Solvency II - Lesson learned?

Table of Content

List of abbreviations

List of equations

List of figures

List of tables

1. Introduction
1.1 Subject and background of the study
1.2 Objectives of this thesis
1.3 Course of the analysis
1.4 Scope and limitations

2. Solvency II - A major European regulatory initiative
2.1 The development of Solvency II
2.2 The three pillar approach
2.3 The current second phase
2.4 Quantitative impact studies
2.5 A risk based economic system
2.5.1 The economic balance sheet
2.5.2 Overall structure of the standard formula
2.5.3 Measurement and assessment of risk

3. Treatment of investment risk under the standard formula
3.1 Interest rate risk
3.1.1 The discount rate
3.1.2 The illiquidity premium
3.2 Equity risk
3.2.1 Symmetric adjustment mechanism
3.2.2 Duration based equity dampener
3.3 Spread risk
3.3.1 Spread risk on bonds
3.3.2 Spread risk on structured credits
3.3.3 Spread risk on credit derivatives
3.4 Illiquidity premium risk
3.5 Property risk
3.6 Currency risk
3.7 Concentration risk
3.8 Counterparty default risk
3.9 Aggregation of risk modules

4. Potential implications caused by Solvency II
4.1 The beginning of an EU wide asset reallocation
4.1.1 Summary of capital requirements of major asset classes
4.1.2 The driver for solvency capital requirements
4.1.3 The changing investment behavior
4.2 The possibility of new risk due to changed market conditions
4.2.1 Negative feedbacks as a consequence of market consistent valuation
4.2.2 A new interesting investment market
4.2.3 Multiple additional threats for the insurers and the market

5. Conceptual drawbacks of Solvency II
5.1 Theory, reality and the model
5.1.1 The independence of price changes
5.1.2 Price changes adhere to a probability distribution
5.2 False confidence in Value at Risk
5.2.1 Underestimation of tail risk
5.2.2 Sub-additive
5.2.3 Different methodology leads to a different Value at Risk
5.3 Black Swans and the Big Bang
5.4 Reliance on credit rating agencies
5.4.1 The non transparent business model
5.4.2 No liability or regulation
5.4.3 Mistakes in the past

6. Conclusion

Appendices

References

List of abbreviations

illustration not visible in this excerpt

List of equations

Equation 3.1: x-and-y formula for calculating the illiquidity premium

Equation 3.2: Equity shock scenario

Equation 3.3: Symmetric adjustment term

Equation 3.4: Aggregation of spread risk sub-modules

Equation 3.5: Spread shock on bonds

Equation 3.6: Spread shock on underlying assets of structured credit

Equation 3.7: Direct spread shock on structured credit

Equation 3.8: Excess exposure

Equation 3.9: Aggregation of the market risk concentration charge

Equation 3.10: Loss given default for derivatives

Equation 5.1: Sub-additive

Equation Appendix.1: Calculation of the BasicSCR

Equation Appendix.2: Calculation of capital requirement for market risk

List of figures

Figure 2.1: The Solvency II balance sheet

Figure 2.2: SCR modules according to standard formula

Figure 3.1: Interest rate stress

Figure 3.2: Discount curve for EUR liabilities under QIS

Figure 3.3: Discount curve and illiquidity premium for EUR liabilities under QIS

Figure 3.4: Effect of the symmetric adjustment mechanism over time

Figure 3.5: Spread solvency capital requirements for bonds

Figure 3.6: Counterparty SCR as percentage of LGD

Figure 4.1: QIS 5 market risk capital requirement for major asset classes

Figure 4.2: Overall market risk sub module charges of Europe’s insurers under QIS

Figure 4.3: Change of median asset allocation for a sample of large euro area insurers

Figure 4.4: Insurers fixed income and equity asset allocation

Figure Appendix.1: The Lamfalussy structure of supervisory committees in the EU

Figure Appendix.2: 3-month LIBOR overnight index swap spread

Figure Appendix.3: The creation of a collateralized debt obligation

List of tables

Table 5.1: Potential loss underestimation of Value at Risk

Table Appendix.1: Correlation matrix for aggregating risk modules

Table Appendix.2: Abbreviations of risk modules’ names

Table Appendix.3: Correlation matrix for aggregating market risk sub-modules

Table Appendix.4: Spread risk factors for bonds

Table Appendix.5: Spread risk factors for exposures to non-EEA governments

Table Appendix.6: The G function for rating class and tenure of the credit risk exposure

Table Appendix.7: Spread risk factors for credit derivatives

1. Introduction

1.1 Subject and background of the study

It may appear somewhat hasty, asking for a lesson learned for a framework which has not yet been implemented. Taking another perspective, it even sounds implausible, to force an industry which has been very successful with managing risks for their customers in the past to use a new regulatory risk framework.¹ Nevertheless, to question whether the lesson has been learned or the usefulness of the introduction of a new risk based regulatory framework, seems to be more up-to-date than it has ever been.

The pace of our time is getting faster. “ Nothing is as consistent as change ” - these wise words uttered by Greek philosopher Pythagoras over 2500 years ago adequately describe today’s world in which change is rather the rule than the exception. The supervisory system for EU insurers which was proofed to be sufficient in 1997 was considered to be insufficient only five years later.² Recently, the latest financial crisis has shown that the strength of companies is not a matter of balance sheet size anymore; it is rather the result of understanding the risk a company takes.³ The cutting-edge Solvency II framework is now going to replace the current existing supervisory system, adopting the latest developments for measuring risk in financial markets. However, with the recent financial crisis in mind, modern financial theories, investment strategies or risk measurement techniques look again like a fancy part of academia without any connection to the real financial world. Basel II, the EU wide regulatory framework for banks which has failed to protect the banking industry from the risk arising in the financial markets, can be quoted as a good example for the necessity of a new framework. As a consequence, Basel III is being developed at the moment.

