CAE Fall Meeting 2011 Accounting and Actuarial Analyis Putting things together Martin Birkenheier, FCAS, Aktuar DAV

Transcription

1 CAE Fall Meeting 2011 Accounting and Actuarial Analyis Putting things together Martin Birkenheier, FCAS, Aktuar DAV

2 Agenda Introduction Methodology / Theory Practical Application incl. Solvency 2 Summary and Outlook 2

3 Introduction 3

4 Introduction What is this talk going to be about? Published IFRS or Local GAAP accounting figures do not always reflect the true picture of the company Often distorted by conservative reserving or profit steering of the management I will show you our approach to reconcile the results of an annual reserve review with the booked financial statements and how we use them in the economic steering of our companies I will also show you the link to Solvency 2 and how this concept can be used for several requirements in Solvency 2 4

5 Introduction ERGO International Operating in over 30 countries ERGO in Europe ERGO in Asia Market position among TOP 5 in life or propertycasualty insurance Market presence ERGO International contributes 22 % of premium income (about 4.4 Bln. ) Non-Life about half of this with ¾ P&C Business and ¼ Legal Overall 30 companies (15 P&C and 15 Legal) with majority shareholding 5

6 Introduction How and why did we come up with this? Reserve Reviews and Profitability Analysis are two core responsibilities of our department Noticed implausible results Tried to come up with a way to monitor the profitability of a given company or line of business based on actuarial best estimates while reconciling these estimates with the accounting figures Over time originally actuarial exercise has received high attention with management and has been established in the regular reporting processes Idea turned out to be applicable to the Solvency 2 environment as well and is currently being implemented for this as well 6

7 Methodology / Theory 7

8 Methodology / Theory Some basics Insurance Accounting 101 Incurred Losses = Paid Losses + Change in Reserves Technical Result = Premium Incurred Losses Expenses Assumptions made Model (up to today) No discounting No MVM For this presentation (for the ease of simplicity) No split for Claims, ALAE, Salvage & Subrogation No split of Basic and Large Losses Net = Gross 8

9 Methodology / Theory Notations AY = Accident Year CY = Calendar Year PY = Prior Years Notations used throughout this presentation Variable Aggregate for all AY For single period Incurred Loss I i Paid Loss P p Reserve R r Ultimate U u Superscripts: B = Booked A = Actuarial Best Estimate E = Excess = Differences between booked and act. Best Estimate 9

10 Methodology / Theory Let s do some (easy) math 1/2 Development Period We know from before: i(k,n+1) = p(k,n+1) + Δr(k) = p(k,n+1) + r(k,n+1) r(k,n) Accident Period Expanding this by adding 0 (past claim payments): i(k,n+1) = p(k,n+1) + r(k,n+1) r(k,n) + (Σp(k) Σp(k)) Rearranging yields: i(k,n+1) = Σp(k) + p(k,n+1) + r(k,n+1) (Σp(k) + r(k,n)) = u(k,n+1) u(k,n) Adding across all AY: I(n+1) = U(n+1) U(n) = u(n+1,n+1) + ΔU Incurred Losses equal payments plus the change in reserves Adding and subtracting past claim payments does not change the value Grouping terms to move from payments and reserves to ultimates Incurred loss equals ultimate loss of most recent accident year plus the change in the ultimate for prior years 10

11 Methodology / Theory Let s do some (easy) math 2/2 Introducing: R B R A = R E Accounting (actual booked losses): i B (k,n+1) = p(k,n+1) + Δr B (k) = p(k,n+1) + r B (k,n+1) r B (k,n) = p(k,n+1) + r B (k,n+1) r B (k,n) + (Σp(k) Σp(k)) = (Σp(k) + p(k,n+1) + r B (k,n+1)) (Σp(k) + r B (k,n)) = (Σp(k) + p(k,n+1) + r A (k,n+1) + r E (k,n+1)) (Σp(k) + r A (k,n) + r E (k,n)) = (Σp(k) + p(k,n+1) + r A (k,n+1)) (Σp(k) + r A (k,n))+ (r E (k,n+1) r E (k,n)) = u A (k,n+1) u A (k,n) + Δ r E (k) In total we have again (compare to before): I B (n+1) = U B (n+1) U B (n) = U A (n+1) U A (n) + Δ R E = u A (n+1,n+1) + Δ A U + Δ R E 11

