Market-consistent embedded value in non-life portfolio

(1)

Market-Consistent Embedded Value

in Non-Life Portfolio

Dimitra Papageorgiou-Siora

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: Dimitra Papageorgiou-Siora Student nr: 10435891

Email: dimitra.papageorgiou168@gmail.com Date: October 21, 2015

Supervisor: Dr. S. Umut Can Second reader: Dr. Katrien Antonio

(2)

Statement of Originality

This document is written by Student Dimitra Papageorgiou-Siora who declares to take full responsibility 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.

(3)

MCEV in Non-Life Portfolio — Dimitra Papageorgiou-Siora iii

Abstract

The aim of this thesis is to provide an implication of the market-consistent embedded value (MCEV) concept to a non-life insurance portfolio. The transfer of MCEV to non-life business can enhance the management of both branches. The non-life model is applied to a mock portfolio representative of the Greek non-life insurance industry. The concept is also tested under different values for several important pa-rameters to check the sensitivity of the model.

Keywords Market Consistent Embedded Value, MCEV, European Embedded Value, Non-Life Insurance, Life Insurance

(4)

Preface

This thesis is submitted in fulfilment of the requirements for the Mas-ter’s degree in Actuarial Science and Mathematical Finance of the Universiteit Van Amsterdam.

Writing a thesis has been hard but in the process of writing I feel I have learned a lot and my internal conception of actuarial crucial matters, and especially of the Embedded Value in insurance industry, has certainly changed. Through all this research, I have dealt with a lot of subjects, in an attempt to give this thesis a broad perspective. I would like to thank my supervisor, Dr. Sami Umut Can, who helped and supported me through all the steps of the thesis as well as the Emeritus Prof. Rob Kaas, who gave me the opportunity to follow the master’s program and be taught by brilliant professionals of the European Community.

I am really happy that this journey is nearing its end. The master has been a springboard for my professional career and I am glad to implement and share all the knowledge I have gained.

(6)

(7)

Chapter 1

Introduction

In view of the introduction of Solvency II and IFRS frameworks, the need for value-based management techniques has aroused in the continuously changing environment of the insurance industry. Under this framework and in order to consolidate the different streams of research, the CFO Forum has developed the Market Consistent Embedded Value calculation for life insurance business. The aim of this thesis research is to de-velop and empirically test this concept on a non-life portfolio which could be a helpful way to overcome the differences in performance measurement between life and non-life insurance businesses, making the concept a powerful management tool.

In general, life and non-life insurance businesses constitute the two major insurance sectors. From the modeling part, these two businesses have unique structure of cash flows and large differences mostly in the duration of assets and liabilities and the risks that each sector is exposed to. More precisely, most life insurance contracts have multiyear payments with monthly or yearly premium payments while non-life contracts usually last for a maximum of one year. Traditionally, the two businesses are managed as separate entities and then pooled in an insurance group in order to achieve the capital allocation and to improve the shareholder value through constant monitoring and measurements of performance. This separation between life and non-life branches has led to different management techniques, a fact that makes the management of a pooled portfolio a complicated issue.

In May 2004 a discussion group composed by the major European insurance com-panies, the CFO Forum, published a paper titled European Embedded Value Principles (EEV Principles). Embedded value calculation is a technique proposed for life insurance business which offered investors a clear picture of the shareholder value, allowing for the implementation of successful new business strategies while embedded value report-ing offered an alternative to the primary accountreport-ing balance sheet and profit and loss account. The intent of these principles was not only to improve the allowance for risk in reported financial results but also to help overcome the differences in the preparation of embedded values and the difficulty in comparing the results across the companies.

However, questions over comparability and consistency still remained. Hence, in an effort to address these difficulties, many insurance companies chose to publish their European Embedded Values on a market consistent basis. The effort of performing the embedded value in a market consistent, risk neutral framework was then formalized by the CFO forum which published and promulgated the document of Market Consistent Embedded Value Principles in June 2008. In this document, the Market Consistent Embedded Value (MCEV) of an insurance company is defined as a measure of the consolidated value of shareholders interest in the covered business. More specifically, MCEV represents the present value of all future shareholder cash flows from the covered in-force business plus the required capital and the free surplus allocated to the covered business while it does not include any values attributable to future sales.

As mentioned above, life and non-life insurance businesses show differences and are 1

(8)

2 Dimitra Papageorgiou-Siora — MCEV in Non-Life Portfolio treated separately using different techniques. Hence, on a management basis, the matter to be solved is that different measures are not directly comparable and cannot be applied to combine different concepts. We consider MCEV to be a congruent valuation technique not only for life but also for non-life insurance. In light of this, MCEV could constitute a useful management tool providing the necessary harmonization since its change from one year to another can be the measurement for quantifying return and risk capital. Thus by transferring its concept from life to non-life insurance business could be a useful approach which could help deal with the difficulties mentioned above while it could also support and promote the management on a group level.

The main idea of this thesis is to develop a technique appropriate and easy to be applied on non-life business that could be directly comparable to life business. Taking under consideration the differences between the two sectors, this could be a compli-cated task. As a first step, we have to consider carefully all the characteristics of the two businesses and their impact on embedded value calculation and then develop a mathematical model that could clearly depict both the MCEV Principles and the spe-cial characteristics. In the rest of the thesis we will try to apply our findings on empirical data of an existing portfolio so as to illustrate the concept and its practical application for management purposes.

The rest of this thesis is structured as follows. In the next section (Chapter 2) we will discuss in detail the concept of embedded value and its history in life insurance companies. Then we will analyze the characteristics of life and non-life insurance, the differences between them and what should be done to apply the technique on a non-life portfolio (Chapter 3). In the following chapter we will develop a mathematical model for the determination of MCEV for a non-life insurance branch (Chapter 4). In Chapter 5 we will examine the application of our model to a real non-life portfolio and in Chapter 6 we will state our conclusions.