One might be led to believe, that these issues do not concern the insurance industry. Insurers are long-term investors and usually follow a rather conservative investment policy. This did not protect them from losses but they were still able to sit out the last crisis, except for AIG which gambled in markets far off from their core business. Financial markets and their volatile behavior have not affected them directly but now Solvency II is going to introduce a market consistent valuation for their assets and liabilities. The value of both sides of their balance sheet, of every insurer in the EU will be linked directly to the financial markets. Changed market conditions will impact on all EU insurers at once. It almost seems unnecessary to mention that a correct measurement of risk arising from the financial markets is therefore of prime concern.

1.2 Objectives of this thesis

In the light of the increased importance of correct risk measurement, the analysis of the new Solvency II framework might provide useful insights on how to obtain greater effectiveness in the handling of risk for insurance companies. Solvency II is still in its development phase and literature is scarce in comparison to a framework like Basel II/III. This thesis will explore the basic principles behind the framework and the overall complex assessment of risk in financial markets within the framework’s context. This is done by shedding some light on how risk is measured within Solvency II and why insurers or investment markets might face certain specific types of risk due this new framework. Furthermore, the impact on investment decisions and financial markets will be analyzed and whether a framework of this size might be able to create new risks by altering the market. The final goal is to figure out whether the way Solvency II measures risk is reliable and useful or if it needs further adaptations.

1.3 Course of the analysis

This thesis is structured in six] chapters. The second chapter seeks to establish the foundations for understanding the reasons behind the introduction of Solvency II, the current state of affairs and the development process. Furthermore, it outlines the principles underlying the framework and its general design. The aim is to provide the reader with the necessary background knowledge to keep track with the several aspects of the further analysis. Chapter three provides a deeper insight into the standard formula of Solvency II and its assessment of financial risk. This is done by analyzing all the risk factors which are covered and, if necessary, their calibration, the reasons for their integration and the associated current discussion. The analysis highlights what has been introduced due to latest experiences, which parameters have changed over time and which are the critical risk factors. Chapter four describes how these rules might affect investment decisions and, since they will apply to all EU insurers, the overall impact on the European financial market. This is done by analyzing different opinions, statistics and studies in order to find evidence for a possible change in investment behavior due to Solvency II. Furthermore, the potential of the framework itself to change market conditions or investment behavior and create new risk sources will be discussed. Chapter five discusses the general theory of risk measurement, more specifically the underlying theory and the statistical and the mathematical concepts behind it. Finally, it covers how the risk associated with certain investments is determined by the opinion of external institutions. This reliance and its drawbacks will be discussed as well.

1.4 Scope and limitations

Solvency II aims to measure all the quantifiable risks of an insurance undertaking. Apart from financial risk, it also takes the risk of the underlying business into account. The focus in this thesis is mainly set on risk arising from the financial markets and how it affects the asset side or liability side of the balance sheet. The methods for calculating the technical provision⁴ of the liability side will not be treated. Only how its cash flows are discounted will be taken into consideration since this depends on data from the financial markets.

Life insurer usually have larger investments in the financial markets which is why examples are mostly given and explained in regard to life insurers. If necessary, some scenarios are also explained by taking property

2. Solvency II - A major European regulatory initiative

2.1 The development of Solvency II

Solvency margin requirements have been in place in Europe since 1973 for non-life and since 1979 for life insurance companies and belong to the first European directives meant to establish a homogeneous insurance industry.⁵ “The solvency margin is the amount of regulatory capital an insurance undertaking is obliged to hold against unforeseen events.”⁶ The drawbacks of the so far existing rules were that they made no attempt to reflect on the development of risk theory and did only focus on the underwriting risk of an insurance company. To modernize the existing rules a work group under the direction of Dr. Helmut Müller, former vice president of the Federal Insurance Commission, was established in 1994.⁷ The results of this workgroup have come to be known as the “Müller Report” which was published in 1997. It came to the conclusion that overall the current solvency rules are still sufficient and contained only some suggestions to adopt the changed market conditions into the established system.⁸ The result of this report were two EU directives which were adopted under the heading of Solvency I in 2002 but it was only a temporary solution since the drawbacks of the established system had still not been solved.⁹ Major changes were only the improvement for calculating the solvency margin, a better intervention for the regulator and the requirement that insurance companies now had to guarantee their solvency at any time during the year.

Solvency I had been implemented in many different ways around Europe and during this process it had finally come apart that those regulations did not satisfy the complex requirements of the European insurance business.¹⁰ The actual risk position of the insurer just did not correlate with the required solvency margin.¹¹ The regulations did not account sufficiently for important risk factors like the risk arising from investment in the financial market.¹² A more fundamental evaluation of the capital adequacy regime for the European insurance industry was needed. It shall harmonize the EU-wide supervisory legislation and Solvency II - A major European regulatory initiative bring it into accordance with those for credit institutions. Thus, at the beginning of 2000 the EU Commission decided to fundamentally reform Solvency I.

