Economic Capital calculations using a „Life DFA“ approach

1. Economic Capital calculations using a „Life DFA“ approach Magyar Aktuáriusi Társaság XV. Altenburger Gyula Szimpózium Balatonvilágos, 2005 május 27-én AMB Generali Holding AG Hrabovszki László

2. Economic Capital calculations using a „Life DFA“ approachAgenda • Background and requirements • The basic concept and calculations • Possible applications Economic Capital 2005.05.27

3. Economic Capital calculations using a „Life DFA“ approachAgenda • Background and requirements • The basic concept and calculations • Possible applications Economic Capital 2005.05.27

4. Why do capital and return need more intensive controlling procedures? Economic risks that were once trivial are gaining in relevance Neglected risks have gained in importance: e.g. Financial guarantees 10 yr risk free government bonds Guaranteed interest rate – New business Approx. Guaranteed interest rate – Business in force The smaller the difference is, the bigger the risk that a loss is incurred 10 year government bonds: 3.48% as of 20th April 2005 In % Economic Capital 2005.05.27

5. Implications for corporate managementQuantifying economic risks and managerial integration Recent accounting standards, solvency requirements and controlling instruments have not allowed for fundamental business risks • Asset Liability Management: • - Longer duration of the actuarial reserves compared to the corresponding bonds portfolio leads to high interest rate sensitivity in the economic capital • - Level of share investment is a main driver of required economic capital • Financial guarantees: • - Long-term implicit options, such as guaranteed interest and lump-sum payment options, require sophisticated valuation, where current accounting methods are rudimentary, and cannot be covered by hedging strategies on the capital market • Inefficient incentive structures: • - New business commissions are determined by the volume of new business acquired and not the added value this creates • - The return on the actual economic capital is used as an indicator for added value, however, as a rule, this has no influence on the rewards paid to top management New accounting standards and solvency requirements increase transparency with respect to economic risk exposure • The increasing importance of a fair value approach to accounting will make economic risks more visible. • As a result, planning, controlling and managing these risks will become more important. Economic Capital 2005.05.27

6. Demands on fully-integrated control systemsStructure of the AMB Generali group’s controlling tool Security Return Publicity Ensure solvency cover cost of capital create transparency Standards Performance Management Capital Management • HGB • IAS/IFRS • Management of the shareholders’ expectations on profit and added value • Calculation of risk adjusted performance • Separation of taxable amounts from non-taxable external factors • Derivation of the total risk exposure and the resulting economic capital requirement for which the shareholder is liable • Ensuring the economic solvency by comparing the required economic capital with that which is available Solvency • Solvency II • Reinsurance regulation Components Components • Performance measurements • Life/Health: NGW • Non-Life: Combined Ratio • Performance indicators • RoEC • RoEV • Embedded Value group/ Economic Capital • Life: ALM/ DFA • Health: ALM • Non-life: DFA • Capital allocation Corporate Governance • Communication of key management figures • Controls/Regulation • Interactive ratings processes fully-integrated control system Economic Capital 2005.05.27

7. Motivation for DFA LifeBuilding a stochastic simulation platform • How high is the level of required capital for the insurance segment life resulting from a complete and consistent economic approach? • How high is the EV in this economic view, if the resulting cash flows are market consistent – i.e. arbitrage free and discounted? open questions • Calculation of the economic capital requirements in a “Fair Value” framework • Creation of a realistic balance sheet • Aggregated pricing of guarantees and options • Derivation of the market consistent Embedded Value • Calculation of the economic capital requirements in a “Fair Value” framework • Creation of a realistic balance sheet • Aggregated pricing of guarantees and options • Derivation of the market consistent Embedded Value steps towards goal • Development of a market consistent simulation environment to calculate economic risks and derive market value balance sheets • Stochastic ascertainment of the market value of commitments with respect to options and guarantees implementation Economic Capital 2005.05.27

