The New NCCI Hazard Groups

The New NCCI Hazard Groups Greg Engl, PhD, FCAS, MAAA National Council on Compensation Insurance CAS Reinsurance Seminar June, 2006 Workers Compensation Session

Agenda History of previous work Impact of remapping Methodology employed Copyright 2006 National Council on Compensation Insurance, Inc. All rights reserved. 2

Current Hazard Groups HG Number of Classes Standard Premium % of Total Premium I 38 1,262,958,374 0.86% II 428 67,150,463,296 45.58% III 318 75,288,994,325 51.10% IV 86 3,623,213,832 2.46% Total 870 147,325,629,827 100.00% Copyright 2006 National Council on Compensation Insurance, Inc. All rights reserved. 3

Assigning Classes to HGs Prior NCCI Method California Approach ELF Based Method Copyright 2006 National Council on Compensation Insurance, Inc. All rights reserved. 4

Prior NCCI Method Hazardousness Excess loss potential Copyright 2006 National Council on Compensation Insurance, Inc. All rights reserved. 5

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) Copyright 2006 National Council on Compensation Insurance, Inc. All rights reserved. 6

California Methodology Group classes with similar loss distributions together Need to precisely define similar Copyright 2006 National Council on Compensation Insurance, Inc. All rights reserved. 7

Crossover Ex ce ss Loss Fa ctors Loss Hazard Group Limit O P 25,000 0.643 0.660 600,000 0.098 0.082 Copyright 2006 National Council on Compensation Insurance, Inc. All rights reserved. 8

0.12 0.10 Crossover California ELF Curves J K L Loss Elimination Ratio 0.08 0.06 0.04 M N O P Q R 0.02 0.00 1 2 3 4 5 6 7 8 9 10 Per Accident Limit ($M) Copyright 2006 National Council on Compensation Insurance, Inc. All rights reserved. 9

0.100 Crossover California ELF Curves 0.095 Loss Elimination Ratio 0.090 0.085 0.080 0.075 J M R 0.070 0.065 0.060 $1,200,000 $1,400,000 $1,600,000 $1,800,000 $2,000,000 $2,200,000 Per Accident Limit Copyright 2006 National Council on Compensation Insurance, Inc. All rights reserved. 10

HG Remapping Rationale What are HGs used for? Determining ELFs Copyright 2006 National Council on Compensation Insurance, Inc. All rights reserved. 11

Kentucky 9/1/04 Filing Excess Loss Pure Premium Factors (Applicable to New and Renewal Policies) Per Accident Hazard Groups Limitation I II III IV $25,000 0.701 0.727 0.813 0.865 $30,000 0.675 0.703 0.794 0.850* $35,000 0.651 0.682 0.777 0.837 $40,000 0.630 0.662 0.761 0.824* $50,000 0.593 0.628 0.732 0.802* $75,000 0.521 0.561 0.674 0.754 $100,000 0.466 0.509 0.628 0.714* $125,000 0.422 0.466 0.589 0.680 $150,000 0.386 0.430 0.555 0.650 $175,000 0.355 0.399 0.525 0.623 $200,000 0.328 0.373 0.498 0.598 $250,000 0.285 0.329 0.452 0.555 $300,000 0.251 0.294 0.413 0.517 $500,000 0.167 0.205 0.308 0.406 $1,000,000 0.088 0.117 0.188 0.262 $2,000,000 0.045 0.064 0.108 0.155 $5,000,000 0.020 0.032 0.053 0.075 * Also applicable to Underground Coal Mine classifications. Copyright 2006 National Council on Compensation Insurance, Inc. All rights reserved. 12

1.0 Kentucky ELPPFs 0.9 0.8 0.7 HG I HG III HG II HG IV ELPPF 0.6 0.5 0.4 0.3 0.2 0.1 0.0 0 1 2 3 4 5 Loss Limit (millions) Copyright 2006 National Council on Compensation Insurance, Inc. All rights reserved. 13

1.0 Kentucky ELPPFs 0.9 0.8 0.7 HG I HG III HG II HG IV ELPPF 0.6 0.5 0.4 0.3 0.2 0.1 0.0 0 1 2 3 4 5 Loss Limit (millions) Copyright 2006 National Council on Compensation Insurance, Inc. All rights reserved. 14