The result of this reform will be the Solvency II framework which is meant to “facilitate the development of a single market for insurance in the EU […].”¹³ While Solvency II is one more plank in building a single market platform for the EU insurance industry, its aims are also to ensure capital adequacy, to strengthen risk management and to protect policyholders. The main objective is to mirror more strongly the actual risk taken by the entire insurance company. Solvency II therefore considers five risk categories:¹⁴ The operational risks (system failures, fraud, etc.), the credit risks (shortfall of reinsurers or debtors), the asset liability mismatch risks (e.g. due to wrong matching of assets to liabilities), the market risks (volatility of the values of investments), and the underwriting risks (calculation of premiums, reinsurance and reservation). Whereby the attempt is being made to design the rules and the new regulatory framework as simple as possible.¹⁵

To achieve this goal the main responsibility for Solvency II is taken by the European Commission, the European Parliament and the European Council as well as the newly established European Insurance and Occupational Pensions Committee (EIOPC) and the Committee of European Insurance and Occupational Pensions Supervisors¹⁶ (CEIOPS).¹⁷ However, the whole project is supported by a variety of organizations like the International Association of Insurance Supervisors (IAIS), the International Accounting Standard Board (IASB) and the European insurance and reinsurance federation (CEA) to name just a few.¹⁸ For its conception, the Solvency II project has been divided into two phases.¹⁹ The aim of the first phase was to determine the general design of a new solvency system. The European Commission therefore assigned the audit firm KPMG to analyze different methodologies to assess the overall financial position of an insurance undertaking from the perspective of prudential supervision.²⁰ The study was published in 2002 and suggested that an approach similar to Basel II for the banking industry, “tailored specifically for insurance companies would help to overcome the drawbacks of many of the solvency margin methodologies”²¹ which have been in place during that time. Furthermore, a second report, better known as Sharma-Report, from the Conference of European Insurance Supervisory Authorities was published which reflected the standpoint of the supervisory authorities on Solvency II.²² Their core statement has been that regulation of capital requirements are not sufficient and have to be extended by qualitative aspects.²³ By these means, it was expected that “[...] in a significant number of cases, problems can be identified and even resolved long before solvency thresholds are breached.”²⁴ Solvency rules capture only certain situations and supervisors therefore need a wide range of other tools and practices. In 2003 the first phase was over and the European Commission published a general outline for a framework directive which is based on three pillars similar to Basel II.²⁵

2.2 The three pillar approach

The three pillars of Solvency II are three main thematic areas which are closely interconnected.

Pillar 1, comprising the quantitative requirements, defines the financial resources needed to maintain solvency. The central aspects are the calculation of the technical provision, the investments and the solvency margin.²⁶ Solvency II harmonizes EU wide the calculation for the technical provisions. This is achieved through improved and coherent calculation methods which consider embedded options and guarantees in insurance contracts as well as the use of a homogeneous discount factor for all. The risk arising from investments is included in this pillar as well. Insurance companies consequently have to hold sufficient capital reflecting the risk of their investments. The overall solvency requirements are the last aspect of Pillar 1. Regulated insurance companies are required to hold a prudent excess of assets over liabilities. This factor is called solvency capital requirements (SCR). “The solvency capital requirement should reflect the amount of capital necessary to meet all obligations over a specified time horizon […].”²⁷ It is a risk based requirement which will cover all the quantifiable risks an insurer or reinsurer faces and is the key solvency control level.²⁸ The SCR can be determined by a standard risk model or by the use of an internal model which has to be accredited by the supervisory authority.²⁹ In case the solvency capital falls below the SCR, the insurance company must re-establish the amount of capital covering the SCR in due time. It needs to get approval from the supervisory authority for a concrete and realizable plan to recover its SCR and will be monitored by the authority but without any further intervention. A second capital requirement, the minimum capital requirement (MCR), is a lower capital requirement and its breach triggers the ultimate supervisory intervention by withdrawing the authorization. Pillar 2, containing the qualitative requirements, is based on the Sharma report and adapts the principles of the supervisory review process set out in the Basel II accord for banks.³⁰ The introduction of an EU wide frame work needs to harmonize these processes especially for the coordination of the supervision in times of a crisis as well as the equal treatment of all insurance companies which should prevent the potential to boost negative market situations.³¹ It also contains qualitative requirements on undertakings for the governance and risk management. It e.g. allows the regulator to impose additional capital add-ons, depending on the assessment of a company’s risk management and corporate governance, as well as whether the measures in Pillar 1 are a true reflection of the risk profile of the insurance company. Any divergence will result in the insurer being required to hold additional solvency capital.³²

Pillar 3, responsible for the market transparency, is market focused and sets out information requirements for reporting to supervisors and public disclosures. Its aim is to promote the market discipline by increasing the supervisory reporting.³³ In addition to this, the aim is to achieve a better market transparency between insurance companies due to public disclosure to the public domain.³⁴ This should help minimize the possibility of an adverse selection since it is assumed that the public is going to choose an insurer with a well working risk management. Problematic is that this could imply the manifestation of the “self-fulfilling prophecies” phenomenon.³⁵ An insurer, which reports to the public that it is in trouble, could get difficulties to write new contracts or old contracts might be canceled. Its overall situation would get worse and the troubles may possibly lead to insolvency.

2.3 The current second phase

The Solvency II project is currently in the second and last phase which started in 2004. The main aim is to create the detailed rules based on the general framework conditions which had been developed in the first phase. This is, among others, done by the development of a standard risk formula, applicable to all insurers, and testing of the implications of Solvency II rules and the standard risk formula by means of several quantitative impact studies. The second phase should have been completed by 2010, was postponed to November 2012 and is now expected to be accomplished at the beginning of 2013.³⁶ With the end of the second phase Solvency II will be mandatory for all EU insurers.

