8/29/2000 1 casualty loss reserve seminar session number 7 workers compensation reserving: how do...

8/29/20001

Casualty Loss Reserve Seminar

Session Number 7

Workers Compensation Reserving:How Do You Slice the Cake?

September 19, 2000

Panelists: Tracy A. Ryan, FCASAssociate Actuary - Liberty Mutual Group

Mark J. Mahon, FCASConsulting Actuary - MBA, Inc.

Moderator: Timothy L. Wisecarver, FCASPresident - Pennsylvania Compensation Rating

Bureau Delaware Compensation Rating

Bureau, Inc.

8/29/20002

Why Do You Slice the Cake?

AvailabilityCredibilityHomogeneity

•Emergence Patterns•Settlement Patterns•Development Patterns•Loss Frequency•Loss Severity

Factors Affecting Decisions ConcerningData Organization

8/29/20003

Slices Related to What Item(s)Are Being Reserved

Benefits vs. Loss Adjustment

Medical Benefits vs. Indemnity Benefits

Medical-Only Benefits vs. Medical Benefits on Indemnity Claims

Vocational Rehabilitation vs. Other Indemnity Benefits

8/29/20004

Slices Related to Who Administers

The Item(s) Being ReservedBranch Office or Region

Business Unit (within an Insured or Self-Insured Risk)

Case Reserver(s)

Insurance Company

PPO/CCO Arrangements vs. “Market” Medical Providers

Producer

Reinsurance Arrangements (Assumed vs. Ceded vs. Direct Business

Self-Administered Losses vs. TPA or Other Vendor-Administered

Voluntary Market vs. Assigned Risk (Services vs. Direct Assignment)

8/29/20005

Slices Related to Rules Applicable

to the Item(s) Being Reserved

•Deductibles (Large vs. Small vs. None)

•Jurisdiction (i.e., USL&HW, FELA, State Act, etc.)

•State of Coverage (for State Act Benefits)

8/29/20006

Slices Related to Special Features

of the Insured(s)

•Industry Group (or Classification(s) )

•Large Accounts vs. Other Policies

•Anomalous Accounts vs. Other Policies

•Loss-Rated vs. Guaranteed Cost Policies

•Participating vs. Non-Participating Policies

8/29/20007

Slices Related to Known or Anticipated Features of Item(s)

Being Reserved

•Large or Catastrophic Losses vs. Other Claims

•Layer of Loss

•Open Cases vs. Closed Cases

•Traumatic vs. Occupational Disease

•Type of Injury (Death, Permanent/Temporary, Total/Partial, Medical Only)

Workers Compensation Reserving How Do You Slice the Cake?

Mark J. Mahon, FCAS, MAAA

MBA, Inc.

8/29/20009

It’s Easy to Want the Data - Receiving It Is Not So Easy

To Start - Keep Things Simple Follow the Client’s Operations Why Do You Want the Data? Time Consuming and Expensive

8/29/200010

Traumatic vs. OccupationalDisease (Black Lung)

Coal Mine Compensation Rating Bureau of Pennsylvania.

8/29/200011

Traumatic vs. Occupational Disease (Black Lung)

Comparison of OD to Traumatic– Cumulative– Long Report Time– Claims take time to Adjudicate– Lifetime Benefits– Low Frequency/High Severity

8/29/200012

The OD System

Frequency times Severity.

8/29/200013

The OD System

IBNR Claims– Uses Typical Accident Year Triangles– Claims assigned to Year based on Last Date

