compared
S.A. Postma
Master’s Thesis to obtain the degree in Actuarial Science and Mathematical Finance University of Amsterdam
Faculty of Economics and Business Amsterdam School of Economics
Author: S.A. Postma
Student nr: 10681302
Date: July 12, 2017
Supervisor: Dr. L. van Gastel Second Supervisor: ir. P. Bijl
Statement of Originality
This document is written by Student Stefanie Postma who declares to take full respon-sibility for the contents of this document. I declare that the text and the work presented in this document is original and that no sources other than those mentioned in the text and its references have been used in creating it. The Faculty of Economics and Business is responsible solely for the supervision of completion of the work, not for the contents.
Abstract
For this thesis we compare the risk margin under Solvency II and the risk adjustment under IFRS Insurance Contracts. Both quantities have a lot in common, but are set in two frameworks with different goals.
Solvency II and IFRS Insurance Contracts are described in general together with the framework’s objective. Within these frameworks the risk margin and the risk adjustment respectively are considered, their objective and methods of calculation, following from the official regulatory documents. After the theoretical comparison comes the imple-mentation for a portfolio of a non-life insurer for three lines of business, namely motor liability, other motor and fire. We select the Cost-of-Capital method for the calculation of the risk margin for both reserving and premium risk. Next the translation is made to the confidence level technique for the calculation of the risk adjustment. With the combination of the theory and practice, we try to connect and compare both quantities, also keeping in mind the different parties of interests and perspective.
Keywords – Solvency II, IFRS, Insurance Contracts, Risk Margin, Risk Adjust-ment, Cost of Capital, Confidence level technique, Comparison, Perspective
Preface vi
1 Introduction 1
2 The main objective of Solvency II and IFRS in general 2
2.1 Solvency II . . . 2 2.1.1 Objective . . . 2 2.1.2 Risk Margin. . . 3 2.2 IFRS . . . 4 2.2.1 Objective . . . 5 2.2.2 Risk Adjustment . . . 6
2.3 Comparing the frameworks . . . 7
3 Different Methods 10 3.1 Risk Margin Method . . . 10
3.2 Risk Adjustment Methods . . . 10
3.2.1 Confidence Level . . . 11
3.2.2 Conditional Tail Expectation . . . 11
3.2.3 Cost of Capital . . . 11
3.2.4 Disclosure . . . 12
4 Implementation 13 4.1 Prior Risk . . . 13
4.1.1 Distributions . . . 13
4.1.2 Calculation of the Risk Margin . . . 14
4.1.3 Risk adjustment . . . 16
4.2 Current Risk . . . 16
4.2.1 Loss ratios . . . 17
4.2.2 Distributions . . . 18
4.2.3 Calculation of the Risk Margin . . . 20
4.2.4 Risk adjustment . . . 21 4.3 Aggregation . . . 22 5 Perspective 24 6 Conclusion 26 6.1 Further Research . . . 27 7 Discussion 28 A Appendix 30 Bibliography 32 v
After four and a half years my study in Actuarial Science and Mathematical Finance has come to an end. And this thesis is the final part. From the beginning it has been a long journey for me. Starting work after my study in Mathematical Science at the University of Leiden and also starting another study at the University of Amsterdam. Especially the working life was a very big and new chapter in my life. Next to the working life, I started going to the university once again. The combination was not always easy but, it has brought me a lot and I am thankful for the opportunity to be able to keep learning. I especially want to thank my colleague Peter Bijl. He helped create the subject of this thesis, delivered valuable input and answered the same questions over and over again. Also I want to thank my supervisor Leendert van Gastel from the University of Amsterdam for supervising this thesis. Your kind and calm words were always welcome. Last but not least I want to thank Teun for his love, support and guidance during this entire process.
Introduction
Solvency II is the new risk-based supervisory framework for the insurance market that entered into effect on January 1st 2016. Within this framework the risk margin is the margin which should be added to the best estimate to provide a market-consistent valuation of the technical provisions. On the other hand the International Financial Reporting Standards, or IFRS, are used for global understanding and guidance for ac-counting standards. For the insurance market these guidelines are covered in IFRS 4 Insurance Contracts. According to this document, the risk adjustment is the compen-sation an entity requires for bearing the uncertainty about and timing of the cash flows that arise as the entity fulfills the insurance contract. According to these definitions, these two concepts seem to have a lot in common. A big difference is the method of calculation. The risk margin is often calculated by the Cost of Capital method and is explicitly described in the latest regulation document of Solvency II. For the risk adjustment only a preference in method is mentioned.
These observations give rise to the following questions:
• Can the common factor in concepts help for the calculation?
• Can the Cost of Capital method be adjusted and used to calculate the risk ad-justment?
• Are there any other methods for calculating both risk margin and risk adjustment? • What are the advantages and disadvantages of these methods?
• Is there one method which can be used for the calculation of both quantities? These questions led to the following central research question for this thesis: How can the risk margin under Solvency II and the risk adjustment under IFRS can be compared and what do both quantities have in common?
This thesis tries to answer the considered central research questions and the several sub-questions mentioned. In Chapter2 the main objective of Solvency II and IFRS are discussed in general as well as the definition of and the thought behind the terms risk margin and risk adjustment. Different methods for the computation of both risk margin and risk adjustment exist. From these described methods both differences and similar-ities will arise. Both methods and the differences and similarsimilar-ities of these methods are described in Chapter 3. Chapter 4 will give an answer to the question of implementa-tion. Followed by Chapter5, where both risk margin, risk adjustment and the methods are considered from different point of view. In Chapter6the research question and sub-questions will be answered and concludes this thesis. And finally, Chapter 7 discusses the interpretation of the risk adjustment.
The main objective of Solvency II
and IFRS in general
In this chapter we will discuss both Solvency II and IFRS in general. This will be done in three sections. The first section discusses the origin and the documents of Solvency II and the second section discusses IFRS. The third and final section will discuss similarities and differences in both frameworks regarding risk margin and risk adjustment. This in preparation for the next chapter.
2.1
Solvency II
Solvency II is the name of an European Union Directive, which is officially called Di-rective 2009/138/EC. It was adopted in November 2009 and it became applicable on 1 January 2016. It replaces 14 existing Directives, together commonly referred to as ’Solvency I’. The official subtitle of the Solvency II-Directive is ’On the taking-up and pursuit of the business of Insurance and Reinsurance’.
For the implementation rules of Solvency II, the European Commission adopted the Delegated Regulation 2015/35, on 10 October 2004 and was published in the Of-ficial Journal on 17 January 2015. The calculation of regulatory capital requirements for several categories of assets held by insurance and reinsurance undertakings was de-scribed in Delegated Regulation 2016/467. This Delegated Regulation was adopted on 25 September 2015 amending Delegated Regulation 2015/35.
2.1.1 Objective
For understanding why Solvency II was adopted and what the main objective was we turn to the preamble of both the Solvency II Directive and the two related Delegated Regulations (EU) 2015/35 and 2016/467.