The decision making for the design and implementation of the Solvency II framework relies heavily on a consensus building process. The existing legislative process in the EU was too time-consuming and not able to keep up with changes and developments in the fast moving, global capital markets. The recommended approach to accelerate the lawmaking in financial services within the European Union is therefore a four level approach,³⁷ better known as Lamfalussy method which is also used for an accelerated development of the second phase of Solvency II.³⁸ Many stakeholders are involved in the Lamfalussy process which is split up as follows:³⁹

The European Commission drafts the European legislation, with advice provided by CEIOPS who compile detailed analysis according to a framework of calls for advice prepared by the European Commission.⁴⁰ Under level 1 the European Commission publishes a Solvency II Framework Directive to be approved by the European Parliament and European Council. This sets out the broad principles and projected outcomes.⁴¹ Under level 2 the EIOPC prepares so- called implementing measures which provide the detailed specifications required to apply the procedures described in the directive. Under level 3 the day-to-day supervision of insurance undertakings is performed by national insurance supervisors, who may prepare common guidelines in order to apply the standards set out in level 1 and level 2. They achieve this through the involvement of four task-force groups (life/nonlife, supervisory reviews, market transparency and questions) of the CEIOPS.⁴² Under the last and final level 4 the European Commission ensures compliance with Solvency II in the member states.

2.4 Quantitative impact studies

The detailed calculation requirements for Pillar I under Solvency II are still being developed by the European Commission. CEIOPS’ part in preparing advice to the European Commission is among others done by acquiring insight into the possible quantitative impacts of this new solvency standard through a series of quantitative impact studies. This has been done at various stages during the development process. A variety of insurers and reinsurers have been invited to take part in these tests and to give feedback on their results. The first quantitative impact study (QIS1) was started at the end of 2005. It focused on the level of prudence in the current technical provisions by benchmarking them against predefined confidence levels.⁴³ Building on the findings of QIS1, the second quantitative impact study (QIS2) in 2006 investigated the effect of the possible restatement of the value of assets and liabilities under the Solvency II framework, as well as some initial options for setting the SCR and MCR.⁴⁴ Under the third quantitative impact study (QIS3) in 2007 the calculation of the technical provision, the SCR and the MCR were amended and updated by taking the results of QIS2 into account.⁴⁵ The fourth quantitative impact study (QIS4) in 2008 focused on the use of full & partial internal models as well as further adaptations and standards regarding calculation of the technical provision and the capital requirements.⁴⁶ The fifth quantitative impact study (QIS5) is currently being carried out until the end of April 2011 and is supposed to be the last impact study. Compared to QIS4, many experiences from the latest crisis were adopted and further detail work was done for calculating the technical provision, the SCR and MCR. The overall aim is “to provide a starting point for an ongoing dialogue between supervisors and insurers and reinsurers in preparation for the new supervisory system.”⁴⁷ To get comparable data in the quantitative impact studies, all participants have to value their assets and liabilities at the same point in time. For QIS5 this scheduled date is the 31 December 2009. Therefore, their assets and liabilities on that date have to be valued by referring to market data of that same date. If different calculation methods are tested, the insurers are asked to provide the result of every calculation. The results of all the quantitative impact studies are anonymized before they are presented to the public. This is done to prevent any disorientation in the market and to protect the participating insurers.

2.5 A risk based economic system

2.5.1 The economic balance sheet

The primary objective for valuating assets and liabilities under Solvency II is an economic, market-consistent approach.⁴⁸ Insurers have to consider the risk that arises from holding a balance sheet item. For both sides of the balance sheet, the amounts should reflect what a willing third party would pay for assets or expect to receive to take over liabilities. “Undertakings must use a mark to market approach in order to measure the economic value of assets and liabilities, based on readily available prices in orderly transactions that are sourced independently […]”.⁴⁹ Where market prices are not available, valuations must be based on market consistent estimates. In case of insurance liabilities, this involves discounting the liability cash flows on the basis of a market derived risk free yield curve. Therefore, the SCR is drawn up by considering assets and liabilities together because market movements can affect both, the asset values and also the discount rates used to derive the present values of the projected liability cash flows. Figure 2.1 shows the basic structure of the Solvency II balance sheet.

illustration not visible in this excerpt

Figure 2.1: The Solvency II balance sheet

Source: Modified illustration in the style of Olesen/Laaksonen (2009), p. 10.

Insurers hold their assets to cover the discounted future liability cash flows, called technical provisions.⁵⁰ The amount of assets above the threshold that covers the technical provision, called net asset value (NAV), is used to fulfill the SCR and MCR. The SCR itself reflects the buffer for risk arising from holding the assets or liabilities.

The main aim of the SCR is to capture unexpected risk.⁵¹ The economic balanced sheet allows to consider the effects of financial risk mitigation techniques which will lead to a reduction of the SCR. Insurers can purchase or issue financial instruments such as derivatives to transfer risk to the financial markets to reduce their asset side risk. The risk arising from their liability side can be reduced by reinsurance agreements. Furthermore, the risk which is transferred to the customer, e.g. due to unit-linked products is not taken into account either. The risk of every asset itself is derived by a look-through approach to examine their economic substance.⁵² This counts i.e. for investments in collective investments funds or structured products in order to assess the risks applying to the assets underlying the investment vehicle.

