The New NCCI Hazard Groups Greg Engl, PhD, FCAS, MAAA National Council on Compensation Insurance CASE Fall Meeting

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 We have 4 HGs, but it feels more like 2. So how do classes get assigned to HGs?� (The numbers are based on five years of data. For most states, the first report of data began during 2001 and the fifth report began during 1997. There is slight variability from state to state in terms of these years, because the states run on slightly different cycles. For instance in one state the oldest policy year might be 7/1/97 to 6/30/98 but in another state it might be 1/1/98 to 12/31/98.) (Data source: J:\Data\250 AES\IR\RET\HG\Hazard Group Remapping\Cluster Analysis\Exhibits\Internal Review Meeting\062905 exhibits\hgexhibit_current)We have 4 HGs, but it feels more like 2. So how do classes get assigned to HGs?� (The numbers are based on five years of data. For most states, the first report of data began during 2001 and the fifth report began during 1997. There is slight variability from state to state in terms of these years, because the states run on slightly different cycles. For instance in one state the oldest policy year might be 7/1/97 to 6/30/98 but in another state it might be 1/1/98 to 12/31/98.) (Data source: J:\Data\250 AES\IR\RET\HG\Hazard Group Remapping\Cluster Analysis\Exhibits\Internal Review Meeting\062905 exhibits\hgexhibit_current)

4. Assigning Classes to HGs Prior NCCI Method California Approach ELF Based Method � let me count the ways.� let me count the ways.

5. Prior NCCI Method Hazardousness �Excess loss potential� Tyranny of terminology Quotes from R-1301: Classifications are distributed among the four Hazard Groups, which effectively categorize the relative extent to which workers are exposed to serious or catastrophic occupational injuries. Three tests were identified as being reasonably representative of excess loss potential and were performed on the data for each class. So how the heck do you measure �excess loss potential�?�Tyranny of terminology Quotes from R-1301: Classifications are distributed among the four Hazard Groups, which effectively categorize the relative extent to which workers are exposed to serious or catastrophic occupational injuries. Three tests were identified as being reasonably representative of excess loss potential and were performed on the data for each class. So how the heck do you measure �excess loss potential�?�

6. 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) Hazardousness Variables Use Principal Components analysis to get a hazardousness score. (All variables are for serious claims. Reduce to freq, indem sev, and tot PP before PC.) This was a good idea and worked pretty well. In CA�Use Principal Components analysis to get a hazardousness score. (All variables are for serious claims. Reduce to freq, indem sev, and tot PP before PC.) This was a good idea and worked pretty well. In CA�

7. California Methodology Group classes with similar loss distributions together Need to precisely define �similar� There was one little problem though�There was one little problem though�

8. Crossover �. Which we call crossover So which is bigger? To me this seems like a problem. The reason I call it crossover is because if you look at the graph� �. Which we call crossover So which is bigger? To me this seems like a problem. The reason I call it crossover is because if you look at the graph�

9. CrossoverCalifornia ELF Curves Zooming in on this a bit� Zooming in on this a bit�

10. CrossoverCalifornia ELF Curves Doesn�t this tell you that maybe you can�t tell the difference between these HGs? Or is there something intrinsic that�s being captured? So we stepped back � Doesn�t this tell you that maybe you can�t tell the difference between these HGs? Or is there something intrinsic that�s being captured? So we stepped back �

11. HG Remapping Rationale What are HGs used for? Determining ELFs What does anybody care about?What does anybody care about?

12. Each HG has a vector of ELFs. Graphically� Each HG has a vector of ELFs. Graphically�

13. Kentucky ELPPFs They are a little smooshed together down low so zooming in� They are a little smooshed together down low so zooming in�

14. Kentucky ELPPFs

15. Kentucky ELPPFs Close, but no crossover. And when you zoom in on the tail� Close, but no crossover. And when you zoom in on the tail�

16. Kentucky ELPPFs

17. Kentucky ELPPFs So I think crossover is bad. So I think crossover is bad.

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 This was our first big breakthrough idea. Ok, so how do you compute a class ELF vector?�This was our first big breakthrough idea. Ok, so how do you compute a class ELF vector?�

19. Excess Ratio Calculations My thumbnail sketch of the 91 Gillam paper �Retrospective Rating: Excess Loss Factors.� This was the 2nd big breakthrough idea.My thumbnail sketch of the 91 Gillam paper �Retrospective Rating: Excess Loss Factors.� This was the 2nd big breakthrough idea.

20. HG RemappingBasic Data For each class code, , we have a vector of ELFs: Credibility weight with current HG ELF vector And so you can graph these� (Used 100K, 250K, 500K, 1M, 5M) More on credibility later. And so you can graph these� (Used 100K, 250K, 500K, 1M, 5M) More on credibility later.

21. Current Hazard Groups (The animation tells the story here.) Note that this looks so weird because the hazard groups were not originally mapped using ELFs. (Based on latest 5 years of CRS data) (Data source: J:\Data\250 AES\IR\RET\HG\Hazard Group Remapping\Cluster Analysis\Exhibits\Internal Review Meeting\062905 exhibits\hgexhibit_current Looks like all 870 classes are included here.) (The animation tells the story here.) Note that this looks so weird because the hazard groups were not originally mapped using ELFs. (Based on latest 5 years of CRS data) (Data source: J:\Data\250 AES\IR\RET\HG\Hazard Group Remapping\Cluster Analysis\Exhibits\Internal Review Meeting\062905 exhibits\hgexhibit_current Looks like all 870 classes are included here.)

