cas spring meeting commentary on the new hazard groups june 18, 2007 jose couret orlando

CAS Spring MeetingCAS Spring Meeting

Commentary on the New Hazard Commentary on the New Hazard GroupsGroups

June 18, 2007June 18, 2007

Jose Couret

Orlando

2

Outline

Motivation

Gauging the Improvement

Excess Loss Factors by Class

Conclusion

MotivationMotivation

4

Motivation Development of New Hazard Groups

Old Hazard Group Mapping– Until recently, hundreds of class codes were condensed into 4

hazard groups--of which hazard groups II and III contained 95% of the exposure.

New Hazard Group Mapping– The number of hazard groups has increased to seven (from four)

under NCCI’s B-1403 filing. – The new hazard groups are a significant improvement.

5

Motivation An ELF is a Weighted Average of the ELFs by Injury Type

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

$0 $100,000 $200,000 $300,000 $400,000 $500,000 $600,000 $700,000 $800,000 $900,000 $1,000,000 $1,100,000 $1,200,000 $1,300,000 $1,400,000 $1,500,000

Fatal PT Major Minor TT

Gauging the ImprovementGauging the Improvement

7

Gauging the ImprovementDiscussion

A key element of the excess percentage is the frequency of loss by injury type. Fatalities and permanent disabilities cost more than other injury types; so when they have high relative frequency, more of the claims cost arises from large losses.

Relative Frequency = claim count for the injury type divided by the claim count for temporary total.

Relative frequency for the more serious injury types should increase as one moves from a lower hazard group to a higher hazard group.– Fatal – Permanent Total– Major Permanent Partial

8

Gauging the ImprovementRelative Frequency by Hazard Group and Injury Type

HG Fatal:TT PT:TT Major:TT Minor:TT TT:TT MO:TT

A 0.001 0.002 0.052 0.350 1.000 5.663 B 0.002 0.004 0.083 0.392 1.000 5.641 C 0.003 0.005 0.099 0.395 1.000 5.050 D 0.004 0.005 0.118 0.387 1.000 4.590 E 0.005 0.006 0.151 0.371 1.000 3.983 F 0.007 0.009 0.198 0.344 1.000 2.970 G 0.013 0.016 0.249 0.394 1.000 2.992

All 0.004 0.006 0.122 0.380 1.000 4.615

Note: Undeveloped, adjusted to Countrywide Level

9




A 0.001 0.002 0.049 0.342 1.000 5.750 B 0.002 0.004 0.084 0.397 1.000 5.704 C 0.003 0.004 0.096 0.393 1.000 5.032 D 0.003 0.005 0.112 0.438 1.000 5.239 E 0.003 0.004 0.091 0.297 1.000 3.866 F 0.006 0.007 0.119 0.397 1.000 3.728 G - - - - - -

All 0.002 0.004 0.089 0.391 1.000 5.285

Classes Formerly in Hazard Group II

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Classes Formerly in Hazard Group III


A - - - - - - B 0.002 0.003 0.062 0.268 1.000 5.371 C 0.004 0.005 0.123 0.407 1.000 5.153 D 0.004 0.005 0.122 0.346 1.000 4.076 E 0.006 0.007 0.158 0.380 1.000 3.998 F 0.007 0.009 0.198 0.340 1.000 2.936 G 0.011 0.013 0.227 0.396 1.000 2.625

All 0.006 0.007 0.164 0.364 1.000 3.730

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0

40

80A

0

40

80B

0

40

80C

0

40

80D

0

40

80E

0

40

80F

0 0. 01725613 0. 03451226 0. 05176838 0. 06902451 0. 08628064 0. 10353677

0

40

80G

Fat al : TT

hg7

Gauging the ImprovementFatal Frequencies– Within and Between Hazard Groups

Hazard Group means are very different.

Is the variation within hazard groups significant?

12

0

40

80A

0

40

80B

0

40

80C

0

40

80D

0

40

80E

0

40

80F

0 0. 00810585 0. 01621169 0. 02431754 0. 03242339 0. 04052923 0. 04863508 0. 05674093

0

40

80G

PT: TT

hg7

Gauging the ImprovementPT Frequencies– Within and Between Hazard Groups

13

0

15

30A

0

1530B

0

15

30C

0

15

30D

0

15

30E

0

15

30F

0. 014 0. 054 0. 094 0. 134 0. 174 0. 214 0. 254 0. 294 0. 334 0. 374 0. 414 0. 454 0. 494 0. 534

0

15

30G

Maj or : TT

hg7

Gauging the ImprovementMajor Frequencies– Within and Between Hazard Groups

14

Gauging the ImprovementPerformance Testing with A Holdout Sample

For each injury type, calculated relative frequency for the even reports (2, 4, 6) and used these to predict the odd reports (3, 5, 7). Discarded greenest year of data (first report).

Estimates are expressed as relativities to the all-class relative frequencies.

