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The New NCCI Hazard Groups Greg Engl, PhD, FCAS, MAAA National Council on Compensation Insurance CASE Fall Meeting September 13, 2006. Agenda. History of previous work Methodology employed Impact of remapping. Current Hazard Groups. Assigning Classes to HGs. Prior NCCI Method

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    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