Contents

Introduction .................................................................................................................................5

Executive Summary ...................................................................................................................9

1. Value Creation in Insurance Companies ...............................................................19

2. Solvency II: From a Constraint to an Opportunity for Sophisticated Internal Management ....................................................................... 35

3. Underwriting Risks and the Economic Capital Model under the Solvency II Constraint ..................................................................................... 49

4. Market and Counterparty Risks in the Economic Capital Model under Solvency II Constraints .............................................................................................. 69

5. Economic Capital Model versus Solvency II Regulatory Capital ....................87

Conclusion ............................................................................................................................... 119

Appendix ..................................................................................................................................121

References ..................................................................................................................................154

Acronyms ....................................................................................................................................157

About the EDHEC Financial Analysis and Accounting Research Centre ............ 160

EDHEC Position Papers and Publications from the last four years ....................161

About Swiss Re .........................................................................................................................167

Printed in France, May 2009. Copyright EDHEC 2009.The opinions expressed in this survey are those of the authors and do not necessarily reflect those of EDHEC Business School and Swiss Re.

3An EDHEC Financial Analysis and Accounting Research Centre Publication


The study it is our pleasure to present to you here was done by the EDHEC Financial Analysis and Accounting Research Centre and is sponsored by Swiss Re. This study is an integral part of our innovative approach to research, an approach in which research is done for business, and this in an attempt to favour a dynamic that puts business at the heart of the researcher’s work.

Since its founding the EDHEC Financial Analysis and Accounting Research Centre has, for two essential reasons, stressed work on Solvency II and IFRS in the insurance industry. First, we believe that the implementation of this new accounting and prudential framework will have a great impact on the perception of risks, not just by insurance companies but also by the financial markets. So, by taking into account this new regulatory framework, valuation methods should also undergo a profound shift. The second reason for this emphasis is that the financial industry is the industry in which the measurement and management of value creation in a risky environment are at their most sophisticated.

This study shows that it may be in the interest of the company to capitalise on the investments required for purely regulatory ends to pursue its own objectives, in particular to perfect or create an economic dashboard, which can be used to improve management of the company. The leading European insurers, forerunners in this domain, show that their economic capital models make it possible to guide their choices, for the company as a whole or for individual lines of business.

By elaborating a management tool for an insurance company under Solvency II constraints, we show the advantages of putting in place such an economic capital model and the degree of complexity needed to create it with the data and simulations required by Solvency II. So this study is of relevance to all insurers, as they are ultimately all compelled to comply with the new Solvency II prudential regulations and their common objective is the satisfaction of their shareholders or members. We also hope that this study will contribute to the debate involving insurance companies, institutional investors, financial analysts, and supervisory authorities.

Finally, this study would not have been possible without the support of our partner Swiss Re, to which we would like to express our warmest gratitude. Swiss Re, the world’s leading reinsurer, is at the forefront in the development and use of economic capital models, and our discussions on the subject made it possible to enrich this publication. The success of this partnership demonstrates yet again the advantages of close cooperation between the business and academic worlds.

Foreword

Philippe Foulquier, PhD,Director of the EDHEC FinancialAnalysis and Accounting Research Centre

4 An EDHEC Financial Analysis and Accounting Research Centre Publication


About the Authors

Philippe Foulquier, PhD, is Professor of Finance and Accounting and Director of EDHEC’s Financial Analysis and Accounting Research Centre. He has a PhD in economic science and is a member of the SFAF (the French Financial Analysts’ Society). He began his career in 1990 in the scientific department of the French insurer UAP, as an internal consultant, notably in asset liability management. He left UAP in 1996 and spent ten years as a sell-side financial analyst in brokerage firms. He was head of the Pan-European insurance sector at Credit Lyonnais Securities Europe, at Enskilda in 2000 and at Exane BNP Paribas in 2003. During this time, he carried out several IPO and international M&A operations. He has been ranked top insurance sector financial analyst in the Extel/Thomson Financial and Agefi international surveys. He joined EDHEC in 2005 to teach financial analysis and accounting and to head the EDHEC Financial Analysis and Accounting Research Centre. He is also actively involved in consulting in both IFRS-Solvency II and corporate valuation issues.

Liliana Arias is a Research Engineer at EDHEC Business School Financial Analysis and Accounting Research Centre. She has an MSc in Finance from EDHEC and an undergraduate degree in Economics from the University San Francisco de Quito in Ecuador. Prior to joining the research centre, Liliana worked as a risk analyst for the Corporate and Investment Banking division at Citigroup. Within the research centre, she actively participates in numerous studies on Solvency II and IFRS.

Introduction

5An EDHEC Risk and Asset Management Research Centre Publ icat ion



Since the turn of the millennium, a profound shift in the management of insurance companies has been underway. The main catalysts of this shift are the growing complexity of risks, the sophistication of the means of measuring them, and the demands made by investors for greater transparency and for higher-quality management. In this environment, prudential (Solvency II) and accounting (IFRS) requirements must also adapt to create new frameworks offering a better view of the risks borne by companies.

All insurers, regardless of their characteristics (public companies, mutual insurers, provident societies) will be subject to the new prudential rules and will thus have to make heavy investments in the data collection, risk measurement, and simulations required by the supervisor.

The objective of our study is to show how, by having these investments respond to objectives more inherent to the company, these Solvency II constraints can be capitalised on. With a fictitious company, we build a management tool for an insurance company subject to Solvency II constraints. We then highlight the contributions this tool makes to the perfecting of the strategy of the company, in particular for the definition of policy for asset allocation, management of capital, asset/liability management, hedging of risks, and the launch of new products. At the heart of this model is value creation for shareholders or mutual members.

To show how to transform Solvency II constraints into an opportunity to perfect company management, we first survey the changes in the ways of measuring performance. So, keeping in mind the major

work done over the last three centuries, we present in the first chapter the genesis of value creation. We show how it is an integral part of the management of an insurance company and responds to the goals of the industry as a whole, including the member-centred mutual insurers. These analyses make it possible to understand the shift from a study of margins to the more complete and relevant market-consistent embedded value and the economic capital models put in place by the leading European insurers.

Chapter II focuses on the differing objectives of regulatory and economic capital, but it also shows the degree to which the Solvency II prudential framework could become an industry benchmark for the creation of economic capital models and thus contribute to the perfecting of insurance company management. This chapter also shows how, by building an economic capital model subject to Solvency II constraints, these constraints can be turned into a management opportunity.

Chapters III and IV present the elaboration of such a management model, and they do so by simulating—based on data from a fictitious insurance company active in six lines of life, property and casualty, and business—the underwriting, market, and counterparty risk modules elaborated by the international supervisor. The construction of this model makes it possible to gauge the complexity required and to determine the feasibility of this construction for all insurers, regardless of their particular features.

Chapter V puts in place an economic capital model subject to Solvency II constraints, a model based on the work done in the

Introduction



preceding chapters. We highlight the contributions made by the model not just to the definition of the strategic objectives of the company but also to the tracking, control, and measure of strategy and management.

Introduction



Introduction

Executive Summary

9



In the last two decades, changes in risks (distribution, extreme risks, correlation), investor culture, managerial practices and regulation have led to profound shifts in corporate management. Value creation, now at the heart of corporate strategy, has gradually become an indispensableapproach to evaluating performance. As a result of the nature of its business, founded on uncertainty and bound by new accounting rules (IFRS) and new prudential rules (Basel II, Solvency II), it is in the financial world that the measure and management of value creation in a risky environment are at their most sophisticated; in many non-financial industries profound management changes are underway as well.

Solvency II is expected to come into effect in 2010: it will introduce a new era for insurance companies. Unlike Solvency I, Solvency II seeks to create a prudential framework that would converge with that used in insurance companies’ internal models, in particular with economic capital models. The trend in managerial practices observed in the past few years is likely to gain momentum; the aim is to improve the integration of risks (identification, measurement and management), consider the cost of capital and create value for shareholders or mutual members. However, data collection and simulations required by the regulator in the new prudential framework will, in view of the quantitative impact studies (QIS) that have already been done, call for heavy investment.

The objective of this study is to show that it is perhaps advisable to capitaliseon these investments made for regulatory ends alone to meet goals more intrinsic to the company, in particular by perfecting or devising an economic dashboard,

a management tool to improve the company’s strategy. The leading European insurers, which are forerunners in this domain, have shown that their economic capital model makes it possible to guide their strategic global and/or local choices for their lines of business, in terms of asset allocation, management of capital, underwriting, asset/liability management and risk hedging.

We use data from a fictitious insurance company to devise a means of managing an insurance company subject to Solvency II constraints. The objective is to show the advantages of having an economic capital model in place and the degree of complexity involved in creating it with the required data and simulations. We then underscore the contributions this management model makes in several domains, such as the allocation of risk-adjusted capital (RAC), the definition of policies for investment, underwriting, launch of new products, provisions, reinsurance, asset/liability management, allocation to lines of business and risk management (definition of accepted bounds, concentration, diversification), as well as communication with the financial markets, rating agencies and the prudential regulator. At the heart of this model lies value creation for shareholders or mutual members.

The study is of relevance to all companies in the insurance industry, regardless of their features, because they are all compelled to adhere to the new Solvency II standards and they all strive to provide shareholder or mutual member satisfaction.

Executive Summary

Solvency II has created a prudential framework likely to give a boost to the trends taking shape……in managerial practices: integration of risks, consideration of the cost of capital, value creation for shareholders or mutual members.

The aim of this study is to show that it may be opportune for a company to capitalise on the investments it has had to make for purely regulatory ends ……to achieve goals more intrinsic to the company, in particular by perfecting its management tools.



Value creation and the cost of capital: a managerial change at the heart of the company…Since the industrial revolution, the measure of company performance has been the subject of wide-ranging studies. Value creation became one of the cornerstones of economic thought in the early nineteenth century and was gradually taken up in the business world over the second half of the twentieth century. Unlike the classic measures of value—measures based on turnover, net income or operating margins—the measure of value creation assumes that the resources of the company (capital and/or debt) have a cost. This approach is applicable to all companies in all industries.

For example, some insurers believe that the third-party liability business performs satisfactorily because it generates a net margin (net income/turnover) as much as three times that generated by the motor own damage business. Yet when the net margin is viewed in the light of allocated economic capital it often turns out that the motor own damage business is more profitable.

Therefore, making allowances for the cost of capital in measuring performance is likely to impose a certain capital discipline on executives and operational managers throughout the operating cycle, as the use of capital does not come without a cost. This notion of a residual profit (the profit generated in excess of the cost of capital) was mentioned by General Motors in the 1920s and first used a few years later by General Electric. But it was not until the 1990s that, as a result of the EVA (economic value added) concept promoted by the firm Stern & Stewart, this measure of performance came into its own.

…even for mutual insurersIt would be reductive to think that value creation consists solely of optimising the profitability of a company. For a mutual undertaking, in the broad definition of the term, and unlike public corporations, the insured and the insurer are one and the same (mutual members), so the profitability of the company is not an end in itself. For a mutual undertaking, value creation is founded on satisfying members by providing insurance products relevant to the features of the affinity group (coverage, services), the prices of which are not very volatile and the margins on which reflect its particularities as defined by the price/service ratio. With the increasing globalisation of the insurance market, the attempt to strike a balance between competitive pricing, coverage, premium refunds, and solvency requires more efficient management. Economic capital models devised around the notion of value creation are thus likely to become indispensable in the world of mutual insurance as well.

Economic capital models founded on value creation: a growing trend…In the early 1990s, the performance of a company in any sector was measured largely by its operating margin, net margin, and the health of its balance sheet. In the insurance business, the development of asset/liability management models in the mid 1990s and the measure of performance in life insurance through embedded value gradually encouraged the leading insurers to create dashboards to steer the creation of value. In view of the investment necessary, only the largest companies have had the means to come up with such dashboards.

Executive Summary

Making the cost of capital an integral part of performance measurement is likely to impose a certain capital discipline on both executive and operational managers, as the use of capital does not come without a cost.

Economic capital models are thus likely to become indispensable in the world of mutual insurance as well.



The objective of the economic capital models involves departing from the single net margin standard to make allowances for the cost of capital. These economic capital models have become genuine tools for strategic decisions.

... that should grow even faster as a result of Solvency II requirementsAs the insurance business is subject to many extreme exogenous variables, financial as well as insurance related, the regulator defines a minimum amount of capital required to do business, so that the insurer will be able to deal with these extreme risks. The current regulatory solvency margin (Solvency I) has never been included by internal models, as it takes a proportional approach to calculating the minimum capital requirement, an approach to the minimum capital requirement founded on historic administrative and accounting data—with variations depending on the country where the company or subsidiary is located—and calculated in standard fashion in proportion to the volumes of business (premiums, claims, or provisions) without explicitly taking into account the notion of risk. Economic capital models, by contrast, take into account the correlation of risks (technical, financial, operational), hedging arrangements (reinsurance, derivatives, securitisation) and the concentration and diversification of risks.

The European Commission, with the backing of CEIOPS (Committee of European Insurance and Occupational Pensions Supervisors), created a new regulatory framework for solvency (CEIOPS, 2007), a framework founded on economic principles of valuation, risk management and internal

risk control. The Solvency II directive is meant to give insurance companies incentives to measure, manage, and control their risks through a cost that translates into the mobilisation of capital. This cost will inevitably encourage companies to optimise their resource allocation and risk management. This is the main point of convergence with the economic capital model, the strategic management tool.

Nonetheless, despite the converging conceptualisation and modelling of risks, regulatory and economic capital are not meant to be equal, as they have different objectives. Regulatory capital is meant above all to ensure a company’s solvency for clients and to avoid any systemic risk; it may have policy designs. Indeed, depending on the calibration of the formula, some activities or risks may be preferred to others. The objective of economic capital is to optimise the profitability of capital, directly for shareholders or indirectly by improving the price/service ratio for mutual members. In this respect, the economic capital model can easily meet regulatory requirements, but first of all it is a strategic management tool based on performance through the measure of value creation.

In practice, the companies that have (or would like to have) internal economic capital models could use much of their information and many of their tests for regulatory purposes. Conversely, the companies that do not have such models could use the information required by the regulator and with possible internal management tools (risk analysis model, reserves, pricing, asset/liability management and so on) devise a dashboard or decision tool in the spirit of the leading companies’ economic capital models. The degree of

Executive Summary

The mobilisation of capital required by Solvency II is a cost that is likely to encourage companies to optimise the way they allocate their resources and manage their risks...…this is the main point of convergence with the economic capital model, the strategic management tool.



sophistication of such a tool will depend on the means available. As we have noted, regardless of their size, legal form, values, and objectives (value creation for shareholders or mutual members), all insurance companies are affected by this prudential reform and thus by its impact on the management of each firm.

The design and sophistication of Solvency II should boost the fundamental trend in managerial practices that has been observed over the last decade. Companies with economic capital models will be in a position to perfect their internal management and to gain a genuine competitive advantage from it.

How management tools can contribute under Solvency II constraintsThe standard formula spelled out in the Solvency II prudential framework can be seen as a simplified internal model that each company can tailor (and is even encouraged to use) to its own particularities, especially in view of its exposure to risks and its ability to manage them. With the standard formula, we have devised a simplified economic capital model subject to Solvency II constraints.

The objective of this economic capital model is to provide every company with a management tool, the foundation of which is the investment necessary to comply with the requirements of the prudential regulator, in terms of both data collection and simulations. This decision tool makes it possible to manage the amount of available capital (the capital structure), allocation to lines of business (in accordance with profitability and the cost and consumption

of capital), exposure to risks (which has an impact on capital requirements), financial autonomy, and solvency. The tool also makes it possible to reallocate surplus capital destructive of value to optimise the profitability of existing activities or to new developments or new business. As capital has a cost, it is indispensable to manage it. The Solvency II prudential framework could become a new standard and constraint for defining the amount of allocated risk-adjusted capital (RAC).

Hitherto, the companies with economic capital models have calculated RAC in keeping with their own perception of risks and the sophistication of their internal models. For example, each company has its own range of weights, although the publication of these weights ultimately attests to a certain heterogeneity. Solvency II is meant to encourage an operational approach to risk exposure, that is, an approach consistent with internal management and/or economic capital models in an attempt to foster the development of these models and to give companies incentives to improve their risk management. The calculation of allocated risk-adjusted capital (RAC) in economic capital models could, as a result of the new solvency requirements, evolve toward greater standardisation.

With a fictitious insurance company whose characteristics are described in appendix 7, we calculated the capital requirement for each line of business (RAC), the company’s profitability per line of business (return on risk-adjusted capital RoRAC) and surplus capital (the difference between available capital and required capital). These three components are at the heart of the economic capital model described below and

Executive Summary

Companies with economic capital models will be in a position to perfect their internal management and to gain a genuine competitive advantage from it.

Solvency II could become a new standard for defining the amount of allocated economic capital.



of our demonstration of the contributions of such models to the management of a company.

The economic capital model makes it possible not only to look at each strategic decision from the perspective of the relevant business unit(s) (line of business, country, region, and so on) but also to gauge the impact on the company as a whole. Indeed, what is best locally is not necessarily appropriate globally: for example, the best acquisition from a strategic and financial point of view in a particular country may not be appropriate, in terms of management priorities, profitability, financing, capital allocation, and so on, for the company as a whole. An analysis of the table above makes it possible not just to see the risk profile and profitability of the company but also to propose strategic management improvements.

In view of its turnover (% premiums), non-life insurance accounts for two-thirds of this company’s business. A large share

of the business is exposed to frequency risks; it thus has a low risk profile. The line of business with the highest risk profile is third-party liability, but it accounts for only 7% of premiums and, at first glance, enjoys a net margin (net earnings/premiums) significantly greater than that enjoyed by the company’s other non-life lines of business (6.1%, as opposed to 3% for property damage, 2.9% for health and 2.3% for motor own damage). Many insurance companies still analyse risk profiles based on net margin and the weight of the turnover or the balance sheet items of individual lines of business in the company as a whole. The ROE (return on equity) of the company—here 11.3%—is calculated to refine this analysis. This calculation is based on published book equity that in no way reflects the economic dimension (under-

Executive Summary

1 - RAC in % = RAC/technical provisions life or RAC/premiums in non life RoRAC = Net profit/RACRAC x = (RoRAC – g)/(CoC – g)where g is the perpetual growth rate of value creation flows, CoC the cost of capital.RAC % of total = RAC/sum of RACA company’s value is based on a combination of a cash flow-asset mixed approach (called goodwill) and a sum-of-the-parts approach.V = net asset value – accounting goodwill + economic goodwillV (RACj) = Σt=1,.., ∞ RACj (RoRACj – CoCj)/(1+ CoCj)t = RAC (RoRACj – gj)/(CoC – gj)where RACj is the economic capital allocated to line of business j. V(RAC) % = V(RAC)/Sum of V(RACj)

Life Non-life

Activity Unit linked

Euro denominated

Motor own

damage

Property damage

Third-party liability

Health Sum Surplus TOTAL

Premiums

Premiums EURm 250 1000 1000 1000 250 200 3700

Premiums % 7% 27% 27% 27% 7% 5% 100%

Capital

RAC in % (Solvency) 0.4% 3.1% 7.1% 10.8% 34.4% 9.9% 12.8%

RAC EURm 5 185 71 108 86 20 474 615

RAC % of total 1% 39% 15% 23% 18% 4% 100%

Profitability

Net margin 0.8% 4.0% 2.3% 3.0% 6.1% 2.9% 3.1%

Net profit EURm 2 40 23 30 15 6 116

RoRAC 35% 21% 33% 28% 18% 29% 24% 5%

Valuation

RAC x 4.7 2.8 3.6 3.1 2.0 3.2 2.9 0.5 1.2

V(RAC) EURm 25 513 256 336 169 64 1364 308 1671

V(RAC) % 2% 38% 19% 25% 12% 5% 100%

Economic capital model1

Source: EDHEC Business School



or over-capitalisation, goodwill, in force, and so on) and as such it is a poor strategic indicator and does not serve as a solid basis for the comparison of the performance of the company and that of other companies in the industry.

If during the analysis the capital required for each line of business is kept in mind, the conclusions are quite different: the riskiest business and the highest margin business—third-party liability—has a greater weight than its share of premiums (7%) would first suggest. Indeed, it consumes 18.3% of total allocated RAC, 2.6 times more than its share of premiums. So the profile of the company is riskier than was suggested by the conventional analysis described in the preceding paragraph. If allocated economic capital2 rather than net margins, ROE or Solvency I (net profit/16% of turnover) is used to measure the performance of third-party liability, one sees that it requires five times more allocated capital given its intrinsic risks (RAC in %, 34.4% vs. 7.1%), and profitability of allocated economic capital (RoRAC) is 18%, as opposed to 33% for motor own damage, 28% for property damage and 29% for health. This results in an implicit valuation of two times allocated capital in third-party liability as opposed to 3.6 times in motor own damage insurance (see RAC x in the table above).

Motor own damage, the business that generates the lowest net margin (2.3%), turns out to be the company’s second most profitable line of business (RORAC of 33% as opposed to 35% for unit-linked business), and this as a result of its modest risk profile (measured here with the Solvency II standard formula, though this measurement could be perfected with an internal model).

With respect to strategic decisions, what main conclusions can be drawn from this dashboard? We will list only two, as each number naturally provides key information for the management of the company.

In terms of RoRAC, the least profitable lines of business are third-party liability and euro-denominated policies; they account for 57% of the total RAC of the company ((185+86)/474). The first means of improving this situation could be to reduce RAC by analysing each of the risk sub-modules. By identifying the greatest consumers of capital, it is possible to identify the actions that can be taken to reduce this consumption. It may be possible to analyse possible risk transfer policies to reduce the capital allocated (RAC) to third-party liability. The numerator in RoRAC may be looked at as well; that is, it is possible to study ways to improve the standardised economic results of these two lines of business (fees, rates offered to the insured, asset allocation, underwriting and financial hedging policy, administrative, management and acquisition costs, portfolio selection, fraud, claims management costs and so on).

Other types of strategic decisions could be considered as well. Has the company’s third-party liability business reached critical mass? If operational and financial management are already optimised and there is no room to improve RoRAC (by steering RAC and net earnings), is it strategically appropriate to maintain this business? If so, might it not need to expand (to attain critical mass)? Such an analysis should naturally be done for each line of business in an attempt to identify possible improvements to RAC as well as to net earnings and risk management.

Executive Summary

2 - Allocated economic capital was calculated with the Solvency II standard formula, which is an initial phase in the improvement in the analysis of risks and of economic performance, but which, as we note above, could be made much more sophisticated with a partial or total internal model.



Another strategic point is the management of capital surpluses. We see that on the basis of RAC the company is valued at an implicit multiple of 2.9 (RAC x line), but that taken as a whole this multiple changes to 1.2. This value destruction stems from the capital surplus: only 43.5% of the company’s available capital is allocated to the insurance business, so 56.5% destroys value. The company should think of ways to improve the allocation of this “dormant” capital, by reinvesting it in existing lines of business to make them more profitable or by moving forward with acquisitions that would make the company bigger or more diversified or, as a last resort, by returning capital to shareholders (dividends, share buybacks) or mutual members (premium refunds).

It would of course be possible to fine tune the strategies resulting from closer analysis.

Risk transfer policy is likely to undergo profound changesIt is our view—and to bring about this change is also one of the objectives of the regulators—that the universe of risk transfers will undergo profound changes. The catalysts of these changes in the culture of the ceding companies and thus in the supply of risk transfers are found in the incentives provided to view these transfers not just by business unit but also from the perspective of the overall company strategy (optimisation of required capital, reallocation of paid-up capital) and in the quantitative and qualitative standardisation brought about by pillars 1 and 2 of Solvency II. We have shown that the treatment and calibration of reinsurance by the European regulator will have a great

impact on the risk transfer policies of the ceding companies, on the rate of coverage as well as on the way insurers divide up the risks they transfer to reinsurers, on the number of reinsurers as well as on their rating and prices.

Nonetheless, the part of the model of underwriting risk based on net premiums leads to calibration errors (as a result of the non-linearity of net premiums and risk transfers) that in turn lead to errors in the capital requirement, errors that are likely to favour policies that do not manage risk optimally over others that do. In this way, the measure and calibration of the formula are decisive, and some reworking is still necessary if the supervisor does not want to cause distortions that are at odds with the objective to create incentives for insurance companies to improve the management of their risks.

ConclusionIn the last ten years, the managerial practices of the leading insurers have undergone profound changes, in particular by making value creation an integral part of their strategic choices. The development of asset/liability management models, embedded value models, and then economic capital models has increased executive and operational management awareness that decisions should be made in the knowledge that capital is not a free resource and that it must be managed accordingly.

At the same time, with the growing complexity of risks, the prudential regulator sought to put in place regulation more consistent with the economic reality and practices of insurers. The transition from Solvency I to Solvency II leads to a

Executive Summary

The measure and calibration of the formula are decisive, and some reworking is still necessary……if the supervisor does not want to cause distortions that are at odds with the objective to create incentives for insurance companies to improve the management of their risks.



determination to calculate the solvency of an insurance company on the basis of a standard formula (or of a partial or full internal model) that converges with that used in economic capital models. In addition to the measure of solvency itself, the regulator seeks to foster the development of internal models likely to improve identification, calibration and management of company risks; it is thus necessary to be consistent with the economic approach taken by the insurance companies.

As for the quantitative impact study (QIS4), the data collection and simulations required by the regulator are a heavy investment for many companies. In our opinion, it would be wise to capitalise on this investment made for purely regulatory ends to pursue goals more intrinsic to the company itself: to perfect or put in place a decision tool, with a view to improving the management of the company and boosting its creation of value. These decision tools make numerous contributions: management of risk-adjusted capital, definition of policy for investment, underwriting, launch of new products, reserves, reinsurance, asset/liability management, allocation of capitalto individual lines of business, risk management (definition of accepted limits, concentration, diversification), and communication with the financial markets, rating agencies, and the prudential regulator.

Just as we were concluding this study, representatives of the European Commission and the European Parliament finally came to an informal agreement, on 26 March 2009, on the Solvency II directive proposal, a consensus reached after a major effort: it involved dropping the notion of “group support”. Group support would have meant

that pan-European companies could have consolidated their capital more heavily at the parent company, by including the benefits of diversification of the subsidiaries active in other European countries, a practice that would have exempted these groups from having to comply with capital requirements in each country. Nonetheless, the notion of group support may be looked at again in three years, after the entry into force of Solvency II.

In addition, CEIOPS is relying on analyses of the results of QIS4 and of the current financial crisis to come up with an improved measurement and calibration of the model. Called into question are the approaches to measuring liquidity, concentration and counterparty risks, the loss given default for financial derivatives, and the correlation of market risks.

We believe that these choices are decisive, all the more so in view of the current financial and economic crisis, as they will have a major impact not just on the effectiveness of the protection of the insured but also on the incentives created to improve insurance company management.

Executive Summary



Executive Summary

1. Value Creation in Insurance Companies

19



In recent years the insurance industry has undergone profound change: competition has grown stiffer, companies have consolidated and expanded overseas, insurance and financial risks have become increasingly complex. To adapt to these changes, modelling has become more and more sophisticated (premiums, reserves, asset/liability management, embedded value).

Since the late 1990s, some leading European insurers have put in place real strategic decision-making tools, tools known as economic capital models. They have several functions: they may serve to define policies for investment, for underwriting, for creation of new products, for reserves, for reinsurance, for asset/liability management, for capital allocation, for capital arbitrage, for risk management (definition of accepted limits, concentration, diversification) or as a means of communication with the financial markets, rating agencies, and the prudential regulator. At the core of these models is value creation.

The primary objective of this chapter is to do an analysis of the academic foundations of value and of its development in the business world (section I) and show the relevance of this notion for the management of a company. Section II analyses the extent of the domain in which it can be applied, in particular in the mutual insurance business, and it will do so even though the objectives and values of this business are centred on the members of the mutual.

The second objective is to show how Solvency II should, as a result of its

nature and sophistication, accelerate the trend in managerial practices that has been observed over the last decade: the inclusion of risk management and the cost of capital in the process of performance measurement and value creation. This trend is a true departure (section III) from traditional approaches focusing on sales and on operating and net margins.

Although not all insurance companies may have the means to create elaborate internal economic capital models, we will show in section IV and in the following chapters that with the data and simulations required by Solvency II it is possible to transform these investments to improve management.

I. Value Creation, at the Heart of Corporate ManagementValue creation is one of the cornerstones of economics. This section looks at the origins of value creation as well as at its accepted academic meanings. The objective is to show how value creation has, over the twentieth century, gradually made its presence felt in business. Unlike traditional indicators of value, indicators based on sales, net profit, or margins, value creation incorporates the notion of performance while taking into account the cost of resources. Taking into account the cost of resources is likely to require that both executive managers and operational managers draw on capital, throughout the business cycle, with a certain discipline, as the use of this capital does not come without costs.

We will show in particular that the objective of creating shareholder value is not at odds with satisfying other stakeholders in the company




(clients, employees, suppliers, banks, governments). So the managerial revolution underway in the leading insurance companies, a revolution sparked by economic capital models, is affecting all those involved in the industry, including mutual insurance companies, whose primary concern is member satisfaction.

I.1. The accepted meanings of value creation: the cornerstone of economicsFor the origins of value creation, it is necessary to go back to the classic economists, who, in fact, make it one of the cornerstones of economics. At the outset, the notion of value was associated with that of labour: the value of a good is represented by the cost of the labour that went into the production of the good. This notion, pioneered by Smith (1904) and further developed by Ricardo (1817), was taken to its political apogee by Marx (1867). At the same time, another school of thought was taking shape: Say (1803), who disagrees with this notion of value, believes instead that the value of a good is the result of its utility to the person who uses it.

Finally, grounded on these two schools of thought, value can be defined on the basis of a transaction (exchange or market value), a function of the cost of production to the seller and on the basis of utility to the buyer (utility value). So it is possible to define an objective value made up of an unchangeable social sense (cost of labour and resources used, observed exchange value) and a subjective value made up of the individual perceptions of those involved (the utility value or the individual and occasional value an economic agent

ascribes to a good or service, depending on its ability to meet a particular need).

The reconciliation of market value and utility was achieved by corporate finance theory (Caby and Hirigoyen 2001). Taking into consideration the existence of a risk-free (or fixed-income) asset and its opportunity cost for any investor, in equilibrium, the exchange value (market value) of a risky asset should converge toward its utility value, as measured by the discounted value of the cash flows it will generate.1 Since the work relying on institutional theories of the firm (theory of ownership rights, of transaction costs, and of agency costs—see Coriat and Weinstein for a review), lenders of equity have been viewed as holders of residual rights2 and as such they bear the totality of the risks. In exchange, they require a utility value (and thus a market value) of their investments (contributors of capital) greater than the opportunity cost, increased by the specific risk of the firm. As a consequence, the maximisation of the market value of capital, that is, of the utility value for the shareholders with respect to the risks they bear, should be the main objective of any financial decision (Albouy 2006).

All the same, in practice, as the manager of the company is privy to information on each stakeholder in the company (clients, employees, suppliers, banks, the state), it is often he who decides how to allocate any surplus to these stakeholders. In an uncertain environment characterised by the incompleteness of contracts, each stakeholder runs a risk in the relationship of information asymmetry that binds him to the manager (Garvey and Swan 1994; Zingales 2000). So now the objective of the firm is to create value not just for


1 - Initially, discounting made allowances only for the temporal value of money. There is a time preference or impatience for immediate consumption (Fisher 1930) measured by the risk-free interest rate. It is not until Markowitz’s (1952) work on the measure of risk and Sharpe’s (1964) and Lintner’s (1965) formalisation of this work with the famous capital asset pricing model (CAPM) that the discount rate incorporates a risk component. Since this work, the discounting of future cash flows has been grounded on a rate that incorporates the opportunity cost of a risk-free investment as well as the risk premium demanded by an investor.2 - The share of the profits generated by a company that goes to the shareholder (variable) is that which remains after the other stakeholders of the company (employees, suppliers, banks, the state) have been paid, in keeping with the terms of a contract that clearly spells out their remuneration (fixed).



shareholders but for all stakeholders. Charreaux and Desbrières (1998) note that all stakeholders are affected each time a strategic decision is made in the company. So these authors speak of stakeholder value. It can be measured at each link in the chain, by taking into consideration the difference between the price paid by the recipient of the value and the minimum price required (opportunity cost) by the contributor of this value.

In this respect, the work of Rappaport (1987) and Slywotzky (1998) shows that the companies that focus on creating value for clients end up creating more shareholder value than do those that focus exclusively on financial indicators of shareholder value. In particular, innovative products and services offered clients make it possible to build a lasting competitive advantage, a source of additional shareholder value. In short, creating shareholder value is not incompatible with the satisfaction of other stakeholders in the company (Denglos 2008). The value created for the shareholder is the final link in a chain whose strength rests on the earlier satisfaction of the other stakeholders. It is nonetheless the ultimate objective.

I.2. Value creation (and measuring value creation) in the corporate world Pinpointing the origin of value creation in the corporate world is not easy, but the notion seems to have been current, in large conglomerates with several businesses, since the start of the twentieth century (Johnson and Kaplan 1987). In classic economic theory, value for the holders of residual rights was initially measured with net income (and/or earnings per share). It is for this reason that in spite of subsequent

developments the price-earnings ratio (P/E), which has several drawbacks (static, dependent on the financial structure), is still so heavily relied on.

Large companies have gradually refined their measure of value creation by incorporating the capital invested by each profit and investment centre. Return on investment (ROI)3 was essential to strategic decision making until the late 1980s. In the 1960s, however, ROI will be called into question (Dearden 1969) and a notion founded on the concept of residual income, a notion that is today standard, will take its place. All the same, it was not until the 1990s, when the consulting firm Stern & Stewart promoted EVA (economic value added),4

that the measure of performance adjusted for cost of capital really came into its own.

In this approach, value creation corresponds to the firm’s profits in excess of the rate of return required by the suppliers of capital (shareholders and creditors). According to Solomons (1965), cited by Bromwoch and Walker (1998), the term residual income was first used by General Electric, even though the president of General Motors in 1923 (A. Sloan) refers to an indicator of this type in the early 1920s. EVA is the capital employed5

multiplied by the difference between return on capital employed (after taxes)6

and the weighted average cost of capital (WACC).7 As the first tool for decentralised financial management, capable of gauging the performance of a unit by applying an embedded required rate of return, EVA is often considered the forerunner of the dashboards and value management (also known as economic capital models) put in place by companies.


3 - ROI or ROIC (return on invested capital) is the net profit divided by the invested capital. 4 - Stern Stewart & Co. has trademarked EVA.5 - Capital invested/employed is the net assets invested throughout the business and investment cycles. It is financed by equity and debt. It is equal to the sum of fixed assets and the need for working capital. 6 - Return on capital employed (ROCE) is the operating profit after taxes divided by capital employed. Although it measures the efficiency of a company’s business from a financial point of view, it is an accounting indicator that fails to make allowances for the notion of risk. 7 - WACC is the overall financing costs for a company, that is, the rate of return required by the suppliers of capital (shareholders and creditors).



EVA will be widely taken up outside consulting firms. Some academic studies (Anctil 1996; Reichelstein 1997; Rogerson 1997) have demonstrated analytically the ability of EVA and of residual income in general to coordinate company objectives in the context of an agency relationship. Many variations have been created: cash flow return on investment (CFROI),8 total shareholder return (TSR),9 the Strategic Planning Associates model,10 the McKinsey and LEK Consulting model for discounting future cash flows, the Marris Q index (price/book value of equity), the Marakon Associates model, the Fruhan and McKinsey model. The interested reader can find a description of these models in appendix 1 (Appendix 1: Value Creation Models) and in the work of Hoarau and Teller (2001) or Caby and Hirigoyen (2001).

Although these indicators of value creation differ, they ultimately have the same conceptual framework:• Operationally, the firm creates value with the resources it has available, that is, the capital employed• Financially, value creation is discounted at the cost of capital (that is, that of resources)• The organisational dimension (organisation of a corporation into profit centres) is associated with a certain allocation of resources and has an impact on the cost of capital• Managerially, the pursuit of the efficient use of resources results in a need for each investment to generate a return greater than the cost of capital. So investment and financing are closely bound up with each other, a message that should also be understood at the operational level.

So then, unlike the traditional indicators of value that are based on sales, net income, or margins, these indicators are closer to the notion of performance, as they include optimisation of the use of resources. This feature is likely to force managers to use capital with a certain discipline throughout the business cycle, as the use of capital has its monetary costs.

The success of these indicators of value creation lies also in the ease with which they can be explained to operational managers and with which they can be made aware of the cost of financial resources. So it is little wonder that some companies have used them to force responsibility on their managers, by putting in place, for example, a system of variable pay indexed to a value creation indicator. Stern, the co-founder of Stern Stewart, goes so far as to speak of employee capitalism (Ehrbar 1999). The value created, as it happens, is shared by shareholders, who see the prices of their shares rise, and managers, who receive bonuses.

We believe that reliance on economic capital models founded on these notions of value creation, currently the province of only a few leading firms, will, in tandem with an increase in management control and risk management, increase in the near future. These models make it possible not just to offer management a broad view of the performance of the company and to optimise the allocation of capital to each operational unit in view of its profitability but also to provide a point of reference for investors, financial analysts, and rating agencies.

The object of this study is to show that in the insurance industry the implementation


8 - CFROI is a variation on ROI that measures the difference between the internal rate of return (IRR) on capital employed and the weighted average cost of capital (WACC) multiplied by the amount of capital employed. The idea is to determine the IRR that leads to a match between the gross value of investments before amortisation and the future after-tax operating cash flows generated over the estimated life of the investments. A simplified version of CFROI involves dividing earnings before interest, taxes, depreciation, and amortisation by capital employed and comparing this ratio to WACC. 9 - TSR is the internal rate of return on an investment made up of the purchase of a share of a company and whose revenue flows are the sum of the dividends and the share price at the end of the period, discounted for the cost of capital. The indicator of the Boston Consulting Group compares a forecasted TSR and a TSR founded on realised results. 10 - The Strategic Planning Associates model relies on the value curve approach, which involves comparing the price/book ratio (the ratio of the market value of a company to its book value possibly adjusted for intangible assets) and the ratio of the return on capital (Rc) to the minimum expected return on capital (Ra). When the price/book ratio is greater than the return on capital/minimum expected return on capital ratio the performance of the firm will, in all likelihood, improve, thus creating value.



of Solvency II forces companies to build internal models or at the very least to make significant investments in the gathering of data that could then be used for other purposes: to refine strategy, to improve management, and thus to increase the profitability of insurance companies. In other words, these data could serve as the foundation of a dashboard for managing the company or even of economic capital models such as those used by the leading European firms.

With our examination of the original notion of value creation, we have shown that this managerial revolution is of relevance to both leading insurers and smaller insurers, and that this is so whatever their legal form (mutual insurance company, public company, provident society, and so on) or end objectives (satisfaction of the mutual member on the premium charged/service provided criterion or of the shareholder on the risk/return criterion).

II. The Concept of Value Creation in Mutual Insurance CompaniesWhat with the widely differing views held by the different groups of mutual insurance societies (as opposed to incorporated or public companies), it seemed worth taking a look in this section at the ways in which these groups are also affected by this managerial revolution, the momentum of which is growing with the work onSolvency II.

As it happens, a reductive version of value creation consists of optimising a company’s profitability. Now, for a mutual insurance company, optimising profitability cannot be an end in itself, as the insured party

and the insurer are one: the mutual member. Is it then necessary to reject the notion of value creation for the mutual insurance universe? Does the economic capital model make no sense for mutual insurance societies? We will show that the answer to these two questions is no, and that Solvency II has been at the origin of much thought in mutual insurance companies (in the rest of the survey we will use the term mutual to differentiate these organisations from incorporated companies or public companies).