of Exposure– Claim Count Development used to estimate

IBNR Claims

8/29/200014

OD Frequency

Three Pieces– Known Claimants Receiving Benefits at the

valuation date (Awarded Claims)– An Estimate of Pending Claims that will be

Awarded– An Estimate of IBNR Claims that will be

Awarded

8/29/200015

The OD System

Awarded Claims

REPORTED DATA TOTAL

TOTAL AW ARDED AWARDED AWARDED

YEAR REPORTED AWARDED PENDING DENIED PENDING IBNR IBNR CLAIMS

1989 20 5 4 11 0.428 2.532 0.271 5.699

1990 28 1 2 25 0.214 2.819 0.302 1.516

1991 27 2 3 22 0.321 2.688 0.288 2.609

1992 20 2 1 17 0.107 2.990 0.320 2.427

1993 8 0 1 7 0.107 3.253 0.348 0.455

1994 8 0 2 6 0.214 3.788 0.405 0.619

1995 10 2 2 6 0.214 4.031 0.431 2.645

1996 5 0 0 5 0.000 5.067 0.542 0.542

1997 2 0 1 1 0.107 5.745 0.615 0.722

1998 0 0 0 0 0.000 7.573 0.810 0.810

TOTAL 128 12 16 100 1.712 40.485 4.332 18.044

Award Ratio: Awarded/(Awarded plus Debied) = 12/(12+100) = 10.7%

8/29/200016

OD Severity

Life Tables Lifetime Benefits Claimant’s Age Annual Benefits Marital Status Escalation (State - No, Federal- Yes)

8/29/200017

OD Severity

Life Tables used to Model Future Benefits

M o rta lity P ro b a b ility Future Future

M ine r's Ta b le o f Benefit Exp ec ted

A g e Liv es P a ym ent A m o unt C O LA P a ym ent

60 46,524 0.9884 $5,935 1.000 $5,866

61 45,449 0.9651 5,935 1.030 5,900

62 44,355 0.9414 5,935 1.061 5,927

63 43,238 0.9171 5,935 1.093 5,948

64 42,096 0.8923 5,935 1.126 5,960

: : : : : :

105 39 0.0007 5,935 3.782 15

106 25 0.0004 5,935 3.895 10

107 16 0.0003 5,935 4.012 7

108 10 0.0002 5,935 4.132 4

109 6 0.0001 5,935 4.256 2

110 0 0.0000 5,935 4.384 0

To ta l 149,977

8/29/200018

OD Severity

Act 57– Only Claims Filed After Mid 1996– WC Benefits Reduced for Social Security– WC Benefits Reduced for Pensions– AMA Guidelines Made it Harder To Achieve

PT Disability Status

8/29/200019

The OD Reserve Three Pieces

>Known Awarded Claims: Sum of Each Claimant’s future payments from

severity model>Pending Claims: Pending Claims x Award Ratio x Average Severity of

Pending Claims>IBNR Claims: IBNR Claims x Award Ratio x Average Severity of

Awarded and Pending Claims

8/29/200020

OD System - Concluding Remarks

Lifetime Payments/Long Tail Relatively Few Claims Parallels Actual Process Reviewed by Interested Parties Expensive Is This Really the Only Way to Make

Estimates?

8/29/200021

Traumatic - Indemnity vs. Medical

Very Common Split Also Breakdown Medical into Medical Only and

Medical on Indemnity Different

– Development– Inflation– Law Changes

8/29/200022

Tail Factor -Inverse Power Curve

Fo rm : ld f = 1 + a *( tim e+c )^(b )

Tra nsfo rm a t io n: ln (Ld f-1) = ln (a ) + b *ln(t im e+c ) Fitted Fitted

Pe rio d Ld f t im e c ln(Ld f-1) ln (tim e+c) D a ta p o ints: 12:24 to 60-72 ln(Ld f-1) Ld f

12:24 1.902 1 3 -0.103 1.386 Reg ressio n Sta tistic s -0.248 1.781

24:36 1.290 2 3 -1.238 1.609 R-Sq ua re 96.4% -0.955 1.385

36:48 1.233 3 3 -1.457 1.792 O b se rv a tio ns 5 -1.533 1.216

48:60 1.144 4 3 -1.938 1.946 a 4.147 -2.021 1.133

60:72 1.085 5 3 -2.465 2.079 b -3.170 -2.445 1.087

72:84 6 3 2.197 -2.818 1.060

84:96 7 3 2.303 -3.152 1.043

96:108 8 3 2.398 -3.454 1.032

108:120 9 3 2.485 -3.730 1.024

120:132 10 3 2.565 -3.983 1.019

: : : : : :