(9)

Chapter 2

Market Consistent Embedded

Value

The idea of embedded value reporting in insurance industry dates back to the 1980s when insurance companies in the Anglo-Saxon countries started embedded value report-ing. Until then there was not a universally accepted basis for financial reporting in the insurance sector. The fact that the available statutory data provided very low valuation led to acquisition bids on some of those companies. This resulted in an increasing de-mand from shareholders and investors for more accurate and reliable information about the value generated by life insurance companies. The traditional historically-oriented accounting information was inadequate to measure the intrinsic value generated by life insurance activities because it did not provide a forward-looking assessment. It was then unavoidable for the embedded value concept to grow. Apart from its significance in cases of acquisitions or mergers, the implementation of internal processes proved to facilitate insurance companies in the monitoring of their business activities.

In May 2004, the European Insurance CFO Forum (CFO Forum), a high-level dis-cussion group formed and attended by the Chief Financial Officers of major European listed, and some non-listed, insurance companies, published EEV Principles in order to bring greater objectivity, comparability and consistency and to improve disclosure to the European insurance industrys embedded value reporting. EEV is a financial mea-surement applied originally to long-term insurance business and provides a means of measurement of the value of an insurance company. In October 2005, the CFO Forum published an additional guidance on EEV reporting, providing the insurance industry with improved sensitivities and disclosures within their financial statements.

The recently emerging accounting and regulatory rules, in particular the Interna-tional Financial Reporting Standards (IFRS) and Solvency II, provided the embedded value with new significance and international attention. According to these regulatory frameworks insurance companies should evaluate their business on a market consistent basis. This is quite recent and unprecedented for many European companies which have practiced a traditionally prudent philosophy based on historical values rather than on market values.

In order to establish a standard for market consistent valuation, the CFO Forum launched in May 2008 the Market Consistent Embedded Value Principles (see European Insurance CFO Forum, 2008a), an update of the EEV Principles. The MCEV concept is an extension of EV in a market consistent, risk neutral framework. MCEV Principles are accepted and applied as the standard form of EV and are compulsory for financial reporting of the CFO Forum members. The concept of the MCEV is considered to be the natural evolution of EV to a basis that provides not only greater comparability across companies but also greater consistency across concepts applied by other financial institutions and the capital markets.

As defined by the CFO Forum, the MCEV for a life insurance business is the consol-3

(10)

4 Dimitra Papageorgiou-Siora — MCEV in Non-Life Portfolio idated value of shareholders interests in the covered business (see European Insurance CFO Forum, 2008a, Principle 1 ) and should be calculated taking into account local legislation and any known future changes. Therefore, the MCEV can be broken down into the value of assets not backing liabilities and the value of future profits emerging from operations and assets backing liabilities.

The business covered under MCEV calculation must be clearly identified and dis-closed and should include as a minimum any contracts that are regarded as long-term or short-term life contracts. According to Principle 3, MCEV represents the present value of shareholders interests in the earnings distributable from assets allocated to the covered business after sufficient allowance for the aggregate risks in the covered business has been made.

Figure 2.1: MCEV Components

As can be seen in Figure 1 and prescribed in MCEV Principles, the MCEV consists of the Free Surplus (FS) allocated to the covered business, the Required Capital (RC) and the Value of In-Force covered business (VIF), whereas the free surplus and the required capital compose the Net Asset Value (NAV). The value of future new business is excluded from the MCEV.

The free surplus (MCEV, Principle 4 ) is defined as the market value of any assets allocated to, but not required to support, the in-force covered business at the valuation date. This means that the free surplus is the market value of any excess of all assets attributed to the covered business but not backing liabilities over the required capital to support the covered business.

The required capital (MCEV, Principle 5 ) is the market value of assets, attributed to the covered business in excess of the amount required to back liabilities for covered business, whose attribution to shareholders is restricted. This amount should be pre-sented from a shareholders perspective and so should be net of funding resources other than shareholder resources. The required capital should meet the level of solvency cap-ital and be in line with the local regulatory requirements, however it should take into account any internal objectives such as internal risk assessment or capital required to obtain a targeted credit rating.

The value of in-force business represents the best estimate of the present value of future profits from in-force business and the assets backing the associated liabilities. However, since the present value of future profits includes costs that investors do not have to bear by directly investing in the capital market, this should be taken into ac-count. Therefore the value of in-force business is calculated as the present value of future profits (PVFP) less the cost of residual non-hedgeable risks (CNHR), the frictional costs of required capital (FCRC) and the time value of options and guarantees (TVOG).

(11)

MCEV in Non-Life Portfolio — Dimitra Papageorgiou-Siora 5 The present value of future profits is the discounted present value of the projected future emergence of shareholders statutory profits, based on projected cash-flows re-sulting from current in-force portfolio. It includes any intrinsic value of the embedded financial options and guarantees and it should be after taxation and net of outward risk reinsurance.

According to Principle 7, allowance must be made for the potential impact on future shareholder cash flows of all financial options and guarantees (TVOG) within the in-force covered business. The time value of financial options and guarantees is calculated using stochastic techniques on a basis that is consistent with that used to calculate the intrin-sic value of shareholder cash flows for both economic and non-economic assumptions. Furthermore, all projected cash flows should be valued using economic assumptions such that they are valued in line with the price of similar cash flows that are traded in the capital markets. This implies that insurance liabilities should be valued as if they were traded assets. However, since insurance liabilities are not usually traded on an open market, assets cash flows that most likely resemble the insurance cash flows are used.