2.5.2 Overall structure of the standard formula

Solvency II offers a range of methods to calculate the SCR: full internal model, standard formula and partial internal model, standard formula with undertaking-specific parameters or the standard formula.⁵³ This allows choosing a method that is proportionate to the nature, scale and complexity of the undertaking’s risk. The internal model has the advantage to reflect the underlying risk in a more accurate way. It is the preferred solution for Solvency II because it will help to understand the specific and complex business risk at a more fundamental level.⁵⁴ On the other hand, the development of such a model is cost and time intensive which would treat especially smaller insurance companies, which do not have the necessary resources, less favorably.⁵⁵ Solvency II offers therefore a standard formula to calculate the capital requirements. The risk factors and principles for the internal model are identical to the standard formula and the calibration of the internal model as well as for the standard formula follows the same principles.⁵⁶

The final version of the standard formula has not yet been published by the European Commission. Considering the development of the standard formula from QIS1 to QIS5, the similarity of the QIS5 standard formula to CEIOPS’ level 2 advice published in 2009 and the fact that QIS5 is supposed to be the last impact study, it is most likely that the final version will be very close to the current QIS5 proposal.⁵⁷ Furthermore, every insurer who wants to use an internal model has to publish the SCRs calculated by an internal model and also by the standard formula for the first two years after the introduction of Solvency II. Every internal model will have to prove its validity by comparison with the standard formula. Therefore, looking at the QIS5 standard formula provides a first, but still slightly rough, figure for the future treatment of risk and the effect on solvency capital requirements under Solvency II.⁵⁸ The calculation of the SCR according to the standard formula is divided into modules⁵⁹ and sub-modules, which reflect different risk categories, as can be seen in Figure 2.2:

Figure 2.2: SCR modules according to standard formula

illustration not visible in this excerpt

Source: Slightly modified illustration in the style of European Commission (2010a), p. 90.

Depending of the kind of business, non-applicable modules do not have to be considered for calculating the SCR. For example; a plain life insurance company does not need to calculate solvency capital for not existing health or non-life obligations. For all market risk submodules and several other sub-modules the calculation of the capital requirement is scenario based. The sub-module’s and module’s contribution to the SCR is determined as the impact of a specified scenario on the NAV of the undertaking.⁶⁰

The overall process of building up the SCR involves aggregating sub-modules into modules and modules into the basic SCR (BSCR) which is the SCR prior to any adjustments. This process involves, at each stage, the use of correlation factors or matrices that reduce sub- module, module and BSCR totals in comparison to the sum of their parts.⁶¹ This process is identical to the variance-covariance approach for measuring risk.⁶² It is therefore not additive and the various scenarios are not assumed to take place simultaneously. Problematical is the determination of such correlation factors. “The setting of the correlation coefficients is intended to reflect potential dependencies found in the tail of the distributions, as well as the stability of any correlation assumptions under stressed conditions.”⁶³ These settings are often based on expert opinions rather than on statistically determined factors and even the settings of the correlation factors of the standard formula have been criticized because no empirical evidence was presented.⁶⁴ The overall SCR is calculated by taking the BSCR and adjusting it to the capital requirement for operational risk as well as to the risk absorbing effect of technical provisions and deferred taxes.⁶⁵

The orange framed modules “market” and its sub modules as well as the “default” module in Figure 2.2 reflect the risk arising from the financial markets for an insurer and will be the main field of attention in the further analysis of this thesis.

2.5.3 Measurement and assessment of risk

For calculating the risk under Solvency II the capabilities of two methods, Value at Risk (VaR) and Expected Shortfall (ES), were discussed during the development process.⁶⁶ VaR is defined as the maximum potential change in value of a portfolio of financial instruments with a given confidence level over a certain time horizon.⁶⁷ ES is the expected value of the loss in those cases where the loss exceeds the predefined confidence level by calculating the average of these exceeded losses.⁶⁸ For example, taking a confidence level of 99.5% and looking at 10000 losses: VaR would be set equal to the 50th largest loss while ES would represent the average of the 50 largest losses. The outcome of both will therefore be different. ES calculates higher losses for the same confidence level especially for skewed distributions and can easily reach a multiple of those obtained by VaR.⁶⁹ It can calculate the risk at the tail of the distribution in a more accurate way but is therefore more complex and requires a greater statistical knowledge to be understood. The advantage of VaR compared to ES is that VaR has become the generally accepted risk measurement for financial risk management and is simpler and easier to communicate to third parties.⁷⁰ VaR has therefore been chosen as the way to measure risk under Solvency II. This is also explained by the fact that ES is said not to be compatible with the use of scenarios within the standard formula.⁷¹ In order to perform an ES analysis, it would require multiple scenarios to describe every position in the tail. This would significantly increase the burden on companies with potentially limited additional value added.

The risk measurement therefore follows a VaR approach with a confidence level of 99.5% over a one-year period⁷² - that is, less than 1 in 200 chance of capital being insufficient to cover liabilities during the next year. For the standard formula this implies that all stress scenarios are calibrated using VaR by taking the same confidence level and period into account.

3. Treatment of investment risk under the standard formula

3.1 Interest rate risk

Interest rate changes have an immediate impact on both sides of the balance sheet of an insurance company.⁷³ The asset side is affected by interest rate sensitive instruments like fixed-income investments, policy loans, or interest rate derivatives.⁷⁴ The impact on the liability side is due to the change of the value of future liability cash-flows which are sensitive to a change in the rate at which those cash-flows are discounted. A risk an insurer faces is that the asset side of the balance sheet cannot compensate for the behavior of the liability side due to an interest rate change and vice versa.⁷⁵ For instance this can occur if the term of a financial instrument on the assets side of the balance sheet is shorter than that on the liability side. A fall in interest rates could result in a negative NAV. One objective of the interest rate risk sub module is to cover this risk.