Starting with the Solvency II Directive, it becomes clear that the main reason is the protection of the policy holder and beneficiaries. According to paragraph (14): ”The protection of policy holders presupposes that insurance and reinsurance undertakings are subject to effective solvency requirements that result in an efficient allocation of capital across the European Union. In light of market developments the current system is no longer adequate. It is therefore necessary to introduce a new regulatory framework.” So here is explicitly mentioned that the current system is ineffective and changes have to be made. In order to accomplish these changes two main methods are described in the Directive. The Solvency Capital Requirement and the calculation and valuation of the technical provisions.
The first method, the Solvency Capital Requirement, is mentioned in paragraph (26). ”The starting point for the adequacy of the quantitative requirements in the insurance
sector is the Solvency Capital Requirement. ... The Solvency Capital Requirement stan-dard formula is intended to reflect the risk profile of most insurance and reinsurance undertakings.” And further on in paragraph (62): ”The Solvency Capital Requirement should reflect a level of eligible own funds that enables insurance and reinsurance under-takings to absorb significant losses and that gives reasonable assurance to policy holders and beneficiaries that payments will be made as they fall due.”
In light of the second method, we turn to paragraph (54). ”The calculation of tech-nical provisions should be consistent with the valuation of assets and other liabilities, market consistent and in line with international developments in accounting and supervi-sion.” Paragraph (55) explains what the value of technical provisions should correspond to. ”The value of technical provisions should therefore correspond to:
• The amount an insurance or reinsurance undertaking would have to pay if it trans-ferred its contractual rights and obligations immediately to another undertaking. • The amount which another insurance or reinsurance undertaking (the reference undertaking) would be expected to require to take over and fulfil the underlying insurance and reinsurance obligations.
The amount of technical provisions should reflect the characteristics of the underlying insurance portfolio. ...” So the value of the technical provisions should be based on directly observable market values, according to paragraph (57). And paragraph (58): ”It is necessary that the expected present value of insurance liabilities is calculated on the basis of current and credible information and realistic assumptions, taking account of financial guarantees and options in insurance or reinsurance contracts, to deliver an economic valuation of insurance or reinsurance obligations. The use of effective and harmonised actuarial methodologies should be required.”
This last paragraph describes exactly why the current system is no longer adequate. The expected present value of insurance liabilities was not done according to these rules. The valuation used was the balance sheet value or book value. It is explicitly mentioned that financial guarantees and options should be taking into account. When using the book value, the uncertainty and risk which covers these products cannot be comprehended into the expected present value of insurance liabilities. A clear example is Equitable Life. [19]
Any reasons concerning the adoption of Solvency II and the ineffectiveness of the current systems are not mentioned in the preamble of the two related Delegated Reg-ulations. The main topics here are the implementation and regulations of the Solvency II-Directive only. All different aspects of both implementation and regulations are dis-cussed. From calculation of best estimates, to supervisory authorities and internal mod-els, but also the definition of good governance is described.Although the first paragraph of Delegated Regulation 2015/35 states: ”In applying the requirements set out in this Regulation, account should be taken to the nature, scale and complexity of the risks inherent in the business of an insurance or reinsurance undertaking.” This is also men-tioned in paragraph (18) of the Solvency II Directive.
The preparation of the new supervisory regime for insurance and reinsurance under-takings and particularly the conduct of all the necessary work for the implementation of the Solvency II-Directive, is one of the main aims of EIOPA in the field of insur-ance for the coming years. EIOPA stands for European Insurinsur-ance and Occupational Pensions Authority. Additionally one of their main goals is better protecting consumers and rebuilding trust in the financial system.
2.1.2 Risk Margin
In the Solvency II-Directive, the risk margin is first mentioned in paragraph (56) of the preamble.
”The assumptions made about the reference undertaking assumed to take over and meet the underlying insurance and reinsurance obligations should be harmonised throughout the Community. In particular, the assumptions made about the reference
undertaking that determine whether or not, and if so to what extent, diversification effects should be taken into account in the calculation of the risk margin should be analysed as part of the impact assessment of implementing measures and should then
be harmonised at Community level.”
The definition of the risk margin according to Article 77(3) of the Solvency II-Directive: ”The risk margin shall be such as to ensure that the value of the technical provisions
is equivalent to the amount that insurance and reinsurance undertakings would be expected to require in order to take over and meet the insurance and reinsurance
obligations.”
The calculation of the risk margin according to Article 77(5) of the Solvency II-Directive: ”When insurance and reinsurance undertakings value the best estimate and the risk
margin separately, the risk margin shall be calculated by determining the cost of providing an amount of eligible own funds equal to the Solvency Capital Requirement
necessary to support the insurance and reinsurance obligations over the lifetime thereof. ...”
Notice that in these two articles both main methods for changing the current system are mentioned, the Solvency Capital Requirement and valuation of the technical provisions, which are mentioned in section2.1.
Both the definition and the calculation of the risk margin mentioned in the Solvency II-Directive are in line with paragraph (18), (19) and (130) of the Delegated Regulation 2015/35. In this Regulation subsection 4, which consists of Articles 37-39, treats the topic of risk margin. Article 37 entitles Calculation of the risk margin and describes the exact formula which needs to be used for the calculation of the risk margin. More information about this method will be given in Chapter 3.
Article 38 is called Reference Undertaking and consists of assumptions for the cal-culation of the risk margin concerning the reference undertaking. This Reference Un-dertaking is important because this is another insurance or reinsurance unUn-dertaking which takes over the whole portfolio of insurance and reinsurance obligations of the insurance or reinsurance undertaking that calculates the risk margin, referred to as the original undertaking. The Reference Undertaking could be seen as the ’ideal’ insurance or reinsurance undertaking. This follows from the other items of Article 38. So in the-ory, what is necessary for the whole portfolio to be taken over by the ideal party? This is completely in line with the whole Solvency II Directive, which tries to focus on an enhanced level of policyholder protection. Here the Solvency Capital Requirement and market risk play important parts. For example that, after the transfer, the reference undertaking raises eligible own funds equal to the Solvency Capital Requirement nec-essary to support the insurance and reinsurance obligations over the lifetime thereof. But also, the assets are selected in such a way that they minimize the Solvency Capital Requirement for market risk that the Reference Undertaking is exposed to.
Finally Article 39 states that the Cost-of-Capital rate is assumed to be equal to 6%.
2.2
IFRS
IFRS stands for International Financial Reporting Standards which are issued by the International Accounting Standards Board (IASB). The IASB is the independent stan-dard-setting body of the IFRS Foundation. The IFRS Foundation is the oversight body of the IASB and includes governance and oversight, undertaken by the Trustees, and support operations.