1.0 Kentucky ELPPFs 0.9 0.8 0.7 HG I HG III HG II HG IV ELPPF 0.6 0.5 0.4 0.3 0.2 0.1 0.0 0 200 400 600 800 1000 Loss Limit (thousands) Copyright 2006 National Council on Compensation Insurance, Inc. All rights reserved. 15

1.0 Kentucky ELPPFs ELPPF 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 HG I HG III HG II HG IV 0.0 0 1 2 3 4 5 Loss Limit (millions) Copyright 2006 National Council on Compensation Insurance, Inc. All rights reserved. 16

0.20 0.18 0.16 0.14 Kentucky ELPPFs HG I HG III HG II HG IV ELPPF 0.12 0.10 0.08 0.06 0.04 0.02 0.00 1000 2000 3000 4000 5000 Loss Limit (thousands) Copyright 2006 National Council on Compensation Insurance, Inc. All rights reserved. 17

HG Remapping Approach Makes sense to sort classes by ELF vectors Class ELF vectors approximated by HG ELF vectors ELF curves characterize loss distribution Copyright 2006 National Council on Compensation Insurance, Inc. All rights reserved. 18

Excess Ratio Calculations R A) = w R ( A µ ) ( i i i R = excess ratio function for injury type i i w i = L L i i L = injury type i i losses µ = mean injury type i i loss Copyright 2006 National Council on Compensation Insurance, Inc. All rights reserved. 19

HG Remapping Basic Data For each class code,, we have a vector of ELFs: x c = c Credibility weight with current HG ELF vector c c ( x, x, K, x 25K 30K 5 c M ) Copyright 2006 National Council on Compensation Insurance, Inc. All rights reserved. 20

Current Hazard Groups 0.250 Excess Ratio at $1M 0.200 0.150 0.100 0.050 0.000 0.200 0.300 0.400 0.500 0.600 0.700 Excess Ratio at $100K Copyright 2006 National Council on Compensation Insurance, Inc. All rights reserved. 21

Current Hazard Groups 0.250 Excess Ratio at $1M 0.200 0.150 0.100 0.050 0.000 0.200 0.300 0.400 0.500 0.600 0.700 Excess Ratio at $100K Copyright 2006 National Council on Compensation Insurance, Inc. All rights reserved. 22

New 4 Hazard Groups Preliminary Mapping 0.250 Excess Ratio at $1M 0.200 0.150 0.100 0.050 0.000 0.200 0.300 0.400 0.500 0.600 0.700 Excess Ratio at $100K Copyright 2006 National Council on Compensation Insurance, Inc. All rights reserved. 23

0.250 New 4 Hazard Groups Preliminary Mapping Excess Ratio at $1M 0.200 0.150 0.100 0.050 0.000 0.200 0.300 0.400 0.500 0.600 0.700 Excess Ratio at $100K Copyright 2006 National Council on Compensation Insurance, Inc. All rights reserved. 24

4 Hazard Group Comparison Number of Classes per Hazard Group Current Mapping New Mapping* 86 38 88 296 HG1 318 428 281 HG2 HG3 HG4 205 * Preliminary Copyright 2006 National Council on Compensation Insurance, Inc. All rights reserved. 25

4 Hazard Group Comparison Percent of Premium Per Hazard Group Current Mapping New Mapping* 2.46% 0.86% 4.78% 26.70% HG1 51.10% 45.58% 37.13% HG2 HG3 HG4 31.39% * Preliminary Copyright 2006 National Council on Compensation Insurance, Inc. All rights reserved. 26

Hierarchical Collapsing of New Mapping A B C D E F G 1 2 3 4 Copyright 2006 National Council on Compensation Insurance, Inc. All rights reserved. 27

New Hazard Groups Preliminary Mapping Number of Classes per HG Percent of Premium per HG 88 55 4.78% 9.33% 57 241 18.69% 17.37% HG A HG B HG C HG D 224 45 160 18.44% 10.14% 21.25% HG E HG F HG G Copyright 2006 National Council on Compensation Insurance, Inc. All rights reserved. 28