240:252 20 3 3.135 -5.792 1.003

P o ssib le Ta il Fa c to rs: 6-10 1.189

6-15 1.251

6-20 1.277

8/29/200023

Tail Factor -Relate to Larger Body

A . Re la tio nsh ip o f C o m p a ny Z to Ind ustry

Lo ss D ev e lo p m ent Fa c to rs Re la t io nsh ip

C o m p a ny Z Insura nc e Ind ustry C o m p a ny Z

P e rio d Fa c to r P e rio d Fa c to r to Ind ustry

12-24 1.902 12-24 1.351 140.8%

24-36 1.290 24-36 1.091 118.2%

36-48 1.233 36-48 1.040 118.6%

48-60 1.144 48-60 1.024 111.7%

60-72 1.085 60-72 1.017 106.7%

72-Ult 72-Ult 1.076

A v era g e o f La test 3: 112.3%

Trend ed : 104.5%

B. Po ssib le Ta il Fa c to rs C o m p a ny Z

Ind ust ry Ta il Re la tio nsh ip Ta il

A v e ra g e -1 1.076 112.3% 1.210

A v era g e -2 1.076 104.5% 1.120

8/29/200024

Tail Factor -Decay Factor

Lo ss Dev e lo p . Fa c to rs Dec a y

P e rio d Fa c to r Fa c to r - 1.0 Fa c to r

A c tua l 12-24 1.902 0.902

24-36 1.290 0.290 32.2%

36-48 1.233 0.233 80.3%

48-60 1.144 0.144 61.8%

60-72 1.085 0.085 59.0%

A v era g e : 58.3%

Med ia n: 60.4%

Se lec ted : 60.0%

P ro jec ted 72-84 1.051 0.0510 60.0%

84-96 1.031 0.0306 60.0%

96-108 1.018 0.0184 60.1%

108-120 1.011 0.0110 59.8%

120-132 1.007 0.0066 60.0%

132:144 1.004 0.0040 60.6%

144:156 1.002 0.0024 60.0%

156:168 1.001 0.0014 58.3%

168:180 1.001 0.0008 57.1%

Ta il Fa c to r - 72 to Ult 1.132

8/29/200025

Traumatic Losses By Injury Type

Death, Permanent Total, Permanent Partial and Temporary Claims

Proportion of Losses by Injury Type– Act 57 Impacts Largest Claims – Severity Subsequent to Law Change should

be Smaller

8/29/200026


Act 57 Also made it Easier to Settle Claims – Fewer Claims Being Reported as PT – Retroactive - Existing PT’s Settled and

Reclassified– Incurred Loss Triangles Double Count

Impact of Settlements– Paid Triangles Overstate Impact

8/29/200027


Permanent Total Claim Count DevelopmentA c c id ent Yea r

Rep o rt 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998

12 m o s. 1 2 2 3 1 3 2 4 2 2

24 m o s. 4 5 4 5 3 6 5 5 6

36 m o s. 8 9 12 7 8 7 9 10

48 m o s. 13 14 13 9 10 12 13

60 m o s. 15 16 18 10 12 12

72 m o s. 15 17 19 10 13

86 m o s. 16 16 19 10

96 m o s. 16 17 19

108 m o s. 16 17

120 m o s. 16

8/29/200028


PT Count Development after Act 57

A c c id ent Yea r

Rep o rt 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998

12 m o s. 1 2 2 3 1 3 2 0 0 0

24 m o s. 4 5 4 5 3 6 1 0 1

36 m o s. 8 9 12 7 8 7 1 0

48 m o s. 13 14 13 9 8 7 2

60 m o s. 15 16 18 10 8 6

72 m o s. 15 17 17 9 6

86 m o s. 16 16 15 8

96 m o s. 14 12 14

108 m o s. 12 10

120 m o s. 11

8/29/200029


Safety Program Impact – Drop in Number of Injuries– Shift to less Severe Accidents

8/29/200030

Losses in Higher Layers

Be Careful - Reserves in Higher Layers may be Inadequate

Loss Development Under Estimates Higher Layers in Most Recent AY– Immature years don’t yet have any big losses– Change in claims handling – Historically there are no Higher Layer Losses in