Three methods used to predict holdout period outcome:

1. No hazard group method

2. Old 4-hazard group method

3. New 7-hazard group method

Note: statistical procedure used to eliminate state differentials.

15

(1) (2) (3) (4) (5)

Holdout Prediction Prediction PredictionHazard Period Without Based On Based OnGroup Relativity HG Old 4-HG New 7-HG

A 0.43643 1.00000 0.61064 0.39589 B 0.48555 1.00000 0.63025 0.49673 C 0.68370 1.00000 0.73183 0.71623 D 1.05510 1.00000 1.09209 0.91244 E 1.30104 1.00000 1.35524 1.33699 F 1.85093 1.00000 1.47003 1.83257 G 2.95338 1.00000 2.39305 3.16405

Mean 1.00000 1.00000 1.00000 1.00000 SSE 5.31575 0.51697 0.06919


Fatal Claims

Approx7x greater

Hold-out period relativities we are trying to predict.

New 7-HG predictions yield lowest sum of squared errors.

Clearly, predictions based on new 7-HG averages from even years more closely track holdout period results.

16


Permanent Total claims


(1) (2) (3) (4) (5)


A 0.50791 1.00000 0.77136 0.50791 B 0.78888 1.00000 0.79082 0.74260 C 0.82907 1.00000 0.85531 0.85528 D 0.92482 1.00000 1.04844 0.90114 E 1.05933 1.00000 1.18931 1.15000 F 1.59147 1.00000 1.25555 1.56268 G 2.46731 1.00000 1.85357 2.24219

Mean 1.00000 1.00000 1.00000 1.00000 SSE 2.82796 0.59179 0.06312

17


Major Permanent Partial Claims


(1) (2) (3) (4) (5)


A 0.48293 1.00000 0.75709 0.45373 B 0.73543 1.00000 0.76893 0.74128 C 0.85706 1.00000 0.83503 0.83793 D 0.95867 1.00000 1.07328 0.97761 E 1.20489 1.00000 1.24724 1.21946 F 1.56231 1.00000 1.30813 1.56371 G 1.77769 1.00000 1.58653 1.81744

Mean 1.00000 1.00000 1.00000 1.00000 SSE 1.32248 0.19285 0.00341

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Gauging the ImprovementComments

Testing suggests that the new hazard groups are superior to the old.

There is great value in having seven sets of benchmark excess loss factors that do not “cross over”.

New hazard groups are still sufficiently heterogeneous for a correlated credibility approach to add value. Even then, the hazard group estimate can serve as the complement of credibility.

May be impractical for bureaus to support ELFs by class. Individual insurers can derive their own credits and debits to adjust hazard group ELFs to class level.

Excess Loss Factors by Class Excess Loss Factors by Class

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0. 25 0. 5 0. 75 1 1. 25 1. 5 1. 75 2 2. 25 2. 5 2. 75 3 3. 25 3. 5 3. 75 4 4. 25

0

10

20

30

40

50

Percent

PT Rel at i vi t y ( Cr edi bi l i t y Adj us t ed, Bef or e Caps )

Excess Loss Factors by ClassRelative Permanent Total (PT) Frequency by Class Code

21

Excess Loss Factors by Class Sample State, $4m XS $1M

0

20

40A

0

20

40B

0

20

40C

0

20

40D

0

20

40E

0

20

40F

0. 02775 0. 03675 0. 04575 0. 05475 0. 06375 0. 07275 0. 08175 0. 09075 0. 09975 0. 10875

0

20

40G

Layer Loss Cos t ( %)

Hazard

Group

22

Excess Loss Factors by Class Sample State, $5m XS $5M

0

20

40A

0

20

40B

0

20

40C

0

20

40D

0

20

40E

0

20

40F

0. 001875 0. 003625 0. 005375 0. 007125 0. 008875 0. 010625 0. 012375 0. 014125 0. 015875 0. 017625

0

20

40G

Layer Loss Cos t ( %)

Hazard

Group

23

Excess Loss Factors by ClassCredibility Procedure Yields Modest Reduction in Sum of Squared Errors

Sum of Squared Prediction Errors by Injury Type

(1) (2) (3) (4)Prediction Prediction Prediction

Injury Based on Based on Based onType HG Raw Even Cred. Proc.Fatal 43.6 65.2 43.5 PT 34.7 83.6 34.6

Major PP 1,425.0 2,201.7 1,405.6 Minor PP 6,756.9 10,360.3 6,558.0 Med. Only 417,260.8 434,837.9 351,270.8

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Excess Loss Factors by ClassQuintiles Test

Utilizing a variation on NCCI’s “Quintiles Test” to measure model performance– Approach used to test Experience Rating Plan

Hazard grouping approximation works best when all classes in a Hazard Group– have the same relative frequency of injuries– same composition of loss by injury type

Our goal: determine if by-class approach improves prediction of injury type relative frequency.