22. Current Hazard Groups (Same as previous slide, but without the animation and with the centroids.) But it seems like we should be able to do a little better than this�(Same as previous slide, but without the animation and with the centroids.) But it seems like we should be able to do a little better than this�

23. New 4 Hazard Groups �and indeed we can. But small classes and large classes get the same size dot��and indeed we can. But small classes and large classes get the same size dot�

24. New 4 Hazard Groups (On to distribution of number of classes and prem by cc.) Claims are total claims in the last 3 years. These are the biggest ones. The columns are: class code, number of claims, % prem, description 8810 405,410 4.48% CLERICAL OFFICE EMPLOYEES NOC 5645 98,912 2.24% CARPENTRY--DETACHED ONE OR TWO FAMILY DWELLINGS. 9082 332,925 2.05% RESTAURANT NOC 8742 132,295 2.03% SALESPERSONS, COLLECTORS OR MESSENGERS--OUTSIDE 8017 261,261 2.02% STORE: RETAIL NOC 7380 124,974 1.95% DRIVERS, CHAUFFEURS & THEIR HELPERS NOC--COMMERCIAL 8380 192,302 1.90% AUTOMOBILE SERVICE OR REPAIR CENTER & DRIVERS. 7229 1.86% TRUCKING�LONG DISTANCE HAULING�ALL EMPLOYEES AND DRIVERS 5190 110,376 1.79% ELECTRICAL WIRING--WITHIN BUILDINGS & DRIVERS. 5183 93,193 1.64% PLUMBING NOC & DRIVERS. 8829 188,140 CONVALESCENT OR NURSING HOME--ALL EMPLOYEES 8018 145,335 STORE: WHOLESALE NOC 9083 138,326 RESTAURANT: FAST FOOD 8033 136,965 STORE: MEAT, GROCERY AND PROVISION STORES COMBINED--RETAIL NOC 8868 135,133 COLLEGE: PROFESSIONAL EMPLOYEES & CLERICAL 3632 134,895 MACHINE SHOP NOC 8833 119,962 HOSPITAL: PROFESSIONAL EMPLOYEES 4484 108,536 PLASTICS MANUFACTURING: MOLDED PRODUCTS NOC. 9052 108,075 HOTEL: ALL OTHER EMPLOYEES & SALESPERSONS, DRIVERS 9101 101,968 COLLEGE: ALL OTHER EMPLOYEES 9015 96,354 BUILDINGS--OPERATION BY OWNER OR LESSEE OR REAL ESTATE MANAGEMENT FIRM: ALL OTHER EMPLOYEES. (On to distribution of number of classes and prem by cc.) Claims are total claims in the last 3 years. These are the biggest ones. The columns are: class code, number of claims, % prem, description 8810 405,410 4.48% CLERICAL OFFICE EMPLOYEES NOC 5645 98,912 2.24% CARPENTRY--DETACHED ONE OR TWO FAMILY DWELLINGS. 9082 332,925 2.05% RESTAURANT NOC 8742 132,295 2.03% SALESPERSONS, COLLECTORS OR MESSENGERS--OUTSIDE 8017 261,261 2.02% STORE: RETAIL NOC 7380 124,974 1.95% DRIVERS, CHAUFFEURS & THEIR HELPERS NOC--COMMERCIAL 8380 192,302 1.90% AUTOMOBILE SERVICE OR REPAIR CENTER & DRIVERS. 7229 1.86% TRUCKING�LONG DISTANCE HAULING�ALL EMPLOYEES AND DRIVERS 5190 110,376 1.79% ELECTRICAL WIRING--WITHIN BUILDINGS & DRIVERS. 5183 93,193 1.64% PLUMBING NOC & DRIVERS. 8829 188,140 CONVALESCENT OR NURSING HOME--ALL EMPLOYEES 8018 145,335 STORE: WHOLESALE NOC 9083 138,326 RESTAURANT: FAST FOOD 8033 136,965 STORE: MEAT, GROCERY AND PROVISION STORES COMBINED--RETAIL NOC 8868 135,133 COLLEGE: PROFESSIONAL EMPLOYEES & CLERICAL 3632 134,895 MACHINE SHOP NOC 8833 119,962 HOSPITAL: PROFESSIONAL EMPLOYEES 4484 108,536 PLASTICS MANUFACTURING: MOLDED PRODUCTS NOC. 9052 108,075 HOTEL: ALL OTHER EMPLOYEES & SALESPERSONS, DRIVERS 9101 101,968 COLLEGE: ALL OTHER EMPLOYEES 9015 96,354 BUILDINGS--OPERATION BY OWNER OR LESSEE OR REAL ESTATE MANAGEMENT FIRM: ALL OTHER EMPLOYEES.

25. 4 Hazard Group ComparisonNumber of Classes per Hazard Group

26. 4 Hazard Group Comparison Percent of Premium Per Hazard Group But the big news is that there won�t be just 4 new HGs �But the big news is that there won�t be just 4 new HGs �

27. Hierarchical Collapsing of New Mapping

28. New Hazard Groups Source: \\ncci\fileshare\Data\250 AES\IR\RET\HG\Hazard Group Remapping\filing\impact\Chart-Movement of Classes-Filing Version 2006-06-23.xls Sheet: PieCharts Source: \\ncci\fileshare\Data\250 AES\IR\RET\HG\Hazard Group Remapping\filing\impact\Chart-Movement of Classes-Filing Version 2006-06-23.xls Sheet: PieCharts

29. New Hazard Groups Nicely separatedNicely separated

30. New Hazard Groups

31. Percent of Premium MovedCurrent Mapping to New 4 Hazard Groups Total moved 274 moved down 2: 9063 YMCA, YWCA, YMHA, YWHA Institution�All Employees and Clerical moved up 2: 3639 Explosives or Ammunition Mfg.: Projectile or Shell Mfg. 4018 Refractory Products Mfg.�All Employees and Drivers (MO state special, like brick mfg, including clay digging and mining) 5505 Paving or Road Surfacing or Scraping NOC and Yards, Drivers (MO state special) (Source: \\ncci\fileshare\Data\250 AES\IR\RET\HG\Hazard Group Remapping\filing\impact\movers_exhibit_current_collapsed_860 classes.xls Sheet:Exhibit) Total moved 274 moved down 2: 9063 YMCA, YWCA, YMHA, YWHA Institution�All Employees and Clerical moved up 2: 3639 Explosives or Ammunition Mfg.: Projectile or Shell Mfg. 4018 Refractory Products Mfg.�All Employees and Drivers (MO state special, like brick mfg, including clay digging and mining) 5505 Paving or Road Surfacing or Scraping NOC and Yards, Drivers (MO state special) (Source: \\ncci\fileshare\Data\250 AES\IR\RET\HG\Hazard Group Remapping\filing\impact\movers_exhibit_current_collapsed_860 classes.xls Sheet:Exhibit)