The Board’s objective was to develop a common, high-quality standard that will ad-dress recognition, measurement, presentation and disclosure requirements for insurance contracts. This has been done through IFRS 4. Starting on 31 July 2003, the Exposure Draft ED 5 ’Insurance Contracts’ was published. Almost a year later, on 31 March 2004, IFRS 4 ’Insurance Contracts’ was issued. Which was effective for annual periods beginning on or after 1 January 2005. After this period there two other Exposure Drafts were published. On 30 July 2010 Exposure Draft ED/2010/8 Insurance Contracts was published and on 20 June 2013 Exposure Draft ED/2013/7, a targeted and revised ex-posure draft, was published. After publication there has been given about half a year to comment the Exposure Drafts. A final standard has been published in May 2017. This standard will also be known as IFRS 17 ’Insurance Contracts’ and will replace IFRS 4. The IASB agreed to split the insurance contracts project into two phases, so that components of the project could be put in place in 2005 without delaying the rest of the project. The first phase addresses the application of existing standards to entities that issue insurance contracts. Phase II is a comprehensive project on accounting for insurance contracts addressing, on a fresh-start basis, all issues unique to insurers. 2.2.1 Objective
According to the official IFRS 4 document from 2004, it is the first IFRS to deal with insurance contracts. And according to the introduction: ”Accounting practices for in-surance contracts have been diverse, and have often differed from practices in other sectors.” The two reasons mentioned for issuing this IFRS:
• To make limited improvements to accounting for insurance contracts until the Board completes the second phase of its project on insurance contracts.
• To require any entity issuing insurance contracts (an insurer) to disclose informa-tion about those contracts.
To be specific, the objective of IFRS 4:
”The objective of this IFRS is to specify the financial reporting for insurance contracts by any entity that issues such contracts (described in this IFRS as an insurer) until
the Board completes the second phase of its project on insurance contracts. In particular, this IFRS requires:
(a) limited improvements to accounting by insurers for insurance contracts.
(b) disclosure that identifies and explains the amounts in an insurer’s financial ments arising from insurance contracts and helps users of those financial state-ments understand the amount, timing and uncertainty of future cash flows from insurance contract.”
Here there is no mentioning of the policy holder or any other beneficiaries. Neither that the current system is no longer adequate and that is therefore necessary to introduce a new regulatory framework. The main reason for issuing IFRS 4 is the need for standards for financial reporting for insurance contracts. This is of a whole other level than the main reason for issuing Solvency II.
This again becomes clear in the objective of Exposure Draft ED/2010/8, but clearly in other words. Paragraph 1 states:
”The objective of this [draft] IFRS is to establish the principles that an entity should apply to report useful information to users of its financial statements about the
amount, timing and uncertainty of cash flows from: (a) insurance contracts that it issues,
(b) reinsurance contracts that it holds, and
(c) financial instruments containing discretionary participation features that it is-sues.”
In the objective of Exposure Draft ED/2013/7 there is a change of tone compared to the objective in the starting document.
”This [draft] Standard establishes the principles that an entity should apply to report useful information to users of its financial statements about the nature, amount,
timing, and uncertainty of cash flows from insurance contracts.” Followed by:
”To meet the objective in paragraph 1, this [draft] Standard requires an entity: (a) to measure an insurance contract it issues using a current value approach that
incorporates all of the available information in a way that is consistent with ob-servable market information; and
(b) to present insurance contract revenue to depict the transfer of promised services arising from an insurance contract in an amount that reflects the consideration to which the entity expects to be entitled in exchange for those services, and to present expenses as the entity incurs them.”
Here uncertainty of cash flows and consistent with observable market information are explicitly mentioned. The resemblance with the objective of Solvency II is quite remark-able.
2.2.2 Risk Adjustment
There is no mentioning of the term risk adjustment in IFRS 4. For this we have to address the two Exposure Drafts. In Exposure Draft ED/2010/8 the following definitions are given in paragraph IN[10] and IN[11] about the measurement model, 35-37 and B67-B103:
”A direct measurement that incorporates current, discounted estimates of future cash flows revised at each reporting date, adjusted for the effects of uncertainty about the
amount and timing of those future cash flows.” - Paragraph IN[10] ”The risk adjustment represents the maximum amount that an insurer would rationally pay to be relieved of the risk that the ultimate fulfilment cash flows exceed those expected. It is remeasured at the end of each reporting period and declines over
time as the insurer is released from risk.” - Paragraph IN[10]
”The risk adjustment shall be the maximum amount the insurer would rationally pay to be relieved of the risk that the ultimate fulfilment cash flows exceed those
expected.” - Paragraph 35
”An insurer shall estimate the risk adjustment at the level of a portfolio of insurance contracts. Therefore, the risk adjustment shall reflect the effects of diversification that
arise within a portfolio of insurance contracts, but not the effects of diversification between that portfolio and other portfolios of insurance contracts.” - Paragraph 36 ”Appendix B provides guidance for estimating the risk adjustment.” - Paragraph 37 Paragraphs B67-B103 in Appendix B address objective and characteristics, techniques for estimating risk adjustments, features of permitted risk adjustment techniques, ap-plication of risk adjustment techniques and risk adjustments and the use of a replicating portfolio. These paragraphs will be used when discussing methods and techniques for computation of the risk adjustment.
In Exposure Draft ED/2013/7 the first definition of the risk adjustment is given in Appendix A Defined terms. Here it states:
”The compensation that an entity requires for bearing the uncertainty about the amount and timing of the cash flows that arise as the entity fulfils the insurance
contract.” And in Paragraph 27:
”When determining the fulfilment cash flows, an entity shall apply a risk adjustment to the expected present value of cash flows used.”
In Appendix B Application guide there is more abbreviation:
”A risk adjustment measured by incorporating diversification benefits to the extent that the entity considers those benefits in setting the amount of compensation it
requires to bear risk (see paragraphs B76-B77).” - Paragraph B37
”The risk adjustment measures the compensation that the entity would require to make the entity indifferent between:
(a) fulfilling an insurance contract liability that has a range of possible outcomes; and (b) fulfilling a liability that will generate fixed cash flows with the same expected
present value as the insurance contract.” - Paragraph B76
”The purpose of the risk adjustment is to measure the effect of uncertainty in the cash flows that arise from the insurance contract. Consequently, the risk adjustment shall
reflect all risks associated with the insurance contract, other than those reflected through the use of market consistent inputs (see paragraph B44). It shall not reflect
the risks that do not arise from the insurance contract, such as investment risk relating to the assets that an entity holds (except when that investment risk affects
the amounts payable to policyholders), asset-liability mismatch risk or general operational risk that relates to future transactions.” - Paragraph 78
Paragraphs B79-B82 there is more information about techniques concerning the risk adjustment. This will also be used further on.
2.3
Comparing the frameworks
Before comparing the two quantities risk margin and risk adjustment, first the main comparison between Solvency II and IFRS 4. One of the main differences between the two frameworks is the focus and point of view. Solvency II focuses on an enhanced level of policyholder protection and Solvency Capital Requirements. IFRS 4, on the other hand, aims to apply uniform accounting standards for all types of insurance and reinsurance contracts. Secondly, Solvency II is said to be more rule-based while IFRS is principle based. This is exactly the point of interest in both these frameworks and the considered risk margin and risk adjustment. The rules for Solvency II are much more prescriptive and comprehensive as compared to IFRS. This freedom in interpretation of IFRS and the rules set for Solvency II can be used to provide synergy between the two regulatory frameworks. The main similarity is the measurement of the asset and liabilities. This will be done on a market consistent basis. The market value of the liabilities is equal to the best estimate of the liabilities increased by a risk margin or risk adjustment. Although Solvency II deals with both sides of the balance sheet, IFRS 4 only deals with the liability side of the balance sheet. Further on, due to the complexity of the content of both frameworks only a global comparison is made. For more detailed comparison, see [13].
