1. Spencer M. Gluck, FCAS New York CAS Seminar on Reinsurance 2007 Hidden Risks in (Re)Insurance Systemic Risks and Accumulation: May 7, 2007

2. 1 Outline  Section 1: Systemic Risks and Accumulation A: Introduction - Model Structure B: Systemic Risks C: Accumulation  Section 2: Examples Impact of Systemic Risks and Accumulation

3. 2 Section 1 – Systemic Risks and Accumulation A: Introduction - Model Structure

4. 3 Introduction  A modeling framework that captures important risks that we may have been missing.  Important applications: –Impact of reinsurance, especially casualty –Cross-lines correlation and whole company models:  Capital adequacy and allocation  ERM

5. 4 Reasons for US P/C Insurer Impairments 1969-2005 *Includes overstatement of assets. Source: A.M. Best: P/C Impairments Hit Near-Term Lows Despite Surging Hurricane Activity, Special Report, Nov. 2005; 2003-20051969-2005

6. 5 Getting the Structure Right  Catastrophe models “understand” the risk that’s being modeled. –The most dangerous risks are those that act in a correlated way on accumulated exposure.  We require a model structure for other types of underwriting risk that reflect the impact of correlation and accumulation.

7. 6 Some Historical Casualty Killers  Runaway Trends –WC: 1970 through 1990 (California, Texas, etc.) –Med Mal: Late 1960’s through early 1980’s (e.g. NY) and then again in the 1990’s. –All casualty 1970’s through early 1980’s.  Extended Downcycles –E.g., early 1980’s, late 1990’s  Latent Losses –E.g. asbestos, environmental, construction defects For the risk model to be meaningful, these types of risk must be captured.

8. Section 1 – Systemic Risks and Accumulation B: Systemic Risks

9. 8 Systemic Risks Are Crucial  Systemic Risks: –Difficult to Measure –Affect all LOB’s -- but –Greatest Impact in Casualty  Systemic Risks Accumulate

10. 9 Elements of Systemic Risk  Time Related Risk –Trend and Development Parameters. –Changing Trends –Simultaneously impact new business and accumulated reserves.  Market Related Risk Also: Casualty catastrophes –But we’re not yet modeling these.

11. 10 Casualty Markets are More Volatile  Price is driven by the lowest estimated costs.  Long tails increase: –Risk of misestimated costs. –Positive cash flows. Therefore: Long tail casualty market cycles are the most severe.

12. 11 Components of Risk Other than diversifying process risk  Limitations of the sample  Uncertainty in other analysis parameters –Trend factors –Loss development factors –Payment patterns  Market Risks (pricing / underwriting) –Imperfect exposure data / on-level process –Actual prices achieved differ from targets –Risk quality changes (underwriting selection)  External Conditions –Changes in inflation –Changes in insurance loss trends / social inflation –Other economic conditions (line specific)  Differences in exposure between the data and the future period

13. 12 Summarized Elements of Systemic Risk  Time Related Risk (i.e. the tail) –Trend and Development Parameters. –Changing Trends –Simultaneously impact new business and accumulated reserves.  Market Related Risk (i.e. the cycle) Also: Casualty catastrophes

14. 13 The Risk Factor Model Model Structure (one LOB, one AY)  Nominal Incremental Paid for accident year i = AY i for a single simulation.  Each RV is sampled once per simulation.  RV’s are mutually independent AY i = A x B x C (F i -E) x D i E : Average date of payment in historical data F i : Average date of payment for period i

15. 14 Risk Factor Model Components: “Process+” Risk AY i = A x B x C (F i -E) x D i  Input Loss Distribution  Reflects both process risk and sample-size related parameter risk –The data “sample” in this case is usually claims at estimated ultimate values, trended to the appropriate prospective level. –Reflects risks that typically do not correlate across lines of business  Alternatively, A can be a placeholder for output from another model.