8. Economic Capital calculations using a „Life DFA“ approachAgenda • Background and requirements • The basic concept and calculations Deriving realistic balance sheets Calculating economic capital • Possible applications Economic Capital 2005.05.27

9. Derivation of the Economic Capital required for Life businessNew EV-Concepts are driving the development of internal capital models Realistic balance sheets are derived based on stochastically generated present values density XS capital market-consistentembedded value economic capital economic capital Value of costs + tax value profit sharing fair value P/H options fair value liabilities • path-dependent discounting of guaranteed cash-flows = value of guarantees • the expected present value of future profit sharing depends on the SAA and management rules describing the dynamic asset-liability interdependency • To what degree are customers financially rational? Assumptions are a main factor in the value of policyholder options Value of guarantees assets liabilities liabilities split Economic Capital 2005.05.27

10. How are results generated?Model framework and implementation strategy Implementation Strategy Model framework • Standard model contains generic products and German accounting rules • Generic products calibrated using EV cash flows • Aim to model fund behaviour – including sensitivities • Asset simulation is similar to bottom-up model • Group model to be implemented in Aachen Economic asset scenario generator -arbitrage free, market consistent scenarios liability model Set of management rules asset model • Endowment model • annuity model • class-related models profit sharing P/H S/H Risk assessment Dynamic adjustment of the SAA Declaration of crediting rate Economic Capital 2005.05.27

11. Modelling management behaviourStep1: Defining the impact parameters and their interdependencies Conceptual View as of 30.12.t Conceptual View as of 30.12.t+1 Economic scenario in t: Pay crediting rate, that was declared Economic scenario: - path-depending realisation of economic scenario - generated through ESG - expected yield curves - expected volatilities next year! Calculate: - path-depending realisation of economic scenario - generated through ESG - free RfB - hidden reserves - SAA - resulting reserve quota (actual RQ) Pay crediting rate, that was declared Calculate RQmin based on percentile default approach of expected yield and current SAA Calculate: If RQmin < actual RQ If RQmin > actual RQ - free RfB - hidden reserves - SAA - resulting reserve quota (actual RQ) - increase equity quota by y% - reduce equity until RQs are matched - Minimum equity quota is x% Recalculate RQmin with new, dynamically adapted SAA Determine new SAA for 1.1.t+1 Declare crediting rate for t+1 as discussed for 30.12.t Economic Capital 2005.05.27

12. Defining a mathematical framework Step 2a: Assessing the actual financial strength Quantitative view Description Definitions • RQ is the relative share of existing (hidden) reserves on assets and liabilities (risk-bearing capital) in % of the mathematical reserves. • Hidden reserves on participations, that are not fungible, are excluded from V, as this position should not be released for profit sharing purposes. • However, at the moment hidden reserves on participations cannot be modelled explicitly due to technical reasons MR: mathematical reserves V= HRINV - HRPART + RfB - TBR with: HRINV : hidden reserves on all assets HRPART : hidden reserves on participations RfB: value of RfB TBR : value of terminal bonus reserve Economic Capital 2005.05.27

13. Defining a mathematical framework Step 2b: Controlling shortfall risks and adjusting the SAA Quantitative view Description Definitions • If the actual RQ is higher than RQmin the equity backing ratio (EBR) can be max. increased by 2%. If the actual RQ is lower than RQmin the EBR is to be decreased until RQ and RQmin are matched. • The EBR floor reflects the fact that the minimum variance portfolio contains an approximate equity-share of 5%. Economic Capital 2005.05.27

14. Defining a mathematical framework Step 2c: Determining the crediting rate Quantitative view Definitions Description • R is the expected running yield for the next period • defines the p/h participation (set to 90%) • Tau is the time horizon to finance a leverage of the crediting yield (pure ceteris-paribus calculus facilitating a smoothed management of reserve levels; initially set to 6 years) • c: maximum increase by 1% maximum rate of 14% minimum rate of guarantee • R can be regarded as the solid basis for determining the crediting rate. It is fueled by expected dividends, rent and coupon payments • The root-term is used to adapt the crediting yield to the current level of capital adequacy. If excess reserves exist, it is assumed that these excess reserves are released continuously within a hypothetical time horizon of t years to finance a leverage of the crediting yield. Economic Capital 2005.05.27

