FCR Recalibration . Presentation to Industry

1. FCR Recalibration .Presentation to Industry Emile Stipp Deloitte Actuarial & Insurance Solutions & Insight ABC 11 August 2005

2. OVERVIEW • PART I: • Broad aims • Conceptual framework • Overview of methodology and data • PART II: • Results • Further discussion points • The way forward Presentation to Industry

3. PART I Presentation to Industry

4. Broad aims • To construct a formula, on the basis of data from Star Returns, and Dynamic Financial Analysis, which would be an appropriate basis for a solvency requirement, for those companies that choose not to use an approved Internal Model • In accordance with work performed by the FSB and the Financial Condition Reporting Sub-Committee of ASSA’s STIC • Taking into account international developments on short-term insurance solvency requirements • The formula should be prudent • And will be a function of capital charges determined to cover: • Insurance risk • Investment risk • Catastrophe risk • Operational risk • Other elements of risk, e.g. underwriting cycle would be explicitly or implicitly included in formula Presentation to Industry

5. Conceptual framework • Progression from industry calibration, to certified model, to internal model: Increasing complexity Industry calibration Certified model Internal model Increasing appropriateness for individual company Increasing cost Increasing usefulness in risk management Presentation to Industry

6. Conceptual framework • Progression from industry calibration, to certified model, to internal model: Industry calibration Certified model Internal model Necessarily approximate Must be prudent for all companies Hence is prudent overall More precise for liabilities But involves judgement And hence requires professional certification Maximum precision for liabilities and assets Also requires professional certification Leads to greatest understanding of risks Provided models are transparent and realistic Presentation to Industry

7. Conceptual framework • All of the above as opposed to current model, which: • Contains heroic approximations • Other than by chance, gives no indication of real risks faced by a company • Prudent for some, and imprudent for others • Its only advantage is that it is simple • The intention is that industry calibrated model would be easy to apply in practice • Although there may be complex maths operating in the background • The industry calibration should walk a tightrope between: • High complexity due to a desire to allow for all possibilities and the individual circumstances of each company; versus • Over-simplification due to a desire to make the formula easy to apply in practice Presentation to Industry

8. Overview of methodology • We first set up programmes that analyse desired aspects of the data contained in STAR returns, dating back to 1990, taking into account changes in layout in 1999 • We identified: duplicate, blank and corrupted files, inconsistent financial year-ends, inconsistencies or changes in company names or structures & made appropriate adjustments • The following were extracted from the data (among other items): • Claims payment run-offs • Outstanding claims reserves • IBNR reserves • Earned premiums • Expenses and commission • We analysed claims run-off using the Bornhuetter-Ferguson (BHF) method • And estimated Ultimate Loss Ratios emerging for each accident year for each company Presentation to Industry

9. Data: ultimate loss ratios before cleansing Presentation to Industry

10. Data: ultimate loss ratios after cleansing Presentation to Industry

11. Data: expenses vs gross written premium Presentation to Industry

12. Data: total asset distribution Presentation to Industry

13. Data: distribution of assets backing liabilities Presentation to Industry

14. Data: distribution of shareholders’ funds Presentation to Industry

15. Data: reinsurance in different classes Presentation to Industry

16. Overview of methodology • Insurance liabilities are: • Outstanding claims liabilities: OCR + IBNR (i.e. claims incurred prior to valuation date – reported and not reported) plus • Premiums liabilities: maximum of UPR and URR (i.e. reserves in respect of future claim payments arising from future events insured under existing policies, assessed on a prospective basis) • Prescribed method will allow for central estimate and prescribed margin on top of that • I.e. insurer would hold capital in respect of insurance risks at least equal to: • Best estimate of liabilities plus additional prescribed margin (75% sufficient) • And Minimum Capital Requirement (MCR) in addition to this to ensure that the company overall has sufficient capital at the 99.5% level • Either using prescribed method (no actuary and with actuary) OR internal model • Taking into account size of insurer • And classes of business written Presentation to Industry

17. Overview of methodology: 99.5% level of capital sufficiency • What does holding sufficient capital at the 99.5% level mean? • We quantify the level of capital an Insurer requires to be protected against adverse results 99.5% of the time • This is equivalent to the worst potential loss a company would face in 200 years of existence Presentation to Industry