Frictional cost of required capital (FCRC) represents the cost of execution of financial transactions that concern the required capital for covered business (Principle 8 ). More specifically, it reflects the impact on the shareholders equity value due to the fact that capital has to be held within the company and cannot be distributed right away. It should allow for taxation and any additional investment expenses on the assets backing required capital and be projected appropriately over the lifetime of the underlying risks. Moreover, allowance must be made in the MCEV for the cost of non-hedgeable risks that are not already allowed for in the time value of options and guarantees or the PVFP (Principle 9 ). The allowance includes the impact of both non-hedgeable financial and non-financial risks. The cost of residual non-hedgeable risks should be calculated using an appropriate method so as to enable a comparison to a cost of capital methodology. The CNHR represents the extra margin that a buyer would require on top of Best Estimate Liability to take over the liabilities in an arms length transaction.

As already mentioned above, under MCEV calculation the value of in-force covered business is taken into account whereas the value of future new business is excluded. In-force covered business can be split into new business and existing business. New business is defined as the business arising from the sale of new contracts signed within the reporting period, whereas existing business is defined as the business arising from the contracts that already exist at the beginning of the reporting period. Apart from these two categories, the renewals should also be taken into account. More precisely, any foreseeable variations in the expected level of renewal premiums in accordance with policy conditions, non-contractual variations in premiums where these are reasonably foreseeable or recurrent single premiums where the level of premium is predefined and reasonably foreseeable, should be included in the valuation.

Apart from the determination of covered business, MCEV can be used for the deter-mination of non-covered business as well. In particular, this is defined by the CFO Forum as the Group MCEV which is composed of the sum of covered business as determined above and non-covered business as the unadjusted IFRS net asset value. The adjust-ments may be required to ensure consistency between the value allocated to covered and non-covered business.

(12)

Chapter 3

Differences between Life and

Non-Life Businesses

The two main businesses in insurance industry, life and non-life, as mentioned, have differences in the modelling of the cash inflows and outflows as well as the duration of assets and liabilities. The MCEV is based on the calculation of the present value of future cash flows, meaning that the different modelling approaches the two businesses need have an effect on the MCEV modelling. Because of the high uncertainty of future cash flows, the calculation could be very complicated. In this section we display a comparison between life and non-life branches.

Both life and non-life businesses are comprised of their liabilities. The liabilities along with the risk drivers, the duration and the amount of risk are those that determine the structure of the assets for each line of business.

Life insurance is a long-term business needing a long-term planning horizon on the assets and liabilities. The main service of life insurance is intermediation in the sense that it provides a certain amount to the insured or their nominated beneficiaries upon a certain event, such as death of the individual who is insured, by a saving and dissaving procedure. The bulk of life insurance contracts are long-term investments requiring pe-riodic payments on a monthly, quarterly or yearly basis. It is common that life products are often issued with embedded options such as minimum return guarantees and bonuses or surrender and cancellation options. In such products it is common for the policyholder to have the right to cancel or resume premium payments so that the contract is not terminated but continues with reduced benefits affecting the policyholders decision to exercise the option or not. It is therefore reasonable that the pricing, management and valuation of such guarantees and options are considered as the most important and difficult financial challenges that insurers face.

Because of the long-term nature, the interest rate component is an important part of life contracts. The discounting of the future cash flows to derive their present values is based on the interest rate. Hence the longer the projecting period the more affect the interest rate has on the calculation and the more important it is.

The risks involved in life insurance products arise mostly because of underwriting risks, such as unexpected death or illness, or market risks such as unexpected movements in markets, low interest rates or rapid price movements. However, the use of mortality tables and other rates makes the prediction of reserves more accurate by reducing the uncertainty. Within life insurance contracts there are slight differences between the various products provided, leading to low diversified portfolios. The reserving is mostly based on the policy reserves and the reserves for premium refund. The latter are reserves held to be provided as bonus to the certain profit participation contracts in case the insurers overall annual profit is higher than the net investment income from its business assets.

The long-term orientation of life insurance products means that the realization of 6

(13)

MCEV in Non-Life Portfolio — Dimitra Papageorgiou-Siora 7 revenues will incur after many years. Regarding claims payments and reserves, life in-surance liabilities can in general be predicted to a limited degree of uncertainty because of their very sturdy and durable structure. This could explain why in life sector there is not extensive need for the use of reinsurance. Non-Life insurance is in general a short-term business although some lines of business are long tailed, such as Motor Third Party Liability. The main service of non-life insurance is risk pooling in the sense that it can protect an individual against losses and damages.

Non-life insurance includes several lines of business, such as Motor Third Party Lia-bility, Other Motor, Marine, aviation and transport, Fire and other damage to property, General Liability, Credit and Suretyship, etc. The coverage period of non-life contracts is usually one year and premiums are paid on a one time basis. For the long tailed lines of business a substantial time period between the premium payment and the claims payment is noted leading to long duration on the liabilities side, in particular six to seven years. This is due to the nature of non-life insurance coverage where claims can also be made after the term of the policy. In contrast, for the short tailed lines of busi-ness, where the claims are made within the term of the contract or at least shortly after the expiration of the policy, the duration of the liabilities is about two years. This leads to significant diversification effects between the different lines of business. Given the duration of the business, the revenues are realized after one year or over a few years.

Comparing with the benefits provided to life contract holders, the claims that arise in non-life contracts display much volatility and are difficult to model. This is mainly due to catastrophe risk which the bulk of contracts are exposed to. Hence, the drivers affecting the cash outflow depend on the underwriting risk which displays extremely high volatility and uncertainty as a result of catastrophe risk, especially when compared to life insurance contracts.

The volatile nature of life risks, combined with the short-term orientation of non-life business leads to a highly uncertain structure of liabilities, resulting in difficulties for actuarial modelling. In order to account for the fluctuations and uncertainty of the liabilities, the reserving is based on actuarially calculated reserves, such as claims reserves and equalization reserves. Claims reserves are those set up for the projected claims while equalization reserves are amounts held for the purposes of preventing cash-flow depletion in the event of a significant unforeseen catastrophe. Such events could be an earthquake or a disastrous fire or a flood. Hence, insurers use the years with low claim costs to set up reserves that will need in years with high claim costs. Apart from the equalization reserve insurers set aside in order to be protected from hazards, there is also need for reinsurance. Depending on the line of business, non-life industry depends on the use of reinsurance. Reinsurance is defined as a means of risk management so that the insurance company has the opportunity to purchase and thus transfer either directly or through a broker its portfolio risk.