Now for the more detailed comparison between the risk margin under Solvency II and the risk adjustment under IFRS. One could imagine why it would be interesting to compare these two terms. Described by different words and in different documents these
terms have a similar concept. The risk adjustment is the compensation that a company requires for bearing the uncertainty about the amount and timing of cash flows that arise as the entity fulfills the insurance contract. The risk margin is defined as the amount, in addition to the present value of future cash flows, which would be required by another insurer to take over and meet the insurer’s obligations. The main difference between the two quantities is the framework they are contained in. The frameworks themselves and the interpretation of the frameworks makes that the two quantities are the same as stand alone, but are different in the framework they belong. Solvency II tries to enhance the level of policyholder protection through the identity of the Reference Undertaking. IFRS tries to give a clear overview of both profit and loss and finally dividend, no Reference Undertaking is needed for this. Due to the reason of existence, it is necessary that the boarders of the framework of Solvency II are much more strict then the ones of IFRS. This also expresses in the methods prescribed for both considered quantities. The risk margin is calculated via the Cost-of-Capital approach, while no exact methods are described for calculating the risk adjustment. This last point will be the point of focus for the thesis and will be carried on in chapter 3.
To be able to give a good comparison between the risk margin and risk adjustment, we also need to consider the balance sheets under Solvency II and IFRS. In the CEIOPS advice paper of March 2007 it states that in Solvency II’s Pillar I is made up of a number of different elements that, in combination, should provide a structured means of assessing whether the insurer has adequate financial resources for the risk it carries. This statement still holds nowadays. The liabilities consist of the technical provisions, the Minimum Capital Requirement (MCR) and the Solvency Capital Requirement (SCR). The technical provisions are the best estimate of the liabilities plus the risk margin, see Figure 2.1.
For the balance sheet under IFRS, Exposure Draft ED/2013/7, paragraph 76, states that an entity shall disclose a reconciliation that separately reconciles the opening and closing balances of the expected present value of the future cash flows, the risk adjust-ment and the Contractual Service Margin (CSR).
In Figure 2.2, a schematic comparison is shown between the Solvency II and IFRS balance. Here the resemblance between both balance sheets and, within there, the risk margin and risk adjustment is made visual.
Figure 2.1: The Solvency II balance sheet. [9]
Different Methods
In this section we will discuss the different methods for the computation of the risk margin and the risk adjustment. The first section will focus on the method for the risk margin and the second second on the methods for the risk adjustment.
3.1
Risk Margin Method
As stated in Chapter2and in the Delegated Regulation 2015/35, the risk margin under Solvency II shall be calculated by the Cost-of-Capital method. Subsection 4 Risk Margin, Article 37 (1) Calculation of the risk margin, Solvency II 2015/35 states the following. The risk margin for the whole portfolio of insurance and reinsurance obligations shall be calculated using the following formula:
RM = CoC ·X
t≥0
SCR(t)
(1 + r(t + 1))(t+1). (3.1)
Here CoC denotes the Cost-of-Capital rate and r(t+1) denotes the basic risk-free interest rate for the maturity of t + 1 years. This basic risk-free interest rate shall be chosen in accordance with the currency used for the financial statements of the insurance and reinsurance undertaking. And SCR(t) denotes the Solvency Capital Requirement, which is non-hedgeable and referred to in Article 38 (2) in the same Delegated Regulation. According to Article 39 of the Delegated Regulation 2015/35 states that the Cost-of-Capital rate shall be assumed to be equal to 6%.
Article 58 is called Simplified calculations of the risk margin. Here it states that simplified methods may be used when calculating the risk margin. This must be done without prejudice to Article 56 Proportionality, which states that about proportionality to the nature, scale and complexity of the underlying risks. But it is not mentioned what these simplified methods are.
3.2
Risk Adjustment Methods
In contrast with one method for the calculation of the risk margin, there are several methods allowed for the calculation of the risk adjustment. Paragraph B73 of the Ex-posure Draft ED/2013/7 states the following:
An insurer shall use only the following techniques for estimating risk adjustments: • Confidence level
• Conditional tail expectation • Cost of capital
A further description of these techniques can be found in the following subsections. 10
3.2.1 Confidence Level
The Exposure Draft ED/2010/8 dedicates a section on the features of permitted risk adjustment techniques, starting with the confidence level technique. It states that this technique expresses the likelihood that the actual outcome will be within a specified interval, and is sometimes referred to as the Value at Risk (VaR). In [10], the use of confidence levels in estimating a risk adjustment is describes as follows:
”The use of confidence levels is the most common quantile method. Risk margin methods based on confidence levels express uncertainty in terms of the extra amount
that must be added to the expected value so that the probability that the actual outcome will be less than the amount of the liability (including the risk margin) over
the selected time period equals the target level of confidence.”
In this context the risk margin mentioned can also be seen as the risk adjustment. It also states some pros and cons of the confidence level technique. For example the benefits of being relatively easy to communicate to users and relatively easy to calculate. However, the usefulness diminishes when the probability distribution is not statistically normal (which is often the case for insurance contracts). When this is the case the selection of the confidence level must take into account additional factors, such as the skewness of the probability function. Therefore judgement is required to determine the confidence level.
3.2.2 Conditional Tail Expectation
The conditional tail expectation is also referred to as tail confidence expectation or tail value at risk and abbreviated by CTE. According to the Exposure Draft ED/2010/8 the CTE technique is an enhancement of the confidence level technique or VaR. A CTE technique provides a better reflection of the potentially extreme losses than the confidence level technique by incorporating the expected value of those extreme losses into the measurement of the risk adjustment. In [12], the CTE technique is described as follows:
”The CTE technique is a modified percentile approach that combines the percentile and mean values of different cases. It basically calculates the mean of the losses within a certain band (or tail) of predefined percentiles. With the CTE technique, the margin is calculated as the probability weighted average of all scenarios in the chosen tail of the distribution less the mean estimate. The CTE technique is an improvement over
the confidence level technique since it smoothes some extreme claims.”
It also states some pros and cons of the CTE technique. The focus of a CTE technique on the tail of the probabilty distribution reflects a fundamental aspect of an insurance contract, namely the fact that the tail is the riskiest part of the distribution. This is also the focus in Solvency II. As part of the estimation of the amount an insurer would rationally pay to be relieved of the risk, significant consideration needs to be given to the tail of the loss distribution. However, if distributions are not particularly skewed one could ask if the CTE technique is the preferred technique. Also here judgement is required to determine the CTE band set.
3.2.3 Cost of Capital
This technique is interesting to analyze from the perspective of a risk adjustment, be-cause this is the prescribed technique for the risk margin under Solvency II.
The Exposure Draft ED/2010/8 states that, for the general purpose of financial reporting, a cost of capital technique can be used to estimate a risk adjustment that reflects the uncertainty about the amount and timing of the future cash flows that will
arise as an insurer fulfills its existing insurance contracts. According to the Exposure Draft, an insurer applies the Cost of Capital technique as follows:
(a) First, the insurer derives an estimated probability distribution for the cash flows. (b) Secondly, the insurer sets a confidence level from that distribution. The confidence level is intended to provide a high degree of certainty that the insurer will be able to fulfill its obligations under existing insurance contracts. The difference between the amount at the confidence level and the expected values (i.e. mean) of claims for the entire probability function indicates a capital amount that corresponds to the high degree of certainty that the insurer will be able to fulfill its obligations under the portfolio of existing contracts, ignoring any risk factors not related to those contracts.
