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

agenda
Agenda
  • History of previous work
  • Methodology employed
  • Impact of remapping
assigning classes to hgs
Assigning Classes to HGs
  • Prior NCCI Method
  • California Approach
  • ELF Based Method
prior ncci method
Prior NCCI Method
  • Hazardousness
  • “Excess loss potential”
hazardousness variables
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)
california methodology
California Methodology
  • Group classes with similar loss distributions together
  • Need to precisely define ‘similar’
hg remapping rationale
HG Remapping Rationale
  • What are HGs used for?
  • Determining ELFs
hg remapping approach
HG Remapping Approach
  • Makes sense to sort classes by ELF vectors
  • Class ELF vectors approximated by HG ELF vectors
  • ELF curves characterize loss distribution
hg remapping basic data
HG RemappingBasic Data
  • For each class code, , we have a vector of ELFs:
  • Credibility weight with current HG ELF vector
4 hazard group comparison percent of premium per hazard group
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%

percent of premium moved current mapping to new 4 hazard groups
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.

number of hazard groups calinski and harabasz

5

6

7

8

9

3310

3213

3442

3297

3102

Number of Hazard GroupsCalinski and Harabasz

Number of HGs

4

CH Statistic

2317

number of hazard groups cubic clustering criterion

5

6

7

8

9

110

108

112

111

125

Number of Hazard GroupsCubic Clustering Criterion

Number of HGs

4

CCC Statistic

89

number of hazard groups
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

three key ideas
Three Key Ideas
  • Map based on ELFs
  • Compute ELFs by class
  • Cluster Analysis
hg remapping objective
HG RemappingObjective

Break C = set of all class codes, into Hazard Groups:

hg remapping basic data1
HG RemappingBasic Data

For each class code, , we have a vector of ELFs:

using hazard groups
Using Hazard Groups
  • (HG mean)
  • approx by for
  • Want as close as possible to
hg remapping method k means
HG Remapping Methodk-means

Splits classes into HGs to minimize

optimal hgs
Optimal HGs
  • % of total variance explained
  • Analogous to an R-squared
  • k-means maximizes this
optimal hgs1
Optimal HGs
  • Want well separated, homogeneous HGs
  • Minimize within variance
  • Maximize between variance
optimal hgs2
Optimal HGs
  • Between variance vs. within variance
  • Have one variance for each variable (ELFs at different attachment points)
  • Need to consider variance-covariance matrices
optimal hgs3
Optimal HGs

Dispersion matrix of whole data set is given by

optimal hgs4
Optimal HGs

Dispersion matrix of HGi is given by

optimal hgs5
Optimal HGs
  • If we let
  • Then
optimal hgs6
Optimal HGs
  • Pooled within group dispersion matrix
  • Weighted between group dispersion matrix
optimal hgs7
Optimal HGs
  • Between variance vs. within variance
  • T = B + W
  • k-means minimizes trace W
credibility
Credibility
  • Compute class ELFs
  • Assign a credibility to each class
  • Use current HG as complement
history
History
  • Hazard Groups were last remapped in 1993
  • Prior to that, Hazard Groups were remapped in 1981
  • Same credibility method used both times
pseudo b hlmann
Pseudo-Bühlmann

where

n = number of claims

pseudo b hlmann1
Pseudo-Bühlmann
  • 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
revenue neutrality
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%.
impact of new hgs on elfs
Impact of New HGs on ELFs
  • ELFs computed by HG
  • New HGs alone change ELFs
  • Extra year of trend
  • Change in ELF Calculations
elf calculation changes
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
movement of classes2
Movement of Classes
  • General movement of classes to lower HGs
  • Classes with high ELFs moving to lower HGs
  • General increase in HGs ELFs
change in hg excess ratios
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
pt average cost per case hazard group 4

HG IV

$413,376

HG 4

$533,913

$ 214,619

$ 450,789

$ 573,275

PT Average Cost per CaseHazard Group 4
pt weight hazard group 4

HG 4

14.5%

HG IV

10.4%

4.1%

12.0%

15.7%

PT WeightHazard Group 4
largest class codes transitioning from ii to b
Largest Class Codes Transitioning From II to B

*Indicates premium 45.1% of 8810 premium.