The risks involved in non-life contracts mostly arise from the uncertainty in catas-trophic events and thus the most important risk that non-life insurance faces is under-writing risk. Because of its short-term nature, surrender value or cancellation behavior is not much relevant to non-life insurance business in the sense that the contracts are usually issued for one year and the premiums are paid either at the beginning of the contract period or within. In non-life business, it is common that the policies follow a premium renewal process on a rolling basis; however this is not broadly analyzed in literature. This means that a remarkable amount of contracts are renewed after their term. In contrast to life insurance, non-life contracts do not usually embed product options.

(14)

8 Dimitra Papageorgiou-Siora — MCEV in Non-Life Portfolio

Figure 3.1: Segmentation per insurance business.

Figure 3.2: Summary of differences between life and non-life businesses. (Source: Diers et al., 2012)

(15)

Chapter 4

Modeling MCEV for a Non-Life

Portfolio

Based on the special characteristics of non-life insurance business and its differences from life insurance, in this section we analyze the modeling approach of the MCEV applied on a non-life portfolio. The modeling procedure can be divided in three areas, the modeling of the external environment, the modeling of the internal environment and the determination of the value of the in-force business.

When modeling the external environment, three major steps are included, namely the modeling of the capital market, claims and renewals. For the modeling of capi-tal market several assumptions have to been set such as the reference yield curve for the determination of risk discount rate and investment return. Concerning the model-ing of claims, as mentioned, there are difficulties in applymodel-ing an appropriate reservmodel-ing methodology which gives accurate projections, quantifying the prediction uncertainties and taking into account all the potential losses. For the renewals, as mentioned, in non-life insurance there is not an extensive literature. Typically, there are no period-ical premium payments, in contrast to the majority of life insurance policies. This is problematic in the context of MCEV when it comes to distinguishing among existing business and renewal business. According to MCEV principle 10 (10.2) the value of the in-force business should anticipate renewal of in-force business, including any reasonably predictable variations in the level of renewal premiums but excluding any value relating to future new business. This leads us to set a reasonable assumption for the renewal contracts in order to model the MCEV.

The methodology for modeling MCEV in life insurance business is fully provided by the European Insurance CFO Forum principles. Based on these principles, we apply all the special features of non-life insurance in the MCEV model. The calculations are based on a projection process of the balance sheet and profit and loss statement according to IFRS (International Financial Reporting Standards).

We first consider a projection period of T years with t=1,.,T and assume a complete settlement of our insurance business in year T. The main liabilities on the balance sheet are shareholder equity (SE0), equalization reserves (ER0) and claim reserves (CR0). On

the asset side, we distinguish between assets backing shareholder equity (BVabse₀ =SE0)

and assets backing liabilities (BVabl₀ =ER0+CR0). The risk-free yield curve at t=0 is

given by predefined swap rates (spot rates srt ). Both investment returns (forward rates frt ) and the discount factors (dt ) are derived from this risk-free yield curve.

According to MCEV Principles, in order to derive the MCEV we need to determine three components, the free surplus (FS), the required capital (RC), and the value of in-force covered business (VIF). Hereby, VIF is calculated as present value of future profits (PVFP) minus the time value of financial options and guarantees (TVFOG) minus the frictional costs of required capital (FCRC) and minus the cost of residual non-hedgeable risks (CRNHR). In contrast to life insurance, non-life contracts have

(16)

10 Dimitra Papageorgiou-Siora — MCEV in Non-Life Portfolio no substantial options and guarantees. We thus set the time value of financial options and guarantees to zero. In a first step, we determine the (1) present value of future profits and then the (2) required capital. In a second step, we evaluate the (3) frictional costs and the (4) costs of residual and non-hedgeable risks. Finally, (5) free surplus is determined.

4.1 Present Value of Future Profits

The present value of future profits (PVFP) is the sum of the discounted annual net income NIt: PVFP = T X t=1 NIt∗ drt; (4.1)

The annual net income consists of earnings before taxes deducted by taxes paid (NIt=EBTt*(1-tr)). Earnings before taxes can be calculated by adding the technical

result Tt and the investment result It at the end of time period t {t 1 . . . ,T}:

EBTt= Tt+ It; (4.2)

The technical result Ttis calculated as gross earned premiums, GEPt, minus changes

in claims reserves, ∆CRt, (∆CRt = CRt - CRt−1), minus changes in equalization

re-serves, ∆ERt, (∆ERt = ERt -∆ERt−1). We deduct claims payments CPt, acquisition

costs ACt, claims settlement expenses costs CSEt and overhead costs OCt:

Tt= GEPt− ∆CRt− ∆ERt− CPt− ACt− CSEt− OCt; (4.3)

The investment result corresponds to the investment income under local GAAP less the associated investment cost. Under Greek local GAAP, the book value of assets may differ from the market value of assets.

For determining the investment result It, it is therefore necessary to project both

book value and market value of the assets backing liabilities (taking into account cash flows related to the insurance contracts and investment cost as well as funding require-ments).