Value creation is interpreted one way in a mutual and another way in an incorporated company. First of all, the mutual member (both the insured party and the insuring party) participates in the life of the mutual undertaking with his vote at general meetings (he may even be elected to the board). The board determines the policies of the mutual undertaking, including the budget for overhead and changes in premiums. When the mutual undertaking makes a profit, the members may be given a premium refund (for example Mutuelle de Poitiers refunded €6.3 million to its members in 2005; Ethias refunded €9 million in 2006). On the other hand, in the event of heavier-than-expected claims, mutual undertakings charging variable premiums may adjust those premiums upwards (for example, in 2000, after the storms Lothar and Martin, MAIF adjusted total premiums upwards by €53.4 million).

So for a mutual undertaking value creation relies on member satisfaction: insurance products well suited to the characteristics of the affinity group (coverage and services), stable premiums, and margins consistent with member needs. According to Facts




and Figures (2008), the combined ratios of mutual undertakings are less volatile than those of public companies and, in an attempt to maintain a price/service ratio satisfactory to their members, their profitability seems deliberately to be kept to less than 10% (as measured by return on equity). Finally, the solvency margin of mutual undertakings is usually greater than that of public companies. Unlike public companies, mutual undertakings have not usually optimised their equity financing. Note, however, that, so as not to distort the analysis, mutuals cannot reduce the accumulated shareholders’ equity and that the bulk of the business for some mutual undertakings is insuring against long-term risks.

In a public insurance company, by contrast, it is a tripartite arrangement: the insured party, the insurer, and the shareholder. The relationship between the insured party and the insurer is a purely commercial one. The insured party is not involved in the insurer’s policy decisions, premium setting or product development. If the insurer is profitable, it can pay dividends to its shareholders. If it loses money, it cannot resort to premium adjustments and must instead appeal to the shareholder (new equity issues). Value creation is done mainly with shareholders (and often management) in mind.

So the mutual and corporate worlds’ contrasting views of the ties between value creation and profit are founded on the fact that profit is merely a tool for the mutual undertaking but an end in itself for the public company. All the same, this difference is not likely to call into question the trend that, for more than a decade now, has been underway in

the management of insurance companies and that will gather momentum with the entry into force of Solvency II.

For one thing, the insurance industry is globalising, and it is become increasingly complex for mutual undertakings to strike a balance among competitive premiums, refunds, and solvency. For another, the Solvency II Quantitative Impact Studies result, for some small or specialised mutuals, in solvency requirements as much as ten times greater than those of Solvency I. And the ability of these insurers to turn to the financial markets is often limited.

To survive in this new environment, some mutuals have advocated more efficient management (some even mention the use of dashboards or decision tools reminiscent of economic capital models) and, failing that, consolidation of those involved in the business. According to Jean-Claude Seys (2006), this consolidation would enable the new entities to benefitfrom the size effect, from diversification of risk, and perhaps even from internationalisation and access to the capital markets through issues of subordinated debt. Consolidation could take place through mergers when the undertakings are involved in similar lines of business, offer similar products, and have similar distribution networks(see the merger of MMA and Azur, for example); or a common controlling entity could also be created (cooperation among mutual undertakings that continue to have a legal existence, as in the case of Covea, an undertaking in a group of mutuals undertakings—SGAM—that is without capital of its own but has a social fund whose members are exclusively mutual insurance undertakings).11


11 - Such a scheme is not unique to the insurance industry: rival carmakers, for example, may develop motors jointly.



We will examine in greater detail the managerial evolution and the suitability of resorting to an economic capital model in section IV.

III. Value Creation and Performance Measurement in Insurance CompaniesFor a closer look at the origins of dashboards or economic capital models and at the suitability of using them, we propose in this section to put in perspective the change in the measure of performance and of value creation in insurance companies. We will show that these decision-making tools have very naturally become standard in certain companies.

III.1. From net asset value to embedded valueIn the early 1990s, as in the manufacturing sector, value creation and the performance in general of an insurance company were measured by operating margins (before and after financial profit, given the weight of the latter in the business), net margin, and the good health of the balance sheet.12

Turnover (insurance premiums), the combined ratio in property and casualty insurance and the financial margin in life insurance13 were the main means of evaluating the strategy of a company. When it came to assessing the health of the balance sheet and pricing an insurance company, the main indicator was net asset value: the book value of shareholders’ equity adjusted for the unrealised capital gains or losses, net of policyholders’ share and net of taxes, and possibly adjusted for other on and off balance sheet items (mainly analysis of the ratio of technical provisions and goodwill). In the literature, there is much talk of wealth valuation

methods that rely on an instant snapshot of the balance sheets and thus on past events alone.

When, in the mid 1990s, the stock market capitalisations of European insurance companies began substantially to exceed their net asset value, methods for the evaluation and measurement of value creation were refined. It turned out that the net asset value multiple (market capitalisation/net asset value) could be greater than one, given the profits generated by the company. Like M. Jourdain, who spoke in prose without realising it, most financial analysts took value creation approaches without knowing they were doing so. Indeed, this net asset value multiple was nothing but the simplification of the ratio of the profitability of insurance companies to the cost of capital.

It can be argued that an insurance company creates value when the net asset value multiple is greater than one. As it happens, the value of an insurance company is the sum of its net asset value and its goodwill. Goodwill is made up of intangible assets, that is, of the value of those prospects of the company that are not included in the balance sheet (for example, the profits that will be generated by a savings insurance contract are often absent from the balance sheet but are nonetheless a source of wealth for the company). So economic goodwill (future cash flows generated by the firm) replaces the book value of goodwill taken from the balance sheet. Unlike the traditional approach, goodwill (GW) makes it possible to view the company as a going concern and to make allowances for future profitability. This goodwill can thus be analysed in terms of the value created by the company,


12 - With its commitments to those it insures, an insurance company must have own funds sufficient to withstand a multitude of external shocks. At the time, the measure was relatively unsophisticated, as asset/liability management models were, for the most part, used only by British or North American insurance companies. 13 - It is the difference between the return on the assets of the company and the payments made to policyholders.



that is, in terms of the profitability of the company with respect to its net asset value (RoNAV and the cost of this capital (rE)). So the valuation (V) of an insurance company can, by making certain assumptions that simplify prospects for cash flow growth, be expressed as a multiple of net asset value:14

V = NAV + GW = NAV * RoNAV/rE

If RoNAV > rE the company creates value and the investor agrees to price it above the net asset value so as to include the future value creation cash flows that it will generate. Conversely, if RoNAV < rE the company destroys value and it is priced at less than its net asset value.

With this dual determination to refine in-house the tracking and management of risks and to improve valuation techniques (in a world where the consolidation of the industry, in and outside the European Union, is gathering momentum) came the development of the notion of embedded value.

Embedded value (EV) can be seen as the value of a life insurance company that stops writing new business. It is often associated with scrap value. It is the sum of net asset value (after deduction of accounting goodwill in life insurance) and of the value of in-force business (VIF), the present value of future profits from existing insurance contracts, less deduction of the implied costs of the risks (cost of capital15). It is calculated net of taxes and of the share owed to policyholders.

Deterministic at the outset, measures of embedded value are gradually becoming uniform. Its sophistication (stochastic

calculation, integration of contract options and guarantees) has led to the creation of European embedded value (EEV) and market-consistent embedded value (MCEV) (CFO Forum 2004; 2005; 2008).

Calculation of embedded value (EV, EEV, MCEV) relies on modelling policyholder behaviour (mortality table, surrender and cancellation rates, average up-front fees, amount of average premium, and so on), on the quality of management (the gap between financial statements and the estimates, commissions, matching of assets and liabilities, hedging policy, profit-sharing policy), and on macroeconomic scenarios (financial markets, inflation, taxation, and so on).

Embedded value, then, has gradually become the standard measure of the creation of value by life insurance: externally (investors, mergers and acquisitions) as well as internally (standard tool for business and risk management). Some insurance companies (AXA and Allianz, for example) have recently modified the features of their products before launch (premiums and guarantees) as a result of the MCEV readings of value creation.

III.2. From the sum of the parts to the economic capital modelIn view of the great differences (risks, profitability, capital requirements) from one branch of insurance to another, it was necessary to refine the approach to value creation, a refinement that began in the late 1990s.

So called sum-of-the-parts valuation methods were thus gradually developed while, at the same time, some leading


14 - Economic goodwill can be expressed as the discounted sum of superprofit (as the Anglo-Saxons call it), that is, of net profit NPt less the cost of capital (NAV*rE where rE is the cost of capital):GW = Σt=1,n(NPt - [NAVt * rE ])/(1+ rE)t15 - In the context of embedded value, the cost of capital is the cost of the capital assets required to ensure the solvency of the insurance company in the event of different scenarios (including extreme shocks).



insurers were creating in-house models per business unit, the forerunners of today’s economic capital models.

Sum-of-the-parts valuation involves replacing net asset value (NAV), as defined in the preceding section, with the sum of risk adjusted capital for each activity j (RACj, determined by the economic solvency requirement for each company as shown by its experience and its exposure to risk) and the surplus or deficit of capital (non-allocated capital). For the capital allocated to each activity RACj it is possible to calculate a return on risk adjusted capital (RoRAC), a cost of capital CoC, possibly a perpetual growth rate gj and thus to determine the value of the company (V) and its creation of value:

V = NAV + GW = NAV + Σj=1,m Σt=0,n [RACjt[RoRACj - CoC)]]/(1+CoC)t

V = (NAV - Σj=1,mRACj) + Σj=1,m RACj * (RoRACj - gj)/(CoC - gj)

The first term is the surplus capital. By design, risk adjusted capital (RAC)includes a margin of safety to cover any possible risk, so the surplus capital is likely to destroy value and should thus be managed actively (share buyback, extraordinary dividends, or acquisitions)

The second term measures value creation. One finds that the risk adjusted capital multiple is greater than or less than one, depending on whether the company creates value (RoRAC >CoC) or destroys it.

With the results for each element of the sum of the parts, it is possible to create the following dashboard, a dashboard widely used by those who value insurance companies.

When the activity under consideration is life insurance, value creation is measured using market consistent embedded value. When it is property and casualty insurance, value creation depends on premiums, shareholders’ equity, reserves, the return on financial assets, and the combined ratio.

Concomitantly, some insurance companies, have, since the start of the new millennium, created economic capital models that rely on an analysis broadly similar to that which, described just above, is used for valuation. To measure the break in the appreciation of the strategy caused by this approach, consider a company active in five lines of business (1: general third-party liability, 2: corporate risk, 3: property damage, 4: assistance, 5: motor insurance).


Activity j RACj RoRACj CoC g RoRACj - CoC %RACj V(RACj)

1 V(RAC1)

2 V(RAC2)

…

…

M V(RACm)

Surplus V(Surplus)

V(NAV)

Dashboard for steering and valuation of an insurance company




This table shows the profile of the company: premiums (in EURm), distribution of premiums (Premiums %), economic solvency margin per line of business (that is, RAC as a percentage of premiums), net margin, return on risk adjusted capital of each line of business (RORAC defined by ratio of standardised net profit to RAC).

With the return on risk adjusted capital (RoRAC) and a perpetual growth rate of cash flows (g), it is possible to determine the value created by the company with respect to its cost of capital. Discounting at a risky rate seems inappropriate to us, as the risk is in the flows to be discounted (Amenc and Foulquier 2006), but the financial markets (most financial analysts, investors, and insurance companies) discount at the risky rate (out of prudence, in case insufficient allowance is made for risk). The valuation ratios are thus shown in keeping with this approach, more familiar to the reader. We have chosen a cost of capital of 8.5%.

When RoRAC is greater than the cost of capital to the company, the company creates value and the implicit valuation multiple in terms of RAC (column RAC x) is greater than one. It is important to notice that this multiple is the result of the RAC valuation

(xRAC= V(RAC)/RAC) as opposed to the result of an a priori assessment performed by certain evaluators. As the table shows, general third-party liability destroys value: the RAC multiple is 0.94. The valuation of the capital allocated to general third-party liability (€1,165m) is thus affected by a coefficient of 0.94 (leading to value destruction) and is thus valued at only €1,098m (V((RAC)). So general third-party liability accounts for only 20.5% of total value but consumes 30% (1,165/3,911) of risk-adjusted capital.

With this dashboard thus defined, what can a manager do to refine or reorient his strategy? In the traditional approach, still taken by most managers (in all industries, including insurance), assessment of strategy relies on analysis of sales and margins. So, at first glance, this company has a low-risk profile, as a large share of the business is exposed to frequent risks. General third-party liability, by contrast, the most volatile in terms of net profit, accounts for only 10% of total premiums. In addition, it delivers margins 2.6 times greater than those of motor insurance (6.5% as opposed to 2.5%). Many insurers can fit this profile, and the composition of the premiums of this


16 - RAC in % = RAC/technical provision life or RAC/premiums in non lifeRoRAC = Net profit/RACRAC x = (RoRAC – g)/(cost of capital – g)The valuation of the company is founded on a mixed cash flow—asset mix approach (called goodwill) combined with a sum of the parts: V = net asset value - accounting goodwill + economic goodwillV (RACj) = Σt=1,.., ∞ RACj (RoRACj – CoCj)/(1+ CoCj)t = RAC (RoRACj - gj)/(CoC - gj)where RACj is the economic capital allocated to line of business i, CoC the cost of capital, g the perpetual growth rate of value creation flows. V(RAC) % = V(RAC)/Sum of V(RACj)

Illustration: Comparison of traditional analysis and analysis founded on economic capital 16


Activity PremiumsEURm

Premiums%

RAC in %of

premiums

RACEURm

Netmargin

Net profit EURm

RoRAC g RACx

V(RAC)EURm

V(RAC)%

General third-party liability

1456 10.4% 80% 1165 6.5% 95 8.1% 2.0% 0.94 1098 20.5%

Corporate risk 897 6.4% 40% 359 4.0% 36 10.0% 1.5% 1.21 436 8.2%

Property damage 4951 35.3% 30% 1485 3.0% 149 10.0% 1.0% 1.20 1782 33.4%

Assistance 745 5.3% 25% 186 3.5% 26 14.0% 1.0% 1.73 323 6.0%

Motor insurance 5963 42.6% 12% 716 2.5% 149 20.8% 1.0% 2.64 1892 35.4%

Sum 14012 100.0% 3911 454 11.6% 1.37 5344 100.0%

Surplus 1000 4.5% 45 4.5% 0.53 529.41

TOTAL 14012 4911 499 1.20 5873



company seems appropriate, in terms of both risks and margins.

All the same, the development of the notion of value creation in a risky environment and economic capital models are turning this view on its head (much as Basel II has just done in the banking industry). Indeed, if capital has a cost and capital (RAC) is allocated to activities in accordance with their risks (for example, 80% in liability, 12% in motor insurance—figures taken from the internal model of a European insurer), the assessment of this strategy is altogether different.

As it happens, this more economic approach makes it possible to verify not only that third-party liability accounts for a greater share of the business (nearly one-third of risk-adjusted capital—1,165/3,911) than that suggested by the more traditional analysis but also that the high net margin (6.5%) is insufficient to offset the large amount of capital required: this line of business destroys value. Third-party liability is valued at 94% of its allocated capital. By contrast, motor insurance, despite its low margins, creates more value than any other line of business. As it uses little capital, it is valued at 2.64 times its allocated capital. This sort of information is likely to lead to changes in strategy along several axes, none of them mutually exclusive: reallocation of capital to lines of business, transfer or expansion of the third-party liability line to attain critical mass, modification of the reinsurance or third-party liability hedging policy in an attempt to reduce the risk and thus the capital allocated to it).

How then can the traditional approach, still the standard for many companies, lead to

a conclusion so different from that drawn from the economic model? As we saw in section I, the difference lies in the notion that capital is a resource that has a cost. For public companies, this notion is not new and their shareholders go over it regularly. For other companies (especially mutual undertakings), in light of the analysis in section II, we see that even if they do not always have problems with capital it is in their interest to put in place an economic capital model. This model can be used as a decision tool to gauge the impact on member satisfaction (through the previously defined price/service ratio) of operational decisions (setting of premiums, launch of a new product or line of business, evaluation of the impact of the offer of an option, new claim management processes, pooling of resources with a mutual undertaking, and so on).

The change in bank acquisition policy in favour of retail banks after the entry into force of Basel II is also worth noting (concomitantly with the refinement of the capital allocation coefficients in favour of this activity). With the weightings of Solvency II, we expect similar changes of strategy in the insurance industry. In fact, some leading European insurers have already modified their strategies in view of their internal economic model (AXA and Allianz, for example).

IV. The Contributions of an Economic Capital Model in a Solvency II EnvironmentThe objective of this section is to analyse in greater detail the foundations of economic capital models, to assess their contributions to company management, and to look at the ways Solvency II fits into this environment




and should accelerate the development of these models.

Since the late 1990s, some insurers have been using economic capital models that they have been perfecting over the years. This decision-making tool enables them to refine in-house their strategic choices and the tracking of these choices and to disclose to the markets information on their performance. In its 2000 annual report, AGF said of its economic capital model: “this approach does not supplant the information transmitted by the financial statements; instead, it sheds relevant economic light on the quality and durability of the results and facilitates the search for and implementation of practical means of creating shareholder value”.

Economic capital can be viewed as the amount of capital a company believes it needs to cover its risks. So it may be viewed as a safety net intended to absorb any extreme losses beyond technical provisions, that is, those resulting from any great failure to meet expectations for average expected cash flow. So, unlike regulatory capital, imposed by the regulator, it is intrinsic to each company.

In particular, an economic capital model addresses two issues:• Capital is not a free resource and it is necessary to include the cost of capital in the measure of the value created by the company.• Return on equity (ROE), the classic measure of profitability, indicates only overall performance and does not make it possible to identify profitability or risk per business unit.

So the economic capital model is built on an allocation of the capital available to the business or reporting units in keeping with their contribution to the total risk of the company (RAC) and on determination of the standardised profit or loss of each unit. Doing the latter involves reposting the accounting profit or loss in such a way as to reflect more accurately the economic performance of the unit, independently of the accounting framework (for example, reposting of provisions for profit sharing), of policy for net profit management, and of the volatility of financial markets. The capital allocated is determined by the insurer, which considers that these capital expenditures must be sufficient to absorb these risks.

The current regulatory solvency margin (Solvency I) was swiftly discarded, as it creates a standard minimum capital requirement proportional to the volume of business (premiums, claims, or provisions) without explicitly making allowances for the notion of risk. Economic capital models, by contrast, include the correlation of risks (technical, financial, operational), hedges (reinsurance, derivatives, securitisation), and the concentration and diversification of risks. In this way, these models enable the company to ward off certain risks (extreme risks, in particular), measure the effects of these risks, and suggest optimal management of them. By calculating the ratio of this economic profit to economic capital, it is thus possible to determine the return on risk adjusted capital per activity j (RoRACj).

So economic capital makes it possible to strengthen the analysis of the profitability of a company by taking into account both




overall company risks and those of each business unit, in keeping with the principles and objectives of value creation. The advantage of the economic capital model is as much in its operational dimension and thus its capacity to aid in company management as in its measure of risks strictly speaking.

Economic capital also meets an objective for the internal management of allocated capital and of risks, in keeping with the often contradictory demands of shareholders and rating agencies: optimisation of capital allocation and of the profitability of the invested capital supplied by shareholders and high capital requirements and appropriate management (diversification of risks, growth prospects, and so on) to obtain a satisfactory rating from rating agencies and bond investors.

Finally, for chief executives, financiers, and managers, the economic capital model provides a common language and a single measure proportional to risk. Its role is to guide the strategic choices made by each unit, and to serve as the foundation of the outside financial communication of some insurance companies, and as such it is a dynamic tool that makes it possible to gauge the efficiency of strategy.

V. ConclusionA profound shift in the management of insurance companies has been underway for the last decade. The major catalysts are the growing complexity of risk, the sophistication of the means of measuring it, the increasing internationalisation and competition in the industry, the

awareness that capital comes with a cost, and accounting and prudential regulatory changes.

In the late 1990s, this new environment encouraged some leading insurers to put in place economic capital models to optimise the management of their businesses. Value creation naturally established itself as a performance measurement standard; it was thus possible to integrate all the issues a company had to deal with.

For the insurers on the crest of the wave, as it were, these economic capital models have become veritable tools for strategic decisions: investment policy, underwriting, launch of new products, reserves, asset/liability management, reinsurance, allocation of capital to individual lines of business, and risk management (definition of accepted limits, concentration, diversification). They are also the foundation of the communication of certain corporations to the financial markets, rating agencies, and the prudential regulator.

In this context, then, the primary objective of our study is to show that Solvency II and its corollary (compelling insurance companies to read and manage their risks better) should, by design, lead to widespread changes in managerial practices revolving around value creation.

Starting with an analysis of the foundations of value creation (in both the academic and business worlds), we have attempted to underscore in this chapter the relevance of the notion of value creation in the management of a company as well as the breadth of the domain in which this notion is, so to speak, legal tender: manufacturing firms, insurers and mutual undertakings (in




spite of their objectives and values focused on the mutual member).

The second objective of this study is to show that the Solvency II constraint, which involves significant costs for data collection and simulation, can be transformed into an opportunity to rethink the culture and fine tune the management of each insurance company (the management of risk, in particular). Indeed, much as with what the banking industry has recently undergone, the measure of regulatory capital as defined by Solvency II has become so sophisticated that it now resembles the measure used in economic capital models: the tools and the underlying measurement concepts are gradually converging. As we will see in chapter II, regulatory capital and economic capital are naturally not meant to be equal amounts, as they do not pursue the same objectives: regulatory capital has to do with ensuring solvency, while economic capital has to do with optimising internal management to achieve satisfactory profitability. In any case, the objective of the internal models favoured by the regulator is to provide information necessary to the determination of Solvency II required capital.

Not all insurance companies have the means to put in place sophisticated internal models, but in the following chapters we will show that with the data and the simulations required by Solvency II it is possible to convert these investments for the purpose of improved management: they should serve as foundations to improve existing management tools in insurance companies (reserves, premiums, asset/liability management).

So Solvency II is likely to provide a boost to a trend that was already taking shape before this reform to the rules for the solvency and capital of insurance companies: a profound shift in managerial practices characterised by the inclusion of risks and the cost of resources (capital) in an attempt to measure the performance of and the value generated by the company.


2. Solvency II: From Constraint to an Opportunity

for Sophisticated Internal Management

35Une publication de l'EDHEC Financial Analysis and Accounting Research Centre



In chapter I we show that value creation is capable of encompassing the entirety of the issues dealt with by insurers, and that this is so whatever their legal form (mutual undertaking, incorporated company, provident society, and so on) or objectives (member satisfaction on the quality/price criterion or shareholder satisfaction on the risk/return criterion).

In this chapter, we will show that as a result of its contents Solvency I is altogether unable to provide the means of elaborating an economic capital model; Solvency II, by contrast, may further hasten the managerial changes that have been underway in the insurance industry in the last decade: improved readings of risks (identification, measurement, and management), of the cost of resources (capital), and thus of the value created for the shareholder or mutual member. In addition, the investment in data collection and the simulations required by the European regulator have turned out to be particularly costly.

This chapter uses these two observations as a starting point; its objective is to show that it is possible to turn the constraints brought about by Solvency II into opportunities to improve existing tools for internal management (reserves, premiums, asset/liability management, reinsurance, embedded value). After all, however sophisticated the insurance company is, it should be capable of calculating the risk-adjusted capital (RAC), a function of underwriting, financial market, counterparty, and operational risks, for each business or reporting unit. These calculations may be products of existing internal or economic capital models, possibly adjusted so as to be

recognised by the regulator as acceptable substitutes for the Solvency II standard formula, or they may be products of the standard formula itself.

Today, then, economic solvency margins defining RAC are the product only of subjective calibrations, specific to the culture and experience of each insurance company and to the sophistication of its models. This subjectivity, all the same, is relative, because the publication of RAC leads to a certain homogeneity per business unit from one corporation to another. With the entry into force of Solvency II, the calculation of RAC could, as a result of new solvency requirements, become more standardised.

As the data and simulations compulsorily provided to the prudential regulator to determine the solvency margin can be used to put in place economic capital models, the use of these models should become more common, in versions of varying degrees of sophistication, depending on the culture and the means of the companies using them. This greater use of these models is, as it happens, one of the objectives of the regulator.

With this chapter, the keystone of the study, it will be possible to show that—as a result of improved management of risk, of the amount of capital allocated to each line of business and of the capital available and required—this decision tool is likely to improve the management of companies and to increase the creation of shareholder or mutual member value.

2. Solvency II: From a Constraint to an Opportunity for Sophisticated Internal Management




17 - For a company with VaR of €1bn at a one-year horizon and at a 99.5% confidence interval, the chances of suffering a loss greater than €1bn over a year are, assuming trading is normal, 0.5%; that is, such a fall in value will occur once every two hundred years.

I. From the Measure of Economic Capital Models to Changes to Solvency IIAs we mention in the introduction, not all insurance companies have the means to put in place sophisticated internal models. All the same, the new prudential framework should act as an accelerator and provide an opportunity to improve internal management. In particular, Solvency II is leading to a sophistication of solvency rules, the underlying bases of which are gradually converging toward those used in economic capital models. On the other hand, the calculation of the capital required by the regulator requires a substantial investment in data collection and simulations. In view of these changes, it seems opportune for each insurance company to use this investment to improve its existing internal management tools (reserves, premiums, asset/liability management, embedded value) and move toward economic capital models of degrees of complexity in keeping with the company’s means.

The preceding chapter examined the foundations of the economic capital model, an examination that enables us to underscore the existence of the current break from the traditional means of performance measurement. The objective of this section is to focus on the measure used in economic capital models in an attempt to examine the ways in which the appearance of Solvency II dovetails with the development of these models. Economic capital addresses the objective of strategic steering of business, steering that relies on the management of risks and the allocation of capital to lines of business in keeping with their economic performance. The ultimate objective is to measure the value

created either directly for the shareholder or indirectly for the mutual, through the member’s increased satisfaction with the price/service ratio.

So it is necessary to determine the economic profitability of each line of business (return on risk-adjusted capital—RoRAC). The types of risks considered and the measure of the capital employed must be defined so as to quantify the minimum amount of capital corresponding to the risk of ruin that the insurer deems acceptable. In other words, the probability distribution of economic capital at a given time horizon should be modelled and the economic capital for the degree of risk deemed acceptable by the company should be defined. The measures usually used to evaluate these risks are Value at Risk (VaR), stress tests, or perhaps a combination of the two. These measures, which are the heart of economic capital models, are also, as we will see in the coming chapters, the measures that have been chosen for Solvency II. We will thus proceed with a brief analysis that will, among other things, underscore the limitations of these measures.

VaR is a probability measure of the risk of the loss that will be borne by a company as a result of future changes in risk factors. It is equal to the maximum potential loss suffered by a company given a particular horizon (often one year) and a confidence interval α (99.97%, for example, is associated with an AA rating).17 It is expressed VaRα (X) = − inf{x: FX (x) ≥α}. The distribution of losses can be estimated with a historic method (observation of past behaviour), a parametric method (probability distribution of the risk factors), or the Monte Carlo method (several thousand random draws in an attempt to ascertain the likelihood of the occurrence of each of the states of nature).



VaR may be a simple concept, easy to compute and interpret, but it is often criticised, as it is not sub-additive and it does not take into account the severity of the loss. Because it is not sub-additive, the overall VaR of a company is not necessarily less than sum of the figures for VaR or each of its components (VaR(X1, …, Xn) > VaR(X1) +…+ VaR(Xn)); now, economic capital is built precisely on a sum of figures for VaR. As a result, highly debatable correlation matrices must be put in place; otherwise, no allowances would be made for diversification. In addition, the correlation of the risk factors is often variable over time and, as we are seeing now, it generally increases in periods of turmoil. Yet most economic capital models assume constant correlation over time. Finally, VaR reduces the view of the risk profile of the company to a single point on the loss distribution and fails to indicate the severity of the fall in value (fatness of the tail distribution).

So a measure of risk derived from VaR, but sub-additive, is attracting growing attention. This measure is tail VaR (also known as expected shortfall, conditional tail expectation, or conditional VaR). Tail VaR18 of confidence interval α is the conditional expectation of the random variable of an amount less than VaR of confidence interval α. Its advantage is that it is more sensitive to the distribution tails and that it is a coherent measure of risk—coherence as defined by Artzner et al. (1999). One of the drawbacks of VaR and of tail VaR, highlighted by the banking and insurance regulators, is that in general these measures rely on the assumption of normal events. Yet rare events are of greater magnitude than the law of normality would have it (fat distribution tails).

The advantage of stress testing19 is that, by offering the opportunity to choose the magnitude of the event, whatever the odds of its occurring, it makes it possible to get around resorting to laws of fat tail distributions. Insurance companies (like Solvency II, as it happens) thus combine stress testing and VaR.

Of course, in a more general manner, it is worth recalling the limitations intrinsic to any method of risk evaluation, limitations that are the result of the quality of data, of the occurrence of rare events that are not present in the simulations, of tested asset and liability valuation problems, and of model risks.

The regulatory reaction to the industry changes described above was tardier. Solvency I should remain in force until at least 2012 and it is much too simplistic (and unrealistic) to serve as a point of reference for the management of insurance companies.

Indeed, the foundations of the current solvency system date to the 1970s. They were updated in 2002, though without really changing the substance, to increase the power of the Commission de contrôle des assurances. Yet in view of the small number of bankruptcies its effectiveness should be underscored. In France, for example, the failure rate of insurance companies is less than 0.25% (less than one company a year), much lower than the failure rate, an estimated 2%, for the rest of the economy.

Solvency I has several drawbacks that make it an inappropriate managerial benchmark for insurance companies (see appendix 2: Solvency I: An Efficient


18 - TailVaRα (X) = TCEα (X) = E[X/X≥VaRα (X)]19 - Stress testing involves analysing the changes in the valuation (often net asset value) resulting from changes in risk factors that reflect extreme events (crisis scenarios).



System with Numerous Drawbacks). It does not take into account: i) the risks of poor operational (costs) and/or financial (assets) management, a major cause of bankruptcy according to the European Commission, ii) investment risks (stock market volatility, exchange rates, interest rates, risks linked to derivatives, to liquidity, to matching, or to credit),20 iii) the risks in the calculation of technical provisions,21 iv) the characteristics of reinsurance programmes,22 and v) risk correlation, dispersion and diversification.

There are several paradoxes that can also be highlighted. As required capital is a percentage of technical provisions in life insurance, the less well provisioned a company is, the less capital the regulator requires. There is also the asymmetric treatment of bond capital gains and losses23 and the total decorrelation of the solvency margin and business prospects (the calculation is done a posteriori, using past financial statements). So it is clear that the current body of rules for insurance capital (Solvency I) cannot serve as a benchmark for the elaboration of an insurance company decision tool.

In the last several years, the complexity of risks has led to a determination to change prudential rules so that they will offer an improved view of every company, in particular with respects to the risks taken on. The finalities may differ, but IFRS, Solvency II, Basel II, new rules for financial conglomerates, and market-consistent embedded value (MCEV) were implemented or are being implemented with the objective of an improved view in mind. With Solvency II, the European Union intends “better to match solvency requirements to the risks insurance companies face

and encourage them to improve their measurement and monitoring of risks”. So it is not the aim of the new solvency system to lay down new rules for provisions or for capital but to encourage companies to use their existing models (models for asset allocation models, for asset/liability management, for embedded value, or for reserves) to develop more sophisticated models to analyse, manage, and control risks. To meet these objectives, Solvency II requires a view of risk broader than that of Solvency I and closer and more Draconian evaluation (distribution of risks, correlation, diversification, extreme risks, and so on). So it also seeks to lead to the determination of a minimum capital requirement and of economic capital that depends on the ability of the company to control its risks (see appendix 3: Solvency II: An Extension of the Notion of Risks).

As with IFRS, the philosophy of Solvency II is to create principles rather than to lay down strict rules; the aim is for each company to put in place or adapt its own model of risk evaluation, a model that should then of course be validated by the regulator. So it seems that with this particular philosophy prudential constraints may have a great impact on the managerial decisions in insurance companies. They are likely to become the standard for economic capital models, and ultimately, for companies that do not yet boast economic capital models, they will serve as an incentive to expand current decision tools.

A new issue is raised then: Are economic capital and regulatory capital compatible? To what extent can regulatory capital serve as a point of reference for economic capital?


20 - By contrast, there is a list of assets and authorised proportions, but it is so crude that it is possible, in theory, for unlisted corporate Colombian debt to back 100% of a company’s insurance commitments. But if an asset is not on the list it cannot be used in calculating the solvency margin. 21 - Not explicitly included in the calculation of the solvency margin are hidden options, floors, and guaranteed rates, major causes of earlier bankruptcies. 22 - Today, under Solvency I, the calculation of the solvency margin does not take into account the specific features of a reinsurance programme. In life insurance, for example, the solvency margin is the sum of two values: i) 4%* gross mathematical reserves GMR * R), where R=(GMR - reinsurance transfers)/GMR cannot be less than 85%. So Solvency I recognises at most 15% of reinsurance transfers with respect to GMR; ii) (0.3% * risk capital charged to the life insurer gross of reinsurance RCG * K), where K=(RCG - reinsurance transfers)/RCG and cannot be less than 50%. So Solvency I recognises at most 50% of reinsurance transfers with respect to RCG. These R and K ratios are those of the latest financial year. In non-life insurance, the solvency margin (we simplify) corresponds to the higher of the two values below:i) (16% * gross premiums * C), where C=(gross claims GC - claims transferred to reinsurers)/GC and cannot be less than 50%. ii) (23% * GC * C), where C=(gross claims GC - claims transferred to reinsurers)/GC and cannot be less than 50%.GC is the average over the last three financial years. The standard reduction of 15% in life insurance and of 50% in property and casualty insurance in the event of reinsurance seems devoid of any grounding in economics. It is often labelled standard because, whatever the type of reinsurance (simple proportional reinsurance with a BB rated reinsurer or sophisticated non-proportional reinsurance, indexed on indices and/or excluding extreme risks, with an AAA rated reinsurer), the 15% and 50% coefficients are applied uniformly.



II. Economic Capital versus Regulatory CapitalThe main objective of Solvency II, like that of Solvency I, is to protect the interests of the insured and those of the beneficiaries of insurance contracts. Solvency I takes a standard approach, founded on historic administrative and accounting data, to determining regulatory capital; there are variations that depend on the country in which the company or subsidiary is located. Solvency II, by contrast, takes a forward-looking and economic approach that is uniform throughout Europe. With the support of CEIOPS (Committee of European Insurance and Occupation Pensions Supervisors), the European Commission created a new framework of solvency rules (Solvency II), published in July 2007, a framework built on economic principles of internal evaluation, management, and control of risks.

The aim of the Directive is thus to encourage insurance companies to measure, manage, and control their risks through the implementation of a cost that results in a mobilisation of capital. This cost will inevitably compel companies to optimise their allocation of resources and their management of risk, optimisation that is a major point of convergence with the economic capital model, a strategic decision tool. In spite of the limitations of this convergence (section II.1), we will show that it is possible to devise an economic capital model for the Solvency II environment, as long as estimates are made at market value and technical reserves are defined with a best estimate and a market value margin (section II.2).

II.1. The conceptual approach of Solvency II favours convergence with economic capital.The aim of the reform of prudential rules led by the supervisor and the European Commission is to encourage insurance companies to measure and control their risks better. To do so, it seems natural for the calculation of regulatory capital to be perceived not as a constraint for insurers but as an incentive for them to develop internal management tools. So the calculation should be similar to those used in economic capital models.

But in spite of converging conceptions and models of risk, regulatory capital and economic capital are not meant to be equal, as they pursue different objectives. The objective of regulatory capital is to keep companies solvent (for their clients and to prevent systemic risk) and it may have policy designs (depending on the calibration of the formulas, some risks or lines of business may be preferred to others). The aim of economic capital is above all to optimise the return on capital (directly by creating shareholding value or indirectly by meeting mutual member demands for a satisfactory price/service ratio). In this respect, the economic capital model can easily satisfy regulatory requirements, but above all it is a performance-based decision tool for companies. So, even though a convergence of the two measures is already underway in the banking industry and is desirable in the insurance industry, it seems unlikely, given the differing ends of regulatory and economic capital, that the amounts will ever be strictly equal.

In practice, the companies that have internal models (or that wish to have one) can convert much of their data and


23 - Capital gains are added to available capital, while capital losses are not deducted in the calculation of the solvency margin. So, when rates are falling, solvency margins are overestimated and include a latent wealth very susceptible to a rise in rates. In addition, this wealth creation is not offset as it should be, with a corresponding revaluation of the liabilities.



their tests for regulatory requirements. Conversely, the companies that do not have internal models will be able to use the data submitted to the regulator and drawn from any existing internal decision tools (risk analysis model, reserves, premiums, asset/liability management, and so on) to create a dashboard or decision model inspired by the economic capital models in use in the leading insurance companies. These models will naturally be of varying degrees of sophistication, depending on the means available for the construction. As we note in the introduction, all insurance companies, whatever their size, legal form, or objectives (creation of shareholder or mutual member value), are affected by this prudential reform.

II.2 Pricing of assets and liabilities other than technical provisions of the economic capital models in keeping with the tenets of Solvency IIIn spite of the incomplete convergence of economic and regulatory capital that we have just mentioned, it is nonetheless preferable for economic capital models or other existing internal decision tools to be elaborated or modified in keeping with the tenets of Solvency II, in particular with respect to the implementation of an economic balance sheet. Naturally, this presupposes that the rules Solvency II lays out to draw up this statement are entirely relevant and compatible with the principles of management of an insurance company. Such seems to be the case. Otherwise, Solvency II would have been nothing but an administrative and regulatory constraint.

The determination of economic capital and regulatory capital relies on an economic valuation, in keeping with market value, of the assets and liabilities. One of the

regulator’s proposals is to value the elements on the balance sheet (other than technical provisions) at fair value as defined by IFRS; that is, at the amount for which they could be exchanged between knowledgeable willing parties in an arm’s length transaction;24 three approaches (from mark to market to mark to model), depending on the information available for completing this evaluation, can be taken. For Solvency II, as a result of their near illiquidity, the economic value of intangible assets is considered nil.

To test the quantitative aspects and the feasibility of the new solvency rules, the European Commission asked CEIOPS to perform quantitative impact studies (QIS). The latest study (QIS4) was done between April and July 2008; its aim was to test the calibration of the formulas intended to determine the MCR and SCR,25 the elements eligible for capital, and the “group” effects. With the data and simulations done by insurers26 in response to QIS4, CEIOPS (2008) was able to compare the balance-sheet structure according to Solvency I and the current Solvency II proposals as formulated in QIS4.


24 - Proposal for a Directive of the European Parliament and of the Council for the taking-up and pursuit of the business of the business of insurance and reinsurance. Solvency II. Art. 73. 10/07/2007. In its appendices TS.III.A. and TS.III.B., QIS4 provides the instructions necessary to determine if IFRS is a satisfactory indicator of economic value in the context of Solvency II. 25 - MCR: Minimum capital requirement and SCR: solvency capital requirement.26 - CEIOPS’s analysis of the data supplied by insurers during QIS4 draws on the participation of 1,412 insurers (“solo” entities) from thirty countries in the European Economic Area (EEA), approximately a third of European insurance undertakings. The responses represent 75% of total life business (in terms of technical provisions), 69% of non-life (in terms of premiums), and 50% of health (in terms of technical provisions). It is worth pointing out that slightly more than a third of the participants are mutual undertakings, that 667 respondents are considered small (less than €100m gross non-life premiums written or than €1bn gross life technical provisions) and 220 large (more than €1bn gross non-life premiums written or than €10bn gross life technical provisions).