The sensitivity of assets or liabilities to interest rate movements is explained by the duration whereby a higher duration means a higher sensitivity for interest rates movements.⁷⁶ For example, a bond with a duration of eight years would be expected to fall 8% in price for every 1% increase in market interest rates.⁷⁷ If the duration of the asset side does not match the duration of the liability side, a mismatch is present referred to as duration gap or duration risk, the most essential risk due to interest rate movements.⁷⁸ E.g. for Germany, a typical life insurer’s asset side has a duration of 6 years compared to a duration of 12 years on the liability side.⁷⁹ Therefore, rising interest rates could be beneficial for the life insurer because the liability side would lose more value than the asset side and the NAV would increase. Unlike life insurers, the liability duration is usually shorter compared to the asset side of P&C insurers.⁸⁰ A rising interest rate would affect them negatively. For this reason Solvency II uses two scenarios, an up-shock and a down-shock, to calculate the interest rate risk. Shocked are all “assets and liabilities for which the net asset value is sensitive to a change in the term structure of interest rates.”⁸¹ The interest rate shock to be applied to the current term structure is specified for each maturity as a percentage change in the current rate. The shocks decrease for longer maturities as can be seen in Figure 3.1:

Figure 3.1: Interest rate stress

illustration not visible in this excerpt

Source: Own illustration. Data taken from European Commission (2010a), p. 111.

For example, a shock of +42% and -31% to the interest term structure of a bond with a maturity of 10 years would be applied. Assuming that this bond has a duration of 8 years and the current interest rate term structure for 10 years would be 3%.⁸² The shocked term structure would be 3% * (1 + 42%) = 4.26% in the up and 3% * (1 - 31%) = 2.07% in the down scenario. This is a difference of 1.26% in the up and -0.93% in the down scenario. As mentioned above, a bond with a duration of eight years would be expected to fall 8% in price for every 1% increase in interest rates. The bond’s value would therefore drop by 1.26% * (- 8) = -10.08% in the up scenario and increase by -0.93% * (-8) = 7.44% in the down scenario. Duration risk is only one of many other risks that can lead to a different behavior of asset and liability side due to changed interest rate conditions. The convexity, the sensitivity of the duration to changes in interest rate, or embedded options and guarantees in insurance contracts are further factors which can lead to different behavior of each side and are taken into account by this module as well.⁸³

The results of both scenarios are used in the end when all risk factors are correlated to create the overall SCR for market risk. This is done because different correlations are assumed between the different modules in a rising interest rate environment and a falling interest rate environment.⁸⁴

3.1.1 The discount rate

“Risk-free yield curves are the basic building blocks for the valuation of future financial claims and long-term risk management.”⁸⁵ The discount rate used for liability valuation is therefore of prime importance to the insurer because the precise risk free discount rate which is applied to the liability cash-flows has to be matched with its assets.⁸⁶ Otherwise, the NAV of the insurer’s balance sheet would be very volatile due to interest rate movements. There have been many discussions about what is to be understood by “risk free”, how to derive the risk free rate for each currency and how to interpolate the long-end of the interest rate in the development process of Solvency II.

There are currently two different kinds of opinions on how to derive a risk free rate for Solvency II. Those are CEIOPS’ and the industry’s opinion. CEIOPS opts for triple A-rated government bonds as proxy for the discount rate which has received widespread criticism from the European industry.⁸⁷ The industry raises concerns that this will lead to distortions in the European financial markets since Germany and France are the only top rated countries.⁸⁸ This approach would e.g. force Greek insurers to divest domestic government bonds and invest in German or French government bonds which would lead to an increase cost of state financing for Greece.

The industry opts for swap rates rather than government bonds. Swap rates have been used as a risk free rate for derivative pricing for a while⁸⁹ but CEIOPS argues that swap rates were not appropriate because they contained a component of credit risk.⁹⁰ The current state of affairs, which is tested in QIS5, in deriving a risk free rate is to adjust inter-bank swaps for credit risk by discounting 10bps from their term structure.⁹¹ It can be argued whether government bonds or swaps are more suitable as a reference risk free rate and should therefore be finally adopted in Solvency II; both have in common that they are characterized by the following issues for insurers:

Even in very liquid and well developed markets it is unlikely to see interest swap contracts or government bonds with maturities of more than 30 years.⁹² This is a problem for valuating life insurance products with a guaranteed benefit payment for up to 40 years and more from the valuation date.⁹³ Therefore, there is no market data available for discounting these liabilities. Solvency II brings up a macroeconomic extrapolation technique to derive the risk-free interest rate term structure beyond the last available market data point. The aim is to get a stable yield curve “which reflects current market conditions and at the same time embodies economical views on how unobservable long term rates are expected to behave.”⁹⁴ This requires an ultimate forward rate (UFR) and an interpolating method between the last available data point and the UFR. The UFR itself is the sum of the expected long-term inflation and the expected real rate of interest.⁹⁵ The long-term inflation rate is derived by taking the inflation target of the central banks since they have been successful in controlling inflation over the last 15-20 years.⁹⁶ Most central banks operate with a target of 2 per cent; the European central bank also aims at an annual inflation target just below 2 per cent. Therefore, the expected long-term inflation is set to 2 per cent per anno. The expected real rate of interest is derived from a study by Dimson, Marsh and Staunton.⁹⁷ They provide a global comparison of annualized bond returns over the last 110 years for 19 major economies whereby the average real bond return over the second half of the 20th century was computed as annually 2.3 percent. This value is taken because the first half of the century was highly characterized by high inflation and hyperinflation⁹⁸ but it still seems slightly beneficial for the insurance industry compared to Sorensen’s study which shows that the expected real interest rate is more likely about to be 1.8%.⁹⁹

Under Solvency II it is set to 2.2 per cent, referring to Dimson, Marsh and Staunton, but without explaining the slightly lower level.¹⁰⁰ In light of the above analysis, the UFR is set to 4.2 per cent per anno, reflecting the 2.0 per cent from the expected inflation rate and 2.2 per cent from the expected risk free return. The last observable liquid forward rate and the UFR are then interpolated between each other by using either a linear extrapolating technique or the so called Smith-Wilson technique.¹⁰¹ The interest rate curve for discounting Euro liabilities used in QIS5 can be seen in Figure 3.2 and shows the Euro swap curve on 31 December 2009. It has been interpolated with the Smith-Wilson technique using an UFR of

Figure 3.2: Discount curve for EUR liabilities under QIS5

illustration not visible in this excerpt

Source: Own illustration. Data taken from CEIOPS (2010f).

