Workers CompensationExcess of Loss Pricing

CAS Reinsurance Pricing Seminar

Moshe D. Goldberg, FCAS

July 29, 2005

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Workers Compensation

Workers Compensation characteristics that cause it to differ from other lines of business

– Extremely long tail

– Annuity-type benefits

– Benefits defined by statute, not by courts

- Indemnity and Medical benefits

- Benefits, to some degree, vary by state

– No policy limits

- Essentially unlimited medical coverage!!

– True No-Fault system (Or is it?)Moshe D. Goldberg, FCASCAS Reinsurance PricingJuly 29, 2005

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WC’s Long Tail

Discounting of case reserves prevalent

– Explicit (lifetime pension cases)

– Implicit (by not inflating projected future payments)

Mortality assumptions used in setting reserves

Effect of unwinding of discount can be quite large on an excess layer

Claims often develop adversely quite late

– Family stops taking care of claimant

– Back injuries “creep” into the layer

Moshe D. Goldberg, FCASCAS Reinsurance PricingJuly 29, 2005

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Example of Impact on Reinsurer

An injured worker is expected to live 10 years.

Weekly indemnity benefits are 500/wk = 26,000/yr

Initial stabilizing medical expenses are 150,000

Annual medical expenses are 50,000/yr

Initial case reserve = 150k+(26k+50k)*10 = 910k

One would expect the loss to the 1Mx1M reinsurer to be zero.

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Implicit Discount Effect

Suppose that instead of the ongoing medical expenses being 50k/yr, they are really inflating at 6% per annum.

The primary company still books the ongoing medical loss at 500k, implicitly discounting them at 6%/yr.

Total undiscounted ongoing medical expenses are really 659k = 50k*(1.0610-1)/.06, instead of the booked 500k

The total undiscounted loss is 1,069k, and the 1Mx1M reinsurer will see 69k of development

Imagine if the time horizon was longer!

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Mortality Assumption Effect

Back to the original example (no growth in medical costs), however, instead of a certain 10 year survival, there was a 50% probability of this worker living only 5 years and 50% of living 15 years.

Losses paid if the claimant lives 5 years = 530k = 150k+(26k+50k)*5

Losses paid if the claimant lives 15 years =1,290k = 150k+(26k+50k)*15

With 50% probability, the 1Mx1M reinsurer will see 290k development

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Example of “Tail” Development for 1Mx1M layer

Acc Month of DevelopmentYear 120 132 144 156 168 180

1990 15,796 17,221 19,079 20,478 22,987 23,7111991 12,107 13,775 15,060 16,996 18,5741992 8,445 9,296 10,139 11,6041993 8,626 10,760 10,9211994 6,533 6,9381995 10,482

AccYear 120 - 132 132 - 144 144 - 156 156 - 168 168 - 180

1990 1.090 1.108 1.073 1.123 1.031 1991 1.138 1.093 1.129 1.093 1992 1.101 1.091 1.144 1993 1.247 1.015 1994 1.062

120 - 132 132 - 144 144 - 156 156 - 168 168 - 180

Wtd Avg 1.126 1.081 1.108 1.109 1.031

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WC Exposure Rating

Moshe D. Goldberg, FCASCAS Reinsurance PricingJuly 29, 2005

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Exposure Rating

Conceptually, exposure rating WC is no different than other lines

– Compute overall expected losses

– Allocate these losses to the layer being priced by a size-of-loss curve.

Practically, WC exposure rating is very different than other lines

– Overall expected loss computation is relatively similar

– However, the allocation to layer is handled vey differently.

Moshe D. Goldberg, FCASCAS Reinsurance PricingJuly 29, 2005

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Exposure Rating

For lines with policy limits, like GL, the rating bureaus publish ILFs, which are based on size-of-loss curves

But WC doesn’t have policy limits. So NOW what do we do?

Retrospective Rating’s Excess Loss Factors (ELFs) to the rescue!