In addition to the interesting information offered by this figure, completeness requires that it be recalled that it was an optional impact study, that it had no effect on the participants, and that it was sometimes carried out by an intermediary (brokers, consultants). As a result, the quality of the information of some insurers could be wanting (for example, some participants used the accounting balance sheet as a substitute for market value) and could thus lead to biased results. In addition, the insufficient precision of the treatment of certain data (deferred taxes, reinsurance receivables, intra-group transfers, and so on) provided by CEIOPS often left things open to interpretation, so there again there may be some biases. All the same, these data provide an interesting idea of the conversion of these balance sheets to market value.

II.3. Best estimate and market value margin valuation of technical provisionsThe approach taken by Solvency II to determining the economic value of technical provisions is that of the current exit value. It is the amount a company would have to pay to another entity if it transferred all its contractual obligations, in normal conditions of competition, to an informed and willing party. It is the sum of two components: the best estimate and the margin of risk (market value margin). Each must be the subject of a separate valuation, unless the insurance and reinsurance commitments are hedgeable, that is, if future cash flows associated with these commitments can be replicated with financial instruments whose market value is observable directly.27

The best estimate “is equal to the probability-weighted average of future cash-flows, taking account of the time value of money, using the relevant risk-free interest rate term structure”. It is calculated gross,


27 - If a component of a contract such as a guarantee or an option is entirely separable and hedgeable, then it is considered a hedgeable component.

Comparison of a QIS4 and Solvency I balance sheet

Source: CEIOPS 2008, p40



without deduction of amounts recoverable from reinsurance and securitisation and must include all flows required to settle obligations over their lifetime on the hypothesis of their liquidation (future fees, inflation, guarantees, options, the insured party’s behaviour, management decisions), discounted at the risk-free interest rate corresponding to each maturity. Reinsurance and securitisation are taken into account in the balance sheet assets adjusted for counterparty risk and later in the calculation of the capital requirement of the company. The calculation of the best estimate can be done with deterministic or stochastic methods. An example of a QIS4 best estimate in life insurance can be found in appendix 8 (Simplified Best Estimate Example Drawn from QIS4).

The risk margin plays the role of adjustment variable to take into account the potential gap between the average and reality to ensure that the insurer will be able to meet its obligations. It is calculated by determining the cost of providing an amount of eligible own funds equal to the solvency capital requirements (cost of capital method). The risk margin is determined for each line of business, net of reinsurance and according to the following method: i) calculation of the annual capital required per line of business (except for market risks already included in the best estimate), ii) calculation of the cost of providing capital by multiplying the annual required by capital by a 6% cost of capital, and iii) discounting of cash flows at the risk-free rate.

With these elements, it is thus possible to define a balance sheet in the Solvency II format:• On the asset side are investments and reinsurance receivables

• On the liability side are own funds used to cover the solvency margins (SCR and MCR), technical provisions calculated with the risk margin and the best estimate, and other debts.

Solvency II balance sheet

ASSET LIABILITIES

Investmentsand other assets

Other debts

Surpluses

SCR

MCR

Reinsurancereceivables

Risk margin(MVM)

Best estimate

Own funds

Technicalprovisions

Again, it is interesting to compare the QIS4 and Solvency I amounts for life and non-life technical provisions.

In the figures below, CEIOPS compares the net technical provisions calculated in keeping with QIS4 and those calculated in keeping with Solvency I for each European country that participated in QIS4 (each bar is a country, but CEIOPS chose to keep contributions anonymous). So, for the first country represented in the figure on the left, in weighted average, the net QIS4 provisions are half those of Solvency I (♦ weighted average = 50%). For all of this country’s contributions to QIS4, this ratio ranges from 50% to 95%, and 50% of the life insurance companies in this country have a ratio between 58% and 82% (25th and 75th percentile). If this figure dealing with life business is looked at Europe-wide, it is clear that, with a few exceptions, this ratio is less than 100%. Much as in France, as we will see in the ACAM figure below, this ratio is very near 100%.




Ratio of net QIS4 life (left) and non-life (right) technical provisions (including the risk margin) to those for Solvency I for each European country

Source: CEIOPS 2008, p118 and 123

The Autorité de Contrôle des Assurances et des Mutuelles (ACAM) did an analysis of French insurers similar to similar to that done by CEIOPS (ACAM 2008).

Ratio of net life QIS4 technical provisions to Solvency I technical provisions for the French insurers that participated in QIS4

0

60

80

100

120

0.9%

101.0% 0.9%

95.8%

4.7%78.3%

3.0%

104.2% 1.0%

99.7%

BE/TP (S1) Coc / TP (S1)

With profit Without profit TotalUnit linked Reinsurance

Source: ACAM, La Conférence du Contrôle, 6 October 2008

Here again, these figures may by biased by the somewhat ill-assorted data and the lack of instructions from the supervisor on certain calculations, thus giving insurers plenty of room for interpretation. ACAM points out in particular a great disparity in the calculation of the risk margin and of the best estimate (given the large number of methods used and the technical specifications that provide few details for


Ratio of net non-life QIS4 technical provisions to Solvency I technical provisions for the French insurers that participated in QIS4

Source: ACAM, La Conférence du Contrôle, 6 October 2008

0

60

80

20

40

100

6%

81%

2%

82%

5%93%

4%

74%

11%

74%

3%

33%

3% 4% 4%

8%11%

10%

79% 82% 85%

71% 73%

51%

BE/TP (S1) Coc / TP (S1) Average 82.7%

Motor, third part

y liability

Motor, other c

lasses MAT

Fire an

d other dam

age

Third-party li

ability

Credit a

nd surety

ship

Legal e

xpenses

Assistan

ce

Miscellan

eous

NP reins p

roperty

NP reins ca

sualty

NP reins M

AT



contracts with discretionary profit sharing and for the treatment of future premiums). In addition to these biases, QIS4 technical provisions are slightly lower than those currently published, given the discounting of cash flows and the nature of the best estimate (shift of implicit prudence toward own funds).

III. Method of Elaborating an Economic Capital Model in a Solvency II EnvironmentThis section is the keystone of our study. Indeed, as we note above, the changes in the rules from Solvency I to Solvency II have led to the implementation of a prudential framework that is converging with that used in economic capital models. This is likely to hasten the trend that was taking shape in managerial practices: improved assessment of risks (identification, measurement, and management), of the cost of resources (capital), and, finally, of value creation for shareholders or mutual members.

In addition, investments in data collection and simulations to be supplied to the supervisor in Solvency II are very costly (see appendix 5: Data Collection and Simulations for QIS4: Major Investments). It would be advisable to capitalise on this investment made for regulatory reasons alone to serve ambitions more intrinsic to the company: to perfect or put in place a management decision tool, in an attempt to improve the management of the company and have it create more value. The leading European insurers, pioneers in this domain, show that their economic capital models have many roles (orientation of global strategy choices as well as those for each line of business,

for asset allocation, for management of capital, for underwriting, for asset/liability management, and for hedging of risks).

The degree of sophistication of internal management tools (reserves, premiums, asset/liability management, reinsurance, embedded value, economic capital) naturally varies greatly depending on the culture of the undertaking, the means it has at hand, its size, its strategy, and so on. So we believe that the smallest common denominator for all the insurance industry will be the requirements for disclosure of information made by the prudential regulator.

Let it be recalled that the objective of this study is to underscore the advantages of using the elements provided to the supervisor to develop an economic capital model that will improve the management of the company, in particular as a result of improvements in the management of risks and the allocation of capital. These data could be relatively “simple” information meant for the Solvency II standard formulas or the product of sophisticated internal models (validated and accepted by the regulator). So the approach that follows concerns all entities in the insurance industry, whatever their degree of sophistication, as ultimately they are all compelled to comply with the new Solvency II prudential standards.

The link between the economic capital model and Solvency II lies in the calculation of risk-adjusted capital. Until now, risk-adjusted capital has been calculated depending on the company’s own perception of its risks and on the sophistication of its model. Indeed, we have seen that Solvency I could in no




way serve as a benchmark and that the standard formulas of Solvency II were hitherto not definitive. In practice, each company has its own weighting range, even if, ultimately, publications attest to certain homogeneity.

We have emphasised the determination of Solvency II to take an operational approach to risk exposure, that is, an approach in keeping with internal management or economic capital models so as to favour their development and give companies an incentive to improve management of their risks. In particular, Solvency II has defined two levels of required capital. The first, the minimum capital requirement (MCR), is the minimum beneath which supervisory intervention is systematic. The second is the solvency capital requirement (SCR), which is a capital target sufficiently high to absorb any unusual shock. The means of calculating the SCR could set standards for improving existing internal management tools or for putting in place an economic capital model of a greater or lesser degree of sophistication. The calculation of the SCR is done to reflect a VaR (with a confidence level of 99.5%) at a time horizon of one year; the six risk modules (themselves broken into sub-modules—see appendix 4: Modular Organisation, Identification and Calibration of Risks) are aggregated.

In short, the calculation of risk-adjusted capital in economic capital models could, under the solvency constraints, move toward more standardised approaches. If the calibration and the modelling of the risks chosen for the prudential framework are consistent (in particular with respect to the perception of the economic reality of insurers),

it is likely that the companies that have an economic capital model or a partial internal model (modelling of certain risks or lines of business) will need only to make a few adjustments for the regulator to approve these models as a substitute for the standard formula defined by Solvency II. The less highly advanced insurers can use the data and simulations supplied to the regulator, data and simulations possibly adjusted to better respond to the needs of the company, to elaborate an economic capital model.

The capital required by Solvency II is the sum of the capital required for operational risk, adjustments (future profit sharing, deferred taxes), and the basic solvency capital requirement (BSCR) derived from the aggregation of the five other risks using a correlation matrix. The risks considered by Solvency II are the following (for a more detailed analysis, see appendix 4):• operational risk “arising from inadequate or failed internal processes, or from personnel and systems, or from external events” (QIS4 2008)• life underwriting risk• non-life underwriting risk (risk having to do with the amount and time at which claims must be settled, with the volume of business, and with pricing rates)• health underwriting risk (health coverage and workers’ compensation)• market risk (stemming from the volatility of the market value of financial instruments• counterparty default risk (the risk of losses arising from the unexpected default or lowering of the credit rating of counterparties, of issuers of risk-mitigating contracts, or of receivables from intermediaries).




So, however sophisticated the insurer may be, it is possible to determine for each line of business j (or reporting unit j) an amount of risk-adjusted capital RACj, a function of the underwriting risks of line of business j, of market risk, of counterparty risk, and of the operational risks of line of business j. This function may be derived from internal models (partial or total), from regulatory-approved economic capital models for the calculation of the Solvency II solvency capital requirement, or from the standard formula defined by the regulator.

If it is derived from the standard formula, reallocations (sometimes non-linear) will be necessary, since the regulator aggregates

certain risk modules for the company as a whole. For example, market risk is calculated not for each line of business but for the entire company, whereas the input for the economic capital model (defined in chapter I, section III.2 and looked at again below) requires assessment of the risks for each line of business. We will come back to these technical points in the following chapters.

So this approach, illustrated in the table below, makes the prudential dimension a constraint in the economic capital model defined in the previous chapter (section III.2.):


Source: QIS4

SCR mkt SCR def SCR life SCR health SCR nl

SCR mkt 1

SCR def 0.25 1

SCR life 0.25 0.25 1

SCR health 0.25 0.25 0.25 1

SCR nl 0.25 0.5 0 0.25 1


RACj = F(SCRj) = F(SCRj underwriting line of business j, SCRj market, SCRj counterparty, SCRj operational)

ActivityPremiums

EURmPremiums

%

RAC in % of

premiums

RACEURm

Net margin

Net profit EURm

RoRAC gRAC

xV(RAC)EURm

V(RAC)%

1

2

…

j

…

m

Sum

Surplus

TOTAL



The creation of this dashboard is not the ultimate aim of this study. The aim is to show that with this decision tool that enables improved management of risks, of the allocation of capital to lines of business, and of available and required capital it is possible to improve strategic decision making in a company and boost value creation.

Given the sophistication of the coming rules for insurance capital, in the following chapters we construct an economic capital model under Solvency II constraints for a fictitious company. This procedure should enable the reader to perceive the advantages of putting in place an economic capital model and the relatively low complexity of elaborating it with data and simulations required (probably after 2012) by Solvency II. With this tool, we will be able in the last chapter of the study to analyse the role it plays in strategic decision making: improved consideration of risks (identification, measurement, and management), of the cost of resources (capital), and, finally, of the creation of shareholder or mutual member value.


3. Underwriting Risks and the Economic Capital Model under

the Solvency II Constraint




As we saw in chapter II, the development of internal models and, more broadly, of economic capital models, is likely to gain momentum with the implementation of Solvency II. This shift is grounded on reasons at once conceptual (convergence of the approaches to the economic capital model and regulatory capital) and operational (exploitation of the investments in data collection and simulation made at the behest of the regulator for company-specific risk management purposes). In the final chapter of this study we will highlight the contributions made by these models to the management of risk, of risk-adjusted capital, of available economic capital and required capital, and, more broadly, to the optimisation of shareholder or mutual member value.

To elaborate the economic capital model described in section III of the preceding chapter, and given the sophistication of prudential rules, we propose to do simulations for a fictitious company (section I) to analyse the measurement of risks and their associated capital needs. Underwriting risks in life insurance, property, and health are analysed in sections II to IV.

According to the calibration offered by Solvency II and the results analysed by the ACAM (2008), in France these underwriting risks account for 17% of required capital (before diversification effects, operational risks, and adjustments

for future profit sharing and deferred taxes) for life insurers and approximately 50% for property and casualty insurers and mixed insurers. Appendix 6 (Weighting of Risk Types in the Composition of the Solvency Capital Requirement in France and in Europe) shows that there are nonetheless great differences from one European country to another (CEIOPS 2008).

I. Features of the Model CompanyThe contribution of our study lies more in the demonstration of the potential of economic capital models to improve risk management and, more broadly, the governance of the company, than in the results of the simulation itself. All the same, for the needs of our demonstration, we have postulated the existence of a fictitious insurance company (which throughout our study we call the model company) and calculated the capital requirements for each risk type so as to create an economic capital model.

This fictitious company has five lines of business:• life (euro-denominated and unit-linked contracts)• motor own damage• property damage• third-party liability• health

Turnover is broken down as follows:

3. Underwriting Risks and the Economic Capital Model under the Solvency II Constraint

Lines of businessLife

unit linked

Lifeeuro

denominated

Motor own damage

Propertydamage


Health Total

Gross premiums in EUR million 250 1 000 1 000 1 000 250 200 3 700

% of total premiums 6,8% 27,0% 27,0% 27,0% 6,8% 5,4% 100,0%


Turnover of the model insurance company by line of business



The characteristics of the balance sheet are synthesised in the table below. The entirety of the data necessary for the components of the risks can be found in appendix 7.

II. Capital Required for Life Underwriting RiskFirst, it is important to note that Solvency II calculates life underwriting risk in an

aggregate fashion for all euro-denominated life insurance and unit-linked (UL) policies. All the same, as a life insurer’s exposure to risk depends greatly on the type of policies under consideration (risks borne by the insurer or not), we differentiate these two types of business (after the fashion of insurer practices in the context of internal models of the embedded value or economic capital type) in our elaboration of the economic capital model. So, as a


Characteristics of the model company


(EURm) Unit linkedEuro

denominatedMotor own

damagePropertydamage


Health Total

Stocks 838 959 105 330 318 5 2554

Bonds 685 4920 392 924 636 99 7657

Property 0 511 26 66 106 0 709

Reinsurance 2 6 3 10 35 1 56

Total assets 1525 6396 525 1330 1095 105 10976

Own funds 23 360 250 300 200 50 1183

Technical provisions 1500 6000 250 1000 875 50 9675

Debt 2 36 25 30 20 5 118

Total liabilities 1525 6396 525 1330 1095 105 10976

Premiums per activity (gross)

250 1000 1000 1000 250 200 3700

Assumptions


Unit linked

Euro denominated

Motor own damage

Propertydamage


Health Total

Asset components %

Stocks 55% 15% 20% 25% 30% 5% 23%

Bonds 45% 77% 75% 70% 60% 95% 70%

Property 0% 8% 5% 5% 10% 0% 6%

Total 100% 100% 100% 100% 100% 100% 100%

Reinsurance assets/technical provisions

0.1% 0.1% 1.0% 1.0% 4.0% 1.0% 0.6%

Technical provisions/premiums 600% 600% 25% 100% 350% 25% 261%

Own funds/technical provisions 1.5% 6% 12%

Own funds/premiums 9% 36% 25% 30% 80% 25% 32%

Debt/own funds 10% 10% 10% 10% 10% 10% 10%



result of this disaggregation, calculating the risk-adjusted capital will require making allowances for possible non-linear effects.

The life underwriting module is defined by the risks covered and by the risks involved in the management of the business. Solvency II thus spells out seven risk sub-modules for life underwriting (k), for which seven capital charges are calculated before (SCRk) and after (nSCRk) allowances are made for the risk-absorbing effects of future profit sharing. The risks considered are:• biometric risks (mortality, longevity, disability-morbidity-illness) for which we calculate required capital SCR mort, SCR long, SCR dis• lapse risks (SCR lapse)• expense risks (SCR exp)• revision risks having to do with non-life claims settled as annuities (SCR rev).

This sub-module does not benefit from the risk-absorbing effect of future profit sharing (SCR rev = nSCR rev)• catastrophe risks (SCR cat)

The calculation of the capital required for life risk (SCR Life) makes it possible to use the process below to define one of the components necessary for the calculation of risk-adjusted capital (RAC) for euro-denominated life business and in unit-linked policies.


Calculation of the components of life RAC

RAC euro denominated = F(SCR euro denominated) (RAC UL is calculated with the same approach)= F(SCR Life euro denominated, SCR market euro denominated, SCR counterparty euro denominated, SCR operational euro denominated)

ActivityPremiums

EURmPremiums

%

RAC in % of

premiums

RACEURm

Net margin

net profit EURm

RoRAC gRAC

xV(RAC)EURm

V(RAC)%

Life euro denominated

Life unit linked

Motor own damage

Property damage


Health

Sum

Surplus

TOTAL

SCR Life euro denominated = √∑r,c Corr SCR life rxc * SCRr*SCRcwhere Corr SCR life rxc are the cells of the correlation matrix of the seven sub-modules (SCRk) of life underwriting.




1 - For the totality of the risk modules, the regulator considers that a loss of value caused by a shock was reposted by a positive change in NAV.2 - For mixed insurance policies, that is, for those providing benefits in the event of death and in the event of survival, QIS4 offers two options: apply the mortality shock scenario while making allowances for the natural offsetting of the survival and death components or unbundle the policies into two separate components (survival and death) and apply the survival and death shocks on the corresponding component. 3 - Article 107, simplification of the standard formula: “Insurance and reinsurance undertakings may use a simplified calculation for a specific sub-module or risk module where the nature, scale and complexity of the risks they face justifies it and where it would be disproportionate to require all insurance reinsurance undertakings to apply the standardized calculation.”

The correlation matrix supplied by QIS4 (QIS4 2008) is:

The capital allocated for each of the seven sub-modules (SCRk) is equal to the change in net asset value (NAV)1 following an upwards and/or downwards shock. The two cases should be differentiated:• for the mortality, longevity, disability, and lapse sub-modules, the capital allocated to risk i (SCR risk i) is calculated from the sum of the changes in NAV of each of the policies n following a given shock:

SCR risk i = ∑n (ΔNAV | shock)

• by contrast, for expense, revision, and catastrophe risks, the calculation of SCR risk j is not done by policy, but directly on the insurer’s net asset values NAV:

SCR risk j =ΔNAV | shock

In the following sections (II.1 to II.7), we present the risk sub-modules for life underwriting. This presentation makes it possible to analyse the risks under consideration, the calibration of these risks with the standard formula and the possible effects of non-linearity in order to proceed with the retreatment necessary (chapter V) to determine risk-adjusted capital. As we have mentioned, for each branch these calculations could, in practice, be fine tuned by and/or tailored to each insurer so that exposure to risks in greater keeping with the characteristics of its portfolio can be determined (supervisor-approved internal model).

II.1. Capital required for mortality riskThe policies for which the amounts to pay out in the event of death are greater than those of technical provisions involve mortality risk.2 The capital charge for mortality risk is equal to the change in the net value of assets as a result of a permanent 10% increase in mortality rates for each age. This charge is calculated before (SCR mort) and after (nSCR mort) allowances are made for the risk-absorbing effect of future profit sharing.

When the risk capital is not subject to significant changes over the life of the policy and when the general simplification criteria are met (article 107, p. 107 of the European directive of July 2007)3, the simulation can be done with the following simplified formula (which we have taken):

SCR mort = (total capital at risk)* q *n* 0.10*1.1((n-1)/2)

where q is the expected average death rate over the next year weighted by the sum insured (specific to each company), n the modified duration of liability cash flows, and 1.1((n-1)/2) the projected mortality increase.

Corr SCR life SCR mort SCR long SCR dis SCR lapse SCR exp SCR rev SCR cat

SCR mort 1 -0,25 0,5 0 0,25 0 0

SCR long -0,25 1 0 0,25 0,25 0,25 0

SCR dis 0,5 0 1 0 0,5 0 0

SCR lapse 0 0,25 0 1 0,5 0 0

SCR exp 0,25 0,25 0,5 0,5 1 0,25 0

SCR rev 0 0,25 0 0 0,25 1 0

SCR cat 0 0 0 0 0 0 1



Simulation with the model companyAssumptionsContracts Unit

linkedEuro

denominated

Gross technical provisions (EURm) 1425 6000

Share reinsured 5% 1%

Share of life insurance contracts contingent on mortality risk

35% 5%

Capital at risk/technical provisions for death benefit contracts

0.10 4.00

Expected average death rate over the next year weighted by the sum insured q

0.3% 0.3%

Modified duration of liability cash flows n

7.64 7.64

Net asset value (NAV) before the shock (EURm)

47 360


ResultsContracts Unit linked Euro denominated

SCR mort (EURm) 0.15 3.74

nSCR mort (EURm) 0.15 0.00


II.2 Capital required for longevity risk Longevity risk is a feature of policies that offer no benefits in the event of death or policies for which a drop in mortality rates would lead to a risk of a rise in technical provisions.4 The capital charge for longevity risk is equal to the change in the value of net assets as a result of a permanent fall of 25% in the mortality rates for each age.

When the average age of the policyholder is sixty years and the general criteria for simplification are met, the simulation can be done with the following simplified formula (which we have taken):

SCR long = TP long * q *n* 0.25 * 1.1((n-1)/2)

where TP long is the technical provisions subject to longevity risk, q the expected average death rate weighted by the sum

insured (specific to each company), n the modified duration of liability cash flows, and 1.1((n-1)/2) the projected mortality increase.


linked Euro

denominated



Share of life insurance contracts contingent on longevity risk

5% 5%

Expected average death rate over the next year weighted by the sum insured q

0.3% 0.3%


7.64 7.64


47 360




nSCR mort (EURm)

0.53 0.00


II.3 Capital required for disability riskDisability risk is a feature of insurance policies for which the payment of benefits (lump sum or annuities) is contingent on some definition of disability or sickness. The capital charge for disability-morbidity-sickness risk (SCR dis) is equal to the change in the net value of assets following a 35% increase in the disability rate for the next year, together with a permanent 25% increase (over best estimate) in the disability rates for each age in the following years.

When there is no significant change in the capital at risk over the term of the policies and when the general criteria for simplification are met, the simulation can be done with the following simplified


4 - For mixed insurance policies, that is, for those providing benefits in the event of death and in the event of survival, QIS4 offers two options: apply the mortality shock scenario while making allowances for the natural offsetting of the survival and death components or unbundle the policies into two separate components (survival and death) and apply the survival and death shocks on the corresponding component.



formula (which we have taken):

SCR dis = (total disability sum at risk)* i *n* 0.35*1.1((n-1)/2)

where i is specific to each company and is the expected number of movements from health to sickness for the coming year weighted by the amount insured/annual payment, n the modified duration of liability cash flows, and 1.1((n-1)/2) the projected disability increase.


linked Euro

denominated



Share of life insurance contracts contingent on disability risk

0.1% 2.0%

Capital at risk/technical provisions for contracts contingent on disability risk

0.10 0.10

Expected average disability rate over the next year weighted by the sum insured i

0.3% 0.3%


7.6 7.6


47 360




nSCR mort (EURm) 0.00 0.00


II.4 Capital required for lapse riskLapse risk relates to the loss, or adverse change in the value of insurance liabilities, losses resulting from changes in the level or volatility of the rates of policy lapses, terminations, changes to paid-up status (cessation of premium payment) and surrenders. The capital required for lapse risk is calculated based on a net

surrender cost,5 that is, on the difference between the amount currently payable on surrender and the best estimate provision in the books reprocessed in the Solvency II format.

Three shocks are tested:• Reduction of 50% in the assumed rates of lapsation in all future years for policies where the surrender strain is expected to be negative. The associated required capital is noted Lapsedown.• Increase by 50% in the assumed rates of lapsation in all future years for policies where the surrender value is expected to be positive. The associated required capital is noted Lapseup. • Mass lapses equal to 30% of the sum of surrender strains of the policies for which the surrender strain is positive. The associated required capital is noted Lapsemass.

The capital required for lapse risk is the greatest of the amounts generated by these three shocks.

SCR lapse = max (lapsedown; lapseup; lapsemass)

If the simplification reflects the nature, scale, and complexity of the risk, if the company is small, or if in the simplified calculation the capital charge for lapse risk is less than 5% of the total SCR before adjustment for the loss-absorbing capacity of technical provisions, the simulation can be done with the following simplified formula (which we have taken):

Lapsedown = 0.5 * ldown * ndown * Sdown

Lapseup = 1.5 * lup * nup * Sup

where ldown, lup are the estimates of average lapsation rates for policies with


5 - The surrender cost is net of any amounts recoverable from policyholders or agents (for example, net of any surrender charge that may apply under the terms of the contract). As such, it may be positive or negative.



negative/positive surrender strain, ndown, nup the average period (in years), weighted by positive/negative surrender strain, and Sdown, Sup the sum of negative/positive surrender strains.

Simulation with the model company6 AssumptionsContracts Unit

linkedEuro

denominated



Average rate of lapsation for the policies with a negative surrender strain

0.5% 0.5%

Surrender strain/technical provisions for policies with negative surrender strain

-2.0% -2.0%

Average rate of lapsation for the policies with a positive surrender strain

3.5% 3.5%

Surrender strain/technical provisions for policies with positive surrender strain

10.0% 17.0%

Average period, weighted by surrender strains, over which the policy with a negative surrender strain runs off ndown

1.5 1.5

Average period, weighted by surrender strains, over which the policy with a positive surrender strain runs off nup

6 6


47 360



SCR lapse (EURm) 1.49 11.13

nSCR lapse (EURm) 1.49 0.00


II.5 Capital required for expense riskExpense risk arises from the changes in the expenses incurred in servicing insurance or reinsurance contracts. If the amount of an expense is already fixed at the valuation date, however, it is not included in the scenario. The capital charge for expense risk is equal to the change in the net value of assets as a result of a 10% increase

(over best estimate) in future expenses and of an expense inflation rate higher than expected by 1% a year.7 If the general simplification criteria are met:

SCR exp = (renewal expenses in the twelve months prior to valuation date)

* n(exp) *(0.1 + 0.005*n(exp))where n(exp) is the average period (in years), weighted by renewal expenses, over which risk runs off.


linkedEuro

denominated



Expense rate 0.2% 0.2%

Average period over which risk runs off, weighted by renewal expenses n(exp)

5 5


47 360



SCR exp (EURm) 1.27 5.57

nSCR exp (EURm) 1.27 0.00


II.6 Capital required for revision riskRevision risk is the risk of adverse variation of the amount of an annuity as a result of an unexpected revision of the process of the settlement of claims (for legal reasons, for example).8 This risk is applicable only to annuities that are genuinely reviewable and to those benefits that can be approximated by a life annuity arising from non-life claims. The capital charge for revision risk is equal to the change in the net value of assets as a result of an increase of 3% in the annual amount payable for annuities exposed


6 - If the scenario that produces the largest net amount is not the one that produces the largest gross amount, the gross amount that is taken is that which produces the largest net amount.7 - For policies with adjustable loadings (policies in which expense loadings or charges may be adjusted within the next twelve months), 75% of these additional expenses can be recovered by increasing the charges payable by policyholders.8 - Annuities whose amount is linked to earnings or another index such as prices or that vary in deterministic value on change of status (a standard annuity that becomes a two-way annuity, for example) should not be classified as genuinely reviewable for these attributes. Annuities subject to legal or other admissibility restrictions are excluded.



to revision risk. The impact should be assessed considering only the remaining run-off period. This sub-module does not benefit from the risk-absorbing effect of future profit sharing.

If the general simplification criteria are met:

SCR rev = 3% * net technical provisions for annuities exposed to revision risk


linkedEuro

denominated



Percentage of annuities elegible for revision risk

0% 0%


47 360



SCR rev (EURm) 0.00 0.00

nSCR rev (EURm) 0.00 0.00


II.7 Capital required for catastrophe riskCatastrophe risk in life insurance stems from extreme events (a pandemic, for instance) that as a result of their nature are not sufficiently well integrated in the capital charges of the other sub-modules of life underwriting risk. The capital charge for catastrophe risk is equal to the change in the net value of assets as a result of a combination of two simultaneous events: an absolute 1.5 per mille increase in the rate of policyholders dying over the following year (e.g., from 1.0 per mille to 2.5 per mille) and an absolute 1.5 per mille increase in the rate of policyholders experiencing morbidity over the following year.

If the general simplification criteria are met:

SCR Cat = = ∑i 0.0015*Capital at riski Capital at riski = SAi + ABi

* Annuity _factor - TPi

where i is each policy for which the payment of benefits (in the form of an annuity or in multiple payments) is contingent on mortality or disability; where for each policy i SAi is the insured sum, net of reinsurance, on death or disability when the benefits are payable as a lump sum (otherwise zero); ABi is the annual amount of benefit, net of reinsurance, payable on death or disability when benefits are not payable in lump sums (otherwise zero); Annuity _factor is the average annuity factor for the expected duration over which benefits may be payable in the event of a claim; and TPi is technical provisions net of reinsurance for each policy i.

Simulations with the model companyAssumptionsContracts Unit

linkedEuro

denominated


% of technical provisions for policies contingent on mortality risk whose benefits payable as a lump sum

95% 90%

Share reinsured of technical provisions for policies contingent on mortality risk

0% 0%

% technical provisions for policies whose benefits are payable on disability definition and as a lump sum

90% 90%

Share reinsured of technical provisions for policies whose benefits are payable on disability risk

0% 0%

Multiple of the amount insured when the benefit is paid as a lump sum as a function of TP

1.1 5

Multiple annualised amount when benefits are paid on death or disability as annuities (net of reins.)

1.1 5

Average annuity factor for the expected duration over which benefits may be payable in the event of a claim

20 20


47 360






SCR cat (EURm) 0.08 2.52

nSCR cat (EURm) 0.08 0.00


II.8. Total capital required for life underwriting riskIn the preceding sections (II.1 to II.7) we calculated the capital required for the seven life underwriting risk sub-modules as spelled out by Solvency II. As we have noted, these calculations could be fined tuned for and/or tailored to each insurer in order to calculate an exposure to risk in greater keeping with its portfolio (supervisor-approved internal model).

Given our intention to elaborate an economic capital model, we have distinguished between euro-denominated and unit-linked policies. We thus determine two capital requirements for life underwriting risk, one for euro-denominated business (SCR Life euro denominated) and another for unit-linked business (SCR Life UL). As we have mentioned, a life insurer’s exposure to risk is heavily dependent on the type of policy (euro-denominated or unit-linked), so our approach seems more consistent with insurance industry practices in

the context of internal models of the embedded value or economic capital type). As a basis for comparison, we have also decided to run a simulation with our model company using the Solvency II approach (aggregated presentation of euro-denominated and unit-linked policies) to highlight possible non-linear effects (see simulation below).

The amounts of capital required for life underwriting risk (SCR Life euro denominated and SCR Life UL) make it possible, with the process described in the introduction to this section II, to determine one of the components necessary to the calculation of risk-adjusted capital for euro-denominated and unit-linked policies. The method for euro-denominated business is shown below (the method for unit-linked business is identical).

RAC euro denominated = F(SCR euro denominated) = F(SCR Life euro denominated, SCR market euro denominated, SCR counterparty euro denominated, SCR operational euro denominated)

where SCR Life euro denominated = √∑r,c Corr SCR Liferxc * SCRr*SCRc with the following correlation matrix:


Corr SCR life Life mort Life long Life dis Life lapse Life exp Life rev Life cat

Life mort 1 -0.25 0.5 0 0.25 0 0

Life long -0.25 1 0 0.25 0.25 0.25 0

Life dis 0.5 0 1 0 0.5 0 0

Life lapse 0 0.25 0 1 0.5 0 0

Life exp 0.25 0.25 0.5 0.5 1 0.25 0

Life rev 0 0.25 0 0 0.25 1 0

Life cat 0 0 0 0 0 0 1



Of the seven sub-modules for life underwriting risk, only the lapse underwriting risk sub-module, for which the greatest of three scenarios determines the required capital, is non-linear. All the same, in our simulation, the calculation based on a distinction between unit-linked and euro-denominated business and the aggregate calculation as in QIS4 leads to the same result. The second absence of linearity lies in the correlation matrix. In our simulation (economic approach), we do one correlation calculation of the seven risk sub-modules of life underwriting risk for unit-linked policies and another for euro-denominated policies. In the QIS4 approach, a single correlation calculation is done for all life insurance policies. In our simulation the difference (1%) is nonetheless slight.

III. Capital Required for Non-Life Underwriting RiskThe non-life underwriting risk module is made up of the risk linked to the uncertainty of underwriting results. This uncertainty has to do the with the amount and timing of the settlement of claims, the volume of business, and the premium rates at which it will be written,9 and

the premium rates that will be necessary to cover the liabilities generated by the business written.

Non-life underwriting risk—SCR NL—is measured with: • two risk sub-modules (premium and reserve risk, SCR NL pr, and catastrophe risk, SCR NL cat)• segmentation of non-life business into twelve lines of business10 • segmentation into fourteen geographic areas.11

This breakdown of premiums and of technical provisions by area and by line of business makes it possible to take into account geographic diversification and the correlation of the risks of these businesses.

The calculation of the capital required for non-life underwriting risk (SCR NL) makes it possible to use the process below to define one of the components necessary to the calculation of the risk-adjusted capital for non-life business (three lines of business for our model company):


9 - The commercial premium payable by the policyholder is composed of the pure (or technical) premium and loadings. This pure premium is equal to the premium rate times the capital insured. The premium rate is a function of the frequency of claims and the average cost of claims for a given risk. 10 - 1) Motor, third-party liability; 2) Motor, other classes; 3) Marine, aviation, transport (MAT); 4) Fire and other damage; 5) Third-party liability; 6) Credit and suretyship; 7) Legal expenses; 8) Assistance; 9) Miscellaneous; 10) Non-proportional reinsurance—property; 11) Non-proportional reinsurance—casualty; 12) Non-proportional reinsurance—MAT.11 - 1) Each country of the EEA; 2) Switzerland; 3) The rest of Europe; 4) Asia (excluding Japan and China); 5) Japan; 6) China; 7) Oceania (excluding Australia); 8) Australia; 9) North America (excluding Canada and the United States); 10) Canada; 11) United States; 12) Each country of South America; 13) Central America; 14) Africa. This segmentation was done for QIS4 and could change as a result of work currently underway to heighten sensitivity to the risks inherent to geographic regions. In addition, an overall threshold of materiality of 5% must be observed for geographic diversification to apply.

Simulation with the model companySynthesis and comparison of QIS4 and “disaggregated” approaches (UL + euro denominated)


SCR (EURm) Eurodenominated

Unit linked Euro denominated + unit linked

Life QIS 4 Life QIS4/Euro den. + Unit linked

Mortality 3.74 0.15 3.89 3.89 100%

Longevity 2.34 0.53 2.87 2.87 100%

Disability 0.13 0.00 0.13 0.13 100%

Lapse 11.13 1.49 12.63 12.59 100%

Expense 5.57 1.27 6.84 6.84 100%

Revision 0.00 0.00 0.00 0.00 -

Catastrophe 2.52 0.08 2.60 2.60 100%

SCR life 16.42 2.61 19.03 18.93 99%



The correlation matrix of the two non-life underwriting risk sub-modules supplied by QIS4 (2008) assumes that the sub-modules are not correlated:

Corr SCR NL SCR NL pr SCR NL cat

SCR NL pr 1 0

SCR NL cat 0 1

In the following sections (III.1 and III.2), we present the two sub-modules for non-life underwriting risk. This presentation makes it possible to analyse the risks considered, the calibration of these risks with the standard formula, and the possible effects of non-linearity to proceed with the retreatment necessary to the calculation of RAC. As we have noted, these calculations could be fine tuned by and/or tailored to each insurer in order to

determine its exposure to risks in greater keeping with the characteristics of its portfolio (a supervisor-approved internal model).

III.1. Capital required for non-life premium and reserve riskPremium risk is the risk that expenses and claims will be greater than premiums received. This risk is present as soon as the policy is issued, as well as before, given the uncertainty as to the premium rates charged and the volume of business underwritten.

Reserve risk stems from the possible underestimate of provisions for claims and from the random nature of future claims payouts.


Calculation of one of the components of property and casualty RAC

RAC motor own damage = F(SCR motor own damage) = F(SCR NL motor own damage, SCR market motor own damage, SCR counterparty motor own damage, SCR operational motor own damage) The property and casualty RAC and the third-party liability RAC are calculated with the same approach

SCR NL motor own damage = √∑r,c Corr SCR NL rxc * SCR NLr*SCR NLcoù Corr SCR NLrxc are the cells of the correlation matrix of the two sub-modules (SCR NLk) of non-life underwiting

(k=pr or cat depending on the sub-module).

ActivityPremiums

EURmPremiums

%

RAC in % of

premiums

RACEURm

Net margin

Net profitEURm

RoRAC gRAC

xV(RAC)EURm

V(RAC)%


Life unit linked

Motor own damage

Property damage


Health

Sum

Surplus

TOTAL



The capital required for premium and reserve risk (SCR NL pr) is determined with a three-step process, calibrated in such a way that, assuming a lognormal distribution of the underlying risk, a risk capital charge consistent with the VaR 99.5% standard is produced.12 To show the overall principles, we provide below a brief look at the three steps; for more information, see appendix 9 (Major Steps in the Calculation of the Premium and Reserve Risk Sub-Module of the Non-Life Underwriting Risk Module).

The first step involves using the standard deviations of the premium sub-risk σ(prem, lob)

and of the reserve sub-risk σ(res, lob) and a correlation coefficient of 0.5 to determine the standard deviation for aggregate premium and reserve risk (σlob) for each line of business (LoB). The standard deviation σ(prem, lob) is a function of the firm-specific standard deviation σ(U,prem, lob), itself a function of the historic volatility ratios of the firm, of the standard deviation of the market σ(M, prem, lob), and of a credibility factor clob defined by QIS4 for each line of business.

In the second step, the effects of geographic diversification are calculated for each line of business. To do so a measure of the geographic volume of premium risk V(prem, lob), a function of the turnover of the insurer, as well as of reserve risk V(res, lob), a function of the best estimate and of the Herfindahl indeed DIVpr, lob (see appendix 9).