15. Defining a mathematical framework Step 2d: Allocating bonuses Quantitative view Definitions Description • TBP: terminal bonus part • RBP: running bonus part • GR: guaranteed rate • omega: ratio splitting running bonus part and the terminal bonus part; defined as: • delta: initial scaling factor set to 4 • At the end of each year, the crediting rate declared in the previous year is to be paid. As the declared rate c is a cumulated profit sharing yield, it is to be broken down into the running bonus part and the terminal bonus part after guaranteed parts are allocated. Economic Capital 2005.05.27

16. Defining a mathematical framework Step 2e: Determining the shareholder’s part Quantitative view Definitions Description • s: shareholder’s part • The shareholder part can be considered as a deterministic factor, solely depending on declared rates of the previous period. • If the targeted realisation of hidden reserves is not sufficient to fund the projected shareholder part, additional hidden reserves are realised. • This mechanism guarantees that the total returns that were expected in the previous period and that were used to declare the p/h and s/h participation in the current period are matched to the actual results. Economic Capital 2005.05.27

17. How can the interdependent rules be validated ? Step 3: Using historical data for simplified back-testing and calibration RQ (min), shortfall probability g of 1% RQ (min), shortfall probability g of 10% VDL (t = 6 years) declared crediting rate (real world) declared crediting rate (real world) declared crediting rate (model world) declared crediting rate (model world) AML (t = 3 years) declared crediting rate (real world) declared crediting rate (real world) declared crediting rate (model world) declared crediting rate (model world) Economic Capital 2005.05.27

18. in € Assets in % Liabilities in % Investments 15.000.000.000 100,00% McEV 548.710.144 3,66% 872.250.773 5,82% Liabilities 14.451.289.856 96,34% Real estate 2.192.785.012 14,62% 333.821.118 2,23% Shares PV tax 11.934.964.215 79,57% 347.700.027 2,32% Bonds PV maintenance Costs 669.939.976 4,47% PV acquisition costs 433.156.916 2,89% PV remaining RfB and UCGs 3.200.103.688 21,33% PV profit sharing 9.466.568.130 63,11% PV guarantees Total assets 15.000.000.000 100,00% Liabilities and S/H Equity 15.000.000.000 100,00% Generating results from the simulationsCreating a balance sheet based on market consistent present values Market value balance sheet as per 31. Dec. 2004 for a life company with a 15%1) investment ratio Case Study: 1) including strategic investments Economic Capital 2005.05.27

19. Economic Capital calculations using a „Life DFA“ approachAgenda • Background and requirements • The basic concept and calculations Deriving realistic balance sheets Calculating economic capital • Possible applications Economic Capital 2005.05.27

20. 1 2 3 How are risk measures derived from stochastic projections? Adequate stress tests are implemented on input parameters Calculate the McEV and the fair value of liabilities in the initial scenario Stress the input parameters to the required level and look up the simulation path representing the targeted confidence level Recalculate the stressed McEV and compare it to the unstressed McEV to derive the economic capital Economic Capital 2005.05.27