layer but because of new severe classes or inflation new losses are expected

8/29/200031


Latest Years’ Lower than HistoricalP o lic y P e rio d

90-91 91-92 92-93 93-94 94-95 95-96 96-97 97-98 98-99 99-00

Lo sses Lim ite d to $250,000

Ultim a te 9,735 14,422 12,928 11,955 14,434 11,442 6,006 11,462 7,185 8,152

G ro ss Lo sse s

Ultim a te 10,995 15,410 14,141 12,907 15,822 11,862 6,697 12,231 7,615 8,542

Ra tio o f G ro ss to $250k

12.9% 6.9% 9.4% 8.0% 9.6% 3.7% 11.5% 6.7% 6.0% 4.8%

Fiv e Yea r Do lla r W e ig hte d A v e ra g e : 9.1% 9.1% 9.1% 9.1% 9.1%

Se lec ted Ra t io : 6.4% 11.5% 9.1% 9.1% 9.1%

Resta ted G ro ss Ultim a te Lo sse s: 12,175 6,697 12,510 7,842 8,897

Lo sses Lim ited to $250k tim es [Se le c ted Ra tio p lus 1.0]

8/29/200032


Immature Years has No Losses

P o lic y P e rio d

90-91 91-92 92-93 93-94 94-95 95-96 96-97 97-98 98-99 99-00

C a se Inc urred Lo sse s XS $250,000

1,100 840 1,000 730 700 240 350 320 0 0

Exc ess Lo ss Dev e lo p m ent Fa c to r

1.145 1.176 1.213 1.304 1.411 1.750 1.974 2.403 2.900 4.500

Ultim a te Lo sses XS $250,000

1,260 988 1,213 952 988 420 691 769 0 0

Resta ted Ultim a te Lo ssses ( Fiv e Yea r A v e ra g e ): 800 800

8/29/200033


Use Industry Statistics to Fill-in Excess Losses– Payroll x Loss Cost x Excess Loss Factor– As AY matures rely on actual data more and

more For Insurers Do Gross, Ceded and Net

Separately

8/29/200034

Losses By Business Segment

Many Self-Insureds have Different Operating Units– E.g., Construction vs. Shipbuilding– Financial Data Already Split– Usually Easy to get Actuarial Data as

Coding already there

8/29/200035

Losses By Business Segment

Many Self-Insureds have Different Operating Units– E.g., Construction vs. Shipbuilding– Financial Data Already Split– Usually Easy to get Actuarial Data as

Coding already there Data by Jurisdiction

– USL&H Benefits Higher than State Benefits

8/29/200036

Combining Data Increases Credibility for Companies with Sparse Data Provides a Guide to Overall Level Use Combined Data as Minimum as usually the Sum

of the Slices are greater than the Total– Less Variation in Total – Smaller Slice with Tail muted by Larger Slice

without Tail– Shifting Losses to Longer Tail Slice

8/29/200037

Keeping Score

Purpose of Slices - Improve Reserve Estimation Accuracy

Keep Tabs on your Estimates - Keep A Scorecard

8/29/200038

Fisc a l Ultim a te Lo sses V a lued a s o f: C ha ng es

Po lic y 3-31-97 to 3-31-98 to 3-31-99 to

Yea r 3-31-97 3-31-98 3-31-99 3-31-00 3-31-98 3-31-99 3-31-00

1992-93 12,399 12,100 12,600 11,928 (299) 500 (672)

1993-94 11,355 11,800 11,800 12,000 445 0 200

1994-95 13,027 13,500 13,700 14,000 473 200 300

1995-96 11,061 10,300 10,900 11,100 (761) 600 200

1996-97 6,563 6,500 5,900 6,000 (63) (600) 100

Sub to ta l 54,405 54,200 54,900 55,028 (205) 700 128

1997-98 9,400 f 9,400 10,600 10,800 0 1,200 200

1998-99 - - 8,450 f 7,500 7,200 - - (950) (300)

1999-00 - - - - 7,400 f 7,700 - - - - 300

2000-01 - - - - - - 7,800 f - - - - - -

Sub to ta l 9,400 17,850 25,500 33,500 0 250 200

To ta l 63,805 72,050 80,400 88,528 (205) 950 328

Keeping Score

Workers Compensation Reserving How Do You Slice the Cake?