(c) Lastly, the insurer estimates the risk adjustment by applying a factor, in the form of an appropriate annual rate, to that capital over the lifetime of the contract and making a further adjustment for the time value of money because the capital will be held in future periods.
Because this is the same technique as under Solvency II the resemblance can be made. Not only the Delegated Regulation 2015/35 states the same technique, but it even captures it in one formula. Notice that the confidence level there is set at 99.5%, the applied factor is equal to the Cost-of-Capital rate of 6% and the appropriate annual rate is the basic risk-free interest rate. Also notice the resemblance between the Solvency Capital Requirement and ’a capital amount that corresponds to the high degree of certainty that the insurer will be able to fulfill its obligations under the portfolio of existing contracts, ...’.
The cost of capital technique reflects almost the entire distribution, and only a relatively small band on the far end of the distribution, beyond the selected confidence level for the capital amount, would not be considered. This is because the confidence level is set at a level that is intended to provide a high degree of certainty that the insurer will be able to fulfill its obligations under existing insurance contracts. Therefore, in setting the confidence level in the cost of capital technique, an insurer takes into account the possibility of low-frequency high-severity losses in all but the extreme tail of the probability distribution. Because this technique takes into account the release of the capital amount over the life of the contract, this technique also reflects how the risk associated with the insurance contract changes over time.
It is important that the confidence level for the capital amount, and the annual rate applied to that capital amount to calculate the risk adjustment, shall be set in such a way that reflects the characteristics of the liability at each point in time.
3.2.4 Disclosure
In the Exposure Draft ED/2013/7 the disclosures are discussed from Paragraph 69 trough 95. According to the Draft the objective of the disclosure requirements is to enable users of financial statements to understand the nature, amount, timing and uncertainty of future cash flows that arise from contracts within the scope of the Draft. The risk adjustment is explicitly mentioned in Paragraph 84. It states that if the entity uses a technique other than the confidence level technique for determining the risk adjustment, it shall disclose a translation of the result of that technique into a confidence level. So even if the Exposure Draft ED/2010/8 states that one of the three techniques mentioned should be used, they strongly recommend the confidence level technique. When using a different technique this should be well explained. Due to this statement the confidence level technique will be the point of interest.
Implementation
The calculation of the risk margin and the confidence level corresponding to the risk adjustment will be done on the portfolio of a non-life insurance company. A non-life insurer encounters both short and long term risks. To be able to give a good representa-tion of these risks, the following lines of business within Property & Casualty are taken into account: Motor Liability, Other Motor and Fire. These are three segments of the Segmentation of Non-Life Insurance Obligations according to the Delegated Regulation 2015/35. Here fire is an example of a line of business with a short term risk. On the other hand, motor liability is more long term risk. For these three lines of business we consider the liabilities. These liabilities consist of reserving and premium liabilities and their risks, also known as prior or reserve risk and current or premium risk respectively. The calculation and comparison of the risk margin and the risk adjustment are done for these lines of business and risks. For convenience, we choose the end of 2016 as reporting period.
The portfolios of the three lines of business are based on the portfolios of the insur-ance company Nationale-Nederlanden. Also the models for prior and current risk are based on models of the insurance company Nationale-Nederlanden.
4.1
Prior Risk
First, we focus on Prior Risk. The model for this risk is used to derive the cash flows and accompanied risk, related to outstanding claims. In this context, outstanding claims refer to losses (or risks) that incur before the reporting date. The output from the Prior Risk model is both the expected cash flows and the statistical distribution of possible outcomes for the outstanding claims. This distribution is determined by the Chain Ladder method in conjunction with the Bootstrap technique and is explained in the next section.
4.1.1 Distributions
The Chain Ladder method uses historical claims grouped along accident and develop-ment periods. When displayed in a table, this results in a triangle of reported claims. This is the so-called development triangle. Future expected payments are predicted by analyzing the historical development of claims and projecting future development of claims with observed historical development patterns. The Chain Ladder projections determine a Best Estimate ultimate loss per accident period. By subtracting the cumula-tive paid claims gross of reinsurance the undiscounted Best Estimate technical provision is determined. Additionally, subtracting the case reserves provides the IBN(E)R, which stands for Incurred But Not (Enough) Reported. The Chain Ladder method is applied on the development triangles of paid claims. These are required to determine the cash flows. If the Best Estimate is based on the triangle with paid claims, the cash flows
Figure 4.1: The statistical distribution following from the Prior Risk model for the line of business Motor Liability.
Figure 4.2: The statistical distribution following from the Prior Risk model for the line of business Other Motor.
follow directly from the Chain Ladder method without a required additional step. To determine the distribution around the future expected cash flows the bootstrap technique is used. The bootstrap technique is a powerful and an easy to implement technique that provides the distributions of reserve estimates. It is shown that the bootstrap method approximates the analytical formula for the prediction error of the Chain Ladder reserve estimates, derived by Mack [16], very closely. The advantage over the analytical method, however, is that besides the prediction error, the Bootstrap delivers a full distribution. And such a distribution can be used to obtain risk related quantities, e.g. confidence level and value at risk. A bootstrap is a simulation method which is used to estimate the underlying distribution of a data set of observations by re-sampling with replacement out of the original sample. Re-sampling is based on the hypothesis that the underlying data of the bootstrap are independent and identically distributed. Here we use a variation of this technique that re-samples the residuals instead of the observations itself to adjust for the fact that development factors are not identically distributed over development periods. The bootstrap technique as described in the article by England and Verrall [14] for the basis for the Prior Risk model. The amount of simulations is equal to 50, 000.
The statistical distribution, following from the Prior Risk model, for the three lines of business are given in Figures4.1,4.2and4.3. These distributions will be the basis of the calculation of the risk margin and risk adjustment.
4.1.2 Calculation of the Risk Margin
The Solvency Capital Requirement or SCR is derived from the Prior Risk model selecting the capital meet the required confidence level of 99.5% under Solvency II. This is one of the main characteristics of Solvency II and in line with the Solvency II Directive paragraph 64 of the preamble:
Figure 4.3: The statistical distribution following from the Prior Risk model for the line of business Fire.
Table 4.1: The duration for the lines of business.
”In order to promote good risk management and align regulatory capital requirements with industry practices, the Solvency Capital Requirement should be determined as the economic capital to be held by insurance and reinsurance undertakings in order to
ensure that ruin occurs no more often than once in every 200 cases or, alternatively, that those undertakings will still be in a position, with a probability of at least 99.5%,
to meet their obligations to policy holders and beneficiaries over the following 12 months. That economic capital should be calculated on the basis of the true risk profile of those undertakings, taking account of the impact of possible risk-mitigation
techniques, as well as diversification effects.”