32. Movement of Classes Ok so why 7 new HGs?� (This is after UW review. Source: J:\Data\250 AES\IR\RET\HG\Hazard Group Remapping\filing\impact\ELF\CW excess ratios by HG (wtd avg of states).v5.xls Sheet: Dist. Of Changes)Ok so why 7 new HGs?� (This is after UW review. Source: J:\Data\250 AES\IR\RET\HG\Hazard Group Remapping\filing\impact\ELF\CW excess ratios by HG (wtd avg of states).v5.xls Sheet: Dist. Of Changes)

33. Number of Hazard GroupsCalinski and Harabasz �An Examination of Procedures for Determining the Number of Clusters in a Data Set,� Glenn W. Milligan and Martha C. Cooper, Psychometrika, v50, no 2, June 1985, pg 159-179 �The Effect of Error on Determining the Number of Clusters,� Cooper & Milligan, published in Proceedings of the International Workshop on Data Analysis, Decision Support, and Expert Knowledge Representation in Marketing and Related Areas of Research, pg 319-328�An Examination of Procedures for Determining the Number of Clusters in a Data Set,� Glenn W. Milligan and Martha C. Cooper, Psychometrika, v50, no 2, June 1985, pg 159-179 �The Effect of Error on Determining the Number of Clusters,� Cooper & Milligan, published in Proceedings of the International Workshop on Data Analysis, Decision Support, and Expert Knowledge Representation in Marketing and Related Areas of Research, pg 319-328

34. Number of Hazard GroupsCubic Clustering Criterion Notice there is a local maximum at 7 HGs. When we view 9 HGs there is crossover.Notice there is a local maximum at 7 HGs. When we view 9 HGs there is crossover.

35. Number of Hazard Groups Don�t want tiny classes deciding how many HGs. That describes the new mapping, now I want to talk about the methodology�Don�t want tiny classes deciding how many HGs. That describes the new mapping, now I want to talk about the methodology�

36. Three Key Ideas Map based on ELFs Compute ELFs by class Cluster Analysis Cluster Analysis falls under predictive modeling, which is currently all the rage.Cluster Analysis falls under predictive modeling, which is currently all the rage.

37. HG RemappingObjective Break C = set of all class codes, into Hazard Groups: �in a way that is somehow optimal. And Cluster Analysis tells us how.�in a way that is somehow optimal. And Cluster Analysis tells us how.

38. HG RemappingBasic Data For each class code, , we have a vector of ELFs: (Used 100K, 250K, 500K, 1M, 5M)(Used 100K, 250K, 500K, 1M, 5M)

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 And it has some nice optimality properties �And it has some nice optimality properties �

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

42. R-squared denominator is total variation Numerator is residual variation (The R2 statistic for a given level of the hierarchy is R2 = 1 - [(Sum(WK))/T] for all N clusters (C1,C2,...,CN) where 1) WK = Sum(|| xJ - xK||2) for all elements xJ in Cluster CK (which has mean xK) and 2) T = Sum(|| xJ - x||2) for all observations xJ and population mean x.) Kirt: �We ran so many iterations, I can't give you one answer. Here are a few things I notice just by looking through some of the outputs: When we ran it using only one attachment point, we consistently got R squareds over 0.9. When we ran it with 2 attachment points (only a handful of times with 250K and 1M), we had slightly lower R squareds, around 0.7-0.8. As we increased the number of attachment points, the R squared produced by fastclus became meaningless since the variables were all correlated. It was all over the place (the lowest I saw was around 0.2.�) denominator is total variation Numerator is residual variation (The R2 statistic for a given level of the hierarchy is R2 = 1 - [(Sum(WK))/T] for all N clusters (C1,C2,...,CN) where 1) WK = Sum(|| xJ - xK||2) for all elements xJ in Cluster CK (which has mean xK) and 2) T = Sum(|| xJ - x||2) for all observations xJ and population mean x.) Kirt: �We ran so many iterations, I can't give you one answer. Here are a few things I notice just by looking through some of the outputs: When we ran it using only one attachment point, we consistently got R squareds over 0.9. When we ran it with 2 attachment points (only a handful of times with 250K and 1M), we had slightly lower R squareds, around 0.7-0.8. As we increased the number of attachment points, the R squared produced by fastclus became meaningless since the variables were all correlated. It was all over the place (the lowest I saw was around 0.2.�)

43. Optimal HGs Want well separated, homogeneous HGs Minimize within variance Maximize between variance So we have to define within and between variance�So we have to define within and 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 This is a matrix�This is a matrix�

46. Dispersion Matrix Trace gives sum of variances. (Def of covariance: x_j=(x_j1,x_j2,�,x_jp), j=1,2,�,n=no. of classes, Sigma hat_ik=(1/n-1)sum_j=1^n(x_ji-xbar_i)(x_jk-xbar_k))Trace gives sum of variances. (Def of covariance: x_j=(x_j1,x_j2,�,x_jp), j=1,2,�,n=no. of classes, Sigma hat_ik=(1/n-1)sum_j=1^n(x_ji-xbar_i)(x_jk-xbar_k))

47. Optimal HGs Dispersion matrix of HGi is given by This is like the within variance of the i-th HG.This is like the within variance of the i-th HG.

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 Who could ask for more than that! Have k-means write-up at hand. (On to credibility.)Who could ask for more than that! Have k-means write-up at hand. (On to credibility.)