Discount rates derived from swap rates as well as government bonds have further problems in common. It is e.g. known that both can be very volatile in a crisis leading to a very volatile balance sheet.¹⁰² What had not been taken into account before the last crisis was the impact of the market’s illiquidity on the valuation of liabilities.¹⁰³ Illiquid markets can lead to a wrong evaluation of the liabilities as it is shown in the next chapter. Therefore, Solvency II which is based upon market consistent valuation had to come up with a solution.

3.1.2 The illiquidity premium

The introduction of an illiquidity premium¹⁰⁴ has been seen as a fundamental step forward by the insurance industry.¹⁰⁵ It is used in addition to the risk-free rate in order to discount the liabilities by reflecting the impact of their market valuation within illiquid markets. In order to understand this concept and its importance for certain insurers it is easier to start looking at the asset side from an investor’s point of view.

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¹ Cf. Lang (2008), p. 388.

² Cf. Buchholz/Sielaff/Wiegard (2008), p. 414.

³ Cf. Institutional Investment Advisors (2010), p. 11.

⁴ The current value of all payments and claims which are expected to be made to the policyholders in the future. 3

⁵ Cf. Sandström (2006), pp. 23 ff.; Straßburger (2006), p. 5.

⁶ Bourdeau (2009), p. 193.

⁷ Cf. Straßburger (2006), p. 6.

⁸ Cf. Buchholz/Sielaff/Wiegard (2008), p. 414; Straßburger (2006), p. 6; Graf (2008), p.11.

⁹ Cf. Graf (2008), pp. 11-12.

¹⁰ Cf. Bourdeau (2009), p. 193; Straßburger (2006), p. 6; Buchholz/Sielaff/Wiegard (2008), p. 414.

¹¹ Cf. European Commission (2002), p. 14.

¹² Cf. Graf (2008), p. 12.

¹³ Cruz (2009), p. xxxi.

¹⁴ Cf. Straßburger (2006), p. 7.

¹⁵ Cf. Graf (2008), p. 13.

¹⁶ As of 1 January 2011, the European Insurance and Occupational Pensions Authority (EIOPA) replaces the Committee of European Insurance and Occupational Pensions Supervisors (CEIOPS).

¹⁷ Cf. Schanté/Caudet (2005), pp. 73-74.

¹⁸ A good overview is given by Schanté/Caudet (2005) on p. 74.

¹⁹ Cf. European Commission (2001), pp. 2ff.

²⁰ The aim of prudential supervision is to protect consumers by ensuring the safety and soundness of financial institutions. Cf. De Haan/Oosterloo/Schoenmaker (2009), p. 299.

²¹ KPMG (2002), p. 242.

²² Cf. European Commission (2002), p. 4.

²³ Cf. Straßburger (2006), p. 8.

²⁴ Sharma (2002), p. 65.

²⁵ Cf. European Commission (2002), pp. 28 ff.; European Commission (2003), p. 6.

²⁶ Cf. Graf (2008), pp. 17-21.

²⁷ European Commission (2005), p.7.

²⁸ Cf. European Commission (2009a), Internet source.

²⁹ Cf. European Commission (2002), pp. 40-41.

³⁰ Cf. Straßburger (2006), p. 10; European Commission (2002), pp. 43-55; Basel Committee (2004), pp. 158 ff.

³¹ Cf. Graf (2008), pp. 22-23.

³² Cf. European Commission (2006), p. 7; Hartung (2005), pp. 57-63.

³³ Cf. Schubert (2005), p. 40.

³⁴ Cf. European Commission (2006), p. 7.

³⁵ Cf. Graf (2008), pp. 23-24.

³⁶ Cf. CEIOPS (2007b), p. 3; FSA (2011), Internetsource; Tower Watson (2010), p. 25.

³⁷ Cf. Alford (2006), p. 398; De Haan/Oosterloo/Schoenmaker (2009), p. 54.

³⁸ Cf. Straßburger (2006), p. 10; Schubert (2005), p. 41.

³⁹ A illustration is given by Figure Appendix.1 on p. 60.

⁴⁰ Cf. CEA (2007), p. 5.

⁴¹ Cf. CEA (2007), p. 5; Schanté/Caudet (2005), p73 ff.; Schubert (2005), p. 41-42.

⁴² Cf. Straßburger (2006), p. 10.

⁴³ Cf. CEIOPS (2005), pp. 1-2.

⁴⁴ Cf. CEIOPS (2006), pp. 1-3.

⁴⁵ Cf. CEIOPS (2007a), pp. 1-5.

⁴⁶ Cf. European Commission (2008c), pp. 3-5.

⁴⁷ European Commission (2010c), p. 4.

⁴⁸ Cf. European Commission (2010a), pp. 6 ff.

⁴⁹ European Commission (2010a), p. 7.

⁵⁰ Under Solvency II the technical provisions are calculated by using a market consistent valuation for hedgeable risks or the sum of a best estimate plus risk margin for non-hedgeable risks.

⁵¹ Cf. European Commission (2010a), p. 270.

⁵² Cf. European Commission (2010a), pp. 109 ff.

⁵³ Cf. European Commission (2010a), p. 93.