In the third step, the standard deviations and volume measures for the premium risk and the reserve risk in the individual LoBs are aggregated (using a matrix of the correlation of the lines of business) to

derive an overall volume measure V and an overall standard deviation σ.

Simulation with the model companyAssumptions

ActivityMotor own

damageProperty damage

Third-partyliability

Gross written premiums (EURm)

1000 1000 250

Share reinsured 3% 10% 15%

Gross written premiums by geographic area

Area 1 60% 60% 100%

Area 2 24% 24% 0%

Area 3 16% 16% 0%

Ratio written premiums/earned premiums

Area 1 105% 103% 105%

Area 2 104% 105% 0%

Area 3 103% 104% 0%

Net written premiums growth rate %

Area 1 1% 3% 5%

Area 2 -1% -2% 0%

Area 3 1% 5% 0%

Gross technical provisions (EURm)

205 740 647,5


Net written premiums by geographic area

Area 1 60% 60% 100%

Area 2 24% 24% 0%

Area 3 16% 16% 0%

Number of historic years considered

5 5 10

Premium risk standard deviation

10% 11% 11%


265 387 276


ResultsActivity Motor own



SCR NL pr (EURm)

262 350 276



12 - The log-normal law for parameters μ and σ has a density function:

μ and σ are the mean and the standard deviation of the logarithm of the variable. The logarithm of the variable is normally distributed with a mean μ and standard deviation σ.



III.2. Capital required for non-life catastrophe riskThe aim of the non-life catastrophe risk sub-module is to make allowances for extreme or irregular events that are not sufficiently captured by the charges for premium and reserve risk. To determine the capital required for catastrophe risks (SCR NL cat), the regulator offers a choice of three possible methods:

Method 1: standard formulaIf no regional scenarios are provided, a standard method is used. The capital charge for non-life catastrophe risk (SCR NL cat) is a function of the estimate of the net written premiums to be issued in the coming year for each line of business (Plob) and of a regulator-supplied catastrophe factor particular to each line of business ct (t=lob=1,...,12).

where:

Method 2: scenariosThe second method integrates regional scenarios supplied by the local supervisor (annex SCR3 TS.XVII.E. QIS4 2008). For the moment, no inter-regional scenario has been supplied. The capital charge for non-life catastrophe risk (SCR NL cat) is a function of the sum of the costs, net of reinsurance, of each specified catastrophe CATi in excess of the materiality threshold, a threshold set at 25% of the

cost of the most severe scenario (defined as the impact on net asset values).

The capital charge for the scenario method is:

NLCAT =

CATi2

i

∑

Method 3: personalised scenariosPersonalised scenarios make it possible for companies to improve the integration of specific features of their business (risks underwritten, geographic concentration), especially when the insurer considers that the calibration obtained under methods 1 or 2 is not representative of its exposure to the risk of man-made or natural catastrophes. The scenarios to be selected are those that the firm considers will exceed the materiality threshold (as defined above). The costs of the scenarios are net of reinsurance to assess the effect of reinsurance treaties and any exceptional costs incurred by the firm in post-event management. There are two options for the calculation:• one on the basis of the occurrence of a single event (storm, flood, earthquake, fire, single explosion) and• another on an annual basis (occurrence of several catastrophic events over the twelve coming months in line with the calibration of the SCR at a 99.5% confidence interval over a one-year horizon)


LoB t ct LoB t ct LoB t ct

Motor. third-party liability

0.15 Third-party liability 0.15 Miscellaneous 0.25

Motor. other 0.075 Credit and suretyship

0.60 Reins. (property) 1.50

MAT 0.50 Legal expenses 0.02 Reins. (casualty) 0.50

Fire 0.75 Assistance 0.02 Reins. (MAT) 1.50

Source: QIS4



Simulation with the model companyGiven the very specific features taken in the scenario methods 2 and 3,13 we have taken method 1 for the simulation with our model company.

AssumptionsActivity Motor own

damagePropertyDamage


Gross written pre-miums (EURm)

1000 1000 250


Risk factor ct 0.075 0.075 0.15


265 387 276


ResultsActivity Motor own

damagePropertyDamage


SCR NL cat (EURm)

73 68 32


III.3. Total capital required for non-life underwriting risk (SCR NL)In the preceding sections (III.1 and III.2), we calculated the capital required for the two non-life risk sub-modules considered by Solvency II. As we note earlier, these calculations could be fine tuned by and/or tailored to each insurer in order to calculate a risk exposure in greater keeping with the characteristics of its portfolio (supervisor-approved internal model).

The capital charges for non-life underwriting risk (SCR NL motor own damage, SCR NL property damage, and SCR NL third-party liability) make it possible, with the process described in the introduction to this section III, to determine one of the components necessary to the calculation of risk-adjusted capital (RAC) for the three non-life lines of business.

With the matrix of correlation (Corr SCR NL) of the risk sub-modules SCR NL pr and SCR NL cat described in the introduction to section III, it is possible to determine the capital required for non-life underwriting risk (SCR NL).

Simulation with the model companyActivity Motor own



SCR NL (EURm) 272 357 277


At this point, the economic capital model and the Solvency II approach to calculating the capital charge for the risks of underwriting each of the non-life lines of business are identical and thus raise no problems of linearity.

All the same, in the introduction to this section III, we saw that the supervisor considered an economic capital requirement for the non-life underwriting risk module (SCR NL) to make allowances for the effects of diversified lines of non-life business. We will do this reposting in determining the overall SCR for each line of business in chapter V. We now provide the Solvency II results:

SCR NL = √∑r,c Corr SCR NLr,c * NLr*NLc

The matrix of the correlation of the three lines of business of the model company is given by QIS4:

Corr SCR NL Motor own damage

Property damage


Motor own damage

1 0.25 0.25

Property damage

0.25 1 0.25


0.25 0.25 1


13 - Annex SCR3 TS.XVII.E of QIS4 provides information on the choice of risks (certain types of natural disasters are envisaged: for example, floods, hail, storms, earthquakes, man-made disasters), the treatment of which differs from country to country (seventeen countries considered: Austria, Belgium, Czech Republic, Denmark, France, Germany, Italy, Iceland, Lithuania, Malta, Norway, Poland, Portugal, Slovakia, Slovenia, Sweden, Great Britain).



IV. Capital Required for Health Underwriting RiskThe health underwriting risk module covers the risks for all health and workers’ compensation guarantees. Health underwriting risk (SCR health) is split into three sub-modules: long-term health (Health LT), practised on a technical basis similar to that of life assurance (it exists only in Austria and Germany), short-term health (Accident and Health ST), and workers’ compensation (Health WC). Like life and non-life underwriting risks, health underwriting risk is calculated based on the capital charges of the sub-modules and by integrating the correlation of these risk sub-modules:

SCR health = √∑r, c CorrHealthr, c*Healthr *Heatlthc

where Healthr and Heatlthc are the capital charges for individual health underwriting sub-modules according to the rows and columns of correlation matrix CorrHealth:

CorrHealth Health LT Accident and Health ST

Health WC

Health LT 1 0 0

Accident and Health ST

0 1 0,5

Health WC 0 0,5 1

Source: QIS4

The determination of the capital required for health underwriting risk (SCR Health) makes it possible, with the process described below, to define one of the components necessary to the calculation of the risk-adjusted capital for health lines of business.


SCR (EURm) Motor own

damage

Property damage


Sum of activities before diversification

benefits

Sum of activities after diversification

benefits

Capital saving related to diversification of non-life

business

Premium and reserve

262 350 276 888 236 73%

Catastrophe 73 68 32 172 104 39%

SCR NL 272 357 277 906 258 72%

Diversification benefit (lines of business) for non-life underwriting risk


Calculation of one of the components of health RAC

RAC health = F(SCR health) = F(SCR health, SCR market health, SCR counterparty health, SCR operational health)

ActivityPremiums

EURmPremiums

%RAC in %

of premiumsRAC

EURmNet

marginNet profit

EURmRoRAC g

RAC x

V(RAC)EURm

V(RAC)%


Life unit linked

Motor own damage

Property damage


Health

Sum

Surplus

TOTAL



In the following sections (IV.1 to IV.3), we present the three health underwriting risk sub-modules. This presentation makes it possible to analyse the risks considered, the calibration of these risks with the standard formula, and the possible non-linearity effects in order to proceed with the reposting necessary to the determination of RAC. As we mention above, these calculations can be fined tuned and/or tailored by each insurer to calculate its exposure to risks in greater keeping with the characteristics of its portfolio (the supervisor-approved internal model).

IV.1. Capital required for long-term healthHealth long-term underwriting risk is split into three components that benefit from the risk-absorbing effects of future profit sharing: expense risk, claim/mortality/cancellation risk and epidemic/accumulation risk.

i) Expense risk in long-term health arises from the difference in expenses estimated during prices and the expenses actually incurred. The Health exp capital charge is a function of gross earned premium (Pay), of the volatility of the expense ratio (σ h exp)14, and of a risk factor (λexp = 2.58) calibrated to produce a capital charge consistent with a VaR of 99.5%:

Health exp =λexp * σ h exp * Pay

ii) Claim risk (or per capital loss risk) is the risk of a difference between the losses assumed in technical provisions when products are priced for mortality or cancellation risk and the losses actually incurred. The capital charge Health cl is a function of gross earned premium (Pay), of the volatility of the claims ratio (σh cl),15 and of a risk factor (λcl = 2.58) set

to generate a capital charge consistent with a VaR 99.5% standard.

Health cl = λcl * σ h cl * Pay

iii) Epidemic risk measures the impact on the insurer’s balance sheet of possible outbreaks of epidemics. Accumulation risk is grounded on the assumption that persons are interdependent. The capital charge Health ac is a function of gross premium earned (Pay) by the firm and in the health insurance market (MPay), of claims expenditure for the accounting year in the health insurance market (claimsay), and of a risk factor (λac = 6.5) calibrated to generate a capital charge consistent with a 99.5% VaR standard and it takes into account the correlation with the other health insurance sub-modules:

Health ac = λ ac * claims ay* (Pay / MPay)

Simulation with the model companyAs the long-term health business exists only in Germany and Austria, we have decided that our model company is not in this business; it is involved only in short-term health and accidents (section IV.3.).

IV.2. Capital required for workers’ compensation riskUnderwriting risk in workers’ compensation has to do with the risks of the liabilities resulting from short- or long-term sick leave: medical treatment and payment of lump-sum indemnities, annuities payable to injured workers and beneficiaries, regular and recurrent payments over a long-term horizon to cover the costs of assistance of a third party. The calculation of the capital required for workers’ compensation underwriting risk is grounded on three risk sub-modules, each them benefiting from the risk-absorbing


14 - The expense ratio is the ratio of expenses to gross earned premiums. Volatility is calculated with “the gross earned premium weighted standard deviation of the expense result in relation to the gross premium over the previous ten-year period.”15 - The previous ten-year period is used to determine volatility. Here again, if the expense history is too short, a standard formula can be used instead (QIS4 p. 180).



effect of future profit sharing: i) premium and reserve (WCompgeneral), ii) underwriting (WCompannuities), and iii) catastrophe (WCompcat).

The regulatory approach to calculating the capital required for the first and third components of risk is similar (although the volatility parameters are different) to that described for the non-life underwriting module: a three-step approach (appendix 9) for premium and reserve risk and the standard method or scenario methods for catastrophe risk. Underwriting risk in workers’ compensation refers to benefits paid in the form of annuities or assistance as a result of workplace accidents. The risk is split into four categories (longevity, disability, revision, and expense) and is measured with the same approach as that taken in life insurance (the impact of correlated shocks on the change in the net value of assets).16

So the capital charge for the workers’ compensation sub-module is defined by:

Wcomp = √∑Corr Wcomp r,c * Wcomp r * Wcomp c

where the correlation matrix of the three risk sub-modules is given by QIS4:

Corr W Comp W comp general

W comp annuities

W comp cat

W comp general 1 0.5 0

W comp annuities 0.5 1 0

W comp cat 0 0 1

Simulation with the model companyWe have chosen not to have our model company be present in this line of business; instead it is present in the accident and short-term health business (section IV.3).

IV.3. Capital required for accident and short-term health riskThe accident and short-term health risk sub-module does not benefit from the risk-absorbing effect of future profit sharing. It is made up of two lines of business (short-term health and accident) with a correlation of 0.5 and of two independent risk components (premium and reserve risk and catastrophe risk).

The approach taken by the regulator to calculate the capital required for each of these two risk components is similar (although the volatility parameters are different) to that described for the non-life underwriting module: a three-step approach (appendix 9) for premium and reserve risk and a standard method or scenario methods for catastrophe risk.

The standard formula for catastrophe risk is:

Accident and health ST CAT = √ [(C1*P1)² + (C2*P2)²],

where P1 and P2 are the estimates of the net written premium in the individual lines of business short-term health and accident and other for the coming year. The catastrophe factors C1 and C2 are equal to 0.1.

Simulation with the model companyWe assume that the model company is present in the two lines of health business described by the regulator: short-term health and accident and other. In addition, we assume that its business is done in a single geographic area (for example, the regulator’s area 1, that is, the European Economic Area).


16 - The shocks whose impact on net asset value is tested are:• for longevity risk, a permanent fall of 25% in the mortality rate for each age• for disability risk, a 35% increase in the disability rate for the coming year together with a permanent increase of 25% in the disability rate in the following years for each age• for revision risk, a 2% annual increase in the amounts payable in the form of annuities and a 5% increase in the amounts payable annually in the form of payments for assistance• for expense risk, future expenses 10% greater than estimated and an inflation rate higher than estimated by 1 percentage point.The correlation of these four shocks is defined by the matrix:

Corr

Ann

uiti

es

Long

evit

y

Dis

abili

ty

Revi

sion

Expe

nse

Longevity 1 0 0 0.25

Disability 0 1 0 0.5

Revision 0 0 1 0.25

Expense 0.25 0.5 0.25 1

Source: QIS4



Premium and reserve riskAssumptionsActivity Short-term

healthAccident & others

Gross written premiums (EURm) 168 32


Ratio written premiums/earned premiums

102% 102%


3% 3%

Gross technical provisions (EURm)

35.7 6.8


Number of historic years considered

7 5

Premium risk standard deviation

3% 5%


52


Results :Activity Short-term health and

accident & others

SCR health ST pr (EURm) 21


Catastrophe riskAssumptionsActivity Short-term

healthAccident & others

Gross written premiums (EURm)

168 32


Risk factor C 0.1 0.1


52


ResultsActivity Short-term health and

accident & others

SCR health ST cat (EURm) 17Source: EDHEC Business School

Capital required for accident and short-term health:Activity Short-term health and accident

& others

SCR health ST (EURm) 27


IV.4 Total capital required for health underwriting riskIn the previous sections (IV.1 to IV.3), we calculated the capital requirements for the three health underwriting risk sub-modules described by Solvency II. As we note above, these calculations could be fine tuned by and/or tailored to each insurer, in order for it to calculate its exposure to risks in greater keeping with the characteristics of its portfolio (a supervisor-approved internal model).

The amounts of capital required for health underwriting risk (SCR Health) make it possible, with the process described in the introduction to this section IV, to determine one of the components necessary to the calculation of risk-adjusted capital for health.

Simulation with the model companySCR HealthActivity Health

SCR health (EURm) 27


The economic capital model and the Solvency II approach to calculating the capital charge for the risks of underwriting health business are identical and thus raise no problems of linearity.

By running simulations on a fictitious company, chapter III has made it possible to study the measurement of the underwriting risks of life, non-life, and health insurance, as well as the capital charges associated with these risks. So we have shown the possible conceptual convergence of the economic and regulatory capital approaches and the operational requirement for heavy investment in data collection simulation for the regulator.




In light of these two analyses, the development of internal models and, more broadly, of economic capital models, should pick up speed with the implementation of Solvency II, and this for firm-specific risk-management improvements as well as for more general management improvements.

This chapter has described the prerequisites for elaborating an economic capital model and analysing its contributions to risk management, to the determination of risk-adjusted capital, to available and required capital, and, more broadly, to the optimal creation of shareholder or mutual member value. With the same objective, the following chapter will deal with market and counterparty risks.


4. Market and Counterparty Risks in the Economic Capital

Model under Solvency II Constraints




Before proceeding in the final chapter of this study (chapter V) to the contributions of economic capital model to risk management and to value creation for shareholders or mutual members, we will look in chapter IV at market (section I) and counterparty (section II) risks, prerequisites for determining risk-adjusted capital (RAC). In the calibration suggested by Solvency IIand the results analysed by the ACAM (2008), market risks are the greatest consumers of capital. In France, they account for 82% of the capital required of life insurers (before the diversification effect, operational risk, and adjustments for profit sharing and deferred taxation), nearly 46% for property insurers, and more than 50% for mixed insurers.

I. Capital Required for Market RiskFirst, in Solvency II the calculation of market risk is done in an aggregate fashion for the entire insurance company, that is, without making distinctions for lines of business. Nonetheless, for the needs of the economic capital model we identify the market risks for each of the six lines of business of our model company. To determine the capital allocated to each line of business it will then be necessary, as a result of this disaggregation, to make allowances for possible non-linear effects.

Market risk arises from the level or volatility of market prices of financial instruments. It is measured by the impact of movements in financial variables (stock prices, interest rates, real estate prices and exchange rates). There are six risk sub-modules (see below). There are thus six capital charges

for each line of business before (SCR Mktk) and after (nSCR Mktk) allowances are made for the risk-absorbing effect of future profit sharing, that is, a total of seventy-two capital charges for market risks (six lines of business x six risk sub-modules x two depending on whether there is a risk-absorbing effect). The risks considered are:• interest rate risk, for which we determine a capital charge SCR Mkt int• equity risk (SCR Mkt eq)• property risk (SCR Mkt prop)• currency risk (SCR Mkt fx)• spread risk (SCR Mkt sp)• risk concentrations (SCR Mkt conc).

The calculation of the capital required for market risk (SCR Mkt) makes it possible to determine one of the components necessary to the calculation of RAC for each of the model company’s six lines of business:

4. Market and Counterparty Risks in the Economic Capital Model under Solvency II Constraints



The correlation matrix provided by QIS4 (2008) is:

This correlation matrix was highly controversial and, as CEIOPS (2009) mentioned in its document on the lessons of the crisis, it is likely to be modified.

The capital required for each of the six sub-modules is equal to the change in the net asset value (NAV) following upwards and/or downwards shocks:

SCR risk i =ΔNAV | shock

In addition, QIS4 mentions several methodological points having to do

with policies in accumulation units, with derivatives, and with collective investment schemes. For unit-linked policies, market risk must be studied when the charges on the policies depend on fund performance. If there are embedded options or guarantees in the policies, exposure to market risk must be analysed. The effect of risk-reduction techniques on the asset side (financial hedging, for example) and on the liability side (hedging instruments, reinsurance) must be taken into account


Calculation of one of the components of RAC

RAC euro denominated = F(SCR euro denominated) = F(SCR Life euro denominated, SCR Mkt euro denominated, SCR counterparty euro denominated, SCR operational euro denominated)

Similar approach for RAC UL, RAC motor own damage, RAC property damage RAC third-party liability and RAC health)

ActivityPremiums

EURmPremiums

%RAC in %

of premiumsRAC

EURmNet

marginNet profit

EURmRoRAC g

RAC x

V(RAC)EURm

V(RAC)%


Life unit linked

Motor own damage

Property damage


Health

Sum

Surplus

TOTAL

SCR Mkt = √∑r,c CorrSCR market rxc * Mktr* Mktcwhere SCR market rxc are the cells of the matrix of the correlation of the six market risk sub-modules (Mktk).

Corr SCR market Mkt interest Mkt equity Mkt property Mkt fx Mkt spread Mkt conc

Mkt interest 1 0 0.5 0.25 0.25 0

Mkt equity 0 1 0.75 0.25 0.25 0

Mkt property 0.5 0.75 1 0.25 0.25 0

Mkt fx 0.25 0.25 0.25 1 0.25 0

Mkt spread 0.25 0.25 0.25 0.25 1 0

Mkt conc 0 0 0 0 0 1



in the evaluation of the risk sub-modules. By contrast, the counterparty risks taken on as a result are dealt with in the counterparty risk module. In chapter V we go over in greater detail the conditions on which risk-reduction techniques are taken into account.

For collective investment schemes, the look-through principle must be applied: risk exposures are allocated to each sub-module. If the collective investment scheme is not sufficiently transparent, the investment mandate of the scheme should be referred to (authorised limits, authorised investment types, and so on) and the share of assets in each risk category chosen in such a way as to maximise the overall charge. The final option is to assume that if the majority of the assets of the collective investment scheme are listed, the collective investment scheme is an equity investment and that if they are not listed it is another risk type.

In the following sections (I.1 to I.6), we present the market risk sub-modules. This presentation makes it possible to analyse the risks considered, the calibration of these risks with the standard formula, and the possible non-linearity effects to proceed with the reposting necessary to the calculation of RAC. As we mention above, these calculations could be fined tuned by and/or tailored to each insurer so that it can calculate its exposure to risks in greater keeping with the characteristics of its portfolio (supervisor-approved internal model).

I.1 Capital required for interest rate riskInterest rate risk is measured by the impact on net asset value (ΔNAV)1 of changes in the term structure of interest rates or

by the impact on the balance sheet of the company (investments in fixed-rate instruments, interest rate derivatives, insurance liabilities, and debts) and on future liability flows (in a manner correlated to the change in the rate at which they are discounted) of interest rate volatility. The upwards (upwardshock) or downwards (downwardshock) interest rate shock that leads to the highest charge is used to determine the capital charge, and this for each year over a twenty-year period (see appendix 10).2

SCR Mkt int = ΔNAV | shock

When the cash flows of the relevant balance sheet item are not sensitive to interest rates (in particular, when it does not have an embedded option or guarantee), the simplified calculation suggested by the regulator involves multiplying the modified duration for each asset or liability by the change in the yield curve. For all durations, the downwards shock is -40% and the upwards shock is +50%. This simplification should not be use for life technical provisions.

It should be underscored that the regulator wants embedded options and guarantees to be priced, all the more so when the bulk of the risk of the policy is borne by the policyholder, as in unit-linked policies. The main embedded options and guarantees in a life insurance portfolio can, of course, be of very different natures: guaranteed minimum rates, profit sharing, annuity conversion options, guaranteed floors for unit-linked policies, guaranteed surrender values, and surrender options. The pricing of these options and guarantees is generally done in accordance with the standards set by the CFO Forum (2008; 2005; 2004), in particular with the so-called


1 - As in QIS4, positive values of ΔNAV signify losses.2 - When a company is exposed to interest rate risk in more than one currency, the capital charge for interest rate risk should be calculated on the basis of an identical relative variation on all relevant yield curves. The term structure is communicated by QIS4.



market-consistent approach. The idea is to take a risk-neutral approach, which involves using expected stochastic cash flows (as determined by several thousand scenario simulations that make it possible to take in the cost of negative changes) discounted at the risk-free rate to calculate the price of these options and guarantees. Models usually simulate the movements of market indices, the dividend rate, inflation, real and nominal rate curves for maturities of between one and thirty years, credit spreads, credit default risks, exchange rates, and so on. In addition, these simulations should reflect policyholder behaviour: (surrenders, and so on), management policies (dynamic investment strategies, hedging, and so on), implicit market-consistent volatilities, the correlation of asset classes, and the correlation of economies.

It is interesting to compare this line-of-business approach (economic capital approach) and aggregate approach taken by Solvency II (regulatory capital approach).


Activity Unit linked Eurodenominated

Motor own damage

Property damage


Health

Bonds (EURm) 663 4920 370 804 550 95

Bond duration 8 8 4 4 9 3

Gross technical provisions (EURm) 1425 6000 205 740 647.5 42.5

Share reinsured 5% 1% 2% 15% 20% 2%

Reinsurance assets (EURm) 1 6 2 7 26 0

Technical provisions duration 8 8 2 2 9 1

Debt (EURm) 2.25 36 25 30 20 5

Debt duration 6 6 6 6 8 4


47 360 265 387 276 52




Motor own damage

Property damage


Health

SCR int (EURm) 4.00 371.24 27.84 39.83 0.00 4.82

nSCR int (EURm) 4.00 349.23 27.84 39.83 0.00 4.82

Results




We see that the QIS4 approach leads to a capital requirement lower than that of the sum of the amounts required for each line of business. This difference is the result of the non-linearity of the interest rate risk module. As it happens, Solvency II tests a downwards shock and an upwards shock and takes the greater of the two on an integrated basis of the lines of business. In our economic capital approach, we consider an upwards and a downwards shock for each of the lines of business. In our simulation, the upwards shock is usually more demanding of capital, although this is not the case, for example, for third-party liability. It is the only non-linearity bias observed and, to calculate the economic

capital for each line of business, we will take another look at it in the following chapter.

I.2 Capital required for equity riskAs in financial theory, two components serve as a basis on which the regulator can measure equity risk:i) idiosyncratic risk, the result of insufficient diversification, a risk dealt with in the concentrations risk sub-module, andii) systemic (or market) risk, which cannot be reduced by diversification and is thus market correlated. It is sensitive to overall economic changes, taxation, interest rates, inflation, and so on.


Total balance sheet

Bonds(EURm) 7403

Bond duration 7

Life gross technical provisions (EURm) 7425

Non life and health gross technical provisions (EURm) 1592.5

Reinsurance assets/technical provisions 1%

Reinsurance assets (EURm) 43

Life technical provisions duration 8

Non life and health technical provisions duration 5

Debt (EURm) 118

Debt duration 6

Net asset value (NAV) before the shock (EURm) 1387

QIS4 assumptions


Total balance sheet

SCR int (EURm) 420

nSCR int (EURm) 398

Results



Euro denominated

Motor own damage

Property damage


Health Sum of activities

Interest rate QIS4

Interest rate QIS4/sum of

activities

SCR int (EURm)

4 371 28 40 0 5 448 420 94%

nSCR int (EURm)

4 349 28 40 0 5 426 398 94%




The regulator puts equities into one of two indices: Global (for equities listed in EEA and OECD countries) and Others (for equities listed only in emerging markets, unlisted equities, hedge funds, and other alternative investments). In QIS4 it is assumed that the beta of the equity portfolio of the insurance companies is identical to that of the indices (Beta = 1).

Two shocks (a 32% drop in the Global index and a 45% drop in the Others index), net of hedging and risk transfers, are used to determine the capital charge SCR Mkt Equity:3

SCR Mkt Equity = √∑r,c CorrIndexr,c

* Mktr * Mktc

where Mktr, Mktc are the capital charges for equity risk per individual index as shown in the lines and columns of the correlation matrix CorrIndex. QIS4 sets the correlation coefficient at 0.75.

In addition, there is an optional method that is currently the subject of debate. This so-called dampener method rests on the theory that the likelihood of an increase in the value of an equity index is low when

this value is high and that it is high when this value is low. The dampener option was tested in QIS4, but only for the market value of equity portfolios (MVEP)4 drawn from the Global index associated with the share (α) of technical provisions for commitments of more than three years (duration k ≥ 3).5

The value of the Global6 equity index is split into a trend component and a cyclical component ct.7 In the dampener approach to the Global index (SCRGlobal index), the capital charge for equity risk is defined by:

SCR Global index = MVEP * ([α*(F(k) + (G(k) * ct))] + [(1- α) * 32%])

where F(k) and G(k) are coefficients defined in the table below:

Duration of the liabilities k

F(k) G(k)

3 to 5 years 29% 0.20

5 to 10 years 26% 0.11

10 to15 years 23% 0.08

More than 15 years 22% 0.07

Source: QIS4


3 - Hedging instruments are allowed only when average protection is afforded over the next year. For example, where an equity option provides protection for the next six months, the determination of the capital requirement should be done assuming that the option covers only half of the current exposure. In addition, hedging programmes other than those in force at the balance sheet date, rolling hedging programmes, for example, are not included. 4 - Excluding equity positions in which a parent has an interest in a subsidiary (see TS.VI.E QIS4).5 - For the share for which the duration is less than three years, the shock (-32%) to the Global equity index is taken. 6 - For the dampener option, QIS4 takes the MSCI Developed Markets index as the equity index.7 - Ct is the difference between the mean of the ten trading days (Ybar 10) before the day when the SCR is calculated and the mean of the last year (around 250 trading days—Ybar 261) that precedes the calculation of the SCR.

Simulation with the model companyAssumptions Activity Unit linked Euro




Health

Global index equities 94.0% 95.0% 95.0% 92.0% 90.0% 95.0%

Global index hedging rate 10.0% 5.0% 0.0% 0.0% 0.0% 0.0%

Other index hedging rate 5.0% 1.0% 0.0% 0.0% 0.0% 0.0%

Efficiency of Global index hedge 90.0% 90.0% 90.0% 90.0% 90.0% 90.0%

Efficiency of Others index hedge 80.0% 80.0% 80.0% 80.0% 80.0% 80.0%

Value of hedge/value of asset hedge (Global)

4.0% 1.0% 1.0% 1.0% 1.0% 1.0%

Value of hedge/value of asset hedge (Other)

4.0% 1.0% 1.0% 1.0% 1.0% 1.0%


47 360 265 387 276 52




Results

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SCR Mkt eq (EURm)

4.0 48.8 31.7 92.6 88.9 1.6

nSCR Mkt eq (EURm)

4.0 26.8 31.7 92.6 88.9 1.6


It is interesting to compare the line-of-business approach (economic capital approach) and the aggregate approach taken by Solvency II (regulatory capital approach)

Comparison of regulatory capital required by the QIS4 approach (global approach) and economic capital (line-of-business approach in keeping with the objective of capital allocation)

QIS4 assumptionsBilan Total

Global index equities 62.5%

Global index hedging rate 3.0%

Other index hedging rate 0.5%

Efficiency of Global index hedge 90.0%

Efficiency of Other index hedge 80.0%

Value of hedge/value of asset hedge (Global)

1.0%

Value of hedge/value of asset hedge (Other) 1.0%


1387


ResultsBilan Total

SCR Mkt eq (EURm) 267

nSCR Mkt eq (EURm) 245


The equity risk sub-module of the market risk module is perfectly linear and the QIS4 and economic capital approaches lead to identical results.

I.3. Capital required for property riskProperty risk makes it possible to calculate the capital charge (SCR Mkt prop) for the changes in market prices for property. It is measured by the change in net assets (ΔNAV) following a 20% fall in the “real estate benchmarks” after allowances are made for investment policy (hedging arrangements, leverage, and so on).

Simulation with the model company Assumptions

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Actifs immobiliers (EURm)

0 511 25 57 92 0

Actif net (NAV) avant le choc (EURm)

47 360 265 387 276 52


Results

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SCR Mkt prop (EURm)

0 21 5 11 18 0

nSCR Mkt prop (EURm)

0 0 5 11 18 0




Euro denominated

Motor own

damage

Property damage



Interest rate QIS4

Interest rate QIS4/

sum of activities

SCR Mkt eq (EURm) 4,0 48,8 31,7 92,6 88,9 1,6 268 267 100%

nSCR Mkt eq (EURm) 4,0 26,8 31,7 92,6 88,9 1,6 246 245 100%






QIS4 assumptionsTotal balance sheet

Real estate assets (EURm) 685

Net asset value (NAV) before shock (EURm)

1387


Total balance sheet

SCR Mkt prop (EURm) 55

nSCR Mkt prop (EURm) 35


The property risk sub-module of the market risk module is perfectly linear and the QIS4 and economic capital approaches lead to identical results.

1.4. Capital required for currency risk (volatility of exchange rates)The currency risk sub-module makes it possible to calculate the SCR Mkt fx capital charge for changes in exchange rates. It is measured with the change in net assets (ΔNAV) following the greater of the capital demands resulting from an 20% rise or fall

in the value of other currencies against the local currency (taking into account hedging arrangements, gearing, and other aspects of investment policy).8

Simulation with the model companyAssumptions and resultsWe assume that the model insurance company has no currency risk as a result of its asset/liability management, coherent investments, and, failing that, a totally efficient hedge against exchange rate risk.

1.5. Capital required for spread riskThe SCR Mkt spread capital charge for the volatility of spreads (the movement of the yield curve) over the risk-free interest rate term structure is measured by the change in net asset value (ΔNAV) following the more adverse of a rise and fall in credit spreads for each of the relevant assets: bonds, structured credit products, and

credit derivatives such as credit-default swaps. In particular, the SCR Mkt spread capital charge is the sum of the three shocks below:• a shock to the market value (MV) of bonds exposed to default risk. This shock is a function of the modified duration of the bonds (mdur), the credit risk rating (F(rating)), and the impact on the liability side for unit-linked policies with embedded options and guarantees (ΔLiabul).9 The capital charge for spread risk of bonds is given by Mktsp

bonds.


8 - The magnitude of the shocks for the currency of an ERM II (European exchange rate mechanism) member state with respect to the euro must respect the limits set by the ERM II (for example, 2.25% for the Danish crown). 9 - QIS4 excludes sovereign bonds as well as assets allocated to policies in which policyholders bear the investment risks. If these policies have embedded options or guarantees, the share of the risk in fact borne by the insurer is taken into account with the term ΔLiabul. The capital charge for bond spread risk is calculated as follows: Mkt sp bonds = ∑i MVi * m(duri)*F (ratingi) + Δ Liab ul.F (and G—see the sub-module for the risk of structured credit products) is calibrated to deliver a shock consistent with a 99.5% VaR:

Note F(Ratingi) G(Ratingi)

AAA 0.25 % 2.13 %

AA 0.25 % 2.55 %

A 1.03 % 2.91 %

BBB 1.25 % 4.11 %

BB 3.39 % 8.42 %

B 5.60 % 13.35 %

CCC or lower 11.20 % 29.71 %

Unrated 2.00 % 100.00 %

Source: QIS 4For example, the loss caused by a shock to the spread for a BBB-rated asset with a term of four years is 5% (1.25*4).


Euro denominated

Motor own damage

Property damage



Interest rate QIS4

Interest rate QIS4/Sum of

activities

SCR Mkt prop (EURm)

0 21 5 11 18 0 55 55 100%

nSCR Mkt prop (EURm)

0 0 5 11 18 0 35 35 100%




• a shock to structured credit products (ABSs, CDOs, and so on10). This shock is a function of the modified duration of these products (ndur) and of the credit risk rating (G(rating)). The capital charge for the spread risk of structured products is Mktsp

struct.11

• a shock to credit derivatives (CDSs, TRSs, CLNs) not held as part of a risk-reduction programme. The capital charge for the spread risk of credit derivative products is noted Mktsp

cd. It is calculated as the more adverse of the changes in the value of the derivative following a widening of 300% or a narrowing of 75% in the credit spreads.

SCR Mkt spread = Mktsp

bonds + Mktspstruct + Mktsp

cd


Results

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SCR Mkt spread (EURm)

0 26 3 10 20 0

nSCR Mkt spread (EURm)

0 4 3 10 20 0


It is interesting to compare the line-of-business approach (economic capital approach) and the aggregate approach taken by Solvency II (regulatory capital approach).


10 - ABS (asset-backed security); CDO (collateralised debt obligation); CDS (credit default swap); TRS (total return swap); CLN (credit-linked note). 11 - Mkt sp

struct = ∑i MVi * n(duri)*G (ratingi)


Eurodenominated

Motor own damage

Property damage


Health

Bonds (EURm) 663 4920 370 804 550 95

% of bonds 99% 99% 99% 99% 99%

% of structured credits 1% 1% 1% 1% 1%

% of credit derivatives (investment not hedging

0% 0% 0% 0% 0%

% non-governement bonds 60% 50% 60% 75% 40%

Non-governement bond portfolio components

cf. appendix 7

Structured credit portfolio components

cf. appendix 7


47 360 265 387 276 52





QIS4 assumptionsActivity Total balance

sheet

Bonds (EURm) 7403

% of bonds 99%

% of structured credits 1%

% of credit derivatives (investment not hedging

0.10%

% non-government bonds 60%

Non-government bond portfolio components

cf. appendix 7

Structured credit portfolio components cf. appendix 7


1387


ResultsBilan Total

SCR Mkt spread (EURm) 59

nSCR Mkt spread (EURm) 37


The spread risk sub-module of the market risk module is perfectly linear, the QIS4 and economic capital approaches lead to identical results.

I.6. Capital required for risk of concentration of market risksThe supervisor deemed it advisable to incorporate market risk concentrations to reflect the risks of additional volatility

inherent to concentrated asset portfolios and of losses of value resulting from the default of an issuer. For the sake of simplicity, QIS4 limited the bounds of this parameter to the risk of the accumulation of exposures to the same counterparty. Other types of concentrations (geographic area, industry sector, and so on) are thus out of bounds.

It is assumed that risk concentrations are present only when the net exposure to a counterparty with a rating higher than or equal to A is greater than 5% (or, for counterparties with ratings lower than A, when this exposure is greater than 3%). This exposure does not count policies where the policyholder bears the investment risk,12 not including sovereign bonds, holdings of more than 20% of the shares of an insurance or financial services company (see treatment of subsidiaries—QIS4, annex SCR 1, TS.XVII.C), or bank deposits of a term of less than three months and a ceiling of €3 million in a bank rated at least AA.

Three steps are taken to calculate the SCR Mkt conc capital charge:• based on total asset (Assetsxl)13 and net exposure of assets at default (Ei), determination of excess exposure (XSi) to counterparty i depending on its rating (the concentration threshold CT is at 5% for a rating of A or higher and at 3% otherwise): XSi = max{0 ; (Ei/Assetsxl) – CT}.


12 - As in the spread risk sub-module, contracts in which the policyholder bears the risk are excluded from the calculation of risk concentrations, but the capital charge is adjusted for the share of the risk borne by the insurer in that event that the policies have embedded options and guarantees (ΔLiabul).13 - For this sub-module of market risk, all the entities in a conglomerate should be treated as a single counterparty. The asset classes considered are stocks and bonds (including bonds held as collateral) and such hybrid instruments as the junior and mezzanine tranches of CDOs. The exposure should be assumed net, that is, it should be assumed, for example, that a put option on a stock or a credit default swap (single name) reduce stock or bond exposure, but the exposure to the risk of option or CDS counterparty default is dealt with in the counterparty risk sub-module (chapter IV, section II).


Euro denominated

Motor own damage

Property damage



Interest rate QIS4


activities

SCR Mkt spread (EURm)

0 26 3 10 20 0 60 59 99%

nSCR Mkt spread (EURm)

0 4 3 10 20 0 38 37 98%




• calculation of the capital charge per issuer (Conci) on the basis of a shock (gi) depending on the credit rating of the counterparty (gi is equal to 0.15, 0.18, 0.30, and 0.73 for ratings of AA-AAA, A, BBB, and lower than BB or unrated respectively): Conci = (Assetsxl * XSi * gi ) + ΔLiabul • calculation of the capital charge for aggregate market concentrations risk SCR Mkt conc assuming independence of the capital required for each counterparty: SCR Mkt conc = √∑ Conci².

Simulation with the model companyFor the sake of simplicity, we assume that for each line of business there is a single net 4% exposure to a BBB-rated counterparty. Since it is assumed that the percentage and the counterparty are the same for each line of business, the sum of the exposures for each of the lines of business leads to a single net exposure of 4% to a BBB-rated counterparty. Unit-linked business in life insurance, of course, is excluded from this module, as spelled out in the method defined in QIS4:

Results Activity

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SCR Mkt conc (EURm)

0 12 1 2 2 0.13

nSCR Mkt conc (EURm)

0 0 1 2 2 0.13


It is interesting to compare the approach by line of business (economic capital approach) to the aggregated approach from Solvency II (regulatory capital approach).