21. SIM# CLASS 2004 2005 Delta SIM# CLASS TERM ZCB 2004 ZCB 2005 Spot 04 Spot 05 Delta 1 2298 EQUITY 100,00% 49,61% -50,39% 1 1841 ZCB 15 0,5392 0,7027 4,20% 2,38% -1,82% 2 3924 EQUITY 100,00% 50,99% -49,01% 2 2298 ZCB 15 0,5392 0,6960 4,20% 2,45% -1,76% 3 3376 EQUITY 100,00% 52,96% -47,04% 3 4233 ZCB 15 0,5392 0,6936 4,20% 2,47% -1,73% 4 3188 EQUITY 100,00% 54,74% -45,26% 4 1991 ZCB 15 0,5392 0,6929 4,20% 2,48% -1,73% 5 1560 EQUITY 100,00% 56,55% -43,45% 5 2307 ZCB 15 0,5392 0,6914 4,20% 2,49% -1,71% 6 4316 EQUITY 100,00% 57,05% -42,95% 6 1720 ZCB 15 0,5392 0,6904 4,20% 2,50% -1,70% 7 4743 EQUITY 100,00% 57,28% -42,72% 7 4316 ZCB 15 0,5392 0,6873 4,20% 2,53% -1,67% 8 3914 EQUITY 100,00% 58,33% -41,67% 8 980 ZCB 15 0,5392 0,6753 4,20% 2,65% -1,55% 9 1841 EQUITY 100,00% 58,73% -41,27% 9 1859 ZCB 15 0,5392 0,6732 4,20% 2,67% -1,53% 10 3352 EQUITY 100,00% 59,12% -40,88% 10 575 ZCB 15 0,5392 0,6690 4,20% 2,72% -1,49% 11 2823 EQUITY 100,00% 59,68% -40,32% 11 1907 ZCB 15 0,5392 0,6690 4,20% 2,72% -1,49% 12 3635 EQUITY 100,00% 59,74% -40,26% 12 1239 ZCB 15 0,5392 0,6687 4,20% 2,72% -1,48% 13 1859 EQUITY 100,00% 60,33% -39,67% 13 3525 ZCB 15 0,5392 0,6635 4,20% 2,77% -1,43% 14 4233 EQUITY 100,00% 60,53% -39,47% 14 1886 ZCB 15 0,5392 0,6628 4,20% 2,78% -1,42% 15 3869 EQUITY 100,00% 60,76% -39,24% 15 4743 ZCB 15 0,5392 0,6611 4,20% 2,80% -1,41% Stressing the input parameters to a confidence level of 99,75%5.000 paths x 0,25% targeted shortfall probability =>13th worst is critical yield curve stress test equity stress test worst paths in t+1 stress scenario • total equity return in t+1 (time horizon of 1 year) is stressed • stressed market value of equities (e.g. 60,33 % x MV equities in base case) is calculated and used as unit value for new run • spot rate of zero-coupon bonds with 15 years to maturity is stressed in t+1 (time horizon of 1 year) • new run for stress testing to be modified in terms of all relevant input parameters (initial and future yield curves, inflation, equity index and deflators as market-consistent discounting factors) Economic Capital 2005.05.27

22. Basic case Stress case I % Stress case II % in € vs. Basic case- vs. Basic case- Scenario Equity crash (99,75%) decreasing yield curve (99,75%) Assets Investments 15.000.000.000 13.970.181.190 -6,87% 16.146.307.858 7,64% Total Assets 15.000.000.000 13.970.181.190 -6,87% 16.146.307.858 7,64% Liabilities McEV 548.710.144 213.173.449 -61,15% 445.994.547 -18,72% Liabilities 14.451.289.856 13.757.007.741 -4,80% 15.700.313.310 8,64% 333.821.118 209.827.193 -37,14% 204.647.876 -38,70% PV tax 347.700.027 347.700.027 0,00% 354.387.017 1,92% PV maintenance costs 669.939.976 669.939.976 0,00% 669.973.615 0,01% PV acquisition costs 433.156.916 349.731.986 -19,26% 369.181.802 -14,77% PV remaining RfB and UCGs 3.200.103.688 2.713.240.429 -15,21% 2.821.286.811 -11,84% PV profit sharing 9.466.568.130 9.466.568.130 0,00% 11.280.836.188 19,17% PV guarantees Liabilities and S/H Equity 15.000.000.000 13.970.181.190 -6,87% 16.146.307.858 7,64% Economic capital for investment risks vs. basic case McEV unstressed 548.710.144 548.710.144 McEV stressed 213.173.449 445.994.547 335.536.695 102.715.597 Economic Capital Total Stress case I Stress case II Aggregation Economic Capital 350.906.494 335.536.695 102.715.597 scenario-derived correlation (equities, bonds) = 0 Recalculating the stressed realistic balance sheets Economic capital derived as D of stressed and unstressed McEV Stressed market value balance sheet as per 31st Dec 2004 for the case study life company Economic Capital 2005.05.27