Tracy A. Ryan, FCAS, MAAA

Liberty Mutual Group

8/29/200040

Large Dollar Deductibles

Primary vs. Excess

Unique Accounts

Industry Segments

IBNR Rule of Thumb

Workers Compensation Reserving

8/29/200041

10

15

20

25

30

35

40

90 91 92 93 94 95 96 97 98p

Calendar Year

$ B

illio

ns

p Preliminary

Impact ofDeductibles

Workers CompensationLarge Dollar Deductibles

Net Written Premium

8/29/200042


Loss Ratio

FirstDolla

r

Large DollarDeductible

Loss

$ 75

$ 15Expens

e $

25

$ 23Premiu

m

$100

$ 38

Loss Ratio

75%

40%

(1)

(2)

8/29/200043


ExampleUlt.Loss(1)

MigrationRate(2)

Ground-upRept. Pattern

(3)

Excess Rept.Pattern

(4)1994 $1,000 10% 91% 22%

1995 $1,000 25% 89% 20%

1996 $1,000 40% 87% 17%

1997 $1,000 45% 82% 14%

1998 $1,000 50% 67% 10%

*Assume deductible level remains the same each year.*Average deductible implies excess loss is 20% of ground-up loss.*Numbers are illustrative only.

8/29/200044


Example

12(1)

24(2)

36(3)

48(4)

60(5)

Ult. Loss(6)

1994 $670 $820 $870 $890 $910 $1,000

1995 $670 $820 $870 $890 $1,000

1996 $670 $820 $870 $1,000

1997 $670 $820 $1,000

1998 $670 $1,000

Total incurred if all remains as first dollar business

8/29/200045


Example

Total first dollar + LDD incurred

12(1)

24(2)

36(3)

48(4)

60(5)

Ult. Loss(6)

1994 $605 $741 $786 $805 $823 $920

1995 $508 $622 $661 $678 $800

1996 $410 $503 $536 $680

1997 $378 $464 $640

1998 $345 $600

8/29/200046

Incurred @12/31/98

(1)

% Rept. @12/31/98

(2)

ImpliedUltimate

(3)

ActualUltimate

(4)

ImpliedReserve

(5)

ActualReserve

(6)1994 $823 91% $904 $920 $81 $97

1995 $678 89% $762 $800 $84 $122

1996 $536 87% $616 $680 $80 $144

1997 $464 82% $566 $640 $102 $176

1998 $345 67% $515 $600 $170 $255

Total $3,363 $3,640 $517 $794


Example

8/29/200047


How to Calculate Ultimate Loss?

Develop losses net of deductible

Develop gross losses and apply a loss

elimination ratio

Apply an expected loss ratio to premium

Use a Bornhuetter-Ferguson approach

Sounds Easy … Right??

8/29/200048


How to Calculate Ultimate Loss? Develop Losses Net of Deductible

– Highly Leveraged Loss Development Factors– Changing Retentions Over Time

Develop Gross Losses & Apply a Loss Elimination Ratio– Selecting the Loss Elimination Ratio– Changing Retentions Over Time

Apply an expected loss ratio to premium– Selecting the Expected Loss Ratio

Use a Bornhuetter-Ferguson approach – See above ...

8/29/200049


Educate your customer (risk manager,

underwriter, internal management, etc.) on the

peculiarities of net deductible loss

- Severity of Excess Claims

- Reporting and Payout Pattern of Excess Claims

- Potential for Catastrophic Claims

- Leveraged Impact of Inflation

4/19/20008/29/2000

Liberty Mutual WC Claims Greater than $500,000

Percent of Total Reported

Claims Dollars

0.05% 9%

4/19/20008/29/2000

NCCI DataWorkers Compensation

Serious Claims vs All Claims

Claim Counts $ Loss

All Claims 250,745 $1,358m

Serious Injuries 5,828 $ 726m

% Serious 2% 53%

4/19/20008/29/2000

Liberty Mutual’s Oldest Open WC Claim

Date of Accident

State

Description

Injury Type

Current Age

Still Paying

September 10, 1937

New Jersey

Bilateral Hand Amputations

Permanent Total

91 Years Old

Weekly Compensation

4/19/20008/29/2000

Acc After After AfterYears 5 Years 10 Years 15 Years1980-1989 1.0 2.1 3.3

For every 1 claim in excess of $500,000 as of 5 years, there will be 3.3 claims in excess of $500,000 as of 15 years.