QIS4 assumptionsActivity Total balance

sheet

Total assets excluding unit-linked, government bonds and reinsurance (EURm)

5764

Net exposure 4%

Counterparty rating BBB


1387


QIS4 resultsActivity Total balance

sheet

SCR Mkt conc (EURm) 17

nSCR Mkt conc (EURm) 5



Activity Eurodenominated

Motor own damage

Property damage


Health


3965 288 774 694 44

Net exposure 4% 4% 4% 4% 4%

Counterparty rating BBB BBB BBB BBB BBB

Net asset value (NAV) before the shock (EURm) 360 265 387 276 52


Assumptions:



Comparison of the regulatory capital required according to QIS4 (global approach) to the economic capital (line of business approach with the goal of capital allocation to line of business)

The market concentrations risk sub-module is not linear because the capital requirement is the square root of the squared concentrations sum (per counterparty). Nevertheless, in our simulation we assumed that the exposure to counterparty risk was identical for each line of business; as a result, global exposure to the counterparty is linear.

I.7. Total capital required for market risk module (SCR Mkt)In the preceding sections (I.1 to 1.6), we calculated the capital required for the six Solvency II market risk sub-modules. As we have noted previously, these calculations could be fined tuned by and/or tailored to each insurer, so that an exposure to risks in greater keeping with the features of its portfolios can be calculated (the supervisor-approved internal model).

To determine the total capital required for market risk (SCR Mkt), the regulator assumes a correlation of the risk sub-modules but looks at the insurer as a whole.

For the purposes of allocating economic capital to each line of business, we will determine a SCR Mktj for each of the six lines of business j. The problems of non-linearity will be dealt with in detail in the following chapter.

SCR Mkt j = √∑r,c CorrSCR Market rxc, j* Mktr j* Mktc j

where CorrSCR Marketrxc are the cells of the matrix of the correlation of the six market risk sub-modules (Mktk) for each line of business j (unit-linked, euro denominated, motor own damage, property damage, third-party liability, and health). We take the correlation matrix provided by QIS4 (2008) for the company as a whole and for each of its lines of business.



Euro denominated

Motor own damage

Property damage



Interest rate QIS4


activities

SCR Mkt conc (EURm)

0 12 1 2 2 0.13 17 17 100%

nSCR Mkt conc (EURm)

0 0 1 2 2 0.13 5 5 100%


Corr SCR market Mkt interest Mkt equity Mkt property Mkt fx Mkt spread Mkt conc

Mkt interest 1 0 0.5 0.25 0.25 0

Mkt equity 0 1 0.75 0.25 0.25 0

Mkt property 0.5 0.75 1 0.25 0.25 0

Mkt fx 0.25 0.25 0.25 1 0.25 0

Mkt spread 0.25 0.25 0.25 0.25 1 0

Mkt conc 0 0 0 0 0 1



Simulation with the model companyMarket risk sub-module capital charges per line of business

II. Capital Required for Counterparty RiskLike the market risk module, the counterparty risk module is an aggregate (the company is taken as a whole). All the same, for the purposes of the economic capital model, we will single out the counterparty risks for each of our model insurer’s six lines of business. To determine capital allocated to each line of business, it will then be necessary, as a result of this disaggregation, to make allowances for possible non-linear effects.

The counterparty default risk module is defined by QIS4 (2008) as “the risk of possible losses due to unexpected default, or deterioration in the credit standing of the counterparties or debtors in relation to risk mitigating contracts, such as reinsurance arrangements, securitisations and derivatives, and receivables from intermediaries, as well as any other credit exposures which are not covered in the spread risk sub-module.”

The definition of the capital required for counterparty default risk (SCR def) makes it possible to calculate one of the

components necessary to the calculation of risk-adjusted capital for each of the model company’s six lines of business.

The capital charge for counterparty default risk is the aggregation of losses given default (LGDi) of each counterparty i depending on its type (reinsurance or SPV, financial derivatives, intermediaries, and other credit exposures) and its probability of default (PDi) as indicated by outside credit ratings:14 • The loss given default on a reinsurance contract or SPV is: LGD = 50% * max (recoverables + gross SCRu/w - net SCRu/w - collateral; 0), where gross/net SCRu/w is underwriting risk gross/net of reinsurance and recoverables are the best estimate of recoverables from the reinsurance contract or SPV. Any collateral held by the counterparty itself should not be taken into account in the calculation. If the collateral bears any default risk, it should be included in the module calculation like receivables from intermediaries and other


14 -

Ratingi PDi Ratingi PDi Ratingi PDi

AAA 0,002 % BBB 0,24 % CCC or lower,

unrated

30,41 %

AA 0,01 % BB 1,20 %

A 0,05 % B 6,04 %

Source : QIS 4

An unrated insurer subject to Solvency II is considered BBB; if it is not subject to Solvency II it is considered CCC.

SCR (EURm) Euro denominated

Unit linked

Motor own damage

Property damage



Interest rate QIS4


activities

Interest rate 371 4 28 40 0 5 448 420 94%

Equity 49 4 32 93 89 2 268 267 100%

Property 21 0 5 11 18 0 55 55 100%

Fx 0 0 0 0 0 0 0 0 -

Spread 26 0 3 10 20 0 60 59 99%

Concentration 12 0 1 2 2 0 17 17 100%

SCR Market 395 6 48 115 111 5 679 568 84%

nSCR Market 351 6 48 115 111 5 635 511 80%


360 47 265 387 276 52 1387 1387




credit exposures (see above). The benefits of the risk-mitigating effects of future profit sharing are left out. • Loss given default on a financial derivative is: LGD = 50%* max (market value + gross SCRmkt - net SCRmkt - collateral; 0), where market value is the value of the financial derivative as defined in article 74 of the proposal for a framework directive.• Loss given default on recoverables from intermediaries and other credit exposures is the best estimate of the credit to intermediaries and any other credit exposures.

When each loss given default (LGDi) has been calculated for each counterparty i, an index of the concentration of the exposure by counterparty type (Hre, Hfd, Hint, and Hoce)15 and an implicit correlation R are calculated via the Herfindahl index16 in order to determine the capital charge Defi for each type of counterparty. The sum of these capital charges produces the capital

required for counterparty default risk (SCR Mkt def).

Simulation with the model companyAssumptions: we have assumed that for each line of business the model insurer had reinsurance arrangements with ten reinsurers, the three largest of which accounted for 61% of the total of the business. Given the individual weights of the seven other reinsurers, the capital required for counterparty risk is nil. The tables below therefore show the assumptions and results only for the three largest reinsurers.


15 - Hre, Hfd, Hint, Hoce

are indices of the concentration of exposure to reinsurers or SPVs (re), to financial derivatives (fd), to recoverables from intermediaries (int), and to other credit exposures (oce). 16 - Herfindahl index = Σ (LDG)²/(Σ LDG)² et R = 0.5+0.5H.For an implicit correlation R less than 1, the determination of Defi is based on the Vasicek distribution: Defi = LGDi * N [(1-R)-0.5*G(PDi) + √(R/(1-R)* G(0.995)] where N is the cumulative distribution function for the standard normal random variable and G is the inverse of this function. For an implicit correlation R greater than 1, Defi = LGDi * min(100*PDi; 1).

Calculation of one of the components of RAC

RAC euro denominated = F(SCR euro denominated) = F(SCR Life euro denominated, SCR Mkt euro denominated, SCR def euro denominated (counterparty), SCR operational euro denominated)

(same approach for RAC UL, RAC motor own damage, RAC property damage, RAC third-party liability et RAC health)

ActivityPremiums

EURmPremiums

%RAC in %

of premiumsRAC

EURmNet

marginNet profit

EURmRoRAC g

RAC x

V(RAC)EURm

V(RAC)%


Life unit linked

Motor own damage

Property damage


Health

Sum

Surplus

TOTAL





AssumptionsTotal balance sheet

Percentage of concentration per reinsurer

Reinsurer 1 27%

Reinsurer 2 17%

Reinsurer 3 17%

Other reinsurers 39%

Total 100%


1387


QIS4 resultsTotal balance sheet

SCR Mkt def (EURm) 0.4

nSCR Mkt def (EURm) 0.4




Motor own damage

Property damage


Health


Reinsurer 1 27% 27% 27% 27% 27% 27%

Reinsurer 2 17% 17% 17% 17% 17% 17%

Reinsurer 3 17% 17% 17% 17% 17% 17%

Other reinsurers 39% 39% 39% 39% 39% 39%

Total 100% 100% 100% 100% 100% 100%


47 360 265 387 276 52


Assumptions


Motor own damage

Property damage


Health

SCR Mkt def (EURm) 0.0035 0.0136 0.4558 0.6796 0.3062 0.0222

nSCR Mkt def (EURm) 0.0035 0.0000 0.4558 0.6796 0.3062 0.0222


Results (economic capital approach per line of business)

SCR (EURm)

Euro denominated

Unit linked

Motor own damage

Property damage



Interest rate QIS4

Interest rate QIS4/

sum of activities

SCR def (EURm)

0.0035 0.0136 0.4558 0.6796 0.3062 0.0222 1.4810 0.4267 29%

nSCR def (EURm)

0.0035 0.0000 0.4558 0.6796 0.3062 0.0222 1.4673 0.4025 27%


Counterparty default risk synthesis



As the set of the preceding risk modules (underwriting and market) and the Vasicek distributions, themselves a function of the Herfindahl index, are used to calculate the counterparty default risk module, it has very many non-linearities.

In conclusion, this chapter has made it possible to calculate the capital charges for market and counterparty risks, charges whose calculation is necessary to the determination of the regulatory capital and to the economic capital required by each of the lines of business of our model insurer, under the constraint of Solvency II. With these results, as well as those from chapter III, and in light of chapters I and II, chapter V will be able to show the contributions that economic capital models can make to risk management and, more broadly, to the creation of value for shareholders or mutual members.


5. Economic Capital Model versus Solvency II Regulatory

Capital




In chapters III and IV, we calculated the capital required for the risk types (life underwriting, non-life, health, market and counterparty risks) for each of the six lines of business of the model insurer. The final phase involves calculating regulatory capital, in keeping with the framework provided by the prudential regulator, for the company as a whole and putting in place, under the constraint of Solvency II, the economic capital model. This model is more sophisticated than that put in place by the regulator, as it defines allocation of capital not just for the company as a whole but also for each of the lines of business it is involved in, a definition that makes possible a more sophisticated dashboard, especially for managing risks and, more broadly, value creation.The complexity lies in the non-linear treatment of some of the modules, and the diversification of risks and lines of business.

The aim of the first section is to calculate regulatory capital. Section II defines the economic capital model under a Solvency II constraint. These two sections serve as the bases for our demonstration of the numerous contributions of this decision model: it contributes to the management of risk-adjusted capital (RAC), to the definition of policies for investment, underwriting, provisioning, reinsurance, asset/liability management, allocation of capital to lines of business, and risk management (definition of accepted limits, concentration, diversification) and to the communication with the financial markets, rating agencies, and the prudential regulator. The heart of this model is the creation of value for the shareholders or mutual members.

Finally, section III shows that Solvency II will lead to a profound shift in risk transfer policies, those involving reinsurance in particular. As it now takes risk transfer policy and the underlying counterparty risks more closely into account, Solvency II favours the management and hedging of risks. We will see, nonetheless, that the measurement and calibration of the formula are decisive, and that a few modifications still need to be made if the regulator wants to avoid causing certain biases that would be at odds with its objective of encouraging improved management of insurance companies.

I. Calculation of Solvency II Regulatory CapitalAs we mentioned in sections II.2 and II.3 of chapter II, there are two levels of capital requirement in the Solvency II framework: the minimum capital requirement (MCR) and the solvency capital requirement (SCR). The MCR is the indispensable minimum for doing business. If this requirement is not met, supervisory intervention is systematic. The SCR is the target capital that every insurance company should aim for, capital that will enable it to absorb most unusual shocks. As such, the SCR is a benchmark for calculating RAC, in internal decision tools as well as in economic capital models. The SCR, with a VaR at 99.5% on a one-year horizon, is the aggregate of the six risk modules (themselves split into sub-modules—see appendix 4).

SCR = BSCR + SCROp – Adj

where BSCR is the basic solvency capital requirement, SCROp is the capital charge for operational risk, and Adj the adjustment for the risk-absorbing effect of future profit sharing and deferred taxes.

5. Economic Capital Model versus Solvency II Regulatory Capital



The following sub-sections (I.1-I.6) deal with the calculation of each of these terms.

I.1. Calculation of the basic solvency capital requirement (BSCR)The BSCR is the aggregate of the capital charges for the five risk modules described in chapters III and IV (life underwriting, non-life, health, market, and counterparty) before operational risk is taken into account and adjustments are made for the risk-absorbing effects of future profit sharing and deferred taxes. To include the benefits of diversification and the correlation of the five risk modules, the BSCR is defined by Solvency II in the following way:

BSCR = √∑r, c Corr SCRr,c* SCRr *SCRc

where Corr SCRr,c are the cells of the correlation matrix.

Simulation with the model company

In this table, the BSCR per line of business is the capital required before taking into account operational risk and the risk-absorbing effects of future profit sharing and deferred taxation, but after taking into account the correlation of the five Solvency II risk modules. It is apparent that the benefits from the diversification of the lines of business (BSCR QIS4 in the table) are substantial, as they make it possible to

reduce by 50% the sum of capital required when the lines of businesses are considered individually ( in the table). We will go over these figures in greater detail in section I.4, in particular with reference to the CEIOPS report (2008) that presents the QIS4 results obtained for European insurers.

I.2. Calculation of the solvency capital requirement for operational risk (SCROp)This risk module covers operational risks not explicitly covered by the other risk modules (chapters III and IV), in particular the risk of loss arising from inadequate or failed internal processes, people, systems, or external events and legal risks. Reputation risks and risks stemming from strategic decisions are not included.

The capital charge for operational risk is a function of the BSCR,1 of annual administrative expenses (gross of reinsurance and not including acquisition expenses) for unit-linked business (Expul), and of the basic capital charge for the operational risk of all business other than unit-linked business (Opln ul):2

SCR Op = min (0.30 * BSCR; OPln ul) + (0.25* Expul)


1 - The capital charge for operational risk is thus capped at 0.3 times the BSCR (article 106(3) of the proposed framework directive).2 - OPln ul = max [0.03*(Earnlife- Earnlife-ul) + 0.02*Earnnon-life+ 0.02*Earnhealth; 0.003*(TPlife-TPlife-ul) + 0.002*TPnon-life + 0.002*TPhealth] where:Earnlife and TPlife are the total earned life premiums and technical provisions gross of reinsuranceEarnlife-ul and TPlife-ul are the total earned life premiums and technical provisions gross of reinsurance for unit-linked policiesEarnnon-life and TPnon-life are the total earned non-life premiums and technical provisions gross of reinsurance, excluding the risk related to annuities in the health and accident lines of business Earnhealth and TPhealth are the total earned non-life premiums and technical provisions, gross of reinsurance and not included in Earnnon-life and TPnon-life.

Corr SCRr,c SCR Mkt SCR def SCR life SCR health SCR NL

SCR Mkt 1 0.25 0.25 0.25 0.25

SCR def 0.25 1 0.25 0.25 0.5

SCR life 0.25 0.25 1 0.25 0

SCR health 0.25 0.25 0.25 1 0.25

SCR NL 0.25 0.5 0 0.25 1

Source: QIS4


Euro denominated

Motor own damage

Property damage



BSCR QIS4

BSCR QIS4 /sum of activities

BSCR 7 400 288 401 323 29 1448 693 48%

n BSCR 7 351 288 401 323 29 1400 636 45%





It should be underscored that the operational risk module is built gross of reinsurance and that it is still founded on a very nearly standard approach. We will return in greater detail to the treatment of risk transfers (of reinsurance as treated by the standard formula of Solvency II, in particular in section III). As it turns out, for each of the lines of business of the model company, the lower of 0.30 * BSCR and OPlnul is always the latter.

QIS4 calculation of operational risk (global approach to the company)Assumptions(EURm) Total balance sheet

Gross technical provisions

Unit linked 1425

Euro denominated 6000

Non-life 1592.5

Health 42.5

Gross earned premiums

Unit linked 255

Euro denominated 1020

Non-life 2250

Health 204

Annual expense rate for unit-linked activity

2%


1387


QIS4 resultsTotal balance sheet

SCR Op (EURm) 75


When the two approaches (by line of business and global) are compared, the results are not identical, as the module is not linear (it has minimum and maximum functions).

So, not including the risk-absorbing effects of future profit sharing and deferred taxes, operational risk requires 11% more capital on top of the BSCR, a requirement somewhat above the European average (ACAM 2008; CEIOPS 2008).


ActivityUnit

linkedEuro

denominated Motor own



Health

Gross technical provisions (EURm) 1425 6000 205 740 648 43

Gross premiums earned (EURm) 255 1020 1044 1050 263 204

Annual expense rate 2%

Net asset value (NAV) before shock (EURm)

47 360 265 387 276 52


Operational risk assumptions for the economic approach per line of business under QIS4


Activity Unit linked Euro denominated

Motor own damage

Property damage


Health

SCR Op (EURm) 3 31 21 21 5 4

Results per line of business (economic approach)



I.3. Calculation of the adjustments for the risk-absorbing effect of future profit sharing and deferred taxesThe adjustment for the risk-absorbing effect of future profit sharing (Adj FDB) is calculated based on the lower of the technical provisions for future discretionary benefits (FDB) and the difference between the BSCR and the nBSCR:3

Adj FDB = min{(√∑r, c CorrSCRr, c* SCRr *SCRc - √∑ r, c CorrSCRr, c* nSCRr * nSCRc) ;

FDB}


Naturally, for the model company, only euro-denominated life insurance policies benefit from the risk-absorbing effect of future profit sharing. When the line-of-business (see sum of activities—total in the table above) and Solvency II (FDB QIS4 after diversif. BSCR) approaches are compared, it is apparent that the risk-absorbing effects of diversification, especially on the market risk modules and on the lines of business, as well as on the five risk modules described in chapters IV and V, are not linear.

Given the profile of the model insurer (six lines of business in which euro-denominated life insurance accounts for only 27% of total premiums), the diversification benefit is more modest than that of the European average, where country profiles are nonetheless highly dissimilar.

In the context of calculating the adjustment for the risk-absorbing effects of deferred taxation (Adj DT), let us recall that the BSCR was calculated based on a balance sheet without deferred tax liabilities and without taking into

account the tax savings in each risk module (in particular, following changes to net assets). AdjDT is the absolute value of the reduction of deferred taxes (Δ Deferred Taxes) following a scenario (SCR shock) corresponding to the immediate loss of basic own funds of the amount BSCR- AdjFDB + SCROp.

Adj DT = Δ Deferred Taxes | SCR shock

Simulation with the model companyWe have assumed a corporate tax rate of 33.33%


3 - The capital charge for the different risks given the risk-absorbing effects of future profit sharing.

Comparison of operational risk according to QIS4 and to an economic approach per line of business



Euro denominated

Motor own damage

Property damage



BSCR QIS4


SCR Op (EURm)

3 31 21 21 5 4 85 75 89%

Comparison of the risk-absorbing effects of future profit sharing according to QIS4 and to an economic approach per line of business



Euro denominated

Motor own damage

Property damage



FDB QIS4 after diversif. BSCR

FDB QIS4/Sum of the activities

Adj FDB (EURm)

0 44 0 0 0 0 44 57 130%

Comparison of the adjustments for deferred taxes according to QIS4 and to an economic approach per line of business



Euro denominated

Motor own damage

Property damage



Deferred taxes QIS4

Def. Taxes QIS4/Sum of activities

Adjustment for deferred taxation (EURm)

3 92 35 54 43 10 237 237 100%



The savings in the capital required for deferred taxation is 33.33% for our model insurer, which is higher than that in the results published by CEIOPS (for example, 20% for French companies, according to the ACAM). This difference may be accounted for by the average tax rate in Europe or by the failure of many of the respondents to QIS4 to make this adjustment. In the end, the effects of the adjustment (FDB and deferred taxes) make it possible to reduce the capital requirement by 42% (by 50% according to the figures from ACAM and CEIOPS).

I.4. Calculation of the overall solvency capital requirementWe have noted previously that the calculation of the overall SCR is done on a one-year horizon using a VaR of 99.5%, based on the aggregation of six risk modules (themselves broken down into sub-modules—see appendix 4).

SCR = BSCR + SCROp - Adj


The weight of the diversification of business in the Solvency II framework should be underscored: the capital requirement in the QIS4 method (after diversification) is €470 million, whereas the sum of the capital required for each of the lines of business (that is, after geographic diversification and diversification of underwriting and market risks and adjustments for risk-absorbing effects but before the diversification of the lines of business benefit) is €1.16 billion.

In addition to this substantial capital savings made possible by the diversification of the lines of business, it is interesting to break down the components of the capital required for each risk type. The following table synthesises the entirety of the calculations made in keeping with the QIS4 risk-adjusted capital method (economic capital).


Calculation of overall SCR per line of business (economic approach) and QIS4 method



Euro denominated

Motor own damage

Property damage



BSCR QIS4


Global SCR (EURm) sum of risk modules

8 267 238 352 284 25 1175 474 40%

Capital required before benefit for diversification of business

(EURm) Unit linked

Euro denominated

Motor own damage

Property damage



SCR u/w 3 16 272 357 277 27 952

n SCR u/w 3 0 272 357 277 27 936

SCR Mkt 6 395 48 115 111 5 679

n SCR Mkt 6 351 48 115 111 5 635

SCR Def 0 0 0 1 0 0 1

n SCR Def 0 0 0 1 0 0 1

BSCR 8 412 320 472 388 32 1633

Operational SCR 3 31 21 21 5 4 85

Adj DPF 0 48 0 0 0 0 48

Adj deferred taxes 3 127 103 141 110 11 495

GLOBAL SCR sum of risk modules 8 267 238 352 284 25 1175




In life insurance, market risk accounts for 98% of the aggregate SCR (sum of the underwriting, market, and counterparty capital requirements). Underwriting risk is relatively modest, given the weight of the savings component. The adjustment factors are the key. They make it possible to reduce substantially (16% for FDB and 28% for deferred taxes)

the life capital charge.


Breakdown of the QIS4 capital required per line of business


Euro Motor own damage

Property damage


Health Total

Reinsurance ratios

Net/gross technical provisions 95% 99% 98% 85% 80% 98%

% premiums reinsured 3% 10% 15% 3%

Underwriting risk module (EURm)

Mortality/prem and reserve for non-life

0.1 3.7 262 350 276 21

Longevity 0.5 2.3

Disability 0.0 0.1

Lapse 1.5 11.1

Expense 1.3 5.6

Revision 0.0 0.0

Catastrophe 0.1 2.5 73 68 32 17

Total underwriting SCR 2.6 16.4 78 102 79 27 304

Market risk module (EURm)

Interest rate 4 371 28 40 0 5

Equity 4 49 32 93 89 2

Property 0 21 5 11 18 0

Fx 0 0 0 0 0 0

Spread 0 26 3 10 20 0

Concentration 0 12 1 2 2 0

Total market SCR 5 330 40 96 92 4 568

Counterparty SCR before diversification (EURm)

0.003 0.014 0.456 0.680 0.306 0.022 1.481

Counterparty SCR after diversification (EURm)

0.001 0.004 0.131 0.196 0.088 0.006 0.427

BSCR u/w + mkt + def (EURm) 7 347 118 198 172 32 873

BSCR after diversification (EURm) 5 307 88 143 124 26 693

Operational SCR after diversification (EURm)

3 27 19 19 5 4 75

Adj FDB (EURm) 0 57 0 0 0 0 57

Adj deferred taxes (EURm) 3 92 35 54 43 10 237

Global SCR after diversification (EURm)

5 185 71 108 86 20 474

NAV (EURm) 47 360 265 387 276 52 1387




The report on the European results published by CEIOPS and ACAM shows that capital requirements differ greatly from one non-life insurer to another, a difference that is the result of the duration of liabilities. The insurers whose liabilities unwind over the long term tend to have capital requirements for underwriting risk greater than those for market risk.

The simulation with a model company shows a relative balance of capital requirements for these two risks (50% for underwriting risk and 45% for market risk). Third-party liability, as it happens, accounts for only 11% of the insurer’s non-life business (not including health) and 7% of its total premiums.

As we have noted above, the capital savings for diversification of risks and lines of business, as well as the adjustments for risk-absorbing effects, are very high. As a result, the ACAM and CEIOPS reports

underscore that ultimately QIS4 involves capital requirements greater than those of Solvency I, but that any increases are largely offset by these diversification effects, so much so that insurance company surpluses are mostly unaffected, whatever the prudential framework (Solvency I or Solvency II).

If capital requirements are broken down no longer by line of business but by risk module, we see that the major component of market risk in life insurance is interest rate risk (77%, as opposed to 11% for equity risk before the diversification benefit). In non-life, equity risk (60%) is a much greater component than interest rate risk (19%), and this as a result of the structure of the assets and the duration of the liabilities. Overall, for the simulation of our model company it is interest rate risk that is the largest single component of the market risk module (52%, as opposed to 32% for equity risk).



Breakdown of the life and non-life SCR



For underwriting risk, in life insurance, capital requirements are fairly homogeneous. Lapse and longevity risks, which each account for approximately one-third of the total capital requirement in the underwriting risk module, are the largest consumers of capital. In non-life insurance, requirements for premium and reserve risks account for between 78% and 90% of capital required for underwriting risk.

The entirety of these calculations thus makes it possible to determine the economic capital required for each line of business under Solvency II. Before we describe the means of going from Solvency II to a dashboard, let us underscore that for pillar II additional capital may be required: these additional requirements are known as capital add-ons.

I.5. Evaluation of capital add-onsAccording to the proposed directive of the European Parliament and Council (2007), as part of supervisory review, the supervisory authorities must assess the adequacy of the strategies and reporting procedures used by insurers to identify, measure, and control their risks. Article 37 stipulates that the solvency capital requirement is the starting point. Nonetheless, if the supervisory authorities believe that risks are inadequately taken into consideration, that the standard formula or the insurer’s internal models fail to reflect the company’s real exposure to risk, or that governance systems are faulty, they may require an additional solvency margin, the so-called capital add-ons.

For the simulation with our model company, we assume that no capital add-on is


Underwriting components per activity


Market SCR components per activity




required. If it were, this capital add-on would naturally be included in the economic capital model and it would increase the figures for risk-adjusted capital.

I.6. Definition of eligible capital and breakdown into tiersIt seems likely that, with the coming into force of Solvency and the changes it will lead to, prudential regulation will have a great impact on the management of own funds, in particular on the choice of capital type (“core” own funds, hybrid and/or subordinate capital instruments) with respect to the three tiers defined by the supervisory authorities and to the SCR and the MCR.

The proposed directive of the European Parliament and Council (2007) defines own funds as the sum of basic own funds (the excess of assets over liabilities, not including own shares directly held by the insurer or subordinated liabilities) and ancillary own funds, which are own funds that, after prior supervisory approval, can be called on to absorb possible losses (unpaid share capital that has not been called up, letters of credit, or, for mutual undertakings, calls for supplementary contributions).

As in the banking world, own funds are broken down into three tiers, on criteria involving:i) subordinationii) loss-absorbencyiii) permanenceiv) perpetual naturev) absence of mandatory servicing costs.

Basic own funds that meet the conditions for subordination, loss-absorbency, and permanence and to a large degree the conditions for a perpetual nature and

absence of servicing costs are eligible for tier 1. Ancillary own funds that meet the conditions for subordination, loss-absorbency, and permanence and to a large degree the conditions for a perpetual nature and absence of servicing costs are classified in tier 2. If basic own funds fail to meet only the condition for permanence (“the item is available, or can be called up on demand, to absorb losses on a going-concern basis, as well as in the case of winding-up”) they are classified as tier 2 funds. Basic or ancillary own funds that do not have the characteristics that would make them eligible for tiers 1 or 2 are classified in tier 3. For example, surplus funds not made available for distribution to policyholders and beneficiaries are classified in tier 1 and letters of credit or claims against members by way of calls for supplementary contributions are in tier 2. Finally, own funds are eligible for these tiers within the following limits.

Eligibility of own funds and limits

SCR MCR

Tier 1 At least one-third At least 50%

Tier 2 The balance The balance

Tier 3 At most one-third

Source: Commission of the European Communities (art. 97, 2007)

Solvency II, of course, is principles-based rather than rules-based. Indeed, so as not to participate in domestic and European debates on the difference between hybrid capital instruments and subordinated liabilities, QIS4 (2008) states: “what is ultimately relevant is the extent to which a particular instrument holds the qualitative characteristics required for classification in a particular tier”.

In addition, QIS4 emphasises the necessity of determining the solvency of the company by making allowances for the inability to




transfer ring-fenced own funds. To simplify our calculations, we assume that our model insurer has no ring-fenced structures.

It is thus very likely that, in an attempt to optimise the management of capital under Solvency II, capital structure offerings, perhaps through hybrid capital instruments or subordinated liabilities, will find takers.

II. Calculation of Economic Capital under Solvency II ConstraintsChapters I and II described the role of value creation in company strategy. Chapters III, IV, and section I of chapter V calculated regulatory capital in keeping with the Solvency II prudential framework. With all these elements, we can now build an economic capital model under Solvency II constraints.

II.1. Elaboration of the economic capital model in the Solvency II environmentThe QIS4 standard formula can, of course, be viewed as an simplified internal model that each insurer can (and is even encouraged to) perfect or fine tune so that it will be suited to its own characteristics, in particular its exposure to risks and its ability to manage them.

The objective of this economic capital model is to provide every company with a steering tool, the foundation of which is the investment—in both data collection and simulations—required to meet the demands of the supervisory authority. This decision tool makes it possible to manage available capital (the capital structure), allocation of capital to lines of business

(by profitability, cost, and consumption of capital), and exposure to risk (which has an impact on capital requirements), financial autonomy and solvency and to reallocate surplus capital destructive of value to optimise existing activities or to develop new business. Capital does not come without a cost, so managing capital is indispensable.

The QIS4 standard formula, in its current form, does not make possible a direct calculation of the allocation of capital per line of business, a calculation necessary to the creation of an economic capital model. Indeed, as it is not the domain of Solvency II, some QIS4 risk modules (especially the market risk module) take the company as a whole rather than each of its lines of business.

So some restatements are necessary, in particular to make allowances for the non-linear effects in certain modules and disaggregate the solvency capital requirement (SCR) for each line of business (allocation of economic capital–risk-adjusted capital). In addition, these adjustments must respect the following constraint: the sum of the capital allocated to each activity (RAC) should be equal to the Solvency II SCR (the standard formula or an internal model). In general, we choose to isolate the non-linear effects4 or the diversification and correlation benefits5

defined by QIS4 through correlation matrices and to reallocate them proportionally to each line of business, depending on the variable linked to these benefits (capital charge for a sub-module, best estimate, and so on). So, with the framework provided by Solvency II, we are able to determine risk-adjusted capital per line of business.


4 - For example, there is non-linearity in the lapse module of life underwriting (the most adverse of three scenarios); in the premium and reserve module of non-life underwriting (the Herfindahl index measures geographic diversification); in the catastrophe sub-module of the non-life underwriting module (the square root of the standard charges calibrated per line of business multiplied by the net written premiums for the coming year). Market risk looks at risk overall rather than by line of business. In this way, there are necessarily biases in the interest rate risk sub-module, where one takes the greater of the capital requirements following an upwards or downwards shock scenario. If the analysis is done per line of business, it is not necessarily the same scenario (upwards or downwards shock) that leads to the greater capital requirement. For example, for third-party liability the greater requirement follows a downwards shock and for motor insurance it follows an upwards shock. It is thus necessary to reallocate capital in proportion to the relevant risk variable.5 - For example, QIS4 provides a matrix of the correlation of the seven life underwriting sub-modules (aggregate unit-linked business and euro-denominated business); of the sub-modules of non-life underwriting risk for each line of business (there is a diversification benefit linked to the number of non-life lines of business on the volatility of claims in past years); of the six market-risk sub-modules (correlation of risks). On the other hand, for the concentrations risk sub-module, according to our assumptions, this risk is nil for each line of business taken individually, but it is positive when the company is viewed as a whole, a circumstance that requires reallocation of this overall amount per line of business in keeping with the amount of its assets eligible for this risk.



The Solvency II regulatory framework may become the new standard and constraint for the definition of RAC and is thus harmonising European practices. The insurance companies that already have internal models may need to adjust them to have them approved by the supervisory authorities. Those that do not have them will, as a result of Solvency II, have made most of the investments required to build them. As we have mentioned in the preceding chapters, these investments involve data collection and the running of simulations to meet European regulatory requirements.

The calculation of RoRAC (return on risk-adjusted capital) and of capital surpluses follows from the Solvency II solvency capital requirements (see appendix 7 for more information).

The economic capital model presented in the table above was built with the characteristics of the model company (see appendix 7)

and under Solvency II constraints (RAC is equivalent to the SCR). Analysis of this table makes it possible not only to take in the risk profile and the profitability of the company but also, as we will see in the following sections, to suggest some means of improving the strategic management of the company.

II.2. Analysis of the profile of the company with the conventional approach (turnover, net margin, and return on equity)The economic capital model is a steering tool put in place by most leading European insurers, the use of which is slowly “trickling down” to rest of the insurance industry (a partial or total model). It makes it possible to assess the impact of each strategic decision not just on the relevant business unit(s) (line of business, country, region, and so on) but also on the company as a whole. After all, not every local optimum is necessarily a global optimum (for example, the best acquisition from a


Economic capital model

Life Non-life


Eurodenominated

Motor owndamage

Property damage


Health Sum Excess TOTAL

Premiums

Premiums EURm 250 1000 1000 1000 250 200 3700

Premiums % 7% 27% 27% 27% 7% 5% 100%

Capital

RAC in % (Solvency) 0.4% 3.1% 7.1% 10.8% 34.4% 9.9% 12.8%

RAC EURm 5 185 71 108 86 20 474 615

RAC % of total 1% 39% 15% 23% 18% 4% 100%

Profitability

Net margin 0.8% 4.0% 2.3% 3.0% 6.1% 2.9% 3.1%

Net profit EURm 2 40 23 30 15 6 116

RoRAC 35% 21% 33% 28% 18% 29% 24% 5%

Valuation

RAC x 4.7 2.8 3.6 3.1 2.0 3.2 2.9 0.5 1.2

V(RAC) EURm 25 513 256 336 169 64 1364 308 1671

V(RAC) % 2% 38% 19% 25% 12% 5% 100%




strategic and financial point of view in a particular country is not necessarily ideal for the parent in terms of management priorities, profitability, financing, capital allocation, and so on).

Lines four and five of the table (Premiums €m and Premiums %) show that the risk profile of the model company is not particularly risky:• one-third (€1.25 billion) of total premiums of €3.7 billion is written in life insurance (with a large savings component, as we saw in chapter III); 20% of this life business (€250 million) is in unit-linked policies• Non-life insurance (damage and health) is mainly formed by motor own damage and property damage (€2 billion), each of them accounting for one-fourth of the company; together they account for 82% of non-life premiums • Third-party liability and health account for only 7% and 5% of the total premiums of the company.

So, in view of its business (frequency risks, for the most part), this company does not seem to have an especially risky profile. The company’s riskiest business is third-party liability, but it accounts for only 7% of premiums and its 6.1% net margin (net earnings/premiums) is, at first glance, substantially higher than that of the other non-life businesses of the company (3% for property damage, 2.9% for health, and 2.3% for motor own damage).

Premium breakdown per activityThird-party liability 7%

Life euro denominated 27%

Motor owndamage 27%

Health5%

Life unit linked 7%

Propertydamage27%

Life 34%Non life 66%


Net margin per activity


Property damage

Motor owndamage

Life eurodenominated

Health Life unit linked

0

1

2

3

4

5

6

7


As we mentioned in chapter II, a great number of insurance companies still rely on net margins and the weight (as a proportion of the total weight of the company) of turnover or balance sheet items of each line of business to determine the risk profile. This analysis is usually refined by determining the return on equity (ROE) of the company; here it is 11.3%.6 It should be noted that this calculation is based on published accounting own funds that in no way reflect the economic dimension


6 - The €615 million surplus generates net earnings of €18.54 million (on the basis of a gross return of 4.5% equal to the cost of the debt and a tax rate of 33.33%). The net earnings of the company are thus €134.3 million. Book value (see appendix 7 and chapter III, section I) comes to €1.183 billion.



(under- or over-capitalisation, goodwill, in force, and so on) and that as a result it is a poor strategic indicator and a poor basis for comparing the performance of the insurer and that of other insurers in the industry.

II.3. Economic capital approach suggests a riskier profile than does conventional analysisIn view of the limitations of the conventional approach and the Solvency II constraints that, as we have noted, require heavy investment in data collection and simulations, we expect the development of economic capital models to pick up speed. The economic capital model makes it possible to observe that the weight of our model insurer’s riskiest and highest margin business—third-party liability—is ultimately greater than its share (7%) of premiums would suggest.

Taking into consideration the Solvency II constraint, we have allocated capital for each activity (RACj) that, in view of its intrinsic risks, ultimately corresponds to an economic solvency margin or to the capital necessary to run a line of business. So, as the line for the RAC in % shows, third-party liability requires a solvency margin of 34.4% (of RAC), more than three times that required by property damage (10.8%) or health (9.9%) and nearly five times more than that required by motor own damage (7.1%). In other words, third-party liability accounts for 7% of the premiums of the company, but it consumes 18.1% of total RAC (86/474), 2.6 times more (18.1/7) than its share of premiums. The motor own damage business, by contrast, accounts for 27% of the total premiums of the company but consumes only 15% (71/474) of RAC.

Lines of business as a share of total premiums and as a share of total risk-adjusted capital

Life unit linked 7%

Motor own damage 27%

Propertydamage 27%


27%

Third-partyliability 7%

Health5%

RAC per activityLife unit linked 1%

Motor owndamage 15%

Property damage 23%


39%

Third-partyliability18%

Health4%


So the company’s risk profile is riskier than suggested by the conventional approach described in the previous paragraph.

This increase in the perceived risk of the company may nonetheless be offset by the net margin substantially higher than that of the other lines of business. In other words, some might note that third-party liability has a relatively modest weight and that in return for its riskier profile it is the best-performing line of business. What of it? If the performance of the third-party




liability business is measured not from its net margin (net earnings/turnover) or profitability (net earnings/shareholders equity) or in keeping with Solvency I (net earnings/(16% of turnover)) but with allocated economic capital7 what lessons can be imparted that will improve the strategy and the management of the company?

The net margin of the third-party liability business (6.1%) is 2.6 times that of the motor own damage business (2.3%) but takes up five times more allocated capital (RAC of 34.4% vs. 7.1%) as a result of its intrinsic risks. So it turns out that profitability measured as the return on risk-adjusted capital (RoRAC) is 18% for third-party liability, 33% for motor own damage, 28% for property damage, and 29% for health.

In short, motor own damage insurance, which has the company’s lowest profit margin (2.3%), turns out to be its second most profitable business (RoRAC of 33%, as opposed to 35% for unit-linked business), given its modest risk profile (measured here with the Solvency II standard formula but perfectible with an internal model).

Net margin and return on economic capital per activity (%)


Propety damage

Motor owndamage


Health

Life unitlinked

0

50

100

150

200

250

300

350

400

Net Margin RoRAC


II.4. The lessons for valuing lines of businessFinancial analysts and investors can use figures for economic return on risk-adjusted allocated capital to come up with valuation models. Hitherto, these approaches had depended excessively on the subjectivity with which the company calculated RoRAC for its lines of business. In addition, companies do not always publish RoRAC and analysts often had to estimate it.

