Post on 31-Dec-2015
CAS Spring MeetingCAS Spring Meeting
Commentary on the New Hazard Commentary on the New Hazard GroupsGroups
June 18, 2007June 18, 2007
Jose Couret
Orlando
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Outline
Motivation
Gauging the Improvement
Excess Loss Factors by Class
Conclusion
MotivationMotivation
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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.
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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
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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
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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
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Gauging the ImprovementRelative Frequency by Hazard Group and Injury Type
Note: Undeveloped, adjusted to Countrywide Level
HG Fatal:TT PT:TT Major:TT Minor:TT TT:TT MO:TT
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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Gauging the ImprovementRelative Frequency by Hazard Group and Injury Type
Note: Undeveloped, adjusted to Countrywide Level
Classes Formerly in Hazard Group III
HG Fatal:TT PT:TT Major:TT Minor:TT TT:TT MO:TT
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?
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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
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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
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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.
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(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
Gauging the ImprovementPerformance Testing with A Holdout Sample
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.
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Gauging the ImprovementPerformance Testing with A Holdout Sample
Permanent Total claims
New 7-HG predictions yield lowest sum of squared errors.
(1) (2) (3) (4) (5)
Holdout Prediction Prediction PredictionHazard Period Without Based On Based OnGroup Relativity HG Old 4-HG New 7-HG
A 0.50791 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
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Gauging the ImprovementPerformance Testing with A Holdout Sample
Major Permanent Partial Claims
New 7-HG predictions yield lowest sum of squared errors.
(1) (2) (3) (4) (5)
Holdout Prediction Prediction PredictionHazard Period Without Based On Based OnGroup Relativity HG Old 4-HG New 7-HG
A 0.48293 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
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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
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Excess Loss Factors by Class Sample State, $5m XS $5M
0
20
40A
0
20
40B
0
20
40C
0
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40D
0
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40E
0
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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
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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.
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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.
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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.
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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.
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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
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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
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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.