This SCR is part of the liabilities of the Solvency II balance sheet, see Figure 2.1. Due to implementation difficulties for the one-year time horizon as stated in para-graph 64, there has been chosen for the full run-off and apply a correction for the 99.5% percentile depending on the cash flow payment pattern duration. The duration is as-sumed to be equal to the sum of the products of the cash flow pattern percentage and the corresponding development year. We assume the the cash flow takes place in the middle of a year.. The duration for line of business x and development year t is given by
Durationx=
X
t
Cash-flow payment pattern%x,t×
t − 1
2
. (4.1)
If the duration is smaller than 1 the standard 99.5% percentile is used, the same as men-tioned in the Directive. If the duration is larger or equal to 1 but smaller or equal than 4, the 99.0% percentile is used. And for a duration larger than 4 the 98.0% percentile is used.
In AppendixA, the cash flow payment pattern is given for the three lines of business. Hence, the corresponding duration is given in Table4.1. This implies that for the lines of business Other Motor and Fire the 99.5% percentile is used to determine the SCR, while for Motor Liability the 98.0% percentile is used due to the high duration. Because this percentile is different for different lines of business, we will refer to this percentile as the SCR-percentile.
Given the distribution around the future expected cash flows, the mean or Best Estimate and standard deviation as well as the corresponding SCR-percentile can be determined. Then the Solvency Capital Requirement is equal to the difference between the SCR-percentile and the Best Estimate.
Table 4.2: The characteristics and SCR of the distributions around the future expected cash flows for the lines of business.
Table 4.3: The SCR/BE-factor FSCR/BEand the projection of the SCR for development
year t for the lines of business, for Prior Risk.
FSCR/BE. Given this SCR/BE-factor and the Statutory Reserve provides the projection
of the SCR at time t = 0. Given this projection, the projection for time t > 0 then follows the same pattern as the cash flow payment pattern given in AppendixA.
For the calculation of the risk margin the only ingredients which are missing are the discounting factors and the Cost-of-Capital rate of 6%. The discounting factor cwt at
time t is given by the following formula: cwt=
1
exp(it−1)t× (exp(it)/ exp(it−1))0.5
. (4.2)
In Appendix Athe discounting factor cwt at time t is given for t = 1 to 24.
For the calculation of the risk margin via the Cost-of-Capital method, formula3.1is followed. The projection of the SCR is multiplied with the discounting factors for every time t and then multiplied with the Cost-of-Capital rate providing the risk margin for the lines of business. This can be found in Table4.4.
4.1.3 Risk adjustment
In order to translate the calculated risk margin into a confidence level corresponding to the risk adjustment, we need the Best Estimate, the risk margin and the distribution around the future expected cash flows. For the confidence level the corresponding per-centile of the Best Estimate plus the risk margin is found. Making this translation, the confidence levels are given in Table4.5.
4.2
Current Risk
The model for Current Risk serves for the assessment of the following underwriting risks:
Table 4.5: The confidence level for Prior Risk for the lines of business.
• The risk of adverse deviation in the value of insurance liabilities resulting from fluctuation in the timing, frequency and severity of insured events that will occur in future periods of coverage. Catastrophic risks however are excluded from the scope of Current Risk.
• The risk of adverse deviation in the value of insurance liabilities resulting from inadequate pricing for future periods of coverage.
These two risks are modeled in combination, and cannot be quantified separately within the model. The combined risks emanating from these two sources are referred to as Current Risk.
4.2.1 Loss ratios
The loss ratio is used as the basis for modeling. The loss ratio, in this context, is the ratio of
• the undiscounted Best Estimate incurred loss of an accident year at the end of that year, gross of reinsurance.
• the gross earned premium of the same accident year.
For the following reasons, the loss ratio gross, and not net of reinsurance, is used: • The effect of reinsurance on the net premium and net incurred loss is not material. • Gross Earned Premium is a better measure for the exposure to Current Risk then Net Earned Premium, as it is not subject to fluctuations of the level of reinsurance premiums for catastrophic risks.
Modeling of Current Risk on the basis of loss ratio is an accepted method that is also applied elsewhere in the insurance market. For the modeling of the loss ratio over multiple future periods, a time series model is used. Also time series modeling is an accepted method that is used elsewhere in the market.
The model is an auto-regressive model of order 0, also known as an AR(0)-process. For simplicity we will assume there is no correlation within the model. By auto-correlation we mean the auto-correlation between loss ratios in successive accident years of the same line of business. Making this assumption will not conflict with the purpose of this thesis. The goal is to give a good reflection of the risk margin of Current Risk. The AR(0)-model can be represented as follows:
LR(t) = LGS + e(t), (4.3)
where LR(t) is the loss ratio in accident period t, LGS is the long term expected loss ratio and e(t) is the error term in accident period t.
In this model structure, loss ratios of a specific line of business in different accident years are assumed to be independent of one another. Therefore auto-correlation of loss ratios does not occur. A higher than expected loss ratio in any year provides no indi-cation whatsoever about the loss ratio in succeeding years. As a result, the effect of an unfavorable loss ratio in any accident year is limited to that particular year, and does not give rise to an adjustment of the anticipated loss ratio in later years. Furthermore,
Table 4.6: The loss ratio and the corresponding information for the line of business of Motor Liability.
the average loss ratio and the spread around the average are assumed to remain con-stant in the historic years used to set model parameters, as well as in the future years included in the model projection. This assumption is used in setting the parameters of the risk process on the basis of recent experience data. If it known that changes have occurred in the modeled risk, for example due to a change in underwriting policy, then parameters can be adjusted to reflect the change.
The loss ratios, together with the gross earned premium and incurred loss in thou-sands of euros, are given for the lines of business. As well as the average, standard deviation and the standard error of the loss ratios. The standard error is equal to the standard deviation divided by the square root of the number of observed annual loss ratios in historic years. The formula for the standard deviation and standard error can be found in Appendix A. The loss ratios and the corresponding information can be found in Table
4.2.2 Distributions
In the modeling of Current Risk, a distinction is made between volatility and uncertainty. Volatility is the unexpected, random fluctuation of the loss ratio from year to year, given the expected loss ratio and other model parameters. For the assessment of the required capital, the confidence level of the loss ratio of the coming year is of interest, as well as the possible dependence thereof with the loss ratios in later years. Uncertainty is the risk that the estimated value of liabilities is incorrect due to estimation errors of parameters of incorrect model structure. Adaptation of model parameters at any point in time will lead to a corresponding change in the value of liabilities over the remaining run-off period. Hence uncertainty risk is related to the entire run-off period of the risk, and not just to the first year of projection. Therefore, uncertainty risk is quantified over a longer period than one year for liabilities with a run-off period exceeding a single year. The uncertainty risk that will manifest itself within a one year time horizon is therefore overestimated: instead of a 99.5 % confidence level over a single year, a 99.5% confidence interval over a longer period is determined. However, separating uncertainty risk in the first year from the uncertainty risk in later years is very difficult to realize in practice. Therefore, to quantify uncertainty risk we assume that the entire risk will manifest itself directly after the balance sheet data at which the Solvency Capital Requirement is determined, leading to corresponding change in value of the modeled liabilities. The
Table 4.7: The loss ratio and the corresponding information for the line of business of Other Motor.
Table 4.8: The loss ratio and the corresponding information for the line of business of Fire.