If it turns out that the Solvency II calibration is relevant from an economic perspective, it is likely that companies and financial analysts will make this prudential framework the standard. As we have mentioned, the solvency capital requirements for each line of business could become a harmonised calculation standard in valuation methods, much as in the approach taken in this study.

To determine the value of the company (V) from that of each of its lines of business (V(RAC)), we have shown in chapter II, section II.2., that the approach taken by the financial markets (net asset value NAV and goodwill GW) is a function of risk-adjusted capital per line of business (RACj), of RoRAC, of the cost of capital CoC, of surplus capital based on adjusted net assets, and possibly a rate of growth towards infinity gj:

V = NAV + GW = NAV + Σj=1,m Σt=0,n [RACjt[RoRACj - CoC)]]/(1+ CoC)t

V = (NAV - Σj=1,mRACj ) + Σj=1,m RACj * (RoRACj - gj) / (CoC - gj)

Discounting at the risky rate does not seem relevant, because the risk is included in the flows to be discounted (Amenc and Foulquier 2006), but the financial markets (most financial analysts, investors, and


7 - The allocated capital (or risk-adjusted capital, RAC) was calculated in keeping with the Solvency II standard formula, which is an initial improvement to the analysis of risks and of economic performance but which, as we have noted, could be made much more sophisticated with a partial or total internal model.



insurance companies) continue to discount at the risky rate (as a precaution, in case risk is insufficiently taken into account). So we have shown the valuation ratios with this approach, more familiar to the reader. We assume a cost of capital of 8.5%.

When RoRAC is greater than the cost of capital to the company, the company creates value and the implicit valuation multiple as a function of RAC (RAC x line) is greater than one. This multiple is the result of the valuation (xRAC = V(RAC)/RAC) and not, contrary to the practices of some analysts, of an a priori appreciation. So the RAC multiple line (RACx) of the dashboard of the economic capital model shows that the lines of business as a whole create value.

Of course, although the third-party liability business generates the highest net margin, it also creates the least value, what with its great consumption of capital. The RAC multiple for third-party liability is 2x, so the valuation of allocated capital for third-party liability (€86 million) comes to €169 million (V(RAC) EURm line). In the end, third-party liability accounts for 7% or premiums, takes up 18.1% of total allocated capital and represents only 16% of the total value of RAC (V(RAC) in % line).

The motor own damage business, by contrast, accounts for 27% of premiums, takes up 15% of allocated capital, and represents 19% of the value.

% of premiums per activity

Life unitlinked

Property damage

Motor own damage



Health

0

5

10

15

20

25

30

RAC per activity

0

5

10

15

20

25

30

35

40

Life unitlinked

Property damage

Motor own damage



Health

Net margin per activity

0

1

2

3

4

5

6

7

8

Life unitlinked

Property damage

Motor own damage



Health




RoRAC per activity

0

5

10

15

20

25

30

35

Life unitlinked

Property damage

Motor own damage



Health

RAC multiple per activity

0

1

2

3

4

5

Life unitlinked

Property damage

Motor own damage



Health

V(RAC) per activity

0

5

10

15

20

25

30

35

40

Life unitlinked

Property damage

Motor own damage



Health

For strategic decisions, then, what main conclusions can be drawn from this dashboard? We will list only two, as each number on the dashboard is in fact a bearer of important information for company management.

II.5. The lessons for strategy (capital allocation, management of surplus)In terms of RoRAC, the least profitable lines of business are third-party liability and euro-denominated policies; they account for 56.5% of the total allocated capital of the company ((185+86)/474). To improve this situation the first thing would be to attempt to reduce RAC by analysing each of the risk sub-modules of chapters III, IV, and V (section I) to pinpoint the greatest consumers of capital and to see what can be done to reduce these capital requirements.

In third-party liability, risk transfers to reduce allocated capital RAC (see section III of this chapter for examples of the sensitivity to reinsurance arrangements) can be studied. The RoRAC numerator should also be looked at; in other words, how to improve the normalised economic profit on these two lines of business (fees, return offered to policyholders, asset allocation, underwriting and financial hedging policy, administrative, management, and acquisition costs, portfolio selection, fraud, claims management costs, and so on.)

Other strategic decisions could be considered as well. Has the company reached a critical mass in third-party liability? If operational and financial management is already optimised and there is really no room to improve RoRAC (by steering RAC and net earnings), is remaining in this business an appropriate strategy? And if it is appropriate,




might it need to expand (to attain critical mass)?

Such analyses should naturally be done for each line of business, and this to identify possible improvements to RAC, to net earnings, and to risk management.

To avoid overloading this analysis, we will focus on only one other strategic point. We see that on the basis of economic capital allocation (RAC) the company is valued at an implicit multiple of 2.9 (RAC x line), but that in the end (the company take as a whole) this multiple changes to 1.2. This value destruction stems from the capital surplus (based on own funds of €1.387 billion from the Solvency II balance sheet, from which one deducts capital allocation (RAC), the debt, and the market-value margin [MVM]; see chapter II). Only 43% of the company’s available capital is allocated to the insurance business (474/(474+615); 57% destroys value. The company would do well to improve allocation of this “dormant” capital, by reinvesting it in existing businesses to improve their profitability and/or making opportune acquisitions that would make it bigger or diversify it or, in the last resort, by returning capital to shareholders (dividends, share buybacks) or mutual members (premium refunds).

It is of course possible to refine the strategies that could be put in place following more detailed analysis (definition of policy for investment, underwriting, new product launches, reserves, reinsurance, asset/liability management, allocation of capital to lines of business, risk management [definition of accepted bounds, concentration, diversification]), but the objective of this section is simply to

demonstrate the feasibility of an economic capital model and to make the reader aware of its contributions to the management of the company.

As this section noted, one of the strategic decisions that should be studied is the policy for the transfer of risks. It is our belief—and one of the regulatory objectives, as it happens—that the culture of those who transfer risks (and therefore the suppliers of risk transfers) is likely to undergo a profound change as a result of incentives to look at these transfers not just locally (business unit) but also globally (optimisation of required capital, reallocation of freed-up capital) and of the quantitative and qualitative standardisation brought about by pillars 1 and 2 of Solvency II. We look at these aspects in greater detail in the following section.

III. Management of Risks and of Required Capital with an Economic Capital Model under Solvency II ConstraintsAs the supervisory authority defines the principles for the attenuation of risk and approves risk transfer instruments, Solvency II should likewise guide the choices made in the province of risk management and required capital. Indeed, one of the great improvements Solvency II makes on Solvency I is that it takes into consideration transfers of risk. Currently, they are dealt with in a standard fashion under Solvency I (see appendix 2—An Efficient System with Numerous Drawbacks).

So, in this new environment, any insurance company will be able to get a read on a combination of instruments (own funds, debt, financial and/or




reinsurance arrangements) from the cost structure as well as the economic and prudential efficiency of each of its sources of financing and risk absorption. In other words, the rationalisation of capital management will involve the rationalisation of risk transfers, on the basis of quantitative evaluations that are in keeping with prudential regulations.

After an introduction to the principles of Solvency II recognition of risk reduction, we analyse the impact of risk transfers on the economic capital requirement. We focus on reinsurance in particular, as it is our belief that, as a result of the change in their views of reinsurance, the criteria guiding the choices of the ceding companies are likely to undergo significant change. Indeed, the companies that have not yet created an overall decision tool in the form of an economic capital model are not currently capable of an exact evaluation of the impact of risk transfers on their available capital (freeing up of capital, reallocation, management of surpluses, holding/transfer arbitrage).

We will conclude by showing that the choice of the treatment for and calibration of reinsurance made by the European supervisory authority will have a great impact on the risk-transfer policies of the ceding companies, and this on the rate of coverage and the ways reinsurance arrangements are assigned to different reinsurers; the number of reinsurers, their ratings, and, finally, their pricing will also have an impact.

The regulation could thus be gamed; such a development would be at odds with the regulatory goal of improved perception and management of risks.

III.1. The economic capital model and the principles of recognition of risk mitigation in accordance with Solvency II (risk management)The preceding chapters have made it possible to define the bounds of risk and importance of managing it. One of the main functions of the economic capital model is to manage risk to optimise capital management. So the Solvency II framework and the economic capital models have a major role in the development of coming means of transferring risk, as they make it possible to quantify the contribution of each of these means.

The figure below shows the connections between risk management policies under Solvency II. Assets are priced at market value or in keeping with the market-consistent principles (see chapter II). Technical provisions are reformatted on the basis of a best estimate and by defining a market-value margin (see chapter II) The Solvency II standard formula (or any supervisor-approved internal model) makes it possible to calculate the capital requirements (SCR and MCR) as well as free assets. For these capital requirements, Solvency II, like Basel II, created a three-tiered quality classification and defined the proportions of capital that are eligible for each of these three tiers (see chapter V, section I.6.).

With this approach, the pursuit of increased available capital and/or of the reduction of required capital makes it possible to improve the management of a company. Risk transfers are one of the preferred means of reducing capital requirements. They make it possible to free up capital that can then be allocated to optimising the bounds of the existing business (insurance and/or financial)




and/or to new developments or lines of business, and this in an attempt to heighten value creation. Here again, in view of the susceptibility of the capital requirement to risk transfer policy, Solvency II has provided a framework as well as Draconian rules that will inevitably have a great influence on the definition of the risk transfer policies of insurance companies.

The supervisor treats separately risk transfers that it takes into consideration in the evaluation of the risk modules and the counterparty risk thus created (for example, for the risk of default of a reinsurer), which is dealt with in a separate module (counterparty risk module—see chapter IV.). In defining these principles, the supervisory authorities took their inspiration from the

requirements made of banks. Whether they are conventional or not, all transfers of asset or liability risk are potentially recognised. But to earn this recognition, they must respect certain principles: the economic effect must take precedence over the legal form, they must be legally effective and enforceable in all relevant jurisdictions, they must be liquid8 as well as of ascertainable value,

explicit, irrevocable, and unconditional, and they must be a direct receivable from the supplier. In addition, the mitigation of risks in the standard formula is restricted to instruments alone and thus excludes processes and controls. So when the capital charge for an investment strategy such as delta hedging or cash-flow matching is calculated the assumption is that the


8 - QIS4 lays down two principles concerning liquidity: the insurer should have written guidance on the liquidity requirements that financial risk-mitigation instruments should meet, in keeping with the objectives of the insurer’s risk management policy, and the risk-mitigating instruments should meet these requirements. The instruments should also have a value over time sufficiently reliable to provide appropriate certainty as to the risk mitigation achieved.


Synthesis of the connections between risk-management policies

Hedgeable Non-hedgeable

At market valueor valued on a

"market-consisitent" basis

Assets

Balance sheet

Free capital

SCR

MCR

Marketconsistent

Risk margin

Best estimate

At least 1/3 of tier 1Balance in tier 2

A most 1/3 of tier 3

At least 50% of tier 1Balance in tier 2

Own funds}

Technical provisions}Increase available

capitalDecrease capital

requirement

Risk mitigation: financial protection and reinsurance in exchange

for additional capital for default risk

Rating Probability of default AAA 0.002% AA 0.01% A 0.05% BBB 0.24% BB 1.20% B 6.40%Others 30.41%

QIS4



company continues to hold its current assets and suffers an instantaneous shock.

To be more effective in a Solvency II framework than those currently available, new means of transferring both financial and underwriting risk are thus likely to see the light of day. At the same time, the risk-transfer policies of insurance companies are likely to be reworked or rationalised; they are likely to be built on more objective and more quantitative bases, and this as a result of the framework created by the supervisory authorities and of the development of economic capital models.

Finally, as the impact of offerings for transferring financial risk (market risk modules) is usually calibrated beforehand by the suppliers of these offerings (banks, reinsurers, asset managers), we expect great cultural changes in the reinsurance landscape, where the global approach to risk management and RAC is still being developed.

III.2. Using reinsurance in a Solvency II framework to mitigate underwriting risksAs we noted in appendix 2, the calculation of the solvency margin does not currently make it possible, in Solvency I, to take into consideration the specific features of a reinsurance programme. The 15% standard deduction from the required solvency margin in life insurance and the 50% deduction in casualty insurance that are allowed in the event of reinsurance seem devoid of any economic foundation.9 In addition, the health of the balance sheets of the reinsurers and the concentration or diversification of a company’s reinsurance

coverage are not taken into account in the calculation of the company’s solvency.

In the Solvency II framework, by contrast, the role of reinsurance is essential to the calculation of the solvency capital requirement (SCR), as the measure of it, although partial, is quantitative, clearly defined, and done on several levels:

i) In the estimate of reinsurance receivables in the balance sheet. In chapter II we saw that the best estimate should be gross of reinsurance contracts and special purpose vehicle arrangements. As a result, receivables from reinsurance contracts and from special purpose vehicles are calculated separately (entered on the asset side of the balance sheet) including the losses expected as a result of counterparty risk,10 the duration of the reinsured liabilities, the time gap between collection and payment, and the possible deposits of the ceding companies. The risk of double counting with the counterparty risk module is often mentioned by insurers, concerns that could lead to modifications to QIS4. The amount of the assets will be affected depend on the reinsurance coverage, a circumstance that could have an impact on the calculation of the SCR, in particular through the market risk module.

ii) In the calculation of the capital charge for the life underwriting risk module (see chapter III). The capital charge is equal to the change in the net asset value following several scenarios.11 A simplified approach (which we have taken) involves calculating the capital requirements for the mortality, longevity, disability, and catastrophe risk sub-modules with net best estimates and capital at risk (insured amount net of technical provisions). For these risk


9 - The calculation of the solvency margin does not currently make it possible, in Solvency I, to take into consideration the specific features of a reinsurance programme). In life insurance, the solvency margin is the sum of two values:i) (4%* gross mathematical provisions GMP *R), where R=(GMP – reinsurance transfers)/GMP and cannot be less than 85%. So Solvency I recognises at most 15% of reinsurance transfers with respect to GMP;ii) (0.3% * capital at risk charged to the life insurer gross of reinsurance GCR * K), where K = (GCR- reinsurance transfers/GCR) and cannot be less than 50%. So Solvency I recognises at most 50% of reinsurance transfers with respect to GCR. These R and K ratios are those of the most recent financial year. In non-life insurance, the solvency margin (we simplify) is the greater of the two values below:i) (16% * gross premiums * C), where C=(gross claims GC – claims transferred to reinsurers)/GC and cannot be less than 50%. ii) (23% * GC * C), where C=(gross claims GC – claims transferred to reinsurers)/GC and cannot be less than 50%. GC is the average over the three most recent financial years. The standard reductions of 15% in life insurance and 50% in non-life insurance seem devoid of any economic foundation. They are often called standard because regardless of the type of coverage (simple proportional from a BB rated insurer or sophisticated non-proportional, indexed to indices, and/or excluding extreme risks and from a AAA insurer), the 15% and 50% coefficients are applied uniformly. 10 - Take, for instance, the example given in QIS4 (2008, TS.II.B.25): if the insurer must pay 100 with a probability of 99% and 10,000 with a probability of 1%, the best estimate of the amount recoverable is 199. If one is sure that the insurer will be able to pay



sub-modules, Solvency II is able to take into consideration most transfers of risk through proportional or non-proportional reinsurance.

iii) In the calculation of the capital charge for the non-life and health underwriting risk module (see chapter III). We have shown that for these businesses Solvency II considered two risk sub-modules: premium and reserve risk and catastrophe risk.

A risk measure of premium volume, determined as a function of net written and earned premiums, and its volatility are used to assess premium risk. The volatility is a function of the volatility of the loss ratios of the company over the last five, ten, of fifteen years, depending on the line of business (by net premiums earned and loss ratios posted in the past) and of the volatility of the market loss ratio.12 So the transfer of risk through reinsurance is founded partly on transferred premiums, a circumstance that is likely to lead to a great underestimate of the efficiency of the coverage of non-proportional arrangements, especially when they have an effect on extreme risks.

The volume of reserve risk, a function of the best estimate, and the market volatility of reserve risk are used to assess reserve risk.

Solvency II offers three means of assessing catastrophe risk: a standard formula (used in our simulation) founded on a standard basis of net written premiums that, again, does not make it possible to take into account in a suitable way non-proportional reinsurance and two scenario-based approaches; these two are more demanding, but they accommodate

tied-up management or commission costs. For the scenario-based methods, the capital charge for non-life catastrophe risk is the square root of the sum of the costs of each catastrophe squared. For a catastrophe to be taken, its cost must exceed a threshold of materiality of 25% of the most adverse scenario.

Naturally, the supervisory authorities encourage the use of internal models when the standard formula does not adequately reflect the real risk exposures of the company, but this is not accessible to all companies. So discussions are underway between insurance industry representatives and regulators to see to what extent improvements can be made to the Solvency II standard formula.

iv) In the allowances made for default risk. For Solvency II to recognise the impact of the risk-mitigation techniques, the credit risk and other risks inherent to this reduction must be taken into consideration in the calculation of the capital requirement. A capital charge in the counterparty risk module integrates the risk of loss-given-default. In chapter IV we saw that it is equal to 50% of the recoverable amount and a function of ratings from rating agencies (two other sources of controversy today), which determines the likelihood of default.

v) Finally, the operational risk module takes into account the entirety of gross pre-transfer risks, which may also seem very conservative.

To evaluate the impact of transfers of risk through reinsurance, we will run a test on our model insurer. We compare three reinsurance arrangements:


the amount of 100, but will default (with a loss-given-default of 50%) if it has to pay the amount of 10,000 the expected loss is: 99%*100*0% + 1%*10,000*50% = 50. The probability of default is 1%, but for QIS4 it is a weighted average of probabilities: (99%*100*0% +1%*10,000*50%)/199 ≈ 50.25%. So the expected loss is: 199*50.25%*50% ≈ 50.11 - The scenarios tested are:• a permanent rise of 10% in the mortality rates for each age for mortality and longevity risks, as well as a permanent fall of 25%. • a rise of 35% in the disability rate for the coming year and of 25% for each age in the following years• a rise and fall of 50% in the lapse rates• an increase in future expenses 10% greater than that of the best estimate, and an increase in expense inflation rate of 1% per year greater than that of the best estimate• an increase of 3% per year in the amounts payable for annuities subject to revision risk (over the remaining run-off period)• simultaneous absolute 1.5 per mille increases in the rate of policyholders’ dying in the coming year and experiencing morbidity in the coming year. 12 - The market standard deviations taken by Solvency II for premium risk of the motor own damage, property damage, third-party liability, and health lines of business are 9%, 10%, 13%, and 3% respectively. The market volatility taken for reserve risk is 7%, 10%, 15%, and 7.5%.



• total absence of reinsurance• reinsurance taken for now to calculate the SCR for the model company presented in chapter III, section I, and appendix 7 (we will call it benchmark reinsurance or benchmark coverage)• doubling of the percentage of premiums transferred.

Simulation of reinsurance arrangements with the model company

Total balance sheet (EURm)

Absence of reinsurance

Benchmark reinsurance

Double benchmark reinsurance

Underwriting SCR 338 304 271

Market SCR 599 568 537

Counterparty SCR 0 0.43 1

BSCR 742 693 646

Global SCR 507 474 442

Reinsurance impact -6% -13%


We see that in spite of our company’s very mixed profile (only a third of the model company’s premiums really benefit from the impact of the transfer of risks to a reinsurer, as the tables below show), the transfer of underwriting risk through reinsurance makes possible substantial reduction of capital

requirements. This reduction is achieved in underwriting as well as market risk (the weight of reinsurance assets in the balance sheet). By contrast, when the number of reinsurers and their ratings (A or AA) are satisfactory, they account for very little of the capital charge for counterparty risk. We will take a close look at counterparty risk and at shifts from one reinsurance policy to another in the following section (section III.3.).

In addition, this simulation tends to underestimate the real benefits of reinsurance in the Solvency II model, as we have not reduced catastrophe risk with coverage of peak risks or volatility of claims with non-proportional protection (and all the more so economically, as we have shown in section III.1., that the supervisory authorities underestimate the effects of reinsurance by neglecting certain types of very widely used coverage).

In the three tables below, we show the detailed results (by risk sub-module and line of business) of the impact of reinsurance coverage.


ActivityUnit

linkedEuro




Health Total

Reinsurance ratios





0.2 3.8 270 397 341 22

Longevity 0.6 2.4

Disability 0.0 0.1

Lapse 1.6 11.2

Expense 1.3 5.6

Revision 0.0 0.0

Catastrophe 0.1 2.5 75 75 38 17


Calculation of economic capital RAC and SCR in the absence of reinsurance coverage






Equity 4 49 32 93 91 2

Property 0 21 5 12 19 0

Fx 0 0 0 0 0 0

Spread 0 26 3 10 21 0


Total market SCR 5 344 43 103 100 5 599


0.000 0.000 0.000 0.000 0.000 0.000 0.000


0.000 0.000 0.000 0.000 0.000 0.000 0.000




3 27 19 19 5 4 75

Adj FDB (EURm) 0 56 0 0 0 0 56



6 193 73 117 98 20 507

NAV (EURm) 47 360 265 387 276 52 1387


Calculation of RAC and SCR with benchmark reinsurance coverage

ActivityUnit

linkedEuro




Health Total

Reinsurance ratios





0.1 3.7 262 350 276 21

Longevity 0.5 2.3

Disability 0.0 0.1

Lapse 1.5 11.1

Expense 1.3 5.6

Revision 0.0 0.0

Catastrophe 0.1 2.5 73 68 32 17




Equity 4 49 32 93 89 2

Property 0 21 5 11 18 0

Fx 0 0 0 0 0 0

Spread 0 26 3 10 20 0


Total market SCR 5 330 40 96 92 4 568


0.003 0.014 0.456 0.680 0.306 0.022 1.481





0.001 0.004 0.131 0.196 0.088 0.006 0.427

BSCR u/w + mkt + def (EURm)

7 347 118 198 172 32 873

BSCR after diversification (EURm)

5 307 88 143 124 26 693


3 27 19 19 5 4 75

Adj FDB (EURm) 0 57 0 0 0 0 57



5 185 71 108 86 20 474

NAV (EURm) 47 360 265 387 276 52 1387


Calculation of RAC and SCR with double the benchmark coverage

ActivityUnit

linkedEuro




Health Total

Reinsurance ratios





0.1 3.7 254 304 210 21

Longevity 0.5 2.3

Disability 0.0 0.1

Lapse 1.4 11.0

Expense 1.2 5.5

Revision 0.0 0.0

Catastrophe 0.1 2.5 71 60 26 16




Equity 4 49 32 92 86 2

Property 0 21 5 11 18 0

Fx 0 0 0 0 0 0

Spread 0 26 3 10 20 0


Total market SCR 5 316 37 89 86 4 537


0.007 0.027 0.468 0.754 0.495 0.024 1.776


0.002 0.009 0.151 0.244 0.160 0.008 0.575




3 27 19 19 5 4 75

Adj FDB (EURm) 0 58 0 0 0 0 58



As expected, the gains from reinsurance are found primarily in the property damage and third-party liability lines of business. The underwriting module makes it possible to save slightly more capital than the market module for all the lines of business benefiting from slightly greater reinsurance coverage. For example, the savings in the market module are greater for euro-denominated life business, health, and motor. The savings from the underwriting module are nonetheless often underestimated, as they do not take into account anything more than proportional improvement of catastrophe risk or non-proportional reinsurance coverage.

To take yet a closer look at the impact of reinsurance on required capital, we compare the savings in the capital charge made by possible by reliance on the three reinsurance strategies detailed above; we look only at third-party liability, that is, without applying the benefit for the diversification of lines of business.


(EURm)

Abse

nce

of

rein

sura

nce

Benc

hmar

k re

insu

ranc

e

Doub

le b

ench

mar

k re

insu

ranc

e

Underwriting SCR

Premium and reserve 341 276 210

Catastrophe 38 32 26

Total underwriting SCR 343 277 212

Market SCR 0 0

Interest rate 10 0 0

Equity 91 89 86

Property 19 18 18

Fx 0 0 0

Spread 21 20 20

Concentration 2 2 2

Total market SCR 115 111 107

Counterparty SCR 0 0.31 0.49

BSCR 458 388 320

Global SCR 332 284 237

Reinsurance impact -15% -29%


The transfer of risks is thus likely to lead to a substantial reduction in the capital required in the Solvency II framework.

In addition, with Solvency II, risks transferred as we have just shown are naturally taken into account, as are the rating of the reinsurer and the weight of each reinsurer in the overall coverage of the company.13 In this way, ratings and diversification have a significant impact on the capital required for default risk and thus on reinsurance policy.

Depending on the final calibrations, an opportunity to arbitrage the cost of reinsurance and the rating of the reinsurer could arise: by reducing the price of the reinsurance, a BBB-rated reinsurer could offset the additional capital charged to the company as a result of the reinsurer’s rating. In an efficient market, it is likely that prices will even out and arbitrage opportunities will disappear. To remain consistent with market practices and to avoid destabilising the market, the standard Solvency II calibration is primordial, as we will see in the following section.


13 - We remind the reader (see chapter IV) that the capital required per counterparty in keeping with its weight in the exposure to reinsurance or to financial derivatives is calculated with the Herfindahl index. This index of concentration is the sum of the squares of the market share of all the companies in the industry.

Adj defered taxes (EURm) 3 88 34 49 37 10 221


5 175 69 99 75 19 442

NAV (EURm) 47 360 265 387 276 52 1387




III.3. The impact of credit quality and of diversification of reinsurance on the capital requirementAs we have just seen, reinsurance as a means of transferring risks comes into play largely in the underwriting and counterparty modules. In this section, we look at the problems of arbitrage (involving the credit quality and diversification of the reinsurers chosen) posed by Solvency II.

To do so, we use several simple examples to examine the ways the diversification and ratings of reinsurers affect the capital charge for counterparty risk. The examples are deliberately somewhat exaggerated; the idea is to highlight the perverse effect Solvency II may have on the choice of reinsurance policy.

First illustration: Combinations of one, two, or three reinsurersTake an insurance company that transfers some of its risk through reinsurance arrangements. It is assumed that in the event of default of all of those who bear these risks the loss (LGD or loss given default) is €500 million. We will show that the insurer’s choice to resort to one, two, or three reinsurers, and above all the chosen allocation (concentration or distribution of risks) will have a great effect on the amount of capital required for counterparty risk. To isolate the effect of this diversification, we assume that all the reinsurers have the same credit rating.

Measure of the total counterparty risk and capital charge for default of one of the two reinsurers, in the context of reinsurance coverage provided by two AA-rated reinsurers.

0

1

2

3

4

5

6

100%

99.9

9%

95%

90%

85%

80%

75%

70%

65%

60%

55%

50%

45%

40%

35%

30%

25%

20%

15%

10%

0.01

% 5% 0%

% held by reinsurer 1

(EUR

m)

Def 1 SCR Def

If an insurance company resorted to but a single AA-rated reinsurer, the capital required for counterparty risk would be €5 million. But if it opts for two AA-rated reinsurers, it saves a substantial amount of capital; and the more unevenly this business is awarded, the more capital the company saves. Coverage divided 50%-50% between two AA-rated reinsurers will lead to a capital savings of 85.4% (€0.73 million). This savings amounts to 89.3% (€0.535 million) when one reinsurer is allocated two-thirds of the business and the other one-third, and at an 85%/15% breakdown the savings attains 98.8% (a requirement of €0.06 million). The Solvency II formula based on a Vasicek function is paradoxical, because, when it resorts to a single reinsurer, the insurance company will need €5 million, but when it transfers 99.99% to one reinsurer and 0.01% to another, it will be subject to no capital requirement for counterparty risk. By splitting its risk fifty-fifty between two reinsurers, its requirement will be reduced by 85.4%.

Coverage provided in equal proportions by three AA-rated reinsurers will result in a capital requirement of €1.28m. The savings on the €5m capital charge for the coverage provided by a single AA-rated reinsurer comes to 74.4% (less than the 85.4% savings for a fifty-fifty split).




Although it is appropriate for Solvency II to encourage diversification of reinsurance coverage in an attempt to spread default risk more widely, the suitability of the calibration, insofar as the capital savings are high, does perhaps raise eyebrows.

Second illustration: Choice of reinsurer by credit ratingTake an insurance company that plans to seek coverage from a single reinsurer. This simulation makes it possible to identify the effect of the reinsurer’s credit rating on the capital required for counterparty risk. To favour comparisons with the preceding illustration, we again assume that LGD is €500 million.

The simulation leads to the following result:Capital requirement for default risk by reinsurer rating

Reinsurer rating SCR counterparty

PDi

AAA 1 0.002%

AA 5 0.01%

A 25 0.05%

BBB 120 0.24%

BB 500 1.20%

B 500 6.04%

CCC or below, unrated 500 30.41%


The capital required for default risk increases by a multiple of approximately five for every fall by one notch; they move proportionally with the probability of default. The counterparty SCR is naturally capped by the LGD.

By contrast, when the ratings are analysed in the presence of several reinsurers, the effects of the ratings are cumulative and, as the third illustration shows, they are no longer proportional.

Third illustration: Combinations of two reinsurers of different credit ratings (the two reinsurers constitute the entire reinsurance coverage)Take an insurance company whose reinsurance coverage is split fifty/fifty between two reinsurers and is seeking the most advantageous split by credit rating. To favour comparisons with the preceding illustrations, we again assume that LGD is €500 million.

The simulation leads to the following results:

Rein

sure

r 1

rati

ng

Rein

sure

r 2

rati

ng

% c

over

ed b

y re

insu

rer

1

Capi

tal c

harg

e fo

r re

insu

rer

1 de

faul

t

Capi

tal c

harg

e fo

r re

insu

rer

2 de

faul

t

Tota

l

AAA AAA 50% 0.02 0.02 0.04

AAA AA 50% 0.02 0.36 0.39

AAA A 50% 0.02 4.26 4.28

AAA BBB 50% 0.02 29.81 29.83

AA AA 50% 0.36 0.36 0.73

AA A 50% 0.36 4.26 4.62

AA BBB 50% 0.36 29.81 30.17

A A 50% 4.26 4.26 8.51

A BBB 50% 4.26 29.81 34.06

BBB BBB 50% 29.81 29.81 59.62


It is interesting to see the multiplicative effect of the ratings. Reinsurance coverage with AAA- and AA-rated reinsurers requires nearly ten times more capital (€0.39 million) than that required (€0.4 million) when the two reinsurers are rated AAA, yet the risk of default of an AA-rated reinsurer that provides 50% of reinsurance coverage is only five times greater.




Likewise, for coverage provided by an AA-rated reinsurer and a BBB-rated reinsurer, the capital requirement for the BBB reinsurer (€29.8 million) is 82.8 times greater than that for the AA-rated reinsurer (€0.36 million); the capital requirement for the two reinsurers is €30.2 million, forty-one times greater than requirement for coverage with two AA-rated reinsurers. The table above shows these combinations.

By combining the three components of the three illustrations above (number of reinsurers, rating, and breakdown of coverage), it turns out to be relatively easy to reduce counterparty risk. For example, with coverage evenly divided between an AA- and an A-rated reinsurer, the capital requirement is €4.62 million. With four AA-rated reinsurers, the capital requirement is €1.5 million. With two AA- and two A-rated reinsurers providing equal shares of coverage, the capital requirement is €5.82 million. By increasing the number of reinsurers, however, it is easy to reduce the capital requirement.

As we stated in the introduction to this section, default risk should be sufficiently well calibrated to the number of counterparties, the share of coverage they provide, and their credit rating, and this to prevent reinsurance choices whose aim is simply to optimise Solvency II capital requirements without reflecting real exposure to risks.

III.4. The Solvency II measure of the impact of non-proportional reinsurance on the capital requirement is inadequate

After our look at the possible distortions to reinsurance policy (combinations of credit ratings and number of reinsurers) caused by Solvency II, we look in this section at the impact of the Solvency II measures and calibration of reinsurance on the type of reinsurance chosen. In section III.2 of this chapter, we saw that the calculation of the capital required for life underwriting risk posed few conceptual problems: the capital required is equal to the change in the value of net assets following different shocks. In spite of the problems of evaluating these shocks in the mortality, longevity, disability, lapse and expense risk sub-modules, Solvency II can accommodate most transfers of risk through proportional and non-proportional reinsurance.

The capital required for non-life underwriting is approached via premium risk, reserve risk, and catastrophe risk. Premium risk is that risk that expenses and claims may be greater than premiums collected. Two measures are used to gauge this risk: one measure of volume and one of volatility. The volume measure is of net written premiums over the past two years and net earned premiums over the past year.

In proportional reinsurance, especially of the quota share sort,14 the premiums net of reinsurance can, in principle, serve as an indicator of risk transfers. In non-proportional reinsurance,15 by contrast, a small percentage of premiums may be transferred to a reinsurer, all while


14 - In proportional reinsurance, the reinsurer and the ceding company share the premiums and the losses of a portfolio at a percentage set in advance. When reinsurance coverage kicks in from the first euro, it is known as quota-share proportional reinsurance. All policies thus have a single underwriting limit. When reinsurance coverage kicks in only for policies exceeding a certain amount (known as a line or retention)—though it still kicks in from the first euro, it is known as surplus-share reinsurance. This enables the ceding company to keep for itself a share of the risks that it has the capacity to bear without resorting to reinsurance. 15 - In conventional non-proportional reinsurance, reinsurance kicks in only at a certain loss threshold (known as the attachment point or priority) and to a certain limit (known as the layer limit or guarantee) in exchange for a percentage of the premiums earned by the ceding company. These arrangements are known as excess of loss (XL) and coverage per claim or per event is expressed in the amount of claims. Another conventional form of non-proportional reinsurance is stop loss (SL), which makes it possible to protect a share of the technical result from frequency risk (catastrophe, for example). It too relies on a threshold and on a reinsurance intervention limit, but the annual coverage is a function of the total premiums earned by the ceding company, which makes it possible to protect a share of the technical result from upwards drifts of claims. This type of reinsurance thus makes possible significant reductions of the volatility of losses. More complex and often customised arrangements can be made to meet the ceding company’s needs more exactly. Such arrangements are often known as unconventional non-proportional reinsurance. These arrangements are naturally not taken into consideration by the Solvency II standard formula, even though the capital they save is real. For example:• standard deviation stop loss is a stop loss as defined above but focusing on the distribution tails, which makes it possible to reduce volatility substantially and keep the loss ratio within certain bounds. When claims are beneath the lower bound, technical profits are transferred to the reinsurer.



transferring only extreme risks, and this to reduce the impact of distribution tails. This strategy makes possible a substantial reduction of the volatility of risks and thus of the consumption of capital. All the same, the capital savings cannot be reflected in an indicator of net premiums. In other words, the amount of net premiums with non-proportional reinsurance coverage may be greater than that obtained with proportional coverage, all else being equal, and could nonetheless lead to an economic capital requirement lower than that of proportional coverage.

The company’s loss ratio (over the last five, ten, or—at most—fifteen years, depending on the line of business) and that of the market are used to gauge the volatility of premium risk. Net premiums earned are used to determine these claims. Here again, analysis of the transfer of risks through reinsurance is thus founded in part on ceded premiums, which is likely to underestimate the efficiency of coverage of non-proportional treaties, especially when they have an effect on the distribution tails (extreme shocks). This approach also underscores a lack of flexibility in the dynamic management or restructuring of reinsurance policy: it assumes a certain stability of reinsurance arrangements over time. Indeed, the volatility observed in the past may reflect the unsuitability of past reinsurance arrangements and is unable to make allowances for any more efficient recent restructuring of such arrangements. Finally, premium (and reserve16) risk is founded only on the volatility of loss ratios, not on their magnitude, which can also lay insurers open to criticism (volatility takes precedence over the quality of pricing).

A lognormal distribution is used to calculate the capital charge—consistent with a 99.5% VaR—for the combined premium and reserve risks. All the same, it is appropriate to use this law to model phenomena characterised by a large number of small independent factors. It is perfectly suitable for the motor own damage line of business, for example. The Poisson law is thus usually used to model the number of losses per contract, and a lognormal law is used to model the average of the claims. All the same, when the distribution tails become fatter (that is, when extreme events are more frequent), this law is no longer relevant. For example, the Pareto principle (or the 80/20 principle, that is, 80% of any effects come from 20% of the causes) is more commonly used to measure the average cost of claims in fire insurance; storm insurance may be modelled with a Weibull law, a law frequently used to model extreme values. So, yet again, in this part of the non-life underwriting module, Solvency II fails to make appropriate allowances for the real savings in the capital required.

The final non-life underwriting risk is the catastrophe sub-module. The standard formula relies on a standard portion of net business written. The use of net premiums as an indicator of the transfer of risk through reinsurance is, as we noted for the measure of the volume of premium risk, unsatisfactory. The scenario-based approach is more demanding but makes possible improved consideration of reinsurance coverage, as the capital charge for catastrophe risk is the square root of the sum of the costs squared of each catastrophe. For a catastrophe to


When, by contrast, they are above the upper bound, the reinsurer covers the losses. • net quota share is a combination of two forms: a quota-share arrangement (see proportional reinsurance) from the first euro of claims to an attachment point and a conventional non-proportional reinsurance arrangement for the part between this attachment point and a layer limit. • run-off involves transferring the entirety of the assets and technical provisions of the ceding company to the balance sheet of the reinsurer (portfolio transfer). A variation involves reinsurance coverage that makes possible the transfer of the risk of upwards drift of losses alone (adverse-development cover or loss portfolio transfer)• risk swaps involve improving the diversification of risks (and thus reducing the capital requirement) by swapping with another insurer portfolios of uncorrelated risks (for example, the risk of a storm in a European country for the risk of a storm in North America)• insurance-linked securities involve structuring insurance risks and placing them in the financial markets. 16 - Reserve risk stems from the underestimation of the amount of reserves for claims and from stochastic nature of future settlement of claims.



be taken, its cost must be higher than an established threshold of materiality, 25% of the cost of the most adverse scenario.

We have shown, then, that though, on the whole, the Solvency II standard formula makes appropriate allowances for the savings in the capital requirement generated by the transfer of risks through proportional reinsure, it fails to do so for non-proportional reinsurance and should thus be reworked.

We present, for example, simulations representing five forms of reinsurance, modelled with the QIS4 standard formula as well as with a partial internal model. This example is taken from a document produced by Hannover Re, Munich Re, and Swiss Re; the document is entitled “Improving the Solvency II standard approach—Toward a better recognition of the risk mitigation effect of the non-proportional reinsurance with the standard approach.”17

As in the approach taken in chapters III and IV, this approach takes a fictitious insurance company and runs simulations to assess the impact of QIS4 on the strategy of the company. This company has four businesses: motor (third-party liability), motor own damage, property damage, and general personal accidents. Five reinsurance arrangements are tested:• the absence of reinsurance (no reins. in the figure)• non-proportional coverage of peak risks with relatively high attachment points in all businesses (PeakRisk)• non-proportional coverage with low attachment points in all lines of business (NP)

• quota-share transfer (to diversify) and non-proportional coverage of the retention with low attachment points for motor (third-party liability) and non-proportional coverage with low attachment points for the other lines of business (MTP Auto50+NP)• quota-share transfer in all lines of business and non-proportional coverage of the retention with a low attachment point (All 50+NP)

The simulations of these arrangements can be seen in the chart below:

Solvency capital requirement (SCR) after reinsurance

No reins. NP ALL50+NP0

50

100

150

200187

177

136

102

143

97

110

7281

59

MTPL50+NPPeakRisk

QIS4 - standard approachQIS4 - partial internal model

Source: Hannover Re, Munich Re, Swiss Re (op. cit.)

