Agenda

1. The New NCCI Hazard Groups Greg Engl, PhD, FCAS, MAAANational Council on Compensation InsuranceCASE Fall MeetingSeptember 13, 2006

2. Agenda • History of previous work • Methodology employed • Impact of remapping

3. Current Hazard Groups

4. Assigning Classes to HGs • Prior NCCI Method • California Approach • ELF Based Method

5. Prior NCCI Method • Hazardousness • “Excess loss potential”

6. Hazardousness Variables For each state, the following seven quantities were measured by class and expressed as ratios to the corresponding statewide value: • Claim Frequency • Indemnity Pure Premium • Indemnity Severity • Medical Pure Premium • Medical Severity • Total Pure Premium • Serious Severity (including Medical)

7. California Methodology • Group classes with similar loss distributions together • Need to precisely define ‘similar’

8. Crossover

9. 1 2 3 4 5 6 7 8 9 10 CrossoverCalifornia ELF Curves

10. CrossoverCalifornia ELF Curves

11. HG Remapping Rationale • What are HGs used for? • Determining ELFs

12. Kentucky 9/1/04 Filing

13. Kentucky ELPPFs

14. Kentucky ELPPFs

15. Kentucky ELPPFs

16. Kentucky ELPPFs

17. Kentucky ELPPFs

18. HG Remapping Approach • Makes sense to sort classes by ELF vectors • Class ELF vectors approximated by HG ELF vectors • ELF curves characterize loss distribution

19. Excess Ratio Calculations

20. HG RemappingBasic Data • For each class code, , we have a vector of ELFs: • Credibility weight with current HG ELF vector

21. Current Hazard Groups

22. Current Hazard Groups

23. New 4 Hazard Groups

24. New 4 Hazard Groups

25. 4 Hazard Group ComparisonNumber of Classes per Hazard Group

26. 4 Hazard Group ComparisonPercent of Premium Per Hazard Group New Mapping Current Mapping 2.5% 0.9% 5.1% 17.9% HG 1 HG 2 45.5% 39.2% HG 3 51.1% HG 4 37.8%

27. C A B D E F G 2 1 3 4 Hierarchical Collapsing of New Mapping

28. New Hazard Groups

29. New Hazard Groups

30. New Hazard Groups

31. Percent of Premium MovedCurrent Mapping to New 4 Hazard Groups 80% 586 70% 60% 50% Percent of Premium 40% 219 30% 20% 10% 51 3 1 0% No Up 1 HG Down 1 HG Up 2 HGs Down 2 Movement HGs Movement * Number above bar represents the number of classes in each category.

32. Movement of Classes

33. 5 6 7 8 9 3310 3213 3442 3297 3102 Number of Hazard GroupsCalinski and Harabasz Number of HGs 4 CH Statistic 2317

34. 5 6 7 8 9 110 108 112 111 125 Number of Hazard GroupsCubic Clustering Criterion Number of HGs 4 CCC Statistic 89

35. Number of Hazard Groups Calinski and Harabasz Number of HGs All Classes 50% Credibility Classes Full Credibility Classes 4 2317 793 433 5 3310 759 393 6 3213 705 450 3442 1025 638 7 8 3297 958 620 9 3102 915 584 Cubic Clustering Criterion Number of HGs All Classes 50% Credibility Classes Full Credibility Classes 4 89 51 37 5 110 50 34 6 108 48 36 59 42 7 112 8 111 57 41 125 9 56 40

36. Three Key Ideas • Map based on ELFs • Compute ELFs by class • Cluster Analysis

37. HG RemappingObjective Break C = set of all class codes, into Hazard Groups:

38. HG RemappingBasic Data For each class code, , we have a vector of ELFs:

39. Using Hazard Groups • (HG mean) • approx by for • Want as close as possible to

40. HG Remapping Methodk-means Splits classes into HGs to minimize

41. Optimal HGs • % of total variance explained • Analogous to an R-squared • k-means maximizes this

42. R-squared

43. Optimal HGs • Want well separated, homogeneous HGs • Minimize within variance • Maximize between variance

44. Optimal HGs • Between variance vs. within variance • Have one variance for each variable (ELFs at different attachment points) • Need to consider variance-covariance matrices

45. Optimal HGs Dispersion matrix of whole data set is given by

46. Dispersion Matrix

47. Optimal HGs Dispersion matrix of HGi is given by

48. Optimal HGs • If we let • Then

49. Optimal HGs • Pooled within group dispersion matrix • Weighted between group dispersion matrix

50. Optimal HGs • Between variance vs. within variance • T = B + W • k-means minimizes trace W