Figure 4.4: The statistical distribution following from the Current Risk model for the line of business Motor Liability, Other Motor and Fire.
Solvency Capital Requirement determined under this approach satisfies this criterion that over one year time horizon, it is sufficient to fund the modeled liabilities at the chosen confidence level. In particular, the Solvency Capital Requirement is sufficient to fund all liabilities over a one year time horizon with at least a 99.5% probability.
Modeling the loss ratios comprises of two parts:
1. Modeling the true values of LGS given LGS∗, the estimation of LGS on the basis of the n observed historic loss ratios, and the estimation error. This component represents the uncertainty risk.
2. Modeling of LR(t) given LGS∗. This component represent the volatility risk. For the first step the chosen probability distribution is equal to the normal distri-bution with mean LGS∗ and standard deviation equal to the standard error of the n observed historic loss ratios, N (LGS∗, SELGS). In the second step the chosen probability
function is equal to the normal distribution with mean randomly chosen from the distri-bution from the first step and standard deviation equal to the corrected sample standard deviation σLGS of the n observed historic loss ratios, N (N (LGS∗, SELGS), σLGS). This
second step provides the simulated loss ratios, denoted by LGSsim(t), for each year
t. Combining this loss ratio LGSsim(t) together with the gross earned premium, the
discounting factor cwt and incurred payment pattern at time t provides the expected
incurred loss at time t. The incurred payment pattern at time t is given in AppendixA. Due to different interpretation for Solvency II and IFRS, there has to be made a different in the projections of the incurred. For both Solvency II and IFRS the volatility risk plays a factor in the first year. The difference needs to be made for year t > 1. Under Solvency II only uncertainty risk is present, but under IFRS volatility risk still plays a factor. And because the simulated loss ratio LGSsim(t) for t > 1 depends on the
regarded framework, there are two distributions around the future expected incurred. The amount of simulations is equal to 50, 000.
The statistical distribution, following from the Current Risk model, for the tree lines of business are given in Figure4.4. These distributions will be the basis of the calculation of the risk margin and risk adjustment.
4.2.3 Calculation of the Risk Margin
The calculation of the risk margin for Current Risk is quite comparable to the calculation done for Prior Risk. The basis is the characteristics and SCR of the distributions around the future expected incurred for the lines of business. The only difference is that this is done for two frameworks. The 99.5% percentile and SCR is only given for Solvency II, because this only provides information in the context of this framework. The information about the Solvency II-distribution is given in Table 4.9 and the information about the IFRS-distribution is given in Table 4.10.
Again, dividing the SCR by the Best Estimate provides a SCR/BE-factor, denoted by FSCR/BE. Given this SCR/BE-factor and incurred loss including claims handling
Table 4.9: The characteristics and SCR of the Solvency II-distributions around the future expected incurred loss for the lines of business.
Table 4.10: The characteristics and SCR of the IFRS-distributions around the future expected incurred loss for the lines of business.
expenses (CHE) provides the SCR at time t = 0. Given this projection, the projection for time t > 0 then follows the same pattern as the incurred payment pattern given in AppendixA.
For the calculation of the risk margin via the Cost-of-Capital method, formula3.1is followed. The projection of the SCR is multiplied with the discounting factors for every time t and then multiplied with the Cost-of-Capital rate providing the risk margin for the lines of business. This can be found in Table4.12.
4.2.4 Risk adjustment
In order to translate the calculated risk margin into a confidence level corresponding to the risk adjustment, we need the Best Estimate under Solvency II, the risk margin and the distribution around the future expected cash flows under IFRS. For the confidence level the corresponding percentile of the Best Estimate under Solvency II plus the risk margin is found. Making this translation, the confidence levels under IFRS are given in Tables 4.13and 4.14.
Table 4.11: The SCR/BE-factor FSCR/BE and the projection of the SCR for
Table 4.12: The risk margin for Current Risk for the lines of business.
Table 4.13: The confidence level for Current Risk for the lines of business Motor Liability and Other Motor.
4.3
Aggregation
According to Annex II of the Delegated Regulation 2015/35, the Segmentation of Non-Life Insurance Obligations for the Non-Non-Life Premium and Reserve Risk Sub-Module, the considered segments are:
(1) Motor vehicle liability insurance
Insurance obligations which cover all liabilities arising out of the use of motor vehicles operating on land (including carrier’s liability).
(2) Other motor insurance
Insurance obligations which cover all damage to or loss of land vehicles (including railway rolling stock).
(4) Fire and other damage to property insurance
Insurance obligations which cover all damage to or loss of property other than those included in the lines of business 5 and 6 due to fire, explosion, natural forces including storm, hail or frost, nuclear energy, land subsidence and any event such as theft.
Annex IV of the same Delegated Regulation provides the correlation matrix of non-life premium and reserve risk. The correlation parameters CorrS(s, t) for the three portfolios is given by CorrS(s, t) = 1 2 4 1 1 0.5 0.25 2 0.5 1 0.25 4 0.25 0.25 1 (4.4)
Here the correlation parameter CorrS(s, t) is equal to the item set in row s and in column t. The headings of the rows and columns denote the number of the segments set out in Annex II. For simplicity, the correlation between premium and reserve risk is set to 0.5. To be able to provide a risk margin and risk adjustment for the total portfolio, the lines of business need to be aggregated. For this aggregation to take place, the aggregated distribution for the Prior Risk model and for the Current Risk model are needed, and additional for the two Risk models combined. Therefore, in order to derive the distribution of the aggregate liability and the aggregate loss ratio across the lines of business, the dependencies between the individual lines of business also need to be
Table 4.15: Aggregation of Prior Risk, Current Risk and the total portfolio.
included. These dependencies can be defined by a copula function. Although there are many copulas, the choice is made for the normal copula family.
According to [17]: In a sense, every joint distribution function for a random vector of risk factors implicitly contains both a description of their dependence structure; the copula approach provides a way of isolating the description of the dependence structure. ... Copulas help in the understanding of dependence at a deeper level. ... The copula approach allows us to combine our more developed marginal models with a variety of possible dependence models and to investigate the sensitivity of risk to the dependence specification.
In [20], the concept of copula and also the normal copula and Monte Carlo simulation are explained. The same concept is used for the modeling and combining of the correlated risks, with the use of Choleski’s algorithm.
After determining the dependencies, the aggregation can be determined using the method of matrix multiplication, also known as the Var-CoVar method. The Var-CoVar method determines the Solvency Capital Requirement for a group of risks in combi-nation, on the basis of the Solvency Capital Requirement of the individual risks and a correlation matrix, CorrS(s, t) here, containing the linear correlations between the risks. Then, the aggregated Solvency Capital Requirement is given by
SCRagg(t) =
s X
i,j
SCRi(t)SCRj(t)ρij, fori, j = 1, . . . , n at time t. (4.5)
Here n is the number of modeled risks, SCRi the Solvency Capital Requirement for risk
i and ρij the linear correlation between risk i and j.
A diversification factor for each time t can be determined when considering the ag-gregated Solvency Capital Requirement and the non-agag-gregated Solvency Capital Re-quirement. Using this diversification factor in combination with the discounting factors cwt and the Cost-of-Capital rate of 6% the aggregated risk margin can be determined.