Moshe D. Goldberg, FCASCAS Reinsurance PricingJuly 29, 2005

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Terminology of WC Size-of-loss curves

“Injury Type” : Description of the seriousness of a WC injury

“Average Cost per Case” : Average severity

“Entry Ratio” : Ratio of a number to the ACPC

“Hazard Group” : Set of classes with similar severity distributions. Currently there are four HGs, but the NCCI is looking at adding more.

“Excess Loss Factor” : Ratio of expected losses in excess of an entry ratio to the overall losses

Moshe D. Goldberg, FCASCAS Reinsurance PricingJuly 29, 2005

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Injury Types

Lost-Time Claim Injury Types

– Fatal

– Permanent Total (PT)

– Major Permanent Partial (PP)

– Minor Permanent Partial

– Temporary Total (TT)

Non-Lost-Time Injury Type

– Medical OnlyMoshe D. Goldberg, FCASCAS Reinsurance PricingJuly 29, 2005

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Average Cost per Case

These are the average severities by:

– State

– Hazard Group

– Injury Type

They are used in computing entry ratios.

Moshe D. Goldberg, FCASCAS Reinsurance PricingJuly 29, 2005

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Excess Loss Factors (ELFs)

ELF(x) = 1 – [LEV(x)/E(X)]

= 1 – Loss Elimination Ratio at x

The “x” is an entry ratio, so E(X) is, by definition, unity.

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Entry Ratio/ELF Example

Injury Type

ACPC Entry Ratio @ 1M

ELF(1M) Inj Type Weight

Fatal 250,000 4.00 0.2385 3%

PT 1,000,000 1.00 0.5677 11%

Major PP 250,000 4.00 0.1395 44%

Minor PP 50,000 20.00 0.0001 16%

TT 10,000 100.00 0.0000 21%

Med Only 500 2,000.00 0.0000 5%

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Example

Suppose we’re pricing the $1M xs $1M layer

Expected Loss Ratio = 75%

ELF(1M) = 0.13; ELF(2M) = 0.06

Losses in the layer = ELF(1M) – ELF(2M) = 7.0%

7.0% of the total losses are in this 1M xs 1M layer

Exposure Loss Cost Rate = 75% * 7.0% = 5.25%

This still needs to be discounted and loadedMoshe D. Goldberg, FCASCAS Reinsurance PricingJuly 29, 2005

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WC Trends

Moshe D. Goldberg, FCASCAS Reinsurance PricingJuly 29, 2005

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WC Trends

The long tail and unlimited medical benefits add to the difficulty in estimating trends for Workers Compensation.

In addition, states can – and do – change the WC benefits, adding to the uncertainty.

Moshe D. Goldberg, FCASCAS Reinsurance PricingJuly 29, 2005

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Source: NCCI, Inc

Used with permission

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Impact of Non-uniform Frequency Trend onExcess of Loss Pricing

Exposure Rating

– Shape of the distribution changes, with more of the losses coming from larger claims

Experience Rating

– Measured ground-up severity trend will increase from the reduced frequency of the smaller claims

– Assuming uniform trend by size of loss, the measured large loss trend will be lower than the measured ground-up trend

– This impact is mitigated by the less-negative frequency trend

Moshe D. Goldberg, FCASCAS Reinsurance PricingJuly 29, 2005

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Example

Two types of claims, small and large.

In year 1, small claims have average severity of 100k, while large claims have average severity of 500k.

In year 1, there are an equal number of small and large claims, say 50 of each claim

Average Severity in year 1 is 300k

= (50*100k + 50*500k)/(50+50)

Moshe D. Goldberg, FCASCAS Reinsurance PricingJuly 29, 2005

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Example, continued

In year 2, there are now 40 small claims (frequency trend = -20%), while there are still 50 large claims (0% frequency trend). Total frequency trend = -10%

The average severity for each claim type increases 10%

– Small claim severity = 110k

– Large Claim Severity = 550k

But, the measured overall severity is now 354k

= (40*110k+50*550k)/(40+50)

This is an 18% increase!

Moshe D. Goldberg, FCASCAS Reinsurance PricingJuly 29, 2005

Page 23

Source: NCCI, Inc.

Used with permission

Page 24

Source: NCCI, Inc.

Used with permission