In each case, reinsurance naturally has a favourable effect on the solvency capital requirement as a result of the drop in the premiums and the best estimate after reinsurance and perhaps in historic loss rates. When the Solvency II and internal approaches are compared, however, one sees that the standard formula recognises but partially the positive effects of non-proportional reinsurance. In addition, whereas the internal model leads to capital


17 - This example is also found in a note from Munich Re: “Impact de la reassurance sur le capital-risque : un exemple pratique,” Solvency Consulting Knowledge Series, September 2008.



savings achieved by an NP arrangement greater than the savings achieved by peak risk coverage (97 vs. 102), the Solvency II standard formula leads to the opposite result (136 vs. 143).

The Solvency II standard formula is a significant advance in the modelling of risk transfers through reinsurance arrangements. Nonetheless, the part of the modelling of underwriting risk founded on net premiums leads to calibration mistakes (as a result of the non-linearity of the net premiums and the risk transfers) and these mistakes lead to erroneous capital requirements that are likely to favour policies that provide less than optimal risk management over other, more appropriate policies.


Conclusion




The Solvency I calculation of the capital requirement is altogether outmoded and arbitrary, insofar as its standard approach, extremely simplistic, has no link to the real economic exposure to the risks borne by insurance companies. To remedy this failing, the international supervisor sought to come up with prudential rules that are in greater keeping with the economic realities of the companies. In addition to the measure of solvency itself, the supervisor is seeking to encourage the development of internal models likely to improve identification, calibration, and management of risk. This objective will be reached only if rules put in place by the supervisor dovetail with the economic approach taken by insurers in their everyday management.

As the quantitative impact studies (QIS) show, the data collection and simulations required by the supervisor are a heavy investment for most companies. The objective of this study was to show that these investments, made for purely regulatory ends, can be capitalised on to pursue goals more intrinsic to the company. The perfecting or elaboration of this managerial tool is likely to improve the management of the company and increase the creation of value for the shareholder or mutual member. We have shown that the contributions of the models to the definition of the strategy, its implementation, and the optimisation of performance, especially with respect to available capital, are many, and that they are likely to encompass the entirety of the issues dealt with by insurers.

As we were concluding this study, on 26 March 2009, representatives of the European Commission and the European Parliament finally reached an informal agreement on the Solvency II project directive, an

agreement that implied the dropping of the notion of group support. This notion of group support will nonetheless come up again three years after the entry into force of Solvency II.

In addition, analysis of the results of QIS4 and of the current crisis is leading the supervisor to adjust the standard formula, and this in an attempt to gauge risks as well as possible and to suit insurers, so that they will have incentives to improve their tools to control and manage risks. The approaches to measuring liquidity risk, risk concentrations, counterparty risk, loss given default, and the correlation of market risks, as well as the allowances made for certain risk-mitigating tools are called into question.

So we are at a critical juncture in the elaboration of Solvency II, as the current choices and modifications will determine the effectiveness of the protection of policyholders as well as the ability of the regulator to encourage insurers to manage better their risks and their companies.

Conclusion

Appendix




Appendix 1Value Creation Models

The objective of this appendix is to discuss very briefly some of the value creation models we mention in chapter 1. We will present cash flow return on investment (CFROI), total shareholder return, the Strategic Planning Associates model, the Marris Q ratio, the Marakon Associates model, and the Fruhan and McKinsey model.

1. CFROI (Cash Flow Return on Investment)CFROI was originally developed by Holt consulting and then taken up by the Boston Consulting Group. It looks at the gap between the internal rate of return (IRR) and weighted average cost of capital. This positive difference multiplied by the amount of capital employed provides an estimate of the value created, while the negative difference multiplied by this capital provides an estimate of the value destroyed. It is important to emphasise that this model looks at the entirety of the economic assets of the company, considered a single investment.

The IRR is calculated by matching the gross value of this investment (before depreciation and adjusted for inflation) and the expected future cash flows generated over the life of the investment. A simplified version of CFROI involves dividing EBITDA (earnings before interest, taxes, depreciation, and amortisation) by the capital invested and comparing this ratio and weighted average cost of capital.

II. Total Shareholder ReturnTotal shareholder return was developed by the Boston Consulting Group and is not observable for unlisted companies.

It is the rate of return on a share over a period, calculated including all dividends received (all cash received as a recurrent or exceptional dividend for a share buyback) and the realised gain:

TSR = (share price end of period – share price beginning of period)

+ dividendsshare price beginning of period

It involves calculating the internal rate of return (IRR) obtained by the shareholder on the basis of dividends and the change in the price of the shares he holds. Although it is simplistic, the advantage of this model is that it favours comparisons or companies or of a company and a market, on the basis of data external to and independent of the size of the companies considered. Variations on this model involve comparing other fundamental indicators of the intrinsic value of the company, indicators such as the price/earnings ratio, free cash flows, economic value added (EVA), and CFROI.

III. The Marris Q RatioThe Marris Q ratio is not a direct measure of value creation, but it does have to do with it. It is the ratio of the market capitalisation of invested equity to the book value of equity. It is thus the inverse of the book to equity ratio.

Q = market capitalisation of invested equity

book value of equity

The Q ratio thus reveals the market’s view of the future strategies of the company, strategies that will lead to a rise or fall in equity. A Q ratio greater than one indicates creation of value: the expected return is greater than the return required by the

Appendix



suppliers of capital (as measured by the average cost of capital). So it includes risk, since it assumes a discounting of future cash flows at the rate of return required by investors.

IV. Strategic Planning Associates ModelThe Strategic Planning Associates model measures value creation by comparing the expected future performance of the company, as measured by the market-to-book-value ratio (M/B), and the results of the strategic decisions made in the past, as shown by the Rc/Ra ratio (where Rc is the performance of the company and Ra the cost of capital). When M/B is greater than Ra/Rc, it is expected that company performance will create value; when it is less, it is expected that value will be destroyed.

V. The Marakon Associates ModelThe Marakon Associates model relies on the approach above to link the return on capital (rc) and the cost of capital (ra) in such a way as to identify four distinct performance situations for a company.

In the “excellence” quadrant the return on equity capital is greater than the cost of capital (rc > ra) and stock market capitalisation is greater than equity capital (M/B > 1). In this approach, the company that is in this situation is likely to repeat its past good performance. In the “revitalisation” quadrant, the market expects that future performance will be better than past performance. In the “rut” quadrant are companies whose mediocre past performance is unlikely to lead to future value creation (return on equity capital lower than the cost of capital). Finally, those in “decline” created value in the past but are likely to destroy it in the future.

Marakon Associates also developed a profitability matrix linking company performance (rc), the cost of capital (ra),

and the growth of the company (g) compared to that of the market (G).

Appendix

Source: Thiertart (1990)



Appendix


Marakon Associates pricing model

Profitability matrix of Marakon Associates model




The aim is to assess the value created by the company and the company’s competitive position. So, when the growth of a line of business (g) is greater than its profitability (rc), the resources produced by the line of business will be unable to keep growth up, even if in the very near term the company is creating value.

VI. Fruhan and McKinsey ModelThe Fruhan and McKinsey model looks at the relationship between M/B and EV/B, where EV is the future economic value of the company estimated with historic cash flows and B is the book value of equity capital. When M/B > EV/B, value is created.

Appendix

Model Fruhan - McKinsey

Source: Lai, L. K., cited by Hax et Majluf (1984)



Appendix 2 Solvency I: An Efficient System with Numerous Drawbacks

The foundations of the current rules for insurance capital date to the 1970s (in particular directives 73/239 for property and casualty insurance and 79/267 for life insurance). As part of Solvency I, work on which was kicked off in 1997 and published in 2002, they were updated. Though they increased the power of the insurance industry regulators, they barely modified the contents of the existing system.

European regulation requires that an insurance company be solvent, that is,that it be sufficiently sound financially to meet its obligations toward its policyholders and its other creditors. Required are:• Sufficient reserves, calculated prudently, that is, providing a margin large enough to absorb any unfavourable changes in the variables making them up. The interest rate is set in accordance with the rules of the supervisory organ of the member state. • Safe, liquid, diversified, and profitable assets. Each member state has drawn up a list of admissible asset classes. • A minimum amount of own funds in excess of the RSM (required solvency margin). In France, for example, the RSM for euro-denominated life insurance contracts is equal to 4% of mathematical reserves and of reserves for the management of policies involving an investment risk, plus a percentage of the capital at risk, a percentage that depends on the term to maturity of the obligations (0.3% for more than five years; 0.15% for between three and five years; 0.1% for less

than three years). Reinsurance contracts can reduce the excess by at most 15%.

In the Solvency I environment, the following count for the RSM: • The paid-up capital or, for a mutual undertaking, the paid-up amount of initial funds, minus self-owned shares.• The French “réserve de capitalisation” or any free or regulatory provisions not associated with obligations toward policyholders.• The carry-forward of the non-dividend gain or loss from the last financial year• Junior securities or borrowings of 25% of the amount of the RSM (or the solvency margin if it is lower). If the debt is of indefinite term, it is raised to 50%.• Unrealised gains on assets when these gains are not out of the ordinary.• An amount equal to 50% of the undertaking’s future profits (upon application, with supporting evidence, by the undertaking to the supervisory authority of the member state in the territory in which its head office is located and with the agreement of that authority); the amount of the future profits is obtained by multiplying the estimated annual profit by a factor that represents the average period left to run on policies.• Provisions for guarantee funds (article R423-16 of the Code des assurances) up to and including the share of contributions made by the company.

Before going on to the drawbacks of the current system to demonstrate the need for European reform, let us emphasise that the existing rules have been particularly effective in Europe. In spite of the significant weakening of insurance company balance sheets as a result of the

Appendix



turmoil in the financial markets, in spite of a significant slowdown in economic growth and an often devastatingly high claims rate, the number of insurance companies going broke has remained very low. In France, for example, the frequency of bankruptcy is less than 0.25% (approximately one company a year), significantly lower than the 2% observed for the rest of the economy.

All the same, Solvency I has several drawbacks:• Every member state has enacted its own rules. Now, it is easy for an insurance company to get around excessive regulation in one country by setting up another company in a country where regulation is not as stringent. The lack of harmonised rules for the solvency of insurance companies can sometimes lead to biases that distort competition. It seems incongruous that the solvency margin of a company in one country should depend on domestic accounting standards rather than on an economic reality shared by all Europe. • In spite of the bankruptcies in Japan and the United States, the views of prudential rules having to do with provisions remains highly administrative and accounting-centred. The calculation of provisions does not always make allowances for the general risks of doing business (inadequate choice of markets or products, ineffective prevention of fraud or human error, legal, tax, or reputation risks, internal risks linked to information systems) and/or risks inherent to the insurance business (mistaken choice or modelling of the underwritten business, changes in the competitive environment). So it is surprising that hidden options such as lower-limit benefits or guaranteed

rates, a cause of earlier bankruptcies, are not always explicitly taken into account in the calculation of the solvency margin. It is also worth noting that this transformation is perhaps the result of the supervisory focus on own funds rather than on provisions. Own funds, of course, are but a buffer in the event of insufficient technical provisions. In other words, a company with satisfactory provisions that is already taking into account economic and financial risks should by definition be able to survive without own funds. So the real issue is with the make-up of provisions. • As for the prudential rules for the allocation of assets, it is surprising that after the turmoil in the stock and credit markets, the notion of risk remains so simplistic. For example, the investment risks that are the volatility of the stock markets, or exchange rates, or interest rates, the risks linked to the use of derivatives, liquidity, matching, or credit risks are not always included in the calculation of the solvency margin. A list of assets and the authorised proportions has been defined, but in such a simplistic way that in theory it is possible for 100% of an insurer’s obligations to be backed by debt issued by privately held Colombian companies. But if an asset is not on this list, it cannot be used in the determination of the solvency margin. • The minimum capital requirement involves several paradoxes. As minimum capital is calculated as a percentage of technical provisions in life insurance, the less well provisioned a company is, the less the capital required of it will be. Another paradox, and not one of the most minor, is the asymmetry of the treatment of bond gains and losses. Unrealised capital gains are added to available capital, whereas

Appendix



unrealised capital losses are not deducted from the calculation of the solvency margin. So, when rates fall, the solvency margins are over-estimated and include unrealised wealth that is very sensitive to a new rise in rates. In addition, this creation of wealth is not offset as it should be, with a re-valuation of liabilities. But except in the mid 1990s there has not been a real bond crash, which perhaps creates a distorted view of the robustness of the current solvency system. • The calculation of the solvency margin does not make it possible to take into account the specific features of a reinsurance programme. The standard reduction of 15% in life insurance and of 50% in property and casualty insurance in the event of reinsurance seems devoid of any economic foundation. • According to the European Commission, the primary cause of bankruptcy is poor operational (costs) and/or financial (assets) management. So it seems paradoxical that the current solvency rules do not have the flexibility to integrate this parameter. • The objective of the solvency system is early detection of any weakness or threat to the insurer’s ability to meet its future obligations toward its policyholders, in particular as a result of a rise in claims or a deterioration of the financial markets. It may seem paradoxical that the monitoring and the rules for calculation are done on past financial statements (total decorrelation of the solvency margin and prospects). As it happens, most European countries are putting in place complementary forward-looking prudential rules to mitigate the effects of this paradox.

In France, for example, specific forward-looking ratios for investments and

reinsurance have been put in place, as have “T3” quarterly asset/liability statements (which introduce the notion of market value), the C6 bis, C8, and C9 statements that test the liquidity of assets in the event of a mass lapses and the quality of reinsurance coverage in the event of great catastrophes (earthquake, epidemic, and so on). With the same objective, in the United Kingdom, the PSB (Prudential Sourcebook) reinforces Solvency I by broadening the notion of risks to include market, credit, insurance, and liquidity risks. Operational risk and the correlation of branches are not yet integrated.

But there is still a broad debate: if it is natural to take into account the risks inherent to new business, should additional mobilisation of capital be required for business that is not yet in the portfolio?

Finally, the correlation and dispersion of risks, which are also the subject of lively debate, are still not directly taken into account in phase I of IFRS or in Solvency I,whereas most leading insurers have already made them part of their internal models, especially those that have economic capital allocation and provision models.

It is evident that the current solvency system is a set of rigid rules, corresponding to an acceptable minimum, so much so that, in general, when a company is found to be in trouble it is often too latefor it to recover. So the current system is an “off-the-rack” set of rules that destroys any incentives for a company to monitor its own risks.

Appendix



Appendix 3Solvency II: An Extension of the Notion of Risk

In recent years, change in the complexity of risks has led to a real determination to adapt accounting and prudential rules, with the objective of offering a better vantage point on any company, especially on the risks it is running. Although the ends are different, the implementation of IFRS, Solvency II, Basel II, new rules for financial conglomerates, and European embedded value (EEV) are converging toward this objective. With Solvency II, the European Union is seeking to draw up solvency requirements more relevant to the risks actually taken on by insurance companies to encourage them to evaluate and control their risks. Analysis of IFRS and Solvency II reveals a shared determination. IFRS attempts to broaden the notion of risk taken into consideration in the accounts, so as to make insurance companies more aware of their real risks and thus to encourage them to understand them better. Solvency II is attempting to encourage a move from an “off-the-rack” system built on minimalist rules to a “custom-made” system that, by broadening the notion of risk and transferring the analysis of their risks to the companies themselves, is well suited to the specific features of each firm. The aim of the new solvency system is not to lay down new rules for capital or provisions but to give companies an incentive to put in place more sophisticated internal models for the analysis, management, and control of risks.

So it is not necessary to revolutionise existing models but to adapt models

for asset allocation, asset/liability management, and/or provisions to the reality of risks.

I. The Foundations of Solvency IITo put in place Solvency II, the European Commission proceeded in two phases:• An initial phase focused on determining the foundations of Solvency II. This phase came to a close on 3 March 2003 after two years of work, with the implementation of an architecture for the prudential oversight system built on three pillars, an architecture similar to that used for Basel II.• In the second phase, more technical, the measures for the new solvency systems’ taking into account of risks are to be spelled out. In 2004 the committee of European insurance and occupational pensions supervisors (CEIOPS) was created to define these measures. The first directive was put in place in July 2007 with the first application planned for 2012. This phase is particularly complex and it is easy to see why the initial objective of a 2007 entry into force was not met.

As with that of IFRS, the philosophy of Solvency II is to foster principles rather than to issue precise directives, so that each company can put in place or adapt its own risk-assessment model, which will then of course have to win independent approval.

The three pillars of the Solvency II architecture are similar to those of Basel II. In 1998, the objective of the Basel Committee, made up of representatives of the central banks and banking supervisory authorities of twelve countries (the body of rules has since been adopted by more than one hundred countries) was to increase the solidity and stability of

Appendix



the international banking system and to reduce the number of competition inequalities in the industry. The contribution of Basel II lies in its adaptation of the rules for bank capital to changes in the risks prevalent in banking. Work on Basel II began in 1998, the reform was published in 2004, and it came into force in 2008.

The prudential objective of Solvency II is very different from that of Basel II. Solvency II, after all, focuses not on individual risks but on the entire set of risks facing each company. In addition, primary motivation for this body of rules is the protection of policyholders from the risk of bankruptcy of any insurance company.

Nonetheless, Basel II provided certain elements for the building of Solvency II: architecture built on three types of rules (known as pillars) and a three-tier ranking of measurements of risk. The banking reform spelled out:• A standard method that classifies risks by external rating• An internal-rating method that relies on the odds of default as identified by the banks • An advanced internal-rating method in which risks are classified by statistical series of the institution concerned.

So the calculation of the risks of bank credit relies either on a standard method founded on rating-agency ratings or on the use of internal models. The McDonough solvency ratio, which took the place of the Cooke ratio, broadened the notion of credit risks to include market and operational risks. It is the ratio of regulatory capital to the sum of credit,

market, and operational risks. It should be greater than 8%. The consequence of Basel II is not an additional capital requirement but a reallocation of capital to each of the businesses, as a result of a weighting of the risks that corresponds to economic reality.

For insurance, the architecture and definition of the measures of risk are largely the result of:• A KPMG report, commissioned by the Internal Market and Services Directorate General and published on 2 May 2002, on risk modelling, technical provisions, asset pricing, reinsurance, the transfer of alternative risk and risk-reduction techniques, the impact of changes to accounting rules, the role of rating agencies, and comparative analyses of solvency systems. The main conclusions of the report are that the three-pillar approach taken by the Basel Committee would be suitable for Solvency II and that the formula for the calculation of the solvency margin should integrate technical, market, and credit risks. KPMG remains circumspect about the integration of operational and asset/liability mismatch risk. • The Sharma report, a report from the conference of the insurance supervisory services of the member states of the European Union, published in November 2002 and grounded on making the problems facing insurance companies common knowledge. It advocates prudential system intervention through preventive or corrective regulatory tools used at any stage of the appearance of problems, from the earliest stage to the final stage detrimental to policyholders. This report also dealt with the definition of good risk management (culture

Appendix



and strategy of the company, decision processes, risk-tracking and information systems), with the principle of prudent financial management, and with reinsurance programmes. These programmes should not just be tailored to the underwriting policy of the insurer, but their quality and liquidity should be studied as well. The amount of capital required should then integrate reinsurance (no longer in a standard fashion) and, more broadly, any means of transferring risk (securitisation, for example). Reinsurance could thus reduce second-pillar but not first-pillar capital needs (see definitions below).

The first phase of Solvency took a three-pillar approach:• The first pillar contains the quantitative requirements and should define the prudential rules for provisions, assets, and capital. The calculation of life technical provisions will be one of the major changes in Solvency II. It should integrate a forward-looking approach, make allowances for the risk of a drift in the factors used as assumptions in the calculation, be founded on a discount rate that depends on the kind of insurance contract and the method of pricing the assets and liabilities, and determine the provisions for supplementary guarantees (explicit valuation of options). In property and casualty insurance, the equalisation provision is being hotly debated as treatment varies greatly from one country to another, just like the determination to set a quantitative benchmark of the level of prudence for provisions for claims. Asset risks are now taken into account quantitatively in the evaluation of the capital requirement (as in the United States).

• The second pillar has to do with qualitative requirements. It is an extension of the statement of the good management practices of Solvency I that the supervisory services would like all insurers to put in place internally. This pillar is grounded on the definition of rules for internal analysis and management of risks (assets and liabilities) with ALM tools and reinsurance. Although the Commission acknowledges that asset/liability management should be strengthened, for the moment it is not planned to change explicitly the capital requirement as a result of the quality of ALM and of the management of mismatches. For this pillar, discussion revolves around the requirements made of the means of tracking exposure to investment risks, requirements founded on an explicit definition of an investment strategy (degree of risk accepted, target composition of portfolio, use of derivatives, liquidity of assets, correlation with the risk profile of liabilities). The insurance supervisory authorities would like to increase their powers of inspection and intervention (to demand capital add-ons, for example), after the fashion of the increase in this power provided for by Solvency I, and this at each link in the chain of the management of risks: typology, analysis, valuation, acceptance, transfer, or reduction and management of risks. • The third pillar has to do with market discipline, with using rules reflecting market demands that companies be more transparent about their exposures and their management of their risks.

This first phase also concluded that the requirement for a regulatory solvency margin is the basis of a prudential regime

Appendix



suited to risks; the calculation method is not yet defined. All the same, a capital requirement may be created to define both the level of capital that leads to an acceptable likelihood of default and the critical threshold beneath which the company is at high risk of bankruptcy. As with the American or Canadian RBC (risk-based capital) systems, a degree of intervention is planned that is a function of the required solvency margin (RSM) multiple depending on a lower limit and a target. If the minimum compulsory threshold is not reached by a company, the supervisor must have the power immediately to withdraw the company’s accreditation to write insurance. This threshold should be relatively low, serve as a safety net, and be the result of a relatively simple formula. Target capital is the capital necessary to deal with the risks of doing business and to converge toward a nearly nil risk of bankruptcy.The formula for calculating it should integrate the particularities of the risk profile of each company, including new business. The idea is to give companies an incentive to measure their own risks. Internal models are perhaps the most appropriate means of defining this target capital.

So, Solvency II may well need to come up with a more progressive solvency control (modulated in keeping with the financial health of the company) at an explicit confidence interval, calculated on the required solvency margin, but the calculation formulas remain to be finalised after the multiple quantitative impact studies define their broad principles.

II. Constraints on the Elaboration of the Solvency II Model and of Internal ModelsThe choice of the formula to define the solvency margin should take into consideration the constraints and objectives of Solvency II, constraints and objectives characterised by:• A determination to make the solvency systems of each member state as uniform as possible. The objective is not to take the smallest common denominator. Unlike those of Basel II, capital requirements are likely to increase for most European insurers (with the likely exception of the large groups that benefit from diversification).• Solvency II is meant to be i) homogeneous (although some countries have already adopted complementary systems of calculating the solvency margin); ii) more complete, by broadening the definition of risks (investment risk and the reduction linked to derivatives hedging are not taken into account in most European countries) and by making allowances for reinsurance and volatility of claims (the risk depends more on the change than on expectations, which alone are taken into account in Solvency I). Reinsurance, in fact, is completely reworked. Risk-based capital (RBC), a solvency model used in the United States, does not integrate it, whereas in Europe it is integrated in a standard fashion, which fosters a search neither for high-quality reinsurers nor for the coverage that would be called for by underwriting policy. • The new calculation rules must be applicable to all companies. In this respect, the Solvency II constraint is broader than that which is initially applied in IFRS, which affects only publicly traded companies.

Appendix



• The cost constraint is not insignificant. Solvency II of course is meant to apply as well to providential societies and small mutual undertakings, which do not have unlimited means of developing sophisticated internal models. • For obvious practical reasons Solvency II is meant to be compatible with IFRS. The problem is that the dates for IFRS II and Solvency II are similar (and Solvency II is even ahead in its decision to define liabilities at market value). So Solvency II has to lay down rules that anticipate the decisions of the IASB, in particular with respect to valuation of technical provisions at market value. Solvency II also relies on the financial conglomerates directive (2002/87) and on the 2005 implementation of EEV (European embedded value) born of the CFO Forum (nineteen of the main European insurers wanted to standardise the methods of communicating embedded value). • Solvency II must not lead to market distortions or systemic risks. Indeed, by underscoring the troubles of some insurance companies, a crisis of confidence among policyholders could lead to a wave of surrenders and weaken these companies while strengthening more adequately capitalised ones. The gradual implementation of tests, as in France (the C6 bis test that is meant to assess the risk of an asset/liability mismatch in different scenarios, the C8 and C9 statements having to do with reinsurance) thus seem to be opportune means of smoothing the transition. For its part, the United Kingdom has put in place resilience tests for insurance companies so that they can test the impact on their technical provisions of interest rate and stock price changes in different scenarios. For reference only, and to confirm this trend, the United States

also put in place additional dynamic stochastic tests to assess the resistance of the financial solidity of a company to interest rate fluctuations simulated in the ALM model of the company under consideration. The American RBC model is currently being perfected (phase II of the C3 project)

All solvency systems (in Europe, the United States, Australia, Canada, Japan) may require a solvency margin, but the calculation of this margin varies greatly from one continent to another. The two main types of calculation rely on the fixed-ratio and RBC concepts (Amenc et al. 2006).

Finally, whether in Europe, the United States, or Australia, recent work seems to demonstrate the suitability of putting in place internal models. As it happens, recent developments outside Europe seem to confirm the trend.

In Australia, for example, insurance will have a choice of two models for the calculation of the required solvency margin:• An internal model developed by each insurance company, a model that reflects most of the risks it has taken on, in particular those inherent to its business profile. These models are naturally subject to regulatory approval. • A model prescribed by law for companies that do not have the means or the intention to develop their own models. This prescribed method is based on an RBC model that integrates investment and technical risks after the fashion of the American model, in addition to the concentration risk meant to integrate catastrophic events.

Appendix



Depending on the sophistication of internal models, a combination of the two methods is accepted.

The other example of a shift toward internal models is the complementary regulation of phase II of the American C3 project. It integrates cash-flow testing for life insurance companies so that they can directly test their own asset/liability management model, the impact of different interest rate scenarios (created by the American Academy of Actuaries) on capital adequacy, and the match of assets and liabilities. It is projected over thirty years and leads to an available surplus or deficit, a surplus or deficit for which allowances are made in the calculation of the solvency margin. The aim of this approach is to give insurance companies an incentive to build their own risk-management models; the incentive to do so is made all the greater by the 50% increase in the RBC coefficients for the companies that do not have such models.

It seems that Solvency II intends to foster the use of internal models for the calculation of target capital. These models could be total or partial, deterministic (tests of different scenarios) or stochastic (Monte Carlo simulation), models based on the probability of bankruptcy or default. With different scenarios, it is possible to calculate both the likelihood of the occurrence of the worst scenarios and the capital necessary to keep the likelihood of bankruptcy or default below a certain limit. According to the European Commission, the prudential rules could be based on extensions of existing internal models, such as asset allocation, ALM, embedded value, dynamic financial analysis (DFA), or the overall risk model.

The latter model has drawn the attention of both Solvency II task forces and large insurance companies. It models the probability distribution of real capital (or economic capital), and its objective is to calculate the need for economic capital as a function of the overall risk deemed acceptable by the company and to define allocations of economic capital to lines of business. This need for economic capital is usually defined:• Either with a Value-at-Risk approach in which it corresponds to a quantile of the distribution function of overall risk (as in Australian regulation)• Or with an expected-shortfall or tail -VaR approach in which it corresponds to the average of the losses occurring at a frequency beneath a threshold. Some insurance companies favour this approach, as it offers a better view of the model of the tail distributions.

The use of tools to measure risk and, more broadly, of these internal models, should also make it possible to fine tune company strategy and the optimisation of capital allocation, in particular to weigh the advantages and disadvantages of allocating capital to the different lines of business (on the basis of RoRAC), the taking on or transfer of risk, reinsurance policy, asset allocation (measure of volatility and performance), and liability management.

The main advantage of these internal models is that they take into account the profile of the company and of its risks. Putting them in place, by contrast, is long and complex (information system capabilities, development and robustness of hypotheses, human resources).

Appendix



Appendix 4Solvency II: Modular Organisation, Identification and Calibration of Risks

The calculation of the solvency capital requirement or the target capital required by the regulator rests on a modular structure of risks. Six risk modules, each

made up of sub-modules, lead to the calculation of required capital, usually following a type of shock for each risk (see the typology of risks and measurement of risks below). Aggregation of these shocks, in keeping with correlation matrices that reveal the dependence of risks and the diversification of risks, leads to the final regulatory capital requirement.

We reproduce this modular structure to define the outline of the internal management models, with a closer look per line of business (chapters III, IV, and V) so as to be able to measure risk-adjusted capital (RAC).

Solvency II rests on the following modular approach:

The calibration for each of these risk modules and sub-modules is defined for each type of risk and in accordance with its own framework. We review below the entire set of risks and their calibration in keeping with the approach tested in QIS4.

Appendix

Solvency II modular structure of risks

Source: CEIOPS

SCR

SCR Health SCR Market SCR CounterpartySCR Life SCR Non Life

Operational SCR

Mortality risk

Longetivity risk

Premium reserve risk

Catastrophe risk

Disability risk

Accident and short term health

Long-term health

Workers' compensation

Lapse risk

Expense risk

Revision risk

Interest rate risk

Equity risk

Property risk

Currency risk

Spread risk

Concentration risk

Catastrophe risk

Adjustments

BSCR

Adjustment for risk-absorbing effect of futurediscretionary benefits



Appendix

LIFE

Mortality risk A permanent 10% increase in mortality rate for each age (for contracts where the amount payable on death is greater than technical provisions held)

Longevity risk A permanent 25% decrease in mortality rate for each age (for contracts where the amount payable on death is less than the technical provisions held)

Disability risk Increase of 35% in disability rates at each age for the next year together with a 25% increase for the following years

Lapse risk Three shocks are tested. The maximum required capital is that which is the greatest as a result of one of these three shocks:• permanent reduction of 50% in the rates of lapsation for contracts for which the surrender strain is expected to be negative• increase of 50% in the rates of lapsation for contracts for which the surrender value is expected to be positive • 30% of the sum of surrender strains for the contracts for the surrender strain is positive.

Expense risk Two simultaneous shocks are tested:• increase of 10% in future expenses compared to best estimate• increase of 1% per year in inflation rate.

Revision risk Increase of 3% in the annual amount payable for annuities exposed to revision risk considering the remaining run-off period.

Catastrophe risk Two simultaneous shocks are tested:• an absolute 1.5 per mille increase in the rate of policyholders dying over the following year• an absolute 1.5 per mille increase in the rate of policyholders experiencing morbidity over the following year.

NON-LIFE

Premium and reserve risk The measure of premium and reserve risk is a function of the volumes underwritten and the volatility of the combined historic ratios per line of business and it is calculated in such a way that, assuming a lognormal distribution of the underlying risk, a risk capital charge consistent with the VaR 99.5% standard is produced.

Catastrophe risk A choice of three approaches:• percentage (catastrophe factor defined by the regulator depending on the line of business specified) of estimated net premium written for the coming year• sum of the costs of each scenario specified by the regulator (regional scenarios) that exceeds a threshold of materiality set at 25% of the cost of the most severe scenario• impact of the change in NAV as a result of a personalised shock scenario: on the basis of a single event or on an annual basis (occurrence of several catastrophic events over the next twelve months in line with the SCR calibration at a 99.5% confidence level at a one-year horizon).

HEALTH

Long-term health • health expense risk as a function of gross premiums earned, of the volatility of the cost ratio, and of a risk factor such that a risk capital charge consistent with the VaR 99.5% standard is produced • claim (mortality or cancellation) risk as a function of gross premiums earned, of the volatility of the claims rate, and of a risk factor such that a risk capital charge consistent with the VaR 99.5% standard is produced• epidemic risk as a function of gross premiums earned (of the company and the market), of claims expenditure in the accounting year for the health insurance market, and of a risk factor calibrated by the regulator such that a risk capital charge consistent with the VaR 99.5% standard is produced.

Typology, measure, and calibration of risks per line of business as defined by the Solvency II modular approach



Appendix

Workers’ compensation • premiums and reserves: approach identical to that used in non-life insurance (three-step approach—appendix 9)• underwriting: four categories (longevity, disability, revision, and expense) of risk, measured with the approach used in life insurance (impact of correlated shocks on changes in NAV)• catastrophe: approach identical to that used in non-life insurance (standard method or scenario methods for catastrophe risk).

Short-term health, accidents, and other • premium and reserve risk as in the approach used in the underwriting risk in non-life (in three phases—appendix 9)• catastrophe risk as in the approach used in the underwriting risk in non-life (standard method, regional scenarios, or personalised scenarios).

MARKET

Interest rate risk Changes in the interest rate term structure each year for a period of twenty years with relative rise or fall (the greater of the two). Simplified approach (not authorised for life technical provisions): upwards shock of 50% and a downwards shock of 40% multiplied by the modified duration.

Equity risk Drop of 32% in the Global equity index and of 45% in the Others index (correlation of the two risks of 0.75). Analysis net of hedging and risk transfers.

Property risk 20% fall in real estate benchmarks, taking into account all direct and indirect exposures to property prices. The property shock takes into account specific investment policy, including hedging arrangements.

Currency risk The greater of the capital charges in the event of a 20% change, rise or fall, in the value of all other currencies against the local currency.

Spread risk Government bonds are exempted from an application of this module, as are assets which are allocated to policies where the policyholders bear the investment risk (unless they have embedded options or guarantees). The greater of the capital charges in the event of a narrowing or widening of the spread with respect to the term structure of the risk-free rate for bonds, structured credit products, and credit derivatives.

Concentration risk Evaluation for the company as a whole of the concentration with respect to each counterparty. Shock depending on the credit rating of the counterparty under consideration.

COUNTERPARTY

Counterparty risk Aggregation of loss-given-default of reinsurance, financial derivatives, intermediary, or any other credit exposures if counterparty i defaults and probability of default of counterparty i.



Appendix 5Data Collection and Simulations for QIS4: Major Investments

In its analysis of the results of QIS4 (2008), CEIOPS (2008) commented on the resources used by the participants to respond to the study. This impact study, of course, was entirely optional and was meant only as an informative test; it had no effect whatsoever on the participants. When Solvency II comes into force, the issue will be very different, since the two levels of capital required by the regulator will have to be officially defined. It is thus likely that insurers will do much fine tuning and make many adjustments, which will lead to additional costs.

It is for this reason that this study seeks to show that it is of interest to the insurer to reorient the investments required by the regulator toward the insurer-specific ends of elaborating internal decision models. The leading European insurers, forerunners in this domain, are showing that their economic capital model has several functions: definition of policy for investment, underwriting, new product launches, provisions, reinsurance, asset/liability management, allocation of capital to the various lines of business, risk management (definition of accepted limits, concentration, diversification) and a means of communication with the financial markets, rating agencies, and the prudential regulator. These multiple functions are dealt with in chapter V. The objective of this appendix is to illustrate with several figures the cost of responding to QIS4.

According to the CEIOPS study, the participants invested on average 3.2 man months to respond to QIS4. Size naturally

accounts for some of the dispersion around the average: larger companies devoted 4.4 man months to it, as opposed to 2.2 for smaller companies.

The figures below show the investments made by line of business and the breakdown of investment by task.

Investment (man months) by participant profile

Life

Non-Life

10th-90th percentile interval

Composite

Reinsurance

Captive0

2

4

6

8

10

25th-75th percentile intervalMedian

Source: CEIOPS 2008

Investment (man months) by participant size and task type

All

unde

rtak

ings

Larg

e un

dert

akin

gs

Smal

l un

dert

akin

gs

Completing overall QIS4 3.2 4.4 2.6

Getting acquainted with the technical specifications

1.0 1.1 0.9

Assessment of best estimate provisions

0.9 1.1 0.8

Calculation of the risk margin 0.4 0.5 0.4

Valuation of assets and other non-insurance liabilities

0.5 0.6 0.4

Calculation of the MCR 0.4 0.5 0.4

Calculation of the SCR 1.0 1.6 0.8

Source: CEIOPS 2008

Appendix



Appendix 6Weighting of Risk Types in the Composition of the Solvency Capital Requirement in France and in Europe

In its analysis of the results of QIS4 (2008), CEIOPS (2008) commented on the composition of the basic solvency capital requirement (BSCR), one of the components of the solvency capital requirement (SCR), in keeping with the modular structure described in appendix 4 and the definition in section I, chapter V.

For each country (although the names of the countries were left off the X axis), CEIOPS thus disclosed the breakdown of the BSCR into the five risk modules it is made up of (life, non-life, health underwriting risk, market, and counterparty) and the benefits of the diversification of these risks (Diversification).

Depending on the participant’s profile (life insurance company, non-life, mixed), certain capital consumption trends appear.

For life insurers, the market risk module seems to require the most capital, as in many countries it accounts for more than half of the BSCR and in some for as much as 80%. In most countries, nonetheless, diversification enables life insurers to reduce this BSCR anywhere from 10 to 30%.

If one focuses on data from the French market drawn from the ACAM (2008) presentation, life insurers stand apart from the European average given the characteristics of their products and their allocation of assets (weights of equities higher than the European average). Even if the ACAM presentation differs from that of CEIOPS, it is interesting to note the 82% weight of the market risk module in the SCR before diversification, reducing to 14% the weight of underwriting risk.

The diversification benefit makes it possible to reduce the BSCR by 11%. The adjustment for the risk-absorbing effect of future profit sharing is substantial, as it reduces the final capital requirement (SCR) by 50% (to which is added 8% for deferred taxation).

Appendix

Composition of BSCR for life insurance companies by European country

Source: CEIOPS (2008)



For non-life insurance companies in Europe, the non-life underwriting module is the major component of the capital charge; in many countries it accounts for between 50 and 80% of the BSCR (even though in some countries market risk and non-life underwriting risk are not equally weighted). The benefits of diversification of the risk modules are, at between 15 and 30%, slightly greater than those in life insurance.

If one focuses on data from the French market drawn from the ACAM (2008) presentation, non-life insurers too stand apart from the European average, as the

market risk and non-life underwriting risk modules are equally weighted (46% and 44% of the BSCR before diversification). This difference stems from a weight of long-term business that is greater than the European average. The diversification benefit, at 20%, is double that of life insurers in France.

Finally, for mixed insurers in Europe, it is harder to identify a clear trend for the community as a whole. Nonetheless, it is clear that the market risk and non-life underwriting risk modules consume a large share of capital. The benefits of diversification, which range from 15 to

Appendix

Composition of SCR for life insurance companies in France

Source: ACAM (2008)

Composition of the BSCR for non-life insurance companies in different European countries

Source: CEIOPS (2008)



40%, are slightly greater than for life and non-life insurers.

For mixed insurers in France, the market risk module, accounting for approximately 50% of capital needs (as measured by the BSCR) ,remains the greatest single contributor to the capital charge. The diversification benefit is relatively high, as it makes it possible to reduce the capital requirement by 25%. The weight of the life business for the mixed French insurers seems relatively high, as adjustments for the risk-absorbing effect of future profit sharing and deferred taxes make it possible to reduce the total required by the regulator (SCR).