⁵⁴ Cf. Bourdeau (2009), pp. 210, 224-225; Graf (2008), pp. 62-63.

⁵⁵ Cf. Lindner/Zierhofer (2008), p. 399.

⁵⁶ Cf. Bourdeau (2009), pp. 224-225.

⁵⁷ Cf. e.g. European Commission (2010c), p. 2.

⁵⁸ Cf. Bourdeau (2009), pp. 210-211, 225.

⁵⁹ A description of each module is given by Table Appendix.2 on p. 66.

⁶⁰ The change of NAV resulting from the scenarios is referred as ∆NAV. ∆NAV is defined to be positive where the scenario results in a loss of NAV. Cf. European Commission (2010a), p. 92.

⁶¹ Cf. Equation Appendix.1 and Table Appendix.1 on p. 66.

⁶² Cf. e.g. Hull (2009), pp. 449-450.

⁶³ Bourdeau (2009), p. 198.

⁶⁴ Cf. Doff (2009), p. 24.

⁶⁵ Cf. European Commission (2010a), pp. 94-95.

⁶⁶ Cf. European Commission (2004), pp. 33-35.

⁶⁷ Cf. Jorion (1997), p. 88.

⁶⁸ Cf. CEA (2006), p. 6; Expected Shortfall is sometimes also called Conditional Tail Expectation, Expected Tail Loss or Tail Value-at-Risk.

⁶⁹ Cf. CEA (2006), p. 4; Straßburger (2006), p. 11.

⁷⁰ Cf. CEA (2006), p. 2.

⁷¹ Cf. CEA (2006), p. 3.

⁷² Cf. European Parliament (2009), p. 43.

⁷³ Cf. Munich Re (2008), p. 4.

⁷⁴ Cf. Meyer-Bullerdiek (2003), pp. 298 ff.; European Commission (2010a), p. 110.

⁷⁵ Cf. Sommerfeld (2009), pp. 438 ff.

⁷⁶ Cf. Bruns/Meyer-Bullerdiek (2008), pp. 283-289; Hull (2009),pp. 87-91; The duration used under Solvency II is the modified duration.

⁷⁷ This is only a rough estimate since duration assumes a linearity between the assets or liabilities price and the interest rate but in reality this relation is more convex than linear. Cf. Bruns/Meyer-Bullerdiek (2008), p. 286; Hull (2009), pp. 90-91; For the sake of simplicity a linearity between price and interest rate is assumed in further calculations. Even Solvency II assumes linearity as will be seen in Chapter 3.3 - Spread risk.

⁷⁸ Cf. Siemßen (2005), p. 133.

⁷⁹ Cf. Kirchner/Zielke (2008), p. 437.

⁸⁰ Cf. Sommerfeld (2009), p. 438; Ludka (2009), pp. 1813-1814.

⁸¹ European Commission (2010, p. 110.

⁸² The term structure for EUR assets and liabilities with a maturity of 10 years under QIS5 is 3.605%. The interest term structure refers to the risk free discount rate used to valuate liabilities under Solvency II (Cf. Chapter 3.1.1 - The discount rate). This assumes that the discount rate for the liabilities reflects the current risk free term structure of the assets.

⁸³ Cf. e.g. European Commission (2010a), pp. 35-39; E.g. embedded options have to be taken into account for calculating the technical provision. This refers to the fact that in times of good market conditions and a high interest rate environment, it is most likely that more life insurance contracts will be canceled because it is more beneficial to invest the money directly in the financial markets: Cf. e.g. Oechslin et al. (2005), pp. 43-45.

⁸⁴ Cf. Chapter 3.9 - Aggregation of risk modules.

⁸⁵ Antonio et. al. (2009), p. 39.

⁸⁶ Cf. Foroughi (2009), pp. 116 ff.

⁸⁷ Cf. Life & Pension (2009a), Internet source.

⁸⁸ Cf. Russel et al. (2009), p. 9; Life & Pension (2009b); Greece’s government debt is currently rated BB which is similar to “junk bonds” and the situation that even their national insurers would invest fewer in Greek government bonds makes it difficult for the country to borrow money.

⁸⁹ Cf. e.g. Hull (2009), p. 494.

⁹⁰ Cf. Life & Pension (2009a), Internet source.

⁹¹ Cf. CRO (2010c), p. 10.

⁹² Cf. Antonio et. al. (2009), p. 39; Ludka (2009), pp. 1813-1814.

⁹³ Cf. CRO (2010b), p.4.

⁹⁴ CEIOPS (2010b), p. 4.

⁹⁵ Cf. European Commission (2010b), p.20.

⁹⁶ Cf. CEIOPS (2010b), p. 6.

⁹⁷ Cf. Dimson / Marsh / Staunton (2000), pp. 1-18.

⁹⁸ German hyperinflation in 1922/1923, which ran at an annual percentage rate in the billions, in Italy an inflation of 344% in 1944, in France 74% in 1946 and in Japan 317% in 1946. Cf. Dimson / Marsh / Staunton (2000), p. 3.

⁹⁹ Cf. Soerensen (2010), p. 7.

¹⁰⁰ Cf. CEIOPS (2010b), p. 10.

¹⁰¹ Cf. CEIOPS (2010b), pp. 12-17.

¹⁰² Cf. Bräutigam (2009), pp. 1247-1250.

¹⁰³ Cf. Pritchard/Trunbull (2009), pp. 3-5.

¹⁰⁴ Illiquidity premium is also often referred as liquidity premium. Both terms refer to the same issue just the point of view is a different one. It can be seen later on that illiquidity premium is a more appropriate term when talking about interest rates.

¹⁰⁵ Cf. Woolner (2009b), Internet source.