25

Excess Loss Factors by Class Quintiles Test Methodology

Discard greenest year of data (first report)

For each injury type, calculated relative frequency relativities (to the hazard group average) from the even reports (2, 4, 6).– Used these to predict the odd reports (3, 5, 7)

Classes within a HG are sorted by credibility-weighted relativity and aggregated into five groups of roughly equal size. – Groupings were created so that the number of TT claim counts in

each quintile is roughly equal.– The lowest 20% of the class relativities belong to the risks in the first

quintile, the next 20% to the second quintile, etc.

26

Excess Loss Factors by Class Observations

(1) (2) (3) (4) (5)

Quintile Odd RelativityPrediction Based

on HGPrediction Based

on Raw Even

Prediction Based on Cred.

Procedure1 0.4951 1.0000 0.3065 0.56482 0.8634 1.0000 0.4260 0.87323 0.9861 1.0000 0.7513 1.00004 1.1269 1.0000 1.3473 1.10385 1.5215 1.0000 2.1547 1.4519

Mean 1.0000 1.0000 1.0000 1.0000SSE 0.5618 0.7315 0.0105

Hazard Group D, Permanent Total Claims

Upwardly sloping relativities are desirable; indicate the credibility procedure tended to identify class difference in relative PT frequency.

Column (2), what we are trying to predict, represents the average relative frequency for the classes in the quintile divided by the corresponding estimate for all of HG D. For example, the relative frequency of PT claims (as a ratio to TT) for the classes within the first quintile was about half of the HG average.

27

Excess Loss Factors by Class Observations (continued)

Goal is to predict the Column (2) frequency relativity for each quintile. Column (3) is a prediction based on the HG average. All entries equal to unity – by assumption every quintile has the HG D relative frequency for PT claims.

The predictions in Column (4) are based on raw class relativities observed for the even years. For example, the classes in the fifth quintile had an even-year relative PT frequency that was 215% of the HG average.

The Column (5) predictions were derived using the multi-dimensional credibility procedure.

Again, the quintiles are ranked by credibility weighted class relativity, not raw relativity.

28

Excess Loss Factors by Class Observations (continued)

(1) (2) (3) (4) (5)

Quintile Odd RelativityPrediction

Based on HGPrediction Based

on Raw Even

Prediction Based on Cred.

Procedure1 0.4951 1.0000 0.3065 0.56482 0.8634 1.0000 0.4260 0.87323 0.9861 1.0000 0.7513 1.00004 1.1269 1.0000 1.3473 1.10385 1.5215 1.0000 2.1547 1.4519

Mean 1.0000 1.0000 1.0000 1.0000SSE 0.5618 0.7315 0.0105

Hazard Group D, Permanent Total Claims

Approx3x greater

Actual Odd year relativities we are trying to predict. Classes

in highest quintile 3x more likely to have a PT claim

Flat relativities significantly underestimate PT frequency for classes in higher quintiles and overestimate lower quintiles

Prediction based on Even years gives too

much credibility to historical experience

There is significant variability of PT frequency within Hazard Group D

29

Excess Loss Factors by Class Sum of Squared Prediction Errors by Hazard Group and Injury Type

Prediction Prediction PredictionInjury Based on Based on Based on

HG Type HG Raw Even Cred. Proc.A Fatal 0.13227 0.94431 0.18952 B Fatal 0.32630 1.79940 0.05637 C Fatal 0.83604 1.39413 0.03376 D Fatal 0.97498 0.87260 0.12111 E Fatal 0.49691 1.44023 0.05096 F Fatal 0.39060 1.35362 0.07280 G Fatal 0.55650 1.23015 0.06035

A PT 0.03941 1.94151 0.57993 B PT 0.38273 1.34145 0.11044 C PT 0.56175 0.55609 0.01180 D PT 0.56183 0.73151 0.01053 E PT 0.73195 0.82350 0.07050 F PT 0.56872 0.53817 0.01812 G PT 1.09139 0.52326 0.07946

A Major 0.58481 0.01988 0.05079 B Major 0.33888 0.03729 0.00870 C Major 0.38001 0.04108 0.00738 D Major 0.18900 0.03928 0.01850 E Major 0.28775 0.07476 0.01030 F Major 0.32418 0.04703 0.01781 G Major 0.58518 0.14046 0.00538

Thinking in R2 terms, the class relativities could be said to "explain" 98% of the "between quintiles” variance for PT/HG D. This is not actually a regression, but the statistic is still impressive by real-life actuarial standards. The use of class relativities dramatically improves the class frequency by injury type estimation.

Supports severity differentials by hazard group for permanent

partial losses.

ConclusionConclusion

31

Conclusion

The new hazard groups are superior to the old.

There is great value in having excess loss factors that do not “cross over”.

A correlated credibility approach can be used to calculate indicated credits/debits to the hazard group ELFs. The actual credit/debit must incorporate underwriting judgment.

cas spring meeting commentary on the new hazard groups june 18, 2007 jose couret orlando

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