4.2 Required Capital

To calculate the required capital, which refers to the amount of assets backing sharehold-ers equity whose distribution to shareholdsharehold-ers is restricted (MCEV Principle 5 ), we con-sider the European Union regulatory rules which are to be implemented on 01/01/2016 (Solvency II) for solvency considerations since this is the level of capital at which the regulator is empowered to take action. We therefore take the required capital as the solvency capital requirement result calculated under the new regime:

RC = SCR II; (4.4)

4.3 Frictional Costs of Required Capital

FCRC reflects the impact on the shareholders equity value due to the fact that capital has to be held within the company and cannot be distributed right away (for example, due to regulatory restrictions). According to Principle 8 (European Insurance CFO Forum, 2008a) frictional costs should reflect investment costs and taxation on assets backing required capital. Thereby, required capital has to be projected appropriately over the lifetime. In order to derive the FCRC, we need to take into account the net

(17)

MCEV in Non-Life Portfolio — Dimitra Papageorgiou-Siora 11 income on the assets backing required capital (NIRCt) and the release of required capital

over the projection horizon (∆RQ_t= RQ_t-RQ_t−1). The present value of these cash flows is then compared to the required capital at t=0:

FCRC = RQ₀−

T

X

t=1

(NIRCt− ∆RQt) ∗ drt; (4.5)

The net income on required capital can be determined by considering the forward rate, investment cost rate, tax rate and discount rate:

NIRC = RQ_t−1∗ (fr_t− icr) ∗ (1 − tr); (4.6)

4.4 Cost of Residual Non-Hedgeable Risks

The cost of residual non-hedgeable risks, CNHR, can be derived using a cost-of-capital approach similar to the risk margin approach under Solvency II. This represents the extra margin that a buyer would require on top of Best Estimate Liability to take over the liabilities on an arms length transaction. Since only liabilities will be involved in such a transaction, only underwriting risks and operational risk are considered. We therefore allocate the relevant risks (underwriting and operational) to companys products using Shapley Euler technique (this is a capital allocation technique). Thereafter the CNHR capital allocated to each product is used in conjunction with the appropriate risk driver for that product to derive a proxy ratio. This ratio, r, is then used to simulate the CNHR capital for future years for each product to determine the cost of capital which is then discounted to t=0: CNHR = T X t=1 RCt∗ drt∗ r; (4.7)

4.5 Free Surplus

The free surplus capital, FS, of the insurance company consists of the difference between the market value of assets backing shareholders equity MVabse₀ and the required capital RC. The market value of assets backing shareholders equity is derived by considering UGL,

(18)

Chapter 5

Application of the MCEV Model

5.1 Construction of Non-Life Portfolio

In order to apply the concept of MCEV, we have constructed a mock non-life insurance company. The figures and numbers used are selected and/or designed to correspond to a Greek insurance company representative of the Greek market. The portfolio is assumed to be healthy, in the sense that the company has the necessary assets to cover for the liabilities. The valuation date is set as the 31st _{of December 2014.}

5.1.1 Existing Business

For the construction of the portfolio of liabilities, the reserves from Taylor and Ashe (1983) are used (Table 5.1). This particular portfolio was also used, among others by Verrall (1991a,b), Mack (1993) and Renshaw, (1989,1994) and consists a good example for deterministic reserve estimation.

In Table 5.1, the rows represent the accident year, when the event took place, while the columns represent the development year. All the amounts are incremental and con-stitute the actual paid claims for each origin period.

The incremental paid claims and the undiscounted best estimates which are shown in Table 5.2 are the first step of the calculation process. The estimation of claims reserves is conducted through deterministic Chain Ladder model, using R programming language. The payment pattern provided in Table 5.3 describes the settlement schedule of the best estimate claims reserves within the next few years.

(19)

MCEV in Non-Life Por tf olio — Dimitra P apageorgiou-Siora 13

Table 5.1: Development triangle of insurance reserves.

Origin Period 1 2 3 4 5 6 7 8 9 10 1 357.848 766.940 610.542 482.940 527.326 574.398 146.342 139.950 227.229 67.948 2 352.118 884.021 933.894 1.183.289 445.745 320.996 527.804 266.172 425.046 3 290.507 1.001.799 926.219 1.016.654 750.816 146.923 495.992 280.405 4 310.608 1.108.250 776.189 1.562.400 272.482 352.053 206.286 5 443.160 693.190 991.983 769.488 504.851 470.639 6 396.132 937.085 847.498 805.037 705.960 7 440.832 847.631 1.131.398 1.063.269 8 359.480 1.061.648 1.443.370 9 376.686 986.608 10 344.014

Table 5.2: Incremental paid claims and best estimates.

Origin Period 1 2 3 4 5 6 7 8 9 10 1 270.061 672.617 704.494 753.438 417.350 292.571 268.344 182.035 272.606 67.948 2 376.125 936.779 981.176 1.049.342 581.260 407.474 373.732 253.527 379.669 94.634 3 372.325 927.316 971.264 1.038.741 575.388 403.358 369.957 250.966 375.833 93.678 4 366.724 913.365 956.652 1.023.114 566.732 397.290 364.391 247.190 370.179 92.269 5 336.287 837.559 877.254 938.200 519.695 364.316 334.148 226.674 339.456 84.611 6 353.798 881.172 922.933 987.053 546.756 383.287 351.548 238.477 357.132 89.016 7 391.842 975.923 1.022.176 1.093.190 605.548 424.501 389.349 264.121 395.534 98.588 8 469.648 1.169.707 1.225.143 1.310.258 725.789 508.792 466.660 316.566 474.073 118.164 9 390.561 972.733 1.018.834 1.089.616 603.569 423.113 388.076 263.257 394.241 98.266 10 344.014 856.803 897.410 959.756 531.636 372.687 341.826 231.882 347.255 86.555

(20)

14 Dimitra P apageorgiou-Siora — MCEV in Non-Life Por tf olio

Table 5.3: Payment Patterns.

t - year 1 2 3 4 5 6 7 8 9 10 Payment Pattern 27,98% 22,37% 16,76% 11,39% 8,36% 6,30% 3,98% 2,38% 0,46%

(21)

MCEV in Non-Life Portfolio — Dimitra Papageorgiou-Siora 15 Hence, the claim payments for each examined year can be derived by multiplying the best estimate claims reserves at the starting period with the payment pattern, as described by the following equation:

CPeb_t = BCReb₀ ∗ preb_t ; (5.1) To derive the discounted best estimate claims reserves, we first discount all the future claims payments and then project the sum of them into the future. This means that at time zero the discounted best estimate claims reserves equal to the sum product of the discounted future claims payments. More specifically:

BCRebDIS_t = (_P_T

i=1CPebi ∗ ri∗ r if t = 0;

BCRebDIS_t−1 ∗ (1 + fr_t) − CPeb_t if t > 0; (5.2) The discount rate used is the discounted spot rate curve as at YE2014, as provided by EIOPA. For the derivation of the forward rates the same yield curve has been used.