16. 15 Risk Factor Model Components: Accident Year Deviation AY i = A x B x C (F i -E) x D i  Structured as an independent random variable multiplied by the overall aggregate losses  Multiply B by expected frequency in a frequency/severity model.  Parametric distribution –Usually mean 1.0  May be considered to reflect: –Market risk (pricing / underwriting) –Non-diversifying frequency risk (contagion) –Differences between past and future exposures

17. 16 Risk Factor Model Components: Trend/Development Parameter Risk AY i = A x B x C (F i -E) x D  Structured as an annualized error  Annual error is compounded from the average date of payment in the experience data to each future payment –The period includes both the “development” and “trend” periods –The structure is appropriate for both trend parameter error and development parameter error  C ~ N(1,σ) or C ~ L-N(0,σ) are reasonable choices.  Compounded error factor for each payment is multiplied by the payment

18. 17 Trend and Development Parameter Risk Long-Tail LOB Short-Tail LOB Future Accident Year Historical Data Ultimate Development Trend

19. 18 Risk Factor Model Components: Future Trend Process Risk AY i = A x B x C (F i -E) x D i  The result of a time series model  The dynamic risk component -- reflects unpredictable changes in future trends / external conditions  Can also be considered as a reflection of specification error  Future trend deviation is modeled as a time series: –First order auto-regressive (AR(1)) –The simplest mean-reverting time series (reverts to mean of zero)

20. 19 Future Trend Process Risk The AR(1) Process  X i (i = 1, 2, …, n) are independent mean zero Normal random variables drawn from the same distribution.  Then define:  is the autocorrelation coefficient.  Annual trend error =  Cumulative trend error for year k = D k =

21. 20 Changing Trends Future Accident Year Historical Data Expected Future Trend

22. 21 Some Pictures from the ERM Book  The estimated trends may be wrong:  Plus the trends may change:

23. 22 Section 1 – Systemic Risks and Accumulation C: Accumulation Over Time

24. 23 Accumulated Risk  Trend and development risks accumulate over many years of underwriting.  Extended down cycles accumulate losses over several years of underwriting.  This appears as reserve risk.  Risk decisions you make now affect reserves for years to come.  The business you write this year absorbs capital for years to come.

25. 24 Drawing Capital for Years to Come Calendar YearExposure Drawing Capital 1The new AY (Premium) 2Reserves for one year old AY 3Reserves for two year old AY 4Reserves for three year old AY 5Reserves for four year old AY 6Reserves for five year old AY etc.

26. 25 “As-If” Reserves: An Approach to Accumulated Risk  Reserves “As If” the company had been writing the business consistently over time.  Equivalent to capital to be allocated in the future.  Can reflect the correlated risks on accumulated exposure.  Can measure the impact of reinsurance over time.

27. 26 Accumulation of Systemic Risks  Trend and development parameter risk is identical (100% correlated) between the new AY and the reserves.  Risk of changing trends is identical (100% correlated) between the new AY and the reserves.  The model for changing trend risk can also be a surrogate for latent losses and emerging exposures.  Market risk is partially correlated between successive AY’s.

28. 27 Section 2 - Examples Impact of Systemic Risk and Accumulation

29. 28 Effect of Systemic Risk Direct Private Passenger Auto PDF

30. 29 Effect of Systemic Risk Direct Private Passenger Auto CDF

31. 30 Effect of Systemic Risk Direct Workers Compensation PDF

32. 31 Effect of Systemic Risk Direct Workers Compensation CDF

33. 32 Effect of Systemic Risk Direct Casualty Multiline PDF

34. 33 Effect of Systemic Risk Direct Casualty Multiline CDF

35. 34 Effect of Systemic Risk Ceded Casualty PDF

36. 35 Effect of Systemic Risk Ceded Casualty CDF

37. 36 Effect of Systemic Risk Ceded Casualty 20 Accounts PDF

38. 37 Effect of Systemic Risk Ceded Casualty 20 Accounts CDF

39. 38 Effect of Systemic Risk and Accumulation Direct Private Passenger Auto PDF

40. 39 Effect of Systemic Risk and Accumulation Direct Private Passenger Auto CDF

41. 40 Effect of Systemic Risk and Accumulation Direct Workers Compensation PDF

42. 41 Effect of Systemic Risk and Accumulation Direct Workers Compensation CDF

43. 42 Effect of Systemic Risk and Accumulation Direct Casualty Multiline PDF

44. 43 Effect of Systemic Risk and Accumulation Direct Casualty Multiline CDF

45. 44 Effect of Systemic Risk and Accumulation Ceded Casualty PDF

46. 45 Effect of Systemic Risk and Accumulation Ceded Casualty CDF

47. 46 Effect of Systemic Risk and Accumulation Ceded Casualty 20 Accounts PDF

48. 47 Effect of Systemic Risk and Accumulation Ceded Casualty 20 Accounts CDF