18. Overview of methodology • Final FCR industry formulation is function of Insurance Risk Capital Charge and Investment Risk Capital Charge • Comments on Catastrophe Risk Charge and Operational Risk Charge later • We first discuss derivation of Insurance Risk Capital Charge… • Conceptual model: Distribution of ULRs Distribution of claims run-off vs reserves Stochastic model generating simulations of ultimate losses and reserving uncertainty for insurers of different sizes and with different size reserves DFA Engine Presentation to Industry

19. Overview of methodology • Conceptual model continued: Stochastic model generating simulations of ultimate losses and reserving uncertainty for insurers of different sizes and with different size reserves DFA Engine Result: distribution of profits and losses Choose 99.5th percentile (i.e. largest loss arising in one year over 200 simulated exposure years) Company-specific adjustments: Reinsurance (proportional and non-proportional) To give net capital required Express 99.5th percentile as a function of GWP and GUPR This function gives gross capital required, including expenses and commission Presentation to Industry

20. Overview of methodology • The DFA engine gives a formula for determining capital at 99.5% sufficiency (and at 99% and 95% - see later) • This formula is expressed as a function of GUPR and GWP • Where GUPR = Gross Unearned Premium Reserve and • GWP = Gross Written Premium (expected over next year) • We chose GWP and GUPR as these numbers are readily verifiable (rather than IBNR and OCR) • By making GWP an estimate for the following year, we also take into account some measure of the company’s growth or decline • But there will be rules issued in respect of such estimation • This formula is complex, and will not necessarily be the final recommended one. However, it gives us a basis for analysis of the appropriate insurance risk capital charge, and companies would not necessarily have to apply formula Presentation to Industry

21. Analysis: Accident: claims development pattern Presentation to Industry

22. Analysis: Accident: Scatter-plot of ULR versus Earned Premium Presentation to Industry

23. Analysis: Accident: Mean Curve relative to Earned Premium Presentation to Industry

24. Analysis: Accident: Standard Deviation relative to Earned Premium Presentation to Industry

25. Analysis: Accident: fitted mean & std deviation curves Presentation to Industry

26. Analysis: Motor: distribution of ULRs Presentation to Industry

27. Analysis: Motor: fitted mean & std deviation curves Presentation to Industry

28. Analysis • Similar analysis was done for all classes of business (ULR as function of EP). In addition to Accident and Motor, also: • Engineering • Guarantee • Liability • Miscellaneous (split) • Miscellaneous (consolidated) • Property • Transport • Now look at reserving uncertainty • For each of above classes, consider ratio of OCR and IBNR to subsequent claim payments and reserves, for different reserve sizes Presentation to Industry

29. Analysis: Motor: Reserving uncertainty: Distribution Presentation to Industry

30. Analysis: Motor: Reserving uncertainty: Scatterplot versus Reserve size Presentation to Industry

31. Analysis: Motor: Reserving uncertainty: Standard Deviation relative to Reserve size Presentation to Industry

32. Analysis: Motor: DFA Model • On the basis of the above, we are in a position to fit Dynamic Financial Analysis, or stochastic, model • E.g. we run 5000 simulations per notional company size of underwriting result given EP and Reserving Ratios given reserve sizes, and parameterise the formula of the format • This allows us to derive, for each class of business, a stand alone gross insurance capital charge, as a function of GWP and GUPR… Presentation to Industry

33. Analysis: Motor: Stand-alone Capital Required: 99.5% level Presentation to Industry

34. Analysis: Motor: Stand-alone Capital Required: 99.5% level Presentation to Industry

35. Analysis: Accident: Stand-alone Capital Required: 99.5% level Presentation to Industry

36. Analysis: Engineering: Stand-alone Capital Required: 99.5% level Presentation to Industry

37. Analysis: Guarantee: Stand-alone Capital Required: 99.5% level Presentation to Industry

38. Analysis: Liability: Stand-alone Capital Required: 99.5% level Presentation to Industry

39. Analysis: Miscellaneous: Stand-alone Capital Required: 99.5% level Presentation to Industry

40. Analysis: Property: Stand-alone Capital Required: 99.5% level Presentation to Industry

41. Analysis: Transport: Stand-alone Capital Required: 99.5% level Presentation to Industry

42. Analysis: insurance risk capital charge • Having fitted this formula for each class of business, we now need to establish how to allow for multiple classes of business • We do this by analysing correlations of ULRs between different classes of business • Noting positive correlation (increasing capital requirement) • And negative correlation (decreasing capital requirement for diversification) • We tested a Generalised Linear Model approach, but did not have sufficient data points in the GLM formulation for statistical significance • Rather set up a methodology with an underlying correlation matrix Presentation to Industry