5.1.2 Renewal Business

In order to capture the full value embedded in the portfolio, it is necessary to take into account any future renewals that will result from the existing portfolio. For the modeling of the portfolio the starting point is the number of contracts that the portfolio includes. In order to identify the development of the underlying portfolio development, we use the following assumptions that are based on experience studies:

Table 5.4: Renewal Assumptions. Average Premium Level PL 250 Average Cancelation Rate cr 13% Best Estimate Loss Ratio LR 40%

For each respective accounting year, the remaining number of existing insurance contracts follows the equation:

ICm_t = ICm₀ ∗ max(1 − t ∗ crm

0; 0); (5.3)

Hence, the Gross Earned Premiums for each respective year equals the number of insurance contracts times the premium level. The total Gross Earned Premiums (GEP) is calculated as the sum of gross earned premiums within each respective year. The total ultimate loss is calculated as the product of GEP and the loss ratio for each respective year.

For the claims payments of renewal business we follow triangular representation as presented in Table 5.5.

(22)

16 Dimitra P apageorgiou-Siora — MCEV in Non-Life Por tf olio

Table 5.5: Claim payments of renewal business.

2015 2016 2017 2018 2019 2020 2021 2015 208.485 143.722 95.195 62.231 38.028 19.778 8.245 2016 177.332 122.246 80.970 52.932 32.346 16.823 2017 146.179 100.771 66.746 43.633 26.664 2018 115.026 79.295 52.521 34.334 2019 83.873 57.819 38.297 2020 52.720 36.344 2021 21.567 2022 2023 2024 2025 2026 2027 2028

(23)

MCEV in Non-Life Por tf olio — Dimitra P apageorgiou-Siora 17

Table 5.6: Claim payments of renewal business.

2022 2023 2024 2025 2026 2027 2028 2015 1.341 2016 7.013 1.141 2017 13.868 5.781 940 2018 20.981 10.912 4.549 740 2019 25.035 15.299 7.957 3.317 540 2020 24.072 15.737 9.616 5.001 2.085 339 2021 14.868 9.848 6.438 3.934 2.046 853 139 2022 2023 2024 2025 2026 2027 2028

(24)

18 Dimitra Papageorgiou-Siora — MCEV in Non-Life Portfolio Tables 5.5 and 5.6 represent the triangle of the claims payments renewal business. The accident years are represented in rows and the calendar years in columns. With respect to a payment for an insurance or reinsurance claim, as accident year is defined the year in which the incurred event that gave rise to that claim took place. Accordingly, as calendar year is defined the year in which the payment took place. Hence, for the cases where the actual calendar year is before the accident year, the future claims payments are zero. In any other case, the future claims payments are calculated as the product of Ultimate Losses and a payment pattern. Since the portfolio is short term the existing business is considered to provide accurate payment pattern which is also used for the development of the future claims of renewal business.

The development of the best estimate claims reserves is derived by summing up the future claims payments for the respective accounting year i and calendar year j:

BCRi,j = T

X

t=j+1

CPi,t; (5.4)

The total best estimate claims reserve at the end of each calendar year is calculated as the sum of the best estimate reserves of all past accident years:

BCRrb_t =

T

X

t=1

BCRi,t; (5.5)

For the discounting of the best estimate claims reserves the factors as calculated based on the spot rates are used.

For the total result of MCEV calculations, independency between the claims set-tlement process of existing and renewal business is assumed. Hence, the total claims payments equal the sum of the claims payments for existing business and claims pay-ments for renewal business. Accordingly, the total best estimate claims paypay-ments (both discounted and undiscounted) equal the sum of the best estimates of existing and re-newal business.

For the derivation of technical result, insurance expenses need to be defined. Tech-nical result consists of gross earned premiums, claims payments, changes in reserves, acquisition costs, claims settlement costs and overhead costs. For this purpose rates to derive acquisition costs, claims settlement costs and overhead costs are needed. Acqui-sition cost expresses the sales costs that are associated with acquiring a new customer. Claims settlement cost includes the total costs charged to complete the settlement of the claim. Overhead costs refer to all ongoing business expenses not including or related to direct labor, direct materials or third-party expenses. Table 5.7 shows all the above rates chosen. They are all based on experience studies for Greek insurance industry.

Table 5.7: Portfolio Rates.

Acquisition Cost Rate acr 13% Claims Settlement Cost Rate cscr 4%

Overhead Costs oc 4%

Hence, acquisition costs are calculated as the product of gross earned premiums and the acquisition cost rate. Accordingly, claims settlement expenses are calculated as the product of claims payments and the claims settlement expenses rate. Overhead costs are derived as the product of overhead cost rate and the best estimate claims reserves.

(25)

MCEV in Non-Life Portfolio — Dimitra Papageorgiou-Siora 19

5.1.3 Statutory Balance Sheet

Since the company is assumed to reside in Greece, the statutory balance sheet follows the rules of Greek local GAAP (Law 400/70). To illustrate the portfolio of assets, a variety of corporate bonds, government bonds, property and shares has been selected. For the purposes of MCEV, the assets are split into assets backing liabilities and assets backing shareholders equity. The book value of assets backing shareholder equity is 7.835.461ewhile the assets backing liabilities amount to 21.004.390e.