Workers Compensation Claims Greater than $500,000

4/19/20008/29/2000

WC Excess Payout Pattern

Retention Approx. Years to Pay Half of Ultimate

$ 0 2.5

$100k 7

$250k 15

$500k 19

$1m 25

4/19/20008/29/2000

How Big Can a WC Claim Be?

A 25 year old quadriplegic

Indemnity benefits = $23,400 per year

Medical costs = $125,000 per year

How much will this claim ultimately cost?

4/19/20008/29/2000

How Big Can a WC Claim Be?YearsUntil Medical InflationDeath 0% 5% 7% 9%

20 $3.0 $4.6 $5.6 $6.9

35 $5.2 $12.1 $18.1 $27.8 50 $7.4 $27.3 $52.0 $103.0

65 $9.6 $58.6 $144.8 $376.3

4/19/20008/29/2000

The Impact of Inflation on Excess Pricing

The customer has a $250,000 LDD policy Expect 1 claim each yearExpected Loss = $360,000Excess loss = $110,000.

Excess premium = $55,000.

Assuming the customer does not change their retention, how much must we charge for next year’s policy if we know losses are growing at 3% per year?

4/19/20008/29/2000

The Impact of Inflation on Excess Pricing

We have to charge 10% more next year. Why?

Expected Loss = $370,800 ($360,000 * 1.03)Excess loss = $120,800.Excess premium = $60,400.

$60,400 / $55,000 = 1.10

8/29/200059

Workers CompensationUnique Accounts

@ 6 months

Claim Closure +17 points

Average Open -36%

Average Paid -32%

To understand how a single large account can impact results, you must look at the diagnostics of the account versus the rest of the book:

8/29/200060

Workers CompensationIndustry Segments

Industry segments studied were contracting, goods and services, manufacturing, office and clerical, and miscellaneous

Over a five year period:-Medical severity increase ranges from 2% to 16%-Indemnity severity change ranges from -2% to 9%

8/29/200061

Workers CompensationBuyouts

Development Expenses Taxes Investment Income Risk charge/profit

8/29/200062

Workers CompensationBuyouts

Policy year 1994

Incurred loss @ 12/99 = $2,500

Paid loss @ 12/99 = $2,450

Ultimate incurred estimate = $2,725

Ultimate paid estimate = $3,185

Average ultimate = $2,955

8/29/200063

Question:

In providing an actuarial reserve analysis to a large national account, the risk manager asked the question for workers compensation: “For every dollar of aggregate case reserve, how much IBNR should I expect?” Answer:

For WC, aggregate IBNR reserves should vary between 80% and 90% of outstanding aggregate case reserves.

Workers CompensationRule of Thumb

8/29/200064

Based on industry data and the following formula:

IBNR Reserve = (Ultimate Loss - Incurred Loss) Case Reserve (Incurred Loss - Paid Loss)

= (100% - % Incurred) (% Incurred - % Paid)

= (1.0 - 1/Incurred CDF)

(1/Incurred CDF - 1/Paid CDF)


8/29/200065

Workers CompensationRule of thumb

Amount of IBNR loss as a percent of case reserveUsing 2 year patterns Using 5 year patterns

MaturityIncurred

CDFPaid CDF

IBNR as a % of case

Incurred CDF

Paid CDF

IBNR as a % of case Selected

12 1.596 4.245 95.5% 1.610 4.376 96.5% 95%24 1.263 2.039 69.1% 1.273 2.084 70.2% 70%36 1.187 1.630 68.8% 1.189 1.642 68.5% 70%48 1.157 1.463 75.1% 1.153 1.458 73.1% 75%60 1.140 1.372 82.8% 1.133 1.360 79.7% 80%72 1.130 1.315 92.4% 1.121 1.300 87.9% 90%84 1.121 1.277 99.0% 1.111 1.260 93.9% 95%96 1.112 1.248 102.8% 1.103 1.230 99.8% 100%

Note: Ratio = (1.00 - 1/Incd CDF)

(1/Incd CDF - 1/Paid CDF)

8/29/200066

Factors Impacting Ratio:

Mix of years - Assumed that case reserves decrease as maturity increases.

Mix of states - Used only countrywide development factors.

Development pattern - Specific company patterns may differ from NCCI pattern.


8/29/2000 1 casualty loss reserve seminar session number 7 workers compensation reserving: how do...

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