New Hazard Groups Preliminary Mapping 0.250 Excess Ratio at $1M 0.200 0.150 0.100 0.050 0.000 0.200 0.300 0.400 0.500 0.600 0.700 Excess Ratio at $100K Copyright 2006 National Council on Compensation Insurance, Inc. All rights reserved. 29

New Hazard Groups Preliminary Mapping 0.250 0.200 Excess Ratio at $1M 0.150 0.100 0.050 0.000 0.200 0.300 0.400 0.500 0.600 0.700 Excess Ratio at $100K Copyright 2006 National Council on Compensation Insurance, Inc. All rights reserved. 30

Percent of Premium Moved Current Mapping to New 4 Hazard Groups (Based on Preliminary New Mapping) Percent of Premium 70% 60% 50% 40% 30% 20% 10% 0% 552 300 15 3 No Movement Up 1 HG Down 1 HG Down 2 HGs Movement * Number above bar represents the number of classes in each category. Copyright 2006 National Council on Compensation Insurance, Inc. All rights reserved. 31

Movement of Classes Based on Preliminary New Mapping Current Mapping Hazard Group I II III IV Total Number of Classes 38 428 318 86 870 % Premium 0.9% 45.6% 51.1% 2.5% 100% New Mapping Hazard Group 1 2 3 4 38 255 3 0 296 0.9% 25.4% 0.5% 0.0% 26.7% 0 164 41 0 205 0.0% 19.6% 11.8% 0.0% 31.4% 0 9 268 4 281 0.0% 0.6% 36.3% 0.2% 37.1% 0 0 6 82 88 0.0% 0.0% 2.6% 2.2% 4.8% Copyright 2006 National Council on Compensation Insurance, Inc. All rights reserved. 32

Number of Hazard Groups Calinski and Harabasz 3600 3200 CH Statistic 2800 2400 2000 4 5 6 7 8 9 Number of Hazard Groups Number of HGs 4 CH Statistic 2317 5 3310 6 3213 7 3442 8 3297 9 3102 Copyright 2006 National Council on Compensation Insurance, Inc. All rights reserved. 33

Number of Hazard Groups Cubic Clustering Criterion 125 CCC Statistic 115 105 95 85 4 5 6 7 8 9 Number of Hazard Groups Number of HGs 4 CCC Statistic 89 5 110 6 108 7 112 8 111 9 125 Copyright 2006 National Council on Compensation Insurance, Inc. All rights reserved. 34

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 7 3442 1025 638 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 7 112 59 42 8 111 57 41 9 125 56 40 Copyright 2006 National Council on Compensation Insurance, Inc. All rights reserved. 35

Three Key Ideas Map based on ELFs Compute ELFs by class Cluster Analysis Copyright 2006 National Council on Compensation Insurance, Inc. All rights reserved. 36

HG Remapping Objective Break C = set of all class codes, into Hazard Groups: C = U HG i i Copyright 2006 National Council on Compensation Insurance, Inc. All rights reserved. 37

HG Remapping Basic Data For each class code,, we have a vector of ELFs: c x c = c c ( x, x, K, x 25K 30K 5 c M ) Copyright 2006 National Council on Compensation Insurance, Inc. All rights reserved. 38

Using Hazard Groups x = (HG mean) i 1 HG i c HG i x c approx by for xc xc xi c HGi Want as close as possible to xi Copyright 2006 National Council on Compensation Insurance, Inc. All rights reserved. 39

HG Remapping Method k-means Splits classes into HGs to minimize k i= 1 c HG i x c x i 2 Copyright 2006 National Council on Compensation Insurance, Inc. All rights reserved. 40

Optimal HGs % of total variance explained Analogous to an R-squared k-means maximizes this Copyright 2006 National Council on Compensation Insurance, Inc. All rights reserved. 41

R-squared R 2 = 1 k i= 1 c HG c i x c x c x x 2 i 2 Copyright 2006 National Council on Compensation Insurance, Inc. All rights reserved. 42

Optimal HGs Want well separated, homogeneous HGs Minimize within variance Maximize between variance Copyright 2006 National Council on Compensation Insurance, Inc. All rights reserved. 43

Optimal HGs Between variance vs. within variance Have one variance for each variable (ELFs at different attachment points) Need to consider variance-covariance matrices Copyright 2006 National Council on Compensation Insurance, Inc. All rights reserved. 44