51. Credibility Compute class ELFs Assign a credibility to each class Use current HG as complement

52. History Hazard Groups were last remapped in 1993 Prior to that, Hazard Groups were remapped in 1981 Same credibility method used both times So if it was good enough for Robin Gillam and Gary Venter, it�s good enough for me. Actually we looked at many alternatives and couldn�t find anything more compelling.So if it was good enough for Robin Gillam and Gary Venter, it�s good enough for me. Actually we looked at many alternatives and couldn�t find anything more compelling.

53. Pseudo-B�hlmann  where n = number of claims Actually this goes back as far as Longley-Cook�s 1962 paper. This has a few nice properties�Actually this goes back as far as Longley-Cook�s 1962 paper. This has a few nice properties�

54. Pseudo-B�hlmann A class with the average number of claims gets 75% credibility. Classes with twice the average number of claims get full credibility. Based on n/n+k Sensible, but no firm foundation. Sensible, but no firm foundation.

55. Pseudo-B�hlmann Credibility Class Codes are arranged by ascending claim count. Drilling down on this a bit� Class Codes are arranged by ascending claim count. Drilling down on this a bit�

56. Pseudo-B�hlmann Credibility (On to skewness of dist.)(On to skewness of dist.)

57. Number of Classes by Claim Count Claims are total claims in the last 3 years. These are the biggest ones. The columns are: class code � number of claims� description 8810 405,410 CLERICAL OFFICE EMPLOYEES NOC 9082 332,925 RESTAURANT NOC 8017 261,261 STORE: RETAIL NOC 8380 192,302 AUTOMOBILE SERVICE OR REPAIR CENTER & DRIVERS. 8829 188,140 CONVALESCENT OR NURSING HOME--ALL EMPLOYEES 8018 145,335 STORE: WHOLESALE NOC 9083 138,326 RESTAURANT: FAST FOOD 8033 136,965 STORE: MEAT, GROCERY AND PROVISION STORES COMBINED--RETAIL NOC 8868 135,133 COLLEGE: PROFESSIONAL EMPLOYEES & CLERICAL 3632 134,895 MACHINE SHOP NOC 8742 132,295 SALESPERSONS, COLLECTORS OR MESSENGERS--OUTSIDE 7380 124,974 DRIVERS, CHAUFFEURS & THEIR HELPERS NOC--COMMERCIAL 8833 119,962 HOSPITAL: PROFESSIONAL EMPLOYEES 5190 110,376 ELECTRICAL WIRING--WITHIN BUILDINGS & DRIVERS. 4484 108,536 PLASTICS MANUFACTURING: MOLDED PRODUCTS NOC. 9052 108,075 HOTEL: ALL OTHER EMPLOYEES & SALESPERSONS, DRIVERS 9101 101,968 COLLEGE: ALL OTHER EMPLOYEES 5645 98,912 CARPENTRY--DETACHED ONE OR TWO FAMILY DWELLINGS. 9015 96,354 BUILDINGS--OPERATION BY OWNER OR LESSEE OR REAL ESTATE MANAGEMENT FIRM: ALL OTHER EMPLOYEES. 5183 93,193 PLUMBING NOC & DRIVERS. Claims are total claims in the last 3 years. These are the biggest ones. The columns are: class code � number of claims� description 8810 405,410 CLERICAL OFFICE EMPLOYEES NOC 9082 332,925 RESTAURANT NOC 8017 261,261 STORE: RETAIL NOC 8380 192,302 AUTOMOBILE SERVICE OR REPAIR CENTER & DRIVERS. 8829 188,140 CONVALESCENT OR NURSING HOME--ALL EMPLOYEES 8018 145,335 STORE: WHOLESALE NOC 9083 138,326 RESTAURANT: FAST FOOD 8033 136,965 STORE: MEAT, GROCERY AND PROVISION STORES COMBINED--RETAIL NOC 8868 135,133 COLLEGE: PROFESSIONAL EMPLOYEES & CLERICAL 3632 134,895 MACHINE SHOP NOC 8742 132,295 SALESPERSONS, COLLECTORS OR MESSENGERS--OUTSIDE 7380 124,974 DRIVERS, CHAUFFEURS & THEIR HELPERS NOC--COMMERCIAL 8833 119,962 HOSPITAL: PROFESSIONAL EMPLOYEES 5190 110,376 ELECTRICAL WIRING--WITHIN BUILDINGS & DRIVERS. 4484 108,536 PLASTICS MANUFACTURING: MOLDED PRODUCTS NOC. 9052 108,075 HOTEL: ALL OTHER EMPLOYEES & SALESPERSONS, DRIVERS 9101 101,968 COLLEGE: ALL OTHER EMPLOYEES 5645 98,912 CARPENTRY--DETACHED ONE OR TWO FAMILY DWELLINGS. 9015 96,354 BUILDINGS--OPERATION BY OWNER OR LESSEE OR REAL ESTATE MANAGEMENT FIRM: ALL OTHER EMPLOYEES. 5183 93,193 PLUMBING NOC & DRIVERS.

58. Number of Classes by Claim Count Again, claims are for the last 3 years.Again, claims are for the last 3 years.

59. Number of Classes by Claim Count So I think someone should write the great American HG Credibility paper. (Again, claims are for the last 3 years.) So I think someone should write the great American HG Credibility paper. (Again, claims are for the last 3 years.)

60. Revenue Neutrality Overall average ELF�s unaffected, therefore no overall premium effect. Individual risks may experience increases or decreases. Individual risk equity improved. For deductibles of $5,000 or less, the impact of the revised credit on the loss cost premium of most risks will be less than 5%.