5.1.4 Required Capital

The capital required to cover the liabilities is based on the European Solvency II leg-islation. For the derivation of the regulatory capitals, we analyze the inherent risks of the portfolio. Therefore, given the nature of the business, reserve and premium risks are identified. Reserve risk refers to the risk arising when the technical provisions set up for incurred claims at the valuation date are insufficient to cover these claims. This means that the claims payments are proved to be greater than expected or that there are differences in expected timing of the claims payments or that there are differences in the expected frequency. Premium risk refers to the risk arising from fluctuations in timing, frequency and severity of the business of future claims. This means that the ex-pected amounts to cover for the business to be written or the unexpired risk on existing contracts differs from the actual amount needed.

According to Solvency II Delegated Acts, the capital requirement for Premium and Reserve risk is delivered by the following equation:

NLpr = 3 ∗ σ ∗ V; (5.6)

Here, σ is defined as the combined standard deviation for nonlife premium and reserve risk and V, refers to the volume measure of business. Hereby, the results for the capital charge are presented in Table 5.8.

Table 5.8: Reserve and Premium risk results. Volume Measure Vres 18.680.856 Vprem 2.228.512 Overall V 20.909.367 Standard Deviation Reserve 9,0% Premium 8,0% Reserve V * σ 1.681.277 Premium V * σ 178.281 Overall s 8,5% Overall V * Overall s 1.777.137 Non-Life Premium & Reserve risk 5.331.411

(26)

5.2 MCEV Results

Table 5.9: MCEV Results - Base Scenario. Free Surplus

FS0 2.449.500

Required Capital

RC0 5.702.514

Value of in - force covered business

PFVP0 5.372.874

FCRC0 37.051

CRNHR0 1.055.184

VIF0 4.280.639

MCEV 12.432.653

As described in Table 5.9, the total MCEV amounts to 12.432.653e, with a free surplus of 2.449.500e, required capital of 5.702.514eand value of in forced business (both existing and renewal) of 4.280.639e. The contribution of the value of in force business corresponds to the 35% of the total MCEV amount. To have a deeper view of the shareholders income we would say that this steams from the free surplus, the required capital (decreased by the frictional cost amount) and the present value of future profits. All the other amounts constitute capital that would be assigned to the policyholders cash flows or to staff, tax, investment and other costs.

Scenario 1:

In the case that the portfolio would not have any renewals steaming from the existing business, it is interesting to have a view on the results of the MCEV amount.

Table 5.10: MCEV Results - Scenario 1 (No renewals). Free Surplus

FS0 2.737.080

Required Capital

RC0 5.414.933

PFVP0 4.411.164

FCRC0 33.213

CRNHR0 964.669

VIF0 3.413.282

6M CEV 11.565.295

Table 5.10 presents the results of the same portfolio that we have analyzed so far, however assuming that there are no renewals in the existing business within the next future years but only the existing business. This means that the cancelation rate is set at 100%. Hence, this settlement of the existing business results to a total MCEV of 11.437.141e, where free surplus amounts to 2.577.237e, required capital is 5.414.933eand the value of in force business is 3.444.970e. As expected the embedded value of the portfolio is reduced since there is no future in flow.

It is interesting to test the movement of the total MCEV amount and of its com-ponents with the movement of the key parameters of the model. This will prove the

(27)

MCEV in Non-Life Portfolio — Dimitra Papageorgiou-Siora 21 robustness of the model while helping us to analyze the impact of a variety of assump-tions and model parameters.

Scenario 2:

Under the base scenario the loss ratio is set at 40%. It is an accurate and appropriate loss ratio, representative of a healthy Greek insurance nonlife portfolio. However, ratios of up to 80% can also be observed in the Greek insurance market. The impact of such a high rate of loss, given that all other parameters remain unchanged, is depicted in this scenario and the results are presented in Table 5.11.

Table 5.11: MCEV Results - Scenario 2 (Loss Ratio). Free Surplus

FS0 2.083.150

Required Capital

RC0 6.068.863

PFVP0 4.372.560

FCRC0 41.913

CRNHR0 1.170.005

VIF0 3.160.642

MCEV 11.312.656

As shown in the Table, if the loss ratio is high the MCEV gets lower. The loss ratio expresses the number of claims over the premiums written. Hence, the result is explained by the fact that more funds need to be paid to the policyholder, under this scenario.

Scenario 3:

So far we have tested the impact of a high cancellation rate (considering no renewals for the portfolio) and of a high loss ratio. Given the uncertainty of Greek market, it would be interesting to check a parallel move of both rates. Hence, this scenario captures the event of a simultaneous increase of losses with an assumption of limited renewal rate. Table 5.12 presents the results for a cancellation rate of 60% and a loss ratio of 80%.

Table 5.12: MCEV Results - Scenario 3 (Loss Ratio / Cancelation Rate). Free Surplus

FS0 2.672.218

Required Capital

RC0 5.479.796

PFVP0 4.419.947

FCRC0 33.960

CRNHR0 985.412

VIF0 3.400.575

MCEV 11.552.588

As we have checked in the previous scenarios, a decrease of either the loss ratio or the cancelation rate causes a depreciation of MCEV amount. However, an interaction between those two parameters reveals that given the high loss ratio, the increase of cancellation enhances the value of MCEV. It would be clearer if we would check the movement within the total amounts.

(28)

Table 5.13: MCEV Results - Comparison of Scenarios.

Base Scenario Scenario 1 Scenario 2 Scenario 3 12.432.653 11.565.295 11.312.656 11.552.588 Change from Base Scenario -6 98% -9 01% -7 08%

The total decreases range between 7% and 9% under these scenarios. Given the large amount of free surplus and required capital, it is not expected a sharp depreciation of MCEV amount. However, the percentages show that given a rise in loss ratio, an increase in cancellation rates adds value to the result.