Optimal HGs Dispersion matrix of whole data set is given by T = c ( ) T x x ( x x) c c Copyright 2006 National Council on Compensation Insurance, Inc. All rights reserved. 45

Dispersion Matrix T = ( n σˆ σ ˆ 1) σˆ σˆ σˆ 11 21 31 41 51 σˆ σˆ σˆ σˆ σˆ 12 22 32 42 52 σˆ σˆ σˆ σˆ σˆ 13 23 33 43 53 σˆ σˆ σˆ σˆ σˆ 14 24 34 44 54 σˆ σˆ σˆ σˆ σˆ 15 25 35 45 55 Copyright 2006 National Council on Compensation Insurance, Inc. All rights reserved. 46

Optimal HGs Dispersion matrix of HG i is given by W i = c HG ( ) T x x ( x x ) i c i c i Copyright 2006 National Council on Compensation Insurance, Inc. All rights reserved. 47

Optimal HGs If we let B i = HG i ( x x) T ( x x) i i Then c HG ( x x) T ( x x) = B + W c c i i i Copyright 2006 National Council on Compensation Insurance, Inc. All rights reserved. 48

Optimal HGs Pooled within group dispersion matrix W = k i= 1 W i Weighted between group dispersion matrix B = k i= 1 B i Copyright 2006 National Council on Compensation Insurance, Inc. All rights reserved. 49

Optimal HGs Between variance vs. within variance T = B + W k-means minimizes trace W Copyright 2006 National Council on Compensation Insurance, Inc. All rights reserved. 50

Credibility Compute class ELFs Assign a credibility to each class Use current HG as complement Copyright 2006 National Council on Compensation Insurance, Inc. All rights reserved. 51

History Hazard Groups were last remapped in 1993 Prior to that, Hazard Groups were remapped in 1981 Same credibility method used both times Copyright 2006 National Council on Compensation Insurance, Inc. All rights reserved. 52

Pseudo-Bühlmann z n = min 1.5, 1 n + k where n = number of claims k = n Copyright 2006 National Council on Compensation Insurance, Inc. All rights reserved. 53

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 Copyright 2006 National Council on Compensation Insurance, Inc. All rights reserved. 54

Pseudo-Bühlmann Credibility 100% 80% % Credibility 60% 40% 20% 0% 0 87 174 261 348 435 522 609 696 783 870 Number of Class Codes (Ordered by Size) Copyright 2006 National Council on Compensation Insurance, Inc. All rights reserved. 55

Pseudo-Bühlmann Credibility Credibility Size Range Claims per Year Number of Classes % Premium 0% Z < 10% 0-237 355 1.2% 10% Z < 20% 238-511 89 1.3% 20% Z < 30% 512-831 61 1.6% 30% Z < 40% 832-1209 56 2.7% 40% Z < 50% 1210-1662 46 2.5% 50% Z < 60% 1663-2216 34 2.5% 60% Z < 70% 2217-2909 46 4.8% 70% Z < 80% 2910-3800 35 4.3% 80% Z < 90% 3801-4987 29 4.0% 90% Z < 100% 4988-6650 18 3.2% Z = 100% 6651 101 71.8% Total 870 100.0% Copyright 2006 National Council on Compensation Insurance, Inc. All rights reserved. 56

Number of Classes by Claim Count 800 833 Number of Classes in Interval 700 600 500 400 300 200 100 0 0 20 40 60 80 50 20 14 3 5 6 1 0 2 0 0 0 1 0 0 1 0 0 0 1 100 120 140 Number of Claims (thousands) 160 180 200 220 240 260 280 300 320 340 360 380 400 420 Copyright 2006 National Council on Compensation Insurance, Inc. All rights reserved. 57

Number of Classes by Claim Count 450 Number of Classes in Interval 400 350 300 250 200 150 100 50 0 2 3 4 5 6 0 1 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Number of Claims (thousands) Copyright 2006 National Council on Compensation Insurance, Inc. All rights reserved. 58

Number of Classes by Claim Count 200 150 100 50 Number of Classes in Interval 0 0 50 100 150 200 250 300 350 400 450 500 550 600 650 700 750 800 850 900 950 1000 Number of Claims Copyright 2006 National Council on Compensation Insurance, Inc. All rights reserved. 59