61. Impact of New HGs on ELFs ELFs computed by HG New HGs alone change ELFs Extra year of trend Change in ELF Calculations

62. ELF Calculation Changes Average with last year�s ELFs Loss limits adjusted for inflation Provides additional stability Additive differential trend adjustmentRecognizes that med loss trend higher than indemnity D5 was implemented last year. Additive adjustment will be implemented this year. see if you can work in the math class "Advanced Impossible" as a prerequisite to understanding the topicD5 was implemented last year. Additive adjustment will be implemented this year. see if you can work in the math class "Advanced Impossible" as a prerequisite to understanding the topic

63. Additive Adjustment to ELFs*all states, all HGs

64. Movement of Classes (This is after UW review. Source: J:\Data\250 AES\IR\RET\HG\Hazard Group Remapping\filing\impact\ELF\CW excess ratios by HG (wtd avg of states).v5.xls Sheet: Dist. Of Changes)(This is after UW review. Source: J:\Data\250 AES\IR\RET\HG\Hazard Group Remapping\filing\impact\ELF\CW excess ratios by HG (wtd avg of states).v5.xls Sheet: Dist. Of Changes)

65. Movement of Classes General movement of classes to lower HGs Classes with high ELFs moving to lower HGs General increase in HGs ELFs Simpson�s Paradox.Simpson�s Paradox.

66. Impact of Remapping on ELFs Old 4 vs new 4 This is at 100k and 1M. Looking at a couple of other limits� (Countrywide excess ratios are calculated as the loss weighted average over 29 states (excludes AL, AZ, DC, FL, GA, IA, ID, KY, MI, UT and WI). Source: J:\Data\250 AES\IR\RET\HG\Hazard Group Remapping\filing\impact\ELF\CW excess ratios by HG (wtd avg of states).v5.xls Sheet: Centroid Exhibit (IV - 4)) Old 4 vs new 4 This is at 100k and 1M. Looking at a couple of other limits� (Countrywide excess ratios are calculated as the loss weighted average over 29 states (excludes AL, AZ, DC, FL, GA, IA, ID, KY, MI, UT and WI). Source: J:\Data\250 AES\IR\RET\HG\Hazard Group Remapping\filing\impact\ELF\CW excess ratios by HG (wtd avg of states).v5.xls Sheet: Centroid Exhibit (IV - 4))

67. Impact of Remapping on ELFs Same general story. (Countrywide excess ratios are calculated as the loss weighted average over 29 states (excludes AL, AZ, DC, FL, GA, IA, ID, KY, MI, UT and WI). Source: J:\Data\250 AES\IR\RET\HG\Hazard Group Remapping\filing\impact\ELF\CW excess ratios by HG (wtd avg of states).v5.xls Sheet: Centroid Exhibit (IV - 4)) Same general story. (Countrywide excess ratios are calculated as the loss weighted average over 29 states (excludes AL, AZ, DC, FL, GA, IA, ID, KY, MI, UT and WI). Source: J:\Data\250 AES\IR\RET\HG\Hazard Group Remapping\filing\impact\ELF\CW excess ratios by HG (wtd avg of states).v5.xls Sheet: Centroid Exhibit (IV - 4))

68. Old and New Hazard Groups Old 4 vs new 7 Note big gap between II and III Note that II is not between C and D. (Countrywide excess ratios are calculated as the loss weighted average over 29 states (excludes AL, AZ, DC, FL, GA, IA, ID, KY, MI, UT and WI). Source: J:\Data\250 AES\IR\RET\HG\Hazard Group Remapping\filing\impact\ELF\CW excess ratios by HG (wtd avg of states).v5.xls Sheet: Centroid Exhibit (IV - 7)) Old 4 vs new 7 Note big gap between II and III Note that II is not between C and D. (Countrywide excess ratios are calculated as the loss weighted average over 29 states (excludes AL, AZ, DC, FL, GA, IA, ID, KY, MI, UT and WI). Source: J:\Data\250 AES\IR\RET\HG\Hazard Group Remapping\filing\impact\ELF\CW excess ratios by HG (wtd avg of states).v5.xls Sheet: Centroid Exhibit (IV - 7))

69. New Hazard Groups New 4 vs new 7. Note that 2 is between C and D. (Countrywide excess ratios are calculated as the loss weighted average over 29 states (excludes AL, AZ, DC, FL, GA, IA, ID, KY, MI, UT and WI). Source: J:\Data\250 AES\IR\RET\HG\Hazard Group Remapping\filing\impact\ELF\CW excess ratios by HG (wtd avg of states).v5.xls Sheet: Centroid Exhibit (IV - 7)) New 4 vs new 7. Note that 2 is between C and D. (Countrywide excess ratios are calculated as the loss weighted average over 29 states (excludes AL, AZ, DC, FL, GA, IA, ID, KY, MI, UT and WI). Source: J:\Data\250 AES\IR\RET\HG\Hazard Group Remapping\filing\impact\ELF\CW excess ratios by HG (wtd avg of states).v5.xls Sheet: Centroid Exhibit (IV - 7))

70. Impact of Remapping on ELFs Just reloading previous slide to set the frame of reference. This is CW. Looking at a couple of states� (Countrywide excess ratios are calculated as the loss weighted average over 29 states (excludes AL, AZ, DC, FL, GA, IA, ID, KY, MI, UT and WI). Source: J:\Data\250 AES\IR\RET\HG\Hazard Group Remapping\filing\impact\ELF\CW excess ratios by HG (wtd avg of states).v5.xls Sheet: Centroid Exhibit (IV - 4)) Just reloading previous slide to set the frame of reference. This is CW. Looking at a couple of states� (Countrywide excess ratios are calculated as the loss weighted average over 29 states (excludes AL, AZ, DC, FL, GA, IA, ID, KY, MI, UT and WI). Source: J:\Data\250 AES\IR\RET\HG\Hazard Group Remapping\filing\impact\ELF\CW excess ratios by HG (wtd avg of states).v5.xls Sheet: Centroid Exhibit (IV - 4))

71. Impact of Remapping in AL High ELFs (Source: J:\Data\250 AES\IR\RET\HG\Hazard Group Remapping\filing\impact\ELF\CW excess ratios by HG (wtd avg of states).v5.xls Sheet: Centroid Exhibit (IV - 4)) High ELFs (Source: J:\Data\250 AES\IR\RET\HG\Hazard Group Remapping\filing\impact\ELF\CW excess ratios by HG (wtd avg of states).v5.xls Sheet: Centroid Exhibit (IV - 4))