Together with the Best Estimate and distribution for the aggregated risk, the confidence level corresponding to the Best Estimate plus the risk margin is found.
Perspective
It is important to consider the different point of views or perspective for this subject. It has become clear from the previous chapters that both the risk margin and the risk adjustment cannot be viewed in the same light because of the different considered frameworks and their different objectives.
Solvency II and the risk margin are much more of interest for the Dutch Central Bank or the tax authorities in terms of risk. The Dutch Central Bank is concerned about the amount of risk an insurance company takes and is willing to take. Solvency II, including the risk margin, take this amount of risk into account. On the other hand, shareholders are more interested in IFRS, because it provides the risk adjustment and the possible dividend an insurance company can provide. Surely shareholders are concerned about the amount of risk an insurance company takes, but they rely on authorities like the Dutch Central Bank to keep this in control. The two main interests of the different parties are thus in line with the objective of the frameworks.
Even though IFRS is more important to shareholders than Solvency II, there also exist more interesting terms in annual reports than a risk adjustment, for example, capital generation or combined ratio for a non-life insurer. Even a term like Solvency ratio tells more about the profit and loss account and dividend of an insurer. Only when considering a portfolio which is in run-off, then the risk adjustment can be seen as future profit. Its goal of measuring uncertainty in the cash flows is then no longer needed.
When considering the perspective of method, one could ask which method of calcu-lation is appropriate and fits its framework best. For the goal of comparison, the Cost of Capital technique is used, because this technique is allowed in both frameworks. The technique, as used in Solvency II, is quite rigid and it is also very sensitive to changes in the yield curve. But with a few adjustments to the technique, it could also be used for the calculation of the risk adjustment and the corresponding confidence level. Such
Figure 5.1: The frameworks, quantities and methods. The Cost of Capital technique was used as a starting point. With the same assumptions used in this technique, the confidence level was calculated, as described in Chapter 4.
an adjustment is for example a different yield curve, one which is a better gauge for market valuation, but also another Cost-of-Capital rate per line of business or entity to give a better representation for each one specific.
Consider IFRS, the choice of not specifically indicating which technique to use to determine the confidence level of the risk adjustment is interesting. Multiple techniques can determine a confidence level. It is key to know well how this level was computed and having good arguments for the chosen technique. Also here the perspective combined with the objective of IFRS becomes clear: The goal is not to have strict rules for calcula-tion but to give guidelines in order to give a good representacalcula-tion of the financial status of the insurer. Figure 5.1 illustrates the two different confidence levels with different assumptions.
The capital which should be considered is explicitly described in both frameworks. Under Solvency II this is the Solvency Capital Requirement, which measures the risk over a one-year time horizon. Article 101(3) of the Solvency II Directive explains the following about the Solvency Capital Requirement:
”The Solvency Capital Requirement shall be calibrated so as to ensure that all quantifiable risks to which an insurance or reinsurance undertaking is exposed are
taken into account. It shall cover existing business, as well as the new business expected to be written over the following 12 months. With respect to existing business, it shall cover only unexpected losses. It shall correspond to the Value-at-Risk
of the basic own funds of an insurance or reinsurance undertaking subject to a confidence level of 99.5 % over a one-year period.”
Under IFRS, the capital that should be considered is the capital over the lifetime of the contract and making a further adjustment for the time value of money because the capital will be held in future periods, according to Paragraph B86(c) of the Exposure Draft ED/2010/8.
It has become clear that the objective for both framework and quantity are different, which also expresses in the method of calculation. Keeping the frameworks and quanti-ties in the right perspective is important and also provides the best insight in either the amount of risk or the amount of dividend of an insurance company. So the perspective comes when placing these quantities in their own framework.
Conclusion
In this thesis, we give a comparison between the risk margin under Solvency II and the risk adjustment under IFRS 4 Insurance Contracts and also explaining what these quantities have in common.
The comparison starts with looking at the official documents of the two frameworks Solvency II and IFRS 4. From these documents it became clear that their objective serve a different goal. For Solvency II, its objective is to protect the policy holder and its beneficiaries in terms of the amount of risk that has been taken by an insurer. For IFRS 4, its objective is to report useful information about the financial status of an insurer. Considering the risk margin and the risk adjustment, it appeared that the thought behind these terms but also their definitions are quite equal.
When describing methods of calculation, we have seen that Solvency II is quite clear on which method to apply, namely the Cost of Capital method. Also which annual rate, interest rate and capital to take into account for the calculation are explicitly mentioned. The definitions are clear. IFRS is less strict, but provides three methods which are allowed. The confidence level technique is preferred, but the Conditional Tail Expectation and Cost of Capital method are also allowed as long as a translation to the confidence level technique is disclosed. So for the calculation, Solvency II is more explicit on the method while IFRS 4 provides more freedom in choice. This can be seen as both an advantage as a disadvantage.
Because Solvency II is strict on the method of calculation, this was the starting point of the implementation of the calculation, due to the clarity in the documentation of Solvency II and also because Solvency II has been effective since 1 January 2016. The calculation of the risk margin was done for the portfolio of a non-life insurer containing three lines of business; motor liability, other motor and fire. Considering reserving and premium risk, the risk margin for the total portfolio was calculated. Next the translation to the confidence level was made, with the use of the Cost-of-Capital method. For this calculation, the same assumptions were made as for the calculation of the risk margin. With this implementation, it was shown that the Cost-of-Capital method can be used for the calculation of both quantities.
Because the Cost of Capital technique is quite rigid and very sensitive to changes in the yield curve, adjustments can help to make the technique more suitable for the calculation of the risk adjustment. When making these adjustments, a well thought judgment about the risk adjustment has to be made. What is the right amount and corresponding confidence level which represents the portfolio best? When doing so, it could be very effective and efficient to use one technique and its implementation for one term in one framework and implement the same technique, with some adjustments, for another, quite comparable term in another framework. So the common factor in the definition of the quantities and the calculation method can help for the calculation in both frameworks.
Finally the different point of views were discussed. When considering the frameworks 26
and their corresponding quantities, it is important to view them in the right perspective. Both frameworks were not introduced with the same objective. The objective of the risk margin and the risk adjustment could be said to be the same. But when regarding each quantity in its own framework it becomes clear that it is important which framework is considered, namely Solvency II for the amount of risk bearing capacity and IFRS for the amount of dividend.
6.1
Further Research
On May 18th 2017 IFRS 17 Insurance Contracts was published. This standard will be effective for annual periods beginning on or after January 1st 2021. IFRS 17 will replace IFRS 4, the current standard considering Insurance Contracts. According to the website of IAS, IFRS 17 establishes the principles for the recognition, measurement, presentation and disclosure of insurance contracts within the scope of this standard. The objective of IFRS 17 is to ensure that an entity provides relevant information that faithfully represents those contracts. This information gives a basis for users of financial statements to asses the effect that insurance contracts have on the entity’s financial position, financial performance and cash flows. This IFRS could be a point of view for further research. Currently IFRS 4 is leading as reporting standard. But what is the comparison with the new IFRS 17? Are there many differences or is it the same standard but with more boundaries, or not? The introduction of this standard provides, next to the challenges of its implementation, a whole new topic for another thesis.