23. Economic Capital calculations using a „Life DFA“ approachAgenda • Background and requirements • The basic concept and calculations • Possible applications Economic Capital 2005.05.27

24. Applying DFA results to internal allocation of capital AMB Generali: Embedded Value allocation steered by equity requirements Allocation: € 2.984 m Economic Capital + € 235 m Excess Capital = € 3.219 m EV Group in Mio. € as per 31.12.2004 (previous year in brackets) 7,3% (5,6%) 235 (178) • Economic Capital in relation to business volume as per 31. Dez. 2004 • Non-Life 28,1% (27,0%) of the earned net premium • Health 3,2% (3,7%)of the technical reserves • Life 2,6% (2,5%) of the technical reserves + € 280 m (€ 504 m) VIF Uplift Life 1) 212 (125) 6,6% (4,0%) 1.806 (1.904) 56,1% (60,3%) 24,5% (24,7%) 788 (781) 178 (169) 5,5% (5,4%) Life (Economic Capital) Financial services (Economic Capital) Health (Economic Capital) Non life (Economic Capital) Excess Capital 1) Uplift EV Life through IFRS shareholder’s equity life Economic Capital 2005.05.27

25. 12.5% RoEC Linking equity requirements to return on a business segment level Can the added value in life insurance be adequately measured? Life: economic profit and loss account Internal risk model for the life segment excess capital 2004 2003 • In Mio. € after tax market-consistent embedded value economic capital economic capital • APE 1) of new business • New business margin • New business value • Operative differences 2) • Realised gains from value in force • Result after tax • 766 • 12,1% • 93 • -11 • 125 • 207 • 1.223 • 10,8% • 132 • -11 • 118 • 239 costs and tax Market value profit sharing Fair value of liabilities Value of guarantees Liability split Assets Liabilities Possible consequences of the increasing importance of a fair value approach • Classic life insurance products such as endowments will create more need for Economic Capital (due to investment, calculation and guarantee risks). Accordingly, the risk adjusted operative profitability of these products will sink. • Unit linked life insurance without guarantees and insurance policies that cover only biometric risks will require comparatively less Economic Capital. The risk adjusted operative profitability of these products could, therefore, be higher in the future. • 1) Annualised premium equivalent = regular premiums plus 1/10 of the single premiums • 2) Only biometric and cost-related variances Economic Capital 2005.05.27

26. European EV (EEV) Market-consistent EV (McEV) Life DFA Solvency II Using DFA Life to calculate EEV and McEVNew challenges demand a common stochastic platform Economic Capital 2005.05.27

27. Disclaimer Some of the statements contained herein are statements of future expectations and other forward-looking statements. These expectations are based on management's current views and assumptions and involve known and unknown risks and uncertainties. The user of such information should recognise that actual results, performance or events may differ materially from such expectations because they relate to future events and circumstances which are beyond our control including, among others, general economic and sector conditions. Neither AMB Generali Holding AG nor any of its affiliates, directors, officers, employees or agents have a duty of care towards any user of the information provided herein nor any obligation to update any forward-looking information contained in this document. Economic Capital 2005.05.27

28. Economic Capital calculations using a „Life DFA“ approach Balatonvilágos, 2005 május 27-én AMB Generali Holding AG László Hrabovszki Head of life actuarial department Email: laszlo.hrabovszki@amb.de