43. Analysis: insurance risk capital charge • Concentration and diversification factor best explained by examples: • Example 1: equal size motor and property… Presentation to Industry

44. Analysis: insurance risk capital charge • Concentration and diversification factor best explained by examples: • Example 2: three classes of business… Presentation to Industry

45. Analysis: insurance risk capital charge • What about underwriting cycle? There is evidence that it exists if we consider average loss ratios across industry Presentation to Industry

46. Analysis: insurance risk capital charge • We have done some analysis by fitting formulae to express underwriting cycle, using: • Adjustment for average loss ratios • ARIMA models • This improved the fit of ULR distributions significantly, and reduced the variability in the data set • BUT gives a false sense of security in our opinion, since: • It does not help us to derive an underwriting cycle “factor” • As we cannot state with any certainty, based on historical data analysis, where we are in the underwriting cycle at the point of the valuation! • Our preferred approach therefore is to specify a formula which applies throughout the underwriting cycle • And takes into account full spectrum of variability over the underwriting cycle • Hence we did not remove effect of underwriting cycle from data before fitting distributions Presentation to Industry

47. Analysis: insurance risk capital charge • Some allowance required for reinsurance • For proportional, make simple allowance by showing all numbers net of reinsurance • BUT also need to take into account credit risk of reinsurer • Do so on asset side: where reinsurance recoverables shown as assets, take into account credit rating of reinsurer when valuing assets – more details on this to follow • For non-proportional, allowance is difficult, as data not yet available, and difficult to quantify the appropriate level of allowance even with data • This would have to be done on an approximate basis at this point • We have just shown figures net of non-proportional on argument that premium approximately equal to value of reinsurance • In certified and internal models, more accurate allowance can be made • And reduction in exposure to catastrophic risks can also be built in Presentation to Industry

48. Analysis: operational risk capital charge • Some debate internationally about appropriate allowance • Some models make no allowance, the argument being: • If you know about operational risk, the solution is not to hold additional capital • Failure due to operational risk often independent of level of capital held beforehand • Remedies should be sought given the circumstances relating to operational risk, e.g. administrative, fraud, mismanagement etc • If an insurer knows enough about fraud or mismanagement risk to quantify it, the solution to such operational risks would lie in addressing the issues, not in holding additional capital • However, we built in appropriate and simple allowance for expenses & commission, based on analysis of historical ratios • As this is important where business growing or declining, for instance • Note that insurance risk capital charge under our DFA model already makes some allowance for growth / decline Presentation to Industry

49. Analysis: investment risk capital charge • We based our analysis on The Smith Model (TSM), calibrated for South Africa • Using similar methods to investment risk capital charge derivation in Life industry • With important difference that there is typically no significant direct link between assets and liabilities over a one-year period • In other words, we can look at assets separately • Group allowable assets under Act (Schedule 1) into broad categories, e.g. bonds, equities, property, cash etc • Allocate assets to liabilities, prescribed margin and MCR (excl investment risk capital charge) • Allocation of assets in increasing order of capital variability, in accordance with TSM • To the extent that assets backing liabilities and MCR subject to stochastic variability, determine additional assets required to protect against a drop in asset values of to-be-specified percentage • Also taking into account effect of drop in such additional assets held • This would be investment risk capital charge • Our model offsets investment returns on assets backing MCR and prescribed margin against capital requirement Presentation to Industry

50. Investment Capital RequirementMethod Overview • Investigate volatility of Asset Values using: • The Smith Model • 10 000 simulations (independent economic scenarios) • Calculate capital requirement to meet solvency with required probability • Solvency defined as: • Assets > Liabilities + MCR over one year time horizon Presentation to Industry