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Workers Compensation
Excess of Loss Pricing
CAS Reinsurance Pricing Seminar
Moshe D. Goldberg, FCAS
July 29, 2005
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
Moshe D. Goldberg, FCAS
CAS Reinsurance Pricing
July 29, 2005
Page 2
- Essentially unlimited medical coverage!!
– True No-Fault system (Or is it?)
WC’s Long Tail

Discounting of case reserves prevalent
– Explicit (lifetime pension cases)
– Implicit (by not inflating projected future
payments)
Moshe D. Goldberg, FCAS
CAS Reinsurance Pricing
July 29, 2005
Page 3

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
Example of Impact on
Reinsurer
Page 4

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.
Implicit Discount Effect
Page 5

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!
Mortality Assumption Effect
Page 6

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
Example of “Tail” Development
for 1Mx1M layer
Acc
Year
1990
1991
1992
1993
1994
1995
Month of Development
120
132
144
156
168
180
15,796
12,107
8,445
8,626
6,533
10,482
17,221
13,775
9,296
10,760
6,938
19,079
15,060
10,139
10,921
20,478
16,996
11,604
22,987
18,574
23,711
Acc
Year
1990
1991
1992
1993
1994
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Wtd Avg
120 - 132
132 - 144
144 - 156
156 - 168
168 - 180
1.090
1.138
1.101
1.247
1.062
1.108
1.093
1.091
1.015
1.073
1.129
1.144
1.123
1.093
1.031
120 - 132
132 - 144
144 - 156
156 - 168
168 - 180
1.126
1.081
1.108
1.109
1.031
WC Exposure Rating
Moshe D. Goldberg, FCAS
CAS Reinsurance Pricing
July 29, 2005
Page 8
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
Moshe D. Goldberg, FCAS
CAS Reinsurance Pricing
July 29, 2005
Page 9
– However, the allocation to layer is handled vey
differently.
Exposure Rating
Moshe D. Goldberg, FCAS
CAS Reinsurance Pricing
July 29, 2005
Page 10

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!
Terminology of WC
Size-of-loss curves
Moshe D. Goldberg, FCAS
CAS Reinsurance Pricing
July 29, 2005
Page 11

“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
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 Only
Moshe D. Goldberg, FCAS
CAS Reinsurance Pricing
July 29, 2005
Page 12
Average Cost per Case

These are the average severities by:
– State
– Hazard Group
– Injury Type

Moshe D. Goldberg, FCAS
CAS Reinsurance Pricing
July 29, 2005
Page 13
They are used in computing entry ratios.
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
Fatal
250,000
4.00
0.2385
3%
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%
500
2,000.00
0.0000
5%
PT
Med Only
Page 15
Entry Ratio @
1M
ELF(1M)
Inj Type Weight
Example
Moshe D. Goldberg, FCAS
CAS Reinsurance Pricing
July 29, 2005
Page 16

Suppose we’re pricing the $1M xs $1M layer

Expected Loss Ratio = 75%

ELF(1M) = 0.13;

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 loaded
ELF(2M) = 0.06
WC Trends
Moshe D. Goldberg, FCAS
CAS Reinsurance Pricing
July 29, 2005
Page 17
WC Trends
Moshe D. Goldberg, FCAS
CAS Reinsurance Pricing
July 29, 2005
Page 18

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.
Source: NCCI, Inc
Used with permission
Page 19
Impact of Non-uniform
Frequency Trend on
Excess 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
Moshe D. Goldberg, FCAS
CAS Reinsurance Pricing
July 29, 2005
Page 20
– This impact is mitigated by the less-negative
frequency trend
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, FCAS
CAS Reinsurance Pricing
July 29, 2005
Page 21
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

Moshe D. Goldberg, FCAS
CAS Reinsurance Pricing
July 29, 2005
Page 22
But, the measured overall severity is now 354k
= (40*110k+50*550k)/(40+50)
This is an 18% increase!
Source: NCCI, Inc.
Used with permission
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Source: NCCI, Inc.
Used with permission
Page 24