72. Impact of Remapping in IL Low ELFs (Source: J:\Data\250 AES\IR\RET\HG\Hazard Group Remapping\filing\impact\ELF\CW excess ratios by HG (wtd avg of states).v5.xls Sheet: Centroid Exhibit (IV - 4)) Low ELFs (Source: J:\Data\250 AES\IR\RET\HG\Hazard Group Remapping\filing\impact\ELF\CW excess ratios by HG (wtd avg of states).v5.xls Sheet: Centroid Exhibit (IV - 4))

73. Change in Excess RatiosHG I to HG 1 (Countrywide excess ratios are calculated as the loss weighted average over 29 states (excludes AL, AZ, DC, FL, GA, IA, ID, KY, MI, UT and WI). Source: J:\Data\250 AES\IR\RET\HG\Hazard Group Remapping\filing\impact\ELF\CW excess ratios by HG (wtd avg of states).v5.xls Sheet: Graphs -HG I-1 )(Countrywide excess ratios are calculated as the loss weighted average over 29 states (excludes AL, AZ, DC, FL, GA, IA, ID, KY, MI, UT and WI). Source: J:\Data\250 AES\IR\RET\HG\Hazard Group Remapping\filing\impact\ELF\CW excess ratios by HG (wtd avg of states).v5.xls Sheet: Graphs -HG I-1 )

74. Change in Excess RatiosHG I to HG 1 Line is (loss) weighted average. (Source: J:\Data\250 AES\IR\RET\HG\Hazard Group Remapping\filing\impact\ELF\CW excess ratios by HG (wtd avg of states).v5.xls Sheet: Graphs -HG I-1 ) Line is (loss) weighted average. (Source: J:\Data\250 AES\IR\RET\HG\Hazard Group Remapping\filing\impact\ELF\CW excess ratios by HG (wtd avg of states).v5.xls Sheet: Graphs -HG I-1 )

75. Change in Excess RatiosHG I to HG 1 (Source: J:\Data\250 AES\IR\RET\HG\Hazard Group Remapping\filing\impact\ELF\CW excess ratios by HG (wtd avg of states).v5.xls Sheet: Graphs -HG I-1) (Source: J:\Data\250 AES\IR\RET\HG\Hazard Group Remapping\filing\impact\ELF\CW excess ratios by HG (wtd avg of states).v5.xls Sheet: Graphs -HG I-1)

76. Change in Excess RatiosHG II to HG 2 A little smaller than I�at least at the high end. (Source: J:\Data\250 AES\IR\RET\HG\Hazard Group Remapping\filing\impact\ELF\CW excess ratios by HG (wtd avg of states).v5.xls Sheet: Graphs -HG II-2 ) A little smaller than I�at least at the high end. (Source: J:\Data\250 AES\IR\RET\HG\Hazard Group Remapping\filing\impact\ELF\CW excess ratios by HG (wtd avg of states).v5.xls Sheet: Graphs -HG II-2 )

77. Change in Excess RatiosHG II to HG 2 (Source: J:\Data\250 AES\IR\RET\HG\Hazard Group Remapping\filing\impact\ELF\CW excess ratios by HG (wtd avg of states).v5.xls Sheet: Graphs -HG II-2 ) (Source: J:\Data\250 AES\IR\RET\HG\Hazard Group Remapping\filing\impact\ELF\CW excess ratios by HG (wtd avg of states).v5.xls Sheet: Graphs -HG II-2 )

78. Change in Excess RatiosHG II to HG 2 (Source: J:\Data\250 AES\IR\RET\HG\Hazard Group Remapping\filing\impact\ELF\CW excess ratios by HG (wtd avg of states).v5.xls Sheet: Graphs -HG II-2 ) (Source: J:\Data\250 AES\IR\RET\HG\Hazard Group Remapping\filing\impact\ELF\CW excess ratios by HG (wtd avg of states).v5.xls Sheet: Graphs -HG II-2 )

79. Change in Excess RatiosHG III to HG 3 Very mild mannered. (Source: J:\Data\250 AES\IR\RET\HG\Hazard Group Remapping\filing\impact\ELF\CW excess ratios by HG (wtd avg of states).v5.xls Sheet: Graphs -HG III-3) Very mild mannered. (Source: J:\Data\250 AES\IR\RET\HG\Hazard Group Remapping\filing\impact\ELF\CW excess ratios by HG (wtd avg of states).v5.xls Sheet: Graphs -HG III-3)

80. Change in Excess RatiosHG III to HG 3 (Source: J:\Data\250 AES\IR\RET\HG\Hazard Group Remapping\filing\impact\ELF\CW excess ratios by HG (wtd avg of states).v5.xls Sheet: Graphs -HG III-3 ) (Source: J:\Data\250 AES\IR\RET\HG\Hazard Group Remapping\filing\impact\ELF\CW excess ratios by HG (wtd avg of states).v5.xls Sheet: Graphs -HG III-3 )

81. Change in Excess RatiosHG III to HG 3 (Source: J:\Data\250 AES\IR\RET\HG\Hazard Group Remapping\filing\impact\ELF\CW excess ratios by HG (wtd avg of states).v5.xls Sheet: Graphs -HG III-3 ) (Source: J:\Data\250 AES\IR\RET\HG\Hazard Group Remapping\filing\impact\ELF\CW excess ratios by HG (wtd avg of states).v5.xls Sheet: Graphs -HG III-3 )

82. Change in Excess RatiosHG IV to HG 4 Pretty big changes at high limits. (Source: J:\Data\250 AES\IR\RET\HG\Hazard Group Remapping\filing\impact\ELF\CW excess ratios by HG (wtd avg of states).v5.xls Sheet: Graphs -HG IV-4 ) Pretty big changes at high limits. (Source: J:\Data\250 AES\IR\RET\HG\Hazard Group Remapping\filing\impact\ELF\CW excess ratios by HG (wtd avg of states).v5.xls Sheet: Graphs -HG IV-4 )