Scenario 4:

Another parameter that is worth to be tested is the acquisition cost. Acquisition cost expresses the cost of business to acquire a new customer and acquisition cost rate is determined as a percentage of gross earned premiums. In the Base Scenario, acquisition cost rate is set at 10%. The following Table (5.14) presents the results after implying the rate at 30% (Scenario 4).

Table 5.14: MCEV Results - Scenario 4 (Acquisition Cost). Free Surplus

FS0 2.449.500

Required Capital

RC0 5.702.514

PFVP0 4.755.915

FCRC0 37.051

CRNHR0 1.055.184

VIF0 3.663.680

MCEV 11.815.694

An increase in the acquisition costs impacts the total MCEV amount since it affects both the present value of future profits and the value of in force business. Hence, the higher the acquisition cost is, the less profitable the business would be.

Scenarios 5 and 6:

So far we have tested the change in MCEV amount caused by the increase or decrease of nonfinancial parameters. Loss ratio, cancellation rate and acquisition cost are amounts related to the insurance business that can be handled and operated within the company. Interest rate summarizes the movement of the market in the sense that it expresses the cost of borrowing money. It is therefore important to test the sensitivity of the model in changes in the interest rate since it would give a picture of the impact of market changes. Scenario 5 assumes that the interest rate follows the shocked up structure of Greek market rate that EIOPA provides. Accordingly, Scenario 6 provides the results using the shocked down risk-free rate.

(29)

MCEV in Non-Life Portfolio — Dimitra Papageorgiou-Siora 23

Table 5.15: MCEV Results - Scenarios 5 & 6 (Interest Rate). Scenario 5 Scenario 6 Free Surplus

FS0 2.460.238 2.448.373

Required Capital

RC0 5.691.775 5.703.640

PFVP0 7.515.319 4.450.467

FCRC0 80.573 32.349

CRNHR0 1.029.122 1.059.177

VIF0 6.405.624 3.358.941

MCEV 14.557.637 11.510.954

The tables above prove the importance of interest rate movements in the model. The stressed term structures affect the present value of future profits and as a result the value of in force business, driving the profitability of the portfolio.

(30)

Chapter 6

Conclusions

The aim of the thesis was to develop the idea of market consistent embedded value in non-life insurance. The concept is analyzed and set by CFO Forum and traditionally is used in life insurance business. The thesis presents how to transfer the design of embedded value from life to non-life by determining assumptions concerning the future development of claims. Furthermore, the impact of varying several assumptions, such as loss ratios, costs and interest rates is tested.

The idea of embedded value in non-life insurance has a number of business and management implications. Given the use of MCEV in life portfolios, the implication in non-life portfolios provides comparable and harmonized information and results that could constitute useful tool to the stakeholders. The change of MCEV from year to year could be the measurement of quantifying return and risk capital. The concept could also assist and promote the management of insurance portfolios on a group level. The insertion of future new business in the modelling adds value to the management of insurance industry and could advance the decision making processes on management level.

(31)

References

American Academy of Actuaries Members of the Life Financial Reporting Committee, (2011). Market Consistent Embedded Value, A public policy practice note, American Academy of Actuaries.

Diers, D., M. Eling, C. Kraus and A. Reuss (2012). “Market-consistent embedded value in non-life insurance: how to measure it and why”, Journal of Risk Finance, 13, 320–346.

England, P. and R. Verrall (1999). “Analytic and bootstrap estimates of prediction errors in claims reserving”, Insurance: Mathematics and Economics, 25, 281–293. England, P. and R. Verrall (1999). “Stochastic claims reserving in general insurance”,

British Actuarial Journal, 8, 443–518.

European Insurance CFO Forum, (2004). European Embedded Value Principles, Pub-lished Principles, CFO Forum,.

European Insurance CFO Forum, (2008a). Market consistent embedded value: Princi-ples, Published PrinciPrinci-ples, CFO Forum,.

European Insurance CFO Forum, (2008b). Market consistent embedded value: Basis of conclusions, Published Principles, CFO Forum,.

European Insurance CFO Forum, (2009). Market consistent embedded value: Basis of conclusions, Published Principles, CFO Forum,.

European Insurance and Occupational Pensions Authority (EIOPA), (2014). Commis-sion Delegated Regulation (EU) 2015/35 , supplementing Directive 2009/138/EC of the European Parliament and of the Council on the taking-up and pursuit of the business of Insurance and Reinsurance (Solvency II),

Insurance Association of Greece. “Insurance in Greece: Annual Report”.http://www. eaee.gr/cms/sites/default/files/annualreport2013_0.pdf.

Insurance Intelligence Center. “Non Life Insurance in Greece, KeyTrends and Oppor-tunities to 2018”.http://www.insurance-ic.com/, consulted on April, 2015. Kaas, R., M.J. Goovaerts, J. Dhaene, and M. Denuit (2008). Modern Actuarial Risk

Theory—Using R, 2nd edition, Springer, Heidelberg.

R Development Core Team (2012). R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria. URL http: //www.R-project.org/. ISBN 3-900051-07-0.

Taylor, G.C. and F.R. Ashe (1983). “Second moments of estimates of outstanding claims”, Journal of Econometrics, 23, 37–61.

Market-consistent embedded value in non-life portfolio

Market-Consistent Embedded Value

in Non-Life Portfolio

Dimitra Papageorgiou-Siora

Contents

Preface

Chapter 1

Introduction

Chapter 2

Market Consistent Embedded

Value

Chapter 3

Differences between Life and

Non-Life Businesses

Chapter 4

Modeling MCEV for a Non-Life

Portfolio

4.1

Present Value of Future Profits

4.2

Required Capital

4.3

Frictional Costs of Required Capital

4.4

Cost of Residual Non-Hedgeable Risks

4.5

Free Surplus

Chapter 5

Application of the MCEV Model

5.1

Construction of Non-Life Portfolio

5.2

MCEV Results

Chapter 6

Conclusions

References