Appendix

Composition of the SCR for non-life insurance companies in France

Source: ACAM (2008)

Composition of the BSCR for mixed insurance companies in Europe

Source CEIOPS (2008)



Appendix

Composition of the SCR for mixed insurers in France

Source: ACAM (2008)



Appendix 7Major Characteristics of the Benchmark Company

Solvency I general hypotheses

Appendix


(EURm) Unit

linkedEuro




Health Total

Stocks 838 959 105 330 318 5 2554

Bonds 685 4920 392 924 636 99 7657

Property 0 511 26 66 106 0 709

Reinsurance 2 6 3 10 35 1 56

Total assets 1525 6396 525 1330 1095 105 10976

Own funds 23 360 250 300 200 50 1183


Debt 2 36 25 30 20 5 118


Premiums per activity (gross)

250 1000 1000 1000 250 200 3700


Unit linked

Eurodenominated

Motor owndamage

Property damage


Health Total

Asset components %

Stocks 55% 15% 20% 25% 30% 5% 23%

Bonds 45% 77% 75% 70% 60% 95% 70%

Property 0% 8% 5% 5% 10% 0% 6%

Total 100% 100% 100% 100% 100% 100% 100%


0.1% 0.1% 1.0% 1.0% 4.0% 1.0% 0.6%

Technical provisions/premiums

600% 600% 25% 100% 350% 25% 261%

Own funds/technical provisions

1.5% 6% 12%

Own funds/premiums 9% 36% 25% 30% 80% 25% 32%

Debt/own funds 10% 10% 10% 10% 10% 10% 10%

ROE 11% 11% 9% 10% 8% 11% 10%



Appendix

Solvency II general hypotheses

(EURm) Unit

linkedEuro




Health Total

Stocks 810 959 99 287 275 5 2435

Bonds 663 4920 370 804 550 95 7403

Property 0 511 25 57 92 0 685

Reinssurance 1 6 2 7 26 0 43

Total assets 1475 6396 495 1157 943 100 10566

Own funds 47 360 265 387 276 52 1387


Debt 2 36 25 30 20 5 118


Premium per activity (gross)

250 1000 1000 1000 250 200 3700



Unit linked

Eurodenominated

Motor owndamage

Property damage


Health

Gross premiums per activity 250 1000 1000 1000 250 200

Asset components %

Stocks 55% 15% 15% 15% 30% 5%

Bonds 45% 77% 80% 80% 60% 95%

Property 0% 8% 5% 5% 10% 0%

Total 100% 100% 100% 100% 100% 100%


0.1% 0.1% 1.0% 1.0% 4.0% 1.0%

Technical provisions/premiums 600% 600% 140% 160% 500% 110%

Own funds/technical provisions 2.0% 6%

Own funds/premiums 25% 40% 80% 25%

Debt/own funds 10% 10% 10% 10% 10% 10%

Duration

Bonds 8 8 4 4 9 3

Technical provisions 8 8 2 2 9 1

Debt 6 6 6 6 8 4

Interest rate used to calculate modified duration

4.65%(8-year interest rate term structure proposed by the CEIOPS)

Benefits distribution rate

Financial yield (%) 5.0%

Tax rate 35%

Discretionary benefits rate 96%



Appendix

Hypotheses for life underwriting risk


Unit linked

Euro denominated

Net technical provisions/gross technical provisions 95% 99%

Mortality risk

Share of life insurance contracts contingent on mortality risk 35% 5%

Capital at risk/technical provisions for death benefit contracts 0.10 4.00

Expected average death rate over the next year weighted by the sum insured q 0.3% 0.3%

Longevity risk

Share of life insurance contracts contingent on longevity risk 5% 5%

Disability risk

Share of life insurance contracts contingent on disability risk 0.1% 2.0%

Capital at risk /technical provisions for contracts contingent on disability risk 0.10 0.10

Expected average disability rate over the next year weighted by the sum insured i 0.3% 0.3%

Lapse risk

Average lapse rate for policies with a negative surrender strain 0.5% 0.5%

Surrender strain/technical provisions for policies with negative surrender strain -2.0% -2.0%

Average rate of lapsation of the policies with a positive surrender strain 3.5% 3.5%

Surrender strain/technical provisions for policies with positive surrender strain 10.0% 17.0%

Average period, weighted by surrender strains, over which the policy with a negative surrender strain runs off ndown

1.5 1.5

Average period, weighted by surrender strains, over which the policy with a positive surrender strain runs off nup

6 6

Expense risk

Expense rate 0.2% 0.2%

Average period over which risk runs off, weighted by renewal expenses n(exp) 5 5

Revision risk

Percentage of annuities elegible for revision risk 0.0% 0.0%

Catastrophe risk

% of technical provisions for policies contingent on mortality risk with benefits payable as a single lump sum

95% 90%

Share reinsured of technical provisions for policies contingent on mortality risk 0.0% 0%

% technical provisions for policies whose benefits are payable on disability definition and as a single lump sum

90% 90.0%

Share reinsured of technical provisions for policies whose benefits are payable on disability risk

0.0% 0%

Multiple of the amount insured when the benefit is paid as a lump sum as a function of TP 1.1 5

Multiple annualised amount when benefits are paid on death or disability as annuities (net of reins.)

1.1 5

Average annuity factor for the expected duration over which benefits may be payable in the event of a claim

20.0 20.0



Appendix

Hypotheses for non-life and health risk

Market risk hypotheses



Motor owndamage

Propertydamage


Short-termhealth

Accident & others

Share of premiums reinsured 3.0% 10.0% 15.0% 2.0% 10.0%

Net written premiums by geographic area

Area 1 59.9% 59.9% 100.0% 100.0% 100.0%

Area 2 24.0% 24.0% 0.0% 0.0% 0.0%

Area 3 16.2% 16.2% 0.0% 0.0% 0.0%

Ratio written premiums/earned premiums by geographic area

Area 1 105% 103% 105.00% 102.0% 102.0%

Area 2 104% 105%

Area 3 103% 104%


Area 1 1.0% 3.0% 5.00% 3.0% 3.0%

Area 2 -1.0% -2.0%

Area 3 1.0% 5.0%

Ratio net/gross best estimate 98.0% 85.0% 80.0% 99.0% 92.0%

Best estimate by geographic area

Area 1 59.9% 59.9% 100.0% 100.00% 100.00%

Area 2 24.0% 24.0% 0.0% 0.00% 0.00%

Area 3 16.2% 16.2% 0.0% 0.00% 0.00%

Interest rate risk Unit

linkedEuro

denominated

Motor own

damage

Property damage


Health Total

Pre shock interest rate 4.65% 4.65% 4.65% 4.65% 4.65% 4.65% 4.65%

Equity risk

Global index equities 94.0% 95% 95% 92% 90% 95% 62%

Global index hedging rate 10% 5% 0% 0% 0% 0% 3%

Other index hedging rate 5% 1% 0% 0% 0% 0% 0%

Efficiency of Global index hedge 90% 90% 90% 90% 90% 90% 90%

Efficiency of Others index hedge 80% 80% 80% 80% 80% 80% 80%

Value of hedge/value of assets hedge (Global)

4% 1% 1% 1% 1% 1% 1%

Value of hedge/value of assets hedge (Other)

4% 1% 1% 1% 1% 1% 1%

Property risk

There are no hypotheses for this module; a 20% drop in the value of the property assets on the balance sheet is applied.

Currency risk

It is assumed that the company manages currency risk with the help of the congruence principle, efficient ALM and/or hedging for currency fluctuations.



Appendix

Spread risk Euro




Health Total

Bonds 98.9% 98.9% 98.9% 98.9% 98.9% 98.9%

Structured credits 1.0% 1.0% 1.0% 1.0% 1.0% 1.0%

Credit derivatives (investment and not hedging)

0.1% 0.1% 0.1% 0.1% 0.1% 0.1%

% non-government bonds 60% 50% 60% 75% 40% 60.3%

Non-government bond portfolio

Rating

AAA 40% 50% 40% 25% 60% 39%

AA 30% 30% 30% 40% 30% 31%

A 24% 15% 20% 29% 9% 23%

BBB 5% 4% 9% 5% 0% 5%

BB 0% 0% 0% 0% 0% 0%

B 0% 0% 0% 0% 0% 0%

CCC or below 0% 0% 0% 0% 0% 0%

Unrated 1% 1% 1% 1% 1% 1%

Total 100% 100% 100% 100% 100% 100%

Structured credits portfolio

Rating

AAA 60% 40% 40% 40% 40% 55%

AA 20% 30% 30% 30% 30% 23%

A 20% 30% 30% 30% 30% 23%

BBB 0% 0% 0% 0% 0% 0%

BB 0% 0% 0% 0% 0% 0%

B 0% 0% 0% 0% 0% 0%

CCC or below 0% 0% 0% 0% 0% 0%

Unrated 0% 0% 0% 0% 0% 0%

Total 100% 100% 100% 100% 100% 100%




ActivityEuro




Health


3965 288 774 694 44

Net exposure 4% 4% 4% 4% 4%

Counterparty rating BBB BBB BBB BBB BBB

Net asset value (NAV) before the shock (EURm) 360 265 387 276 52

Total balance sheet

Total assets excluding unit-linked, government bonds and reinsurance (EURm) 5764

Net exposure 4%

Counterparty rating BBB

Net asset value (NAV) before the shock (EURm) 1387



Appendix

Hypotheses for counterparty risk

Activity Unit linked Euro




Health


Reinsurer 1 27% 27% 27% 27% 27% 27%

Reinsurer 2 17% 17% 17% 17% 17% 17%

Reinsurer 3 17% 17% 17% 17% 17% 17%

Other reinsurers 39% 39% 39% 39% 39% 39%

Total 100% 100% 100% 100% 100% 100%

ActivityMotor own



Short-termhealth

Accident &others

Reinsurance gains applied to the loss ratio in basis points

Reinsurer 1 160 230 246 50 50

Reinsurer 2 160 230 246 50 50

Reinsurer 3 160 230 246 50 50



Appendix 8Simplified Best Estimate Example Drawn from QIS4

A simplified approach, proposed by QIS4, can be taken to calculate the best estimate of a life insurance policy with future discretionary benefits. The steps are:• calculation of the future value of future cash flows at the rate offered policyholders• calculation of the guaranteed best estimate• and of the total best estimate.

We will look in detail at each of these steps:• Calculation of the future value of the cash flow that the policyholder/beneficiary will receive at term. This future value depends on an interest rate offered by the insurer:

YT = S0 ∏ (1+ RT)

S0 is the amount insured at the moment of the valuation, RT lthe interest rate paid to the policyholder, and YT a benefit to be paid at date T.

The interest rate paid to the policyholder may be either a minimum guaranteed rate (δ) or a minimum guaranteed rate combined with a discretionary rate e (β*I), set as a function of the return received by the insurer on investment (I) adjusted for the technical interest rate (r).1 In this way, it is possible to establish the following relationship :

RT = max [(β*I – r)/ (1+ r) ; δ]

• Calculation of the guaranteed best estimateThe minimum guaranteed benefit is a function of the discount rate of guaranteed future cash flows:

BE garantee = S 0 (1+ δ) T * VT

where VT is the risk-fee discount factor.

• Calculation of the total best estimateThe total best estimate corresponds to a discounting of the benefit to be paid YT which integrates the guaranteed minimum rate and the discretionary rate. The return on the insurer’s investments is a function of a forward rate (m(f)), calculated from the risk-free rate.

So the valuation of technical provisions for life insurance policies is similar to that of options. First, an intrinsic value, which does not take into account the effect of the time value of the future benefit, is determined:

Intrinsic value = S0 * ∏ (1+ m (f T) * VT

Then, to integrate the time value, the future return on investments (f) is adjusted by the volatility of the return on stocks and bonds:

f*T = fT + [σB (1-WE) + σ E WE] / √ T

where, according to QIS4, σB = 2.5% et σE = 15%. WE is the fraction of equity investments.

The simplification for the total best estimate (the guarantee plus a discretionary share) is:

BE ≈ S0 Vt ∏ [1+m(f t*)]

The value of future discretionary benefits is thus:

FDB = BE – BE garantee

Appendix

1 - The financial aspect of life insurance is founded on financial capitalisation characterised by the use of a so-called technical interest rate. It is used to set premiums for policies and to calculate the insurer’s obligations to its policyholders.



Appendix 9Major Steps in the Calculation of the Premium and Reserve Risk Sub-Module of the Non-Life Underwriting Risk Module

The capital charge (SCR NL pr) for the combined premium and reserve risk in non-life business is a function of the measures of volume (V) and the volatility of the combined ratio of the overall portfolio (σ):2

SCR NL pr =ρ (σ)*V

where ρ (σ) is a function of the volatility of the combined ratio calculated in such a way that assuming a lognormal distribution of the underlying risk (approximately ρ (σ) = 3σ)), a risk capital charge consistent with the VaR 99.5% standard is produced.

ρ (σ) = exp (N0.995*√log(σ²+1)) _ 1

√σ²+1

To calculate the measures of volume (V) and of the volatility of the combined ratio (σ), the regulator suggests a three-step approach: • Step 1: calculation of V and σ for each line of business LOB• Step 2: integration of the geographic diversification benefit for each line of business LOB• Step 3: aggregation of measures of V and σ to calculate overall measures.

Step I: Calculation of volume measures and standard deviations (for premium and reserve risk) per line of business LOB and geographic zone j. This step is broken down into five smaller components. (i to v).

• The measure of the volume of premium risk V(prem, j, lob) for the line of business LOB in geographic zone j is a function of net

premiums written for the coming year Pj

lobt, written, of those for the preceding year

Pj, lobt-1, written and of net premiums earned

during the forthcoming year Pj, lobt earned.

V (prem, j, lob) = max (Pj, lobt, written;

Pj, lobt earned; 1.05*Pj, lob

t-1, written)

• The volume measure of reserve risk is equal to the best estimate of claims outstanding PCO j, lob for line of business LOB in geographic area j.

V (res, j, lob) = POC j, lob

• The standard deviation σ(prem, lob) of premium risk is a function of the standard deviation σ(U, prem, lob), specific to the insurance company under consideration, of that σ(M, prem ,lob) of the market, and of a credibility factor clob defined for the lines of business:

s ( prem , lob ) = clob • s ( U , prem , lob )

2 + (1 − clob ) • s ( M , prem , lob )2

The estimate of the standard deviation σ (U,prem,lob) specific to the company is a function of the volatility of historic loss ratios LR :

s ( U , prem , lob ) =1

nlob −1( ) • V( prem , lob )

• Ploby ,e • LRlob

y − mlob( )2

y

∑

où :

nlob is the number of historic years (at most five, ten or fifteen, depending on the LoB). The number should not take into account the first three years after start up of the line of business;

V( prem ,lob ) = V( prem , j ,lob )

j

∑ is the sum of the volume measure of premium risk per line of business (lob) in geographic area j ;

LRloby is the net loss ratio in each of the lines

of business and for historic years y=t-1, t-2,…, t-n.

Appendix

2 - The combined ratio is based on technical provisions discounted as in Solvency II, not as in Solvency I.



Py,elob =

Pj ,loby ,earned

j

∑ is the sum of earned net premiums in each line of business for the period (y=forthcoming year -1).

mlob =Plob

y ,e • LRloby

y∑Plob

y ,e

y∑ is the premium-

weighted average of historic loss ratios.

The market-wide estimate of the standard deviation for premium risk in the individual line of business is determined by QIS4 as follows:

The credibility factor is a function of the number of historic years for which data are available:

• The standard deviation σ(res, lob) ) for reserve risk in the individual line of business LOB is determined by QIS4 as follows:

• The standard deviation for the premium and reserve risk σ(lob) for each line of business LOB, is defined by aggregating the standard deviation of the two sub-risks σ(res, lob) and σ(res, lob) under the assumption of a correlation coefficient of α = 0.5 :

Step II:Integration of the geographic diversification benefit for each line of business.

Diversification is not allowed for the miscellaneous (line 9) and credit and suretyship insurance (line 6) lines of business.

The geographically diversified volume measure for premium and reserve risk

Vlob is a function of the volume measures of premium risk V(prem, lob), of reserve risk V(res, lob)

4 and of the Herfindahl index

DIVpr, lob5 : Vlob = (V (prem, lob) + V (res, lob)) *

(0.75+0.25*DIV pr,lob)

Step III: Aggregation of volumes and standard deviation for each line of business.

• The overall volume measure V is determined as follows: (V = ∑lob Vlob).

Appendix

3 - On the basis of the QIS4 results for the credibility factor for premium risk, CEIOPS is studying the suitability of putting in place a credibility factor per line of business for reserve risk as well. 4 - V(prem, lob) = ∑j V(prem, j, lob) and V(res, lob) = ∑j V(res, j, lob).5 - The Herfindahl index is calculated as DIVpr, lob = ∑(V(prem, j, lob) + V(res, j, lob))²/ [∑(V(prem, j, lob) + V(res, j, lob))]².

LOB = 1 2 3 4 5 6 7 8 9 10 11 12

σ (M,prem, lob) 9% 9% 12.5% 10% 12.5% 15% 5% 7.5% 11% 15% 15% 15%

Source: QIS4

clob Number of historic years of data available (excluding the first three years after the line of business was first written

Maximum value of nlob

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

15 0 0 0 0 0 0 0.64 0.67 0.69 0.71 0.73 0.75 0.76 0.78 0.79

10 0 0 0 0 0.64 0.69 0.72 0.74 0.76 0.79 - - - - -

5 0 0 0.64 0.72 0.79 - - - - - - - - - -

Source: QIS 4

LOB3 = 1 2 3 4 5 6 7 8 9 10 11 12

σ(res, lob) 12 % 7 % 10 % 10 % 15 % 15 % 10 % 10 % 10 % 15 % 15 % 15 %

Source: QIS 4

s ( lob ) =

s ( prem ,lob )V( prem ,lob )( )2

+ 2a s ( prem ,lob )s ( res .lob )V( prem ,lob )V( res .lob ) + s ( res ,lob )V( res ,lob )( )2

V( prem ,lob ) + V( res ,lob )



• The overall standard deviation is a function of σ(lob) the standard deviation of each line of business in the first step, of volume measures Vlob for the lines of business in the second step, of a matrix of the correlation of the lines of business:

The correlation matrix CorrLob is specified as follows:

Appendix

CorrLob 1 2 3 4 5 6 7 8 9 10 11 12

1: Motor (third-party) 1

2: Motor (other) 0.5 1

3: MAT 0.5 0.25 1

4: Fire 0.25 0.25 0.25 1

5: Third-party liability 0.5 0.25 0.25 0.25 1

6: Credit 0.25 0.25 0.25 0.25 0.5 1

7: Legal exp. 0.5 0.5 0.25 0.25 0.5 0.5 1

8: Assistance 0.25 0.5 0.5 0.5 0.25 0.25 0.25 1

9: Misc. 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 1

10: Reins. (property) 0.25 0.25 0.25 0.5 0.25 0.25 0.25 0.5 0.25 1

11: Reins. (casualty) 0.25 0.25 0.25 0.25 0.5 0.5 0.5 0.25 0.25 0.25 1

12: Reins. (MAT) 0.25 0.25 0.5 0.5 0.25 0.25 0.25 0.25 0.5 0.25 0.25 1

Source: QIS4



Appendix 10 Information about the Market Risk Module

I. Information on the change in the term structure of interest ratesThe interest rate term structure is provided by the regulator. For the QIS4 tests, it was the following:

The shocks that must be tested on the term structure of interest rates to determine the capital charge for interest rate risk are:

For example, the “stressed” ten-year interest rate R1(10) in the upward stress scenario is determined as:

R1(10 ) = R0 (10 ) • (1 + 0,42) These upwards and downwards shocks make it possible to determine two new interest rate structures with which changes in the net value of assets and liabilities can be analysed.

Appendix

Year 1 2 3 4 5 6 7 8 9 10

Rate 4.6960% 4.5262% 4.5097% 4.5330% 4.5529% 4.5797% 4.6137% 4.6529% 4.6975% 4.7417%

Year 11 12 13 14 15 16 17 18 19 20

Rate 4.7843% 4.8197% 4.8508% 4.8775% 4.9006% 4.9197% 4.9365% 4.9514% 4.9648% 4.9769%

Maturity t (years) 1 2 3 4 5 6 7

Relative change sup(t) 0.94 0.77 0.69 0.62 0.56 0.52 0.49

Relative change sdown(t) -0.51 -0.47 -0.44 -0.42 -0.40 -0.38 -0.37

Maturity t (years) 8 9 10 11 12 13 14

Relative change sup(t) 0.46 0.44 0.42 0.42 0.42 0.42 0.42

Relative change sdown(t) -0.35 -0.34 -0.34 -0.34 -0.34 -0.34 -0.34

Maturity t (years) 15 16 17 18 19 20+

Relative change sup(t) 0.42 0.41 0.40 0.39 0.38 0.37

Relative change sdown(t) -0.34 -0.33 -0.33 -0.32 -0.31 -0.31

Source: QIS4

Year 1 2 3 4 5 6 7 8 9 10

Upwards shock curve 9.11% 8.01% 7.62% 7.34% 7.10% 6.96% 6.87% 6.79% 6.76% 6.73%

Downwards shock curve 2.30% 2.40% 2.53% 2.63% 2.73% 2.84% 2.91% 3.02% 3.10% 3.13%

Year 11 12 13 14 15 16 17 18 19 20

Upwards shock curve 6.79% 6.84% 6.89% 6.93% 6.96% 6.94% 6.91% 6.88% 6.85% 6.82%

Downwards shock curve 3.16% 3.18% 3.20% 3.22% 3.23% 3.30% 3.31% 3.37% 3.43% 3.43%

Modified term structure of interest rates




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References



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• Smith, A. 1904. An inquiry into the nature and causes of the wealth of nations. Edited by E. Cannan. London: Methuen & Co. Available from: http://www.econlib.org/library/Smith/smWN.html; accessed May 2009.

• Solomons, D. 1965. Divisional performance: Measurement and control. Homewood: Irwin.

• Thiertart, R. A. 1990. La stratégie d’entreprise. Paris: McGraw-Hill.

• Zingales, L. 2000. In search of new foundations. Journal of Finance 55(4): 1623-53.

References



Acronym Expression

ACAM Autorité de Contrôle des Assurances et Mutuelles

Adj Adjustment for risk-absorbing properties of future profit sharing and deferred taxation

Adj DT Adjustment for risk-absorbing properties of deferred taxation

Adj FDB Adjustment for risk-absorbing properties of future discretionary benefits

ALM Asset/liability management

ANA Adjusted net assets

BE Best estimate

BSCR Basic solvency capital requirement

BV Book value

CAPM Capital asset pricing model

CAT Catastrophe

CEIOPS Committee of European Insurance and Ocupational Pensions Supervisors

CFROI Cash flow return on investment

Conci Risk concentration charge per counterparty

Defi Counterparty default risk requirement

DFA Dynamic financial analysis

DIV Herfindahl index used for geographic diversification

DPS Discretionary profit sharing

EBITDA Earnings before interest, taxes, depreciation and amortisation

EEA European Economic Area

EEV European embedded value

EV Embedded value

EVA Economic value added

Expul Amount of last year’s administrative expenses (gross of reinsurance) for unit-linked business

g Perpetual growth rate

Gross SCR u/w Capital requirement, gross of reinsurance, for underwriting risk

GW Goodwill

Health cl Capital charge for long-term health claims risk

Health exp Capital charge for long-term health expense risk

Health LT Capital charge for long-term health underwriting risk

Health WC Capital charge for workers' compensation underwriting risk

Heath ac Capital charge for long-term health accumulation risk

Hfd Concentration index for financial derivatives exposure

Hint Concentration index for receivables from intermediaries

Hoce Concentration index for other credit exposures

Hre Concentration index for reinsurance exposure

IFRS International financial reporting standards

LGDi Loss given default per counterparty i

LOB Line of business

MAT Marine, aviation, transport

MCEV Market-consistent embedded value

MCR Minimum capital requirement

Mkt sp bonds Capital charge for spread risk of bonds

Mkt spcd Capital charge for credit derivatives

Acronyms



Mkt spstruct Capital charge for spread risk of structured credit

MV Market value

MVEP Market value of equity portfolios drawn from Global index

MVM Market value margin

n BSCR Net basic solvency capital requirement

n SCR Net solvency capital requirement

n SCR Mkt k Net solvency capital requirement for equity risk per activity k

NAV Net asset value

Net SCR u/w Solvency capital requirement, net of reinsurance, for underwriting risk

NP Net profit

OECD Organisation for Economic Co-operation and Development

OPln ul Basic operational charge for all businesses except unit linked

Pay Company’s gross earned premiums

PBR Price book ratio

PDi Counterparty i default probability

PSB Prudential source book

TP Technical provisions

QIS Quantitative Impact Study

R Implicit correlation

RAC Risk-adjusted Capital

Rc Return on capital

RoNAV Return on net asset value

ROCE Return on capital employed

ROE Return on equity

ROI Return on investment

ROIC Return on invested capital

RoRAC Return on risk-adjusted capital

RSM Required solvency margin

SCR Solvency capital requirement

SCR cat Capital charge for catastrophe risk

SCR def Capital charge for default risk

SCR dis Capital charge for disability, morbidity and sickness

SCR exp Capital charge for expense risk

SCR health Capital charge for health underwriting risk

SCR lapse Capital charge for lapse risk

SCR life Capital charge for life underwriting risk

SCR long Capital charge for longevity risk

SCR Mkt Capital charge for market risk

SCR Mkt conc Capital charge for market concentration risk

SCR Mkt eq Capital charge for equity risk

SCR Mkt fx Capital charge for currency risk

SCR Mkt int Capital charge for interest rate risk

SCR Mkt k Capital charge for market risk per activity k

SCR Mkt prop Capital charge for property risk

SCR Mkt sp Capital charge for spread risk

Acronyms



SCR mort Capital charge for mortality risk

SCR nl Capital charge for non-life underwriting risk

SCR NL cat Capital charge for non-life catastrophe risk

SCR NL pr Capital charge for non-life premium and reserve risk

SCR op Capital charge for operational risk

SCR rev Capital charge for revision risk

SPV Special purpose vehicle

TSR Total shareholder return

UL Unit linked

V(RAC) RAC valuation

V (prem, lob) Volume measure for premium risk

V (res, lob) Volume measure for reserve risk

VaR Value at risk

WACC Weighted average cost of capital

Wcomp annuities Capital charge for workers' compensation underwriting risk

Wcomp CAT Capital charge for workers compensation catastrophe risk

Wcomp general Capital charge for workers compensation premium and reserve risk

XSi Excess exposure to counterparty i

Acronyms



The Financial Analysis and Accounting Research Centre was created in 2006 around the theme of company valuation. Cultural and technological changes now make it possible to use multiple dynamic analyses, the cornerstone of which is the discount rate. There is an abundance of academic research into the determination of the discount rate, but the gap between academe and business seems to be growing wider by the day. In practice, those who do the valuations often oversimplify, invalidating their reasoning; they may even ignore theory and transform the discount rate into a black box to hide the absence of objective and academic foundations in the determination of the risk premium and of beta.

The objective of the EDHEC Financial Analysis and Accounting Research Centre is to call into question certain financial paradigms, in particular that which consists of separating idiosyncratic risk—because it is diversifiable—from the risk premium and to provide the financial markets (financial analysts, investors, companies, rating agencies, auditors) with new light on the discount rate and to recommend new ways to determine it.

The great diversity of backgrounds is one of the advantages of the Centre (specialists in financial analysis, in accounting, in law, researchers from academe or from business), and it allows the Centre to take a multi-disciplinary approach to financial analysis: company valuation, the impact of IFRS and Solvency II on insurance companies, the impact of IFRS on the valuation and pricing of risk, the growing use of fairness opinions, the status of the outside expert, and the measurement of intangible assets.

About the EDHEC Financial Analysis and Accounting Research Centre



EDHEC Risk and Asset Management Research Centre

2009 Position Papers• Amenc, N. Quelques réflexions sur la régulation de la gestion d'actifs (June).

• Sender, S. The European pension fund industry again beset by deficits (May).

• Lioui, A. The undesirable effects of banning short sales (April).

• Gregoriou, G., and F.-S. Lhabitant. Madoff: A riot of red flags (January).

2009 Publications• Amenc, N., F. Goltz, A. Grigoriu, and D. Schroeder. The EDHEC European ETF survey (May).

• Martellini, L., and V. Milhau. Measuring the benefits of dynamic asset allocation strategies in the presence of liability constraints (March).

• Le Sourd, V. Hedge fund performance in 2008 (February).

• La gestion indicielle dans l'immobilier et l'indice EDHEC IEIF Immobilier d'Entreprise France (February).

• Real estate indexing and the EDHEC IEIF Commercial Property (France) Index (February).

• Amenc, N., L. Martellini, and S. Sender. Impact of regulations on the ALM of European pension funds (January).

• Goltz, F. A long road ahead for portfolio construction: Practitioners' views of an EDHEC survey. (January).

2008 Position Papers • Amenc, N., and S. Sender. Assessing the European banking sector bailout plans (December).

• Amenc, N., and S. Sender. Les mesures de recapitalisation et de soutien à la liquidité du secteur bancaire européen (December).

• Amenc, N., F. Ducoulombier, and P. Foulquier. Reactions to an EDHEC study on the fair value controversy (December). With the EDHEC Financial Analysis and Accounting Research Centre.

• Amenc, N., F. Ducoulombier, and P. Foulquier. Réactions après l’étude. Juste valeur ou non : un débat mal posé (December). With the EDHEC Financial Analysis and Accounting Research Centre.

• Amenc, N., and V. Le Sourd. Les performances de l’investissement socialement responsable en France (December).

• Amenc, N., and V. Le Sourd. Socially responsible investment performance in France (December).

EDHEC Position Papers and Publications from the last four years



• Amenc, N., B. Maffei, and H. Till. Les causes structurelles du troisième choc pétrolier (November).

• Amenc, N., B. Maffei, and H. Till. Oil prices: The true role of speculation (November).

• Sender, S. Banking: Why does regulation alone not suffice? Why must governments intervene? (November).

• Till, H. The oil markets: Let the data speak for itself (October).

• Amenc, N., F. Goltz, and V. Le Sourd. A comparison of fundamentally weighted indices: Overview and performance analysis (March).

• Sender, S. QIS4: Significant improvements, but the main risk for life insurance is not taken into account in the standard formula (February). With the Financial Analysis and Accounting Research Centre.

2008 Publications• Amenc, N., L. Martellini, and V. Ziemann. Alternative investments for institutional investors: Risk budgeting techniques in asset management and asset-liability management (December).

• Goltz, F., and D. Schröder. Hedge fund reporting survey (November).

• D’Hondt, C., and J.-R. Giraud. Transaction cost analysis A-Z: A step towards best execution in the post-MiFID landscape (November).

• Amenc, N., and D. Schröder. The pros and cons of passive hedge fund replication (October).

• Amenc, N., F. Goltz, and D. Schröder. Reactions to an EDHEC study on asset-liability management decisions in wealth management (September).

• Amenc, N., F. Goltz, A. Grigoriu, V. Le Sourd, and L. Martellini. The EDHEC European ETF survey 2008 (June).

• Amenc, N., F. Goltz, and V. Le Sourd. Fundamental differences? Comparing alternative index weighting mechanisms (April).

• Le Sourd, V. Hedge fund performance in 2007 (February).

• Amenc, N., F. Goltz, V. Le Sourd, and L. Martellini. The EDHEC European investment practices survey 2008 (January).

2007 Position Papers • Amenc, N. Trois premières leçons de la crise des crédits « subprime » (August).

• Amenc, N. Three early lessons from the subprime lending crisis (August).

• Amenc, N., W. Géhin, L. Martellini, and J.-C. Meyfredi. The myths and limits of passive hedge fund replication (June).




• Sender, S., and P. Foulquier. QIS3: Meaningful progress towards the implementation of Solvency II, but ground remains to be covered (June). With the EDHEC Financial Analysis and Accounting Research Centre.

• D’Hondt, C., and J.-R. Giraud. MiFID: The (in)famous European directive (February).

• Hedge fund indices for the purpose of UCITS: Answers to the CESR issues paper (January).

• Foulquier, P., and S. Sender. CP 20: Significant improvements in the Solvency II framework but grave incoherencies remain. EDHEC response to consultation paper n° 20 (January).

• Géhin, W. The Challenge of hedge fund measurement: A toolbox rather than a Pandora's box (January).

• Christory, C., S. Daul, and J.-R. Giraud. Quantification of hedge fund default risk (January).

2007 Publications• Ducoulombier, F. Etude EDHEC sur l'investissement et la gestion du risque immobiliers en Europe (November/December).

• Ducoulombier, F. EDHEC European real estate investment and risk management survey (November).

• Goltz, F., and G. Feng. Reactions to the EDHEC study "Assessing the quality of stock market indices" (September).

• Le Sourd, V. Hedge fund performance in 2006: A vintage year for hedge funds? (March).

• Amenc, N., L. Martellini, and V. Ziemann. Asset-liability management decisions in private banking (February).

• Le Sourd, V. Performance measurement for traditional investment (literature survey) (January).

2006 Position Papers • Till, H. EDHEC Comments on the Amaranth case: Early lesson from the debacle (September).

• Amenc, N., and F. Goltz. Disorderly exits from crowded trades? On the systemic risks of hedge funds (June).

• Foulquier, P., and S. Sender. QIS 2: Modelling that is at odds with the prudential objectives of Solvency II (November). With the EDHEC Financial Analysis and Accounting Research Centre.

• Amenc, N., and F. Goltz. A reply to the CESR recommendations on the eligibility of hedge fund indices for investment of UCITS (December).




2006 Publications

• Amenc, N., F. Goltz, and V. Le Sourd. Assessing the quality of stock market indices: Requirements for asset allocation and performance measurement (September). • Amenc, N., J.-R. Giraud, F. Goltz, V. Le Sourd, L. Martellini, and X. Ma. The EDHEC European ETF survey 2006 (October).

• Amenc, N., P. Foulquier, L. Martellini, and S. Sender. The impact of IFRS and Solvency II on asset-liability management and asset management in insurance companies (November). With the EDHEC Financial Analysis and Accounting Research Centre.

EDHEC Financial Analysis and Accounting Research Centre2009 Publications• Foulquier, P. Solvabilité II : une opportunité de pilotage de la performance des sociétés d’assurance (May).

2008 Position Papers • Amenc, N., F. Ducoulombier, and P. Foulquier. Reactions to an EDHEC study on the fair value controversy (December). With the EDHEC Risk and Asset Management Research Centre.

• Amenc, N., F. Ducoulombier, and P. Foulquier. Réactions après l’étude. Juste valeur ou non : un débat mal posé (December). With the EDHEC Risk and Asset Management Research Centre.

• Escaffre, L., P. Foulquier, and P. Touron. The fair value controversy: Ignoring the real issue (November).

• Escaffre, L., P. Foulquier, and P. Touron. Juste valeur ou non : un débat mal posé (November).

• Sender, S. QIS4: Significant improvements, but the main risk for life insurance is not taken into account in the standard formula (February). With the EDHEC Risk and Asset Management Research Centre.

2007 Position Papers • Sender, S., and P. Foulquier. QIS3: Meaningful progress towards the implementation of Solvency II, but ground remains to be covered (June). With the EDHEC Risk and Asset Management Research Centre.

2006 Position Papers • Foulquier, P., and S. Sender. QIS 2: Modelling that is at odds with the prudential objectives of Solvency II (November). With the EDHEC Risk and Asset Management Research Centre.




2006 Publications• Amenc, N., P. Foulquier, L. Martellini, and S. Sender. The impact of IFRS and Solvency II on asset-liability management and asset management in insurance companies (November). With the EDHEC Risk and Asset Management Research Centre.

EDHEC Economics Research Centre2009 Position Papers • Chéron, A. Quelle protection de l’emploi pour les seniors ? (January).

• Courtioux, P. Peut-on financer l’éducation du supérieur de manière plus équitable ? (January).

• Gregoir, S. L’incertitude liée à la contraction du marché immobilier pèse sur l’évolution des prix (January).

2008 Position Papers • Gregoir, S. Les prêts étudiants peuvent-ils être un outil de progrès social ? (October).

• Chéron, A. Que peut-on attendre d'une augmentation de l'âge de départ en retraite ? (June).

• Chéron, A. De l'optimalité des allégements de charges sur les bas salaires (February).

• Chéron, A., and S. Gregoir. Mais où est passé le contrat unique à droits progressifs ? (February).

2007 Position Papers • Chéron, A. Faut-il subventionner la formation professionnelle des séniors ? (October).

• Courtioux, P. La TVA acquittée par les ménages : une évaluation de sa charge tout au long de la vie (October).

• Courtioux, P. Les effets redistributifs de la « TVA sociale » : un exercice de microsimulation (July).

• Maarek, G. La réforme du financement de la protection sociale. Essais comparatifs entre la « TVA sociale » et la « TVA emploi » (July).

• Chéron, A. Analyse économique des grandes propositions en matière d'emploi des candidats à l'élection présidentielle (March).

• Chéron, A. Would a new form of employment contract provide greater security for French workers? (March).

2007 Publications• Amenc, N., P. Courtioux, A.-F. Malvache, and G. Maarek. La « TVA emploi » (April).

• Amenc, N., P. Courtioux, A.-F. Malvache, and G. Maarek. Pro-employment VAT (April).

• Chéron, A. Reconsidérer les effets de la protection de l'emploi en France. L'apport d'une approche en termes de cycle de vie (January).




2006 Position Papers • Chéron, A. Le plan national d’action pour l’emploi des seniors : bien, mais peut mieux faire (October).

• Bacache-Beauvallet, M. Les limites de l'usage des primes à la performance dans la fonction publique (October).

• Courtioux, P., and O. Thévenon. Politiques familiales et objectifs européens : il faut améliorer le benchmarking (November).

EDHEC Leadership and Corporate Governance Research Centre2009 Position Papers• Petit, V., and V. Boulocher. Equipes dirigeantes : comment développer la légitimité managériale ? (May).

• Petit, V. Leadership : ce que pensent les top managers (May)

• Petit, V., and I. Mari. La légitimité des équipes dirigeantes : une dimension négligée de la gouvernance d'entreprise (January).

• Petit, V., and I. Mari. Taking care of executive legitimacy: A neglected issue of corporate governance (January).

EDHEC Marketing and Consumption Research Centre – InteraCT2007 Position Papers • Bonnin, Gaël. Piloter l’interaction avec le consommateur : un impératif pour le marketing. (January).




Swiss Re is a leading and highly diversified global reinsurer. The company operates through offices in more than 20 countries.

Founded in Zurich, Switzerland, in 1863, Swiss Re offers financial services products that enable risk-taking essential to enterprise and progress. Its clients comprise insurance companies, captives, governments, NGOs, financial institutions as well as large companies.

For over 145 years now, Swiss Re has committed itself to identifying and evaluating emerging risks. Hence, the Group has gained comprehensive expertise in managing risk and capital and has the ability to offer new solutions required by the new risk landscape, characterised by more interconnected and complex risks. Swiss Re is well positioned to be the preferred reinsurer for insurable risks, which include natural catastrophes on the rise, terrorism, pandemics and ageing population.

The company offers traditional reinsurance products and related services for property and casualty, as well as the life and health business, which are complemented by insurance-based corporate finance solutions and supplementary services for comprehensive risk management. Swiss Re is the industry leader in insurance-linked securities.

Swiss Re's ambition is to provide innovative and sustainable reinsurance solutions and to meet continued demand for significant solvency support. The Group's strong value proposition and its outstanding execution capabilities mean that it is well positioned to assist clients in achieving their ambitious goals in terms of insurance risk-taking or insurance sales growth.

Find out more about Swiss Re on www.swissre.com Or contact directly Client Markets, Swiss Re Europe S.A., Succursale de Paris by phone +33 1 43 18 30 00 or +33 1 43 18 30 94

Compagnie Suisse de Réassurances SA Mythenquai 50/60 Boîte postale 8022 Zurich - Switzerland Tél. : +41 43 285 2121 - Fax +41 43 285 2999 www.swissre.com

Swiss Re Europe S.A., Succursale de Paris 7, rue de Logelbach 75847 Paris Cedex 17 - France Tél.: +33 1 43 18 3000 - Fax +33 1 42 12 9140

About Swiss Re

EDHEC Financial Analysis and Accounting Research Centre393-400 promenade des AnglaisBP 311606202 Nice Cedex 3 - FranceTel.: +33 (0)4 93 18 32 53E-mail: joanne [email protected]: www.edhec.com

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