83. Change in Excess RatiosHG IV to HG 4 Good deal of variation around average. Source: J:\Data\250 AES\IR\RET\HG\Hazard Group Remapping\filing\impact\ELF\CW excess ratios by HG (wtd avg of states).v5.xls Sheet: Graphs -HG IV-4 ) Good deal of variation around average. Source: J:\Data\250 AES\IR\RET\HG\Hazard Group Remapping\filing\impact\ELF\CW excess ratios by HG (wtd avg of states).v5.xls Sheet: Graphs -HG IV-4 )

84. Change in Excess RatiosHG IV to HG 4 Pretty big changes at the high limits�and this is just the impact of the remapping. (Source: J:\Data\250 AES\IR\RET\HG\Hazard Group Remapping\filing\impact\ELF\CW excess ratios by HG (wtd avg of states).v5.xls Sheet: Graphs -HG IV-4 ) Pretty big changes at the high limits�and this is just the impact of the remapping. (Source: J:\Data\250 AES\IR\RET\HG\Hazard Group Remapping\filing\impact\ELF\CW excess ratios by HG (wtd avg of states).v5.xls Sheet: Graphs -HG IV-4 )

85. Change in HG Excess Ratios Biggest increases at higher limits in HG I and IV Considerable variation by state Total change due to remapping, trend, and calculation changes �.now let�s drill down a little and see what�s going on with HG 4��.now let�s drill down a little and see what�s going on with HG 4�

86. Excess Ratio Calculations My thumbnail sketch of the 91 Gillam paper �Retrospective Rating: Excess Loss Factors.� Weights and ACCs determine ELFs So let�s look at the changes in weights and ACCs� My thumbnail sketch of the 91 Gillam paper �Retrospective Rating: Excess Loss Factors.� Weights and ACCs determine ELFs So let�s look at the changes in weights and ACCs�

87. % Change in Average Cost per Case

88. PT Average Cost per CaseHazard Group 4 (Not developed, trended, or on-leveled. I think it�s 1st-5th report, Casey said 3rd-5th. Source: \\boca2\crs\dfsroot\ProdData\INTRAAPPS\_Reference\ELFs for HG Remapping Filing\cw data\HG 4 ACC comparisons & inj wts - SUMMARY ONLY.xls)(Not developed, trended, or on-leveled. I think it�s 1st-5th report, Casey said 3rd-5th. Source: \\boca2\crs\dfsroot\ProdData\INTRAAPPS\_Reference\ELFs for HG Remapping Filing\cw data\HG 4 ACC comparisons & inj wts - SUMMARY ONLY.xls)

89. % Change in Injury Type Weights F is only up from .3 to .7.F is only up from .3 to .7.

90. PT WeightHazard Group 4 (Source: \\boca2\crs\dfsroot\ProdData\INTRAAPPS\_Reference\ELFs for HG Remapping Filing\cw data\HG 4 ACC comparisons & inj wts - SUMMARY ONLY.xls) (Source: \\boca2\crs\dfsroot\ProdData\INTRAAPPS\_Reference\ELFs for HG Remapping Filing\cw data\HG 4 ACC comparisons & inj wts - SUMMARY ONLY.xls)

91. Impact of Remapping vs. Trend, and ELF Calculation Changes

92. Change in Excess RatiosHG I to HG 1 (AL excluded because the med only curve was updated due to a large med only being reclassified.) (GA excluded because there was a law only filing so new data was used and not just trended forward a year like in the other states.) Source: J:\Data\250 AES\IR\RET\HG\Hazard Group Remapping\filing\impact\ELF\CW excess ratios by HG (wtd avg of states).v6.xls Sheet: All States (AL excluded because the med only curve was updated due to a large med only being reclassified.) (GA excluded because there was a law only filing so new data was used and not just trended forward a year like in the other states.) Source: J:\Data\250 AES\IR\RET\HG\Hazard Group Remapping\filing\impact\ELF\CW excess ratios by HG (wtd avg of states).v6.xls Sheet: All States

93. Change in Excess RatiosHG II to HG 2 (Source: J:\Data\250 AES\IR\RET\HG\Hazard Group Remapping\filing\impact\ELF\CW excess ratios by HG (wtd avg of states).v6.xls Sheet: All States) (Source: J:\Data\250 AES\IR\RET\HG\Hazard Group Remapping\filing\impact\ELF\CW excess ratios by HG (wtd avg of states).v6.xls Sheet: All States)

94. Change in Excess RatiosHG III to HG 3 Still pretty tame, but not nearly as tame as just the remapping. (Source: J:\Data\250 AES\IR\RET\HG\Hazard Group Remapping\filing\impact\ELF\CW excess ratios by HG (wtd avg of states).v6.xls Sheet: All States) Still pretty tame, but not nearly as tame as just the remapping. (Source: J:\Data\250 AES\IR\RET\HG\Hazard Group Remapping\filing\impact\ELF\CW excess ratios by HG (wtd avg of states).v6.xls Sheet: All States)

95. Change in Excess RatiosHG IV to HG 4 (Source: J:\Data\250 AES\IR\RET\HG\Hazard Group Remapping\filing\impact\ELF\CW excess ratios by HG (wtd avg of states).v6.xls Sheet: All States) (Source: J:\Data\250 AES\IR\RET\HG\Hazard Group Remapping\filing\impact\ELF\CW excess ratios by HG (wtd avg of states).v6.xls Sheet: All States)

96. Change in Excess RatiosHG I to HG 1 Remapping impact is actually not that big compared to the total. (Source: J:\Data\250 AES\IR\RET\HG\Hazard Group Remapping\filing\impact\ELF\CW excess ratios by HG (wtd avg of states).v6.xls Sheet: All States) Remapping impact is actually not that big compared to the total. (Source: J:\Data\250 AES\IR\RET\HG\Hazard Group Remapping\filing\impact\ELF\CW excess ratios by HG (wtd avg of states).v6.xls Sheet: All States)