12 Methodology / Theory First Results Incurred Losses = Ultimate of Accident Year + Change in Ultimate for Prior Years + Change in Excess Reserve Technical Result = Premium Expenses - Incurred Loss = Premium Expenses - Ultimate of Accident Year - Change in Ultimate for Prior Years - Change in Excess Reserve => Now possible to split P&L into latest accident year and prior year effects 12

13 Methodology / Theory Graphical Representation Actuarial Estimates Accounting Data Analysis of Change in Ultimate will be expanded to Actual vs. Expected (Experience Variance & Assumption Change) 13

14 Practical Applications 14

15 Practical Applications Introduced concepts are part of steering process Actuarial Report (AR) Annual Report of Actuarial and Accounting Information to ERGO Headquarter Reconciled with audited Accounting Data to ensure consistency of data and applicability of results Reserve Analysis Derive Best Estimate Reserves/Ultimates by line of business using well established actuarial methods based on the AR reported data Use results to assess reserve strength of the company Profitability Analysis Translate results of the reserve analysis into P&L format Separately identify drivers of technical result to increase transparency and support business decisions 15

16 Practical Applications Retrospective Profitability Analysis 16

17 Practical Applications Excursion back to Reserve Reviews Reserve Analysis: Statement about Reserve Adequacy In our reserve reviews we usually state our opinion about the reserve adequacy including a quantification of the excess reserve (relationship of the booked to the best estimate reserve) We also compare the development of this reserve surplus from year to year Held Reserves Best Estimate Reserves Reserve Surplus 5 0 Change in Reserve Surplus -5 Change in Reserve Surplus as shown above equals the change in reserve surplus as shown in the graph before This way we have a link between a pure reserve analysis and the profitability analysis Current reserve surplus can be used for result steering of the company, reserve deficiency should be avoided 17

18 Practical Applications Challenging of Planning Assumptions 18

19 Practical Applications Relation to Solvency 2 Definitions of Premium and Reserve Risk Premium Risk: Negative deviation of ultimate losses for the accident year as estimated at the end of the year from the originally planned losses Reserve Risk: Negative deviation of ultimate estimated at the end of the year from ultimate estimated at the beginning of the year How does method shown relate to definitions above? Accident Year result closely linked to definition of premium risk as we project AY losses/profit as well as estimate ultimate after first development year (consistent to definition above). Difference between them corresponds to Premium Risk Change in Ultimate, i.e. Actuarial Runoff Result, from two consecutive reserve analyses corresponds to definition of Reserve Risk 19

20 Practical Applications Relation to Solvency 2 Backtesting Backtesting Internal Model Compare actual observations made to model in order to check model consistency and applicability First split for insurance risk between premium and reserve risk Example below shows Reserve Risk Table Year Change in BE Realization of Reserve Risk Quantile % % % 20

21 Summary and Outlook 21

22 Summary and Outlook Key Messages Comprehensive system to transform results of reserve analysis into P&L information Identify drivers of technical result and reconcile them to accounting figures Possibility to challenge planning assumptions and project corresponding reserve strength development Possible Model Developments Discounting Will be included to fit with S2 requirements AvE Actual vs. Expected Analysis to identify driver of change in Ultimate Experience Variance/Assumption Change for Variation Analysis MVM Include Market Value Margin to fit with S2 requirements Better Net Modelling Currently use of internal model to calculate recoveries 22

23 Thank you very much for your attention! 23