97. Change in Excess RatiosHG II to HG 2 (Source: J:\Data\250 AES\IR\RET\HG\Hazard Group Remapping\filing\impact\ELF\CW excess ratios by HG (wtd avg of states).v6.xls Sheet: All States) (Source: J:\Data\250 AES\IR\RET\HG\Hazard Group Remapping\filing\impact\ELF\CW excess ratios by HG (wtd avg of states).v6.xls Sheet: All States)

98. Change in Excess RatiosHG III to HG 3 Again, this is the most mild mannered, but total impact still dwarfs remapping impact. (Source: J:\Data\250 AES\IR\RET\HG\Hazard Group Remapping\filing\impact\ELF\CW excess ratios by HG (wtd avg of states).v6.xls Sheet: All States) Again, this is the most mild mannered, but total impact still dwarfs remapping impact. (Source: J:\Data\250 AES\IR\RET\HG\Hazard Group Remapping\filing\impact\ELF\CW excess ratios by HG (wtd avg of states).v6.xls Sheet: All States)

99. Change in Excess RatiosHG IV to HG 4 Now the gap actually narrows a bit. (Source: J:\Data\250 AES\IR\RET\HG\Hazard Group Remapping\filing\impact\ELF\CW excess ratios by HG (wtd avg of states).v6.xls Sheet: All States) Now the gap actually narrows a bit. (Source: J:\Data\250 AES\IR\RET\HG\Hazard Group Remapping\filing\impact\ELF\CW excess ratios by HG (wtd avg of states).v6.xls Sheet: All States)

100. Key Transitions Moral: need to look at where the action is, i.e. the main transitions. (Source: J:\Data\250 AES\IR\RET\HG\Hazard Group Remapping\filing\impact\ELF\CW excess ratios by HG (wtd avg of states).v5.xls Sheet: Dist. Of Changes) Moral: need to look at where the action is, i.e. the main transitions. (Source: J:\Data\250 AES\IR\RET\HG\Hazard Group Remapping\filing\impact\ELF\CW excess ratios by HG (wtd avg of states).v5.xls Sheet: Dist. Of Changes)

101. Largest Class Codes Transitioning From II to B

102. Largest Class Codes Transitioning From II to C

103. Change in HG II Excess Ratios (Source: J:\Data\250 AES\IR\RET\HG\Hazard Group Remapping\filing\impact\ELF\CW excess ratios by HG (wtd avg of states).v5.xls Sheet: Graphs -HG II-B & C) (Source: J:\Data\250 AES\IR\RET\HG\Hazard Group Remapping\filing\impact\ELF\CW excess ratios by HG (wtd avg of states).v5.xls Sheet: Graphs -HG II-B & C)

104. Change in HG II Excess Ratios (Source: J:\Data\250 AES\IR\RET\HG\Hazard Group Remapping\filing\impact\ELF\CW excess ratios by HG (wtd avg of states).v5.xls Sheet: Graphs -HG II-B & C) (Source: J:\Data\250 AES\IR\RET\HG\Hazard Group Remapping\filing\impact\ELF\CW excess ratios by HG (wtd avg of states).v5.xls Sheet: Graphs -HG II-B & C)

105. Change in HG II Excess Ratios (Source: J:\Data\250 AES\IR\RET\HG\Hazard Group Remapping\filing\impact\ELF\CW excess ratios by HG (wtd avg of states).v5.xls Sheet: Graphs -HG II-B & C) (Source: J:\Data\250 AES\IR\RET\HG\Hazard Group Remapping\filing\impact\ELF\CW excess ratios by HG (wtd avg of states).v5.xls Sheet: Graphs -HG II-B & C)

106. Change in HG II Excess Ratios (Source: J:\Data\250 AES\IR\RET\HG\Hazard Group Remapping\filing\impact\ELF\CW excess ratios by HG (wtd avg of states).v5.xls Sheet: Graphs -HG II-B & C) (Source: J:\Data\250 AES\IR\RET\HG\Hazard Group Remapping\filing\impact\ELF\CW excess ratios by HG (wtd avg of states).v5.xls Sheet: Graphs -HG II-B & C)

107. Change in HG III Excess Ratios (Source: J:\Data\250 AES\IR\RET\HG\Hazard Group Remapping\filing\impact\ELF\CW excess ratios by HG (wtd avg of states).v5.xls Sheet: Graphs -HG III-E & F) (Source: J:\Data\250 AES\IR\RET\HG\Hazard Group Remapping\filing\impact\ELF\CW excess ratios by HG (wtd avg of states).v5.xls Sheet: Graphs -HG III-E & F)

108. Change in HG III Excess Ratios (Source: J:\Data\250 AES\IR\RET\HG\Hazard Group Remapping\filing\impact\ELF\CW excess ratios by HG (wtd avg of states).v5.xls Sheet: Graphs -HG III-E & F) (Source: J:\Data\250 AES\IR\RET\HG\Hazard Group Remapping\filing\impact\ELF\CW excess ratios by HG (wtd avg of states).v5.xls Sheet: Graphs -HG III-E & F)

109. Change in HG III Excess Ratios (Source: J:\Data\250 AES\IR\RET\HG\Hazard Group Remapping\filing\impact\ELF\CW excess ratios by HG (wtd avg of states).v5.xls Sheet: Graphs -HG III-E & F) (Source: J:\Data\250 AES\IR\RET\HG\Hazard Group Remapping\filing\impact\ELF\CW excess ratios by HG (wtd avg of states).v5.xls Sheet: Graphs -HG III-E & F)

110. Change in HG III Excess Ratios (Source: J:\Data\250 AES\IR\RET\HG\Hazard Group Remapping\filing\impact\ELF\CW excess ratios by HG (wtd avg of states).v5.xls Sheet: Graphs -HG III-E & F) (Source: J:\Data\250 AES\IR\RET\HG\Hazard Group Remapping\filing\impact\ELF\CW excess ratios by HG (wtd avg of states).v5.xls Sheet: Graphs -HG III-E & F)

111. Largest Class Codes Transitioning From III to E

112. Largest Class Codes Transitioning From III to F