Loss Adjustment Expense Reserving

Adam D. Hartman, ACAS

Casualty Loss Reserve Seminar

September 14, 1999

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Purpose To introduce basic reserving methodologies

for loss adjustment expenses that are not tracked on an accident year basis

To contrast different methodologies for allocating such reserves to accident year

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Discussion Topics Defining Terms (see Appendix) What’s Really Important Methodologies for Estimating Loss

Adjustment Expense Reserves Methodologies for Allocating LAE

Reserves to Accident Year Other Considerations

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What’s Really Important Identifying the components of LAE Understanding the way in which the

components are incurred Understanding the timing of the

corresponding expense payments

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LAE captured in accident year detail

Examples– External Legal Expenses– External Adjuster/Appraiser– Internal Legal Expenses (?)

Basic Methodologies– “chain-ladder” development– cumulative paid-to-paid– incremental paid-to-paid– generalized Cape Cod

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LAE captured at calendar year aggregate level Cannot be directly converted into accident

year triangles Basic Methodologies

– Transaction method (Brian)– “Classical” CY paid-to-paid– Kittel’s correction to “Classical”– Wendy Johnson method

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Transaction method

“ULAE” Reserve = Sum over t {X(t)*n(t)}

where– X(t) = Avg. cost of transaction t– n(t) = number of transaction type t required to close a

claim file (whether reported or not)– X(t) determined by time study– Var[X(t)] may be high– n(t) estimated using history

Very accurate, whole lotta work

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“Classical” Paid-to-Paid

Assumptions– 50% of ULAE paid at report – 50% of ULAE paid at close – ULAE outstanding is proportionate to losses

outstanding– Loss reserves are accurate– Age of claims does not affect p (see next slide)– ULAE, losses are paid at the same time and rate– Loss inflation% = ULAE inflation%

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“Classical” Paid-to-Paid

Paid-to-paid Ratio

PPR = Sum {CY Paid ULAE} Sum {CY Paid Losses}

(1-p) = % of “ULAE” unpaid on claims currently open.

50% paid at report,50% paid at close>>p=.5 Indicated “ULAE” Reserve

= PPR * [(1-p)*Case Reserve+ IBNR]

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“Classical” Paid-to-Paid

Appropriate only if…– line is short-tailed, stable– low/stable inflation– consistent claim reporting and closing patterns

For long-tail, rapidly-growing lines in high inflation– Historical (paid ULAE)/(paid loss) may be high– Classical Reserve > W Johnson Reserve

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Kittel’s Correction to “Classical” paid-to-paid Paid losses do not accurately represent work

done by Claims Dept.– do not account for opens during year still open at

December 31st

Replace [sum Paid ULAE/sum Paid losses] with

____Sum_Paid ULAE _

Sum[(1-p)*Paid Loss + p * Incd Loss]

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Kittel’s Assumptions

50% of ULAE incurred at report 50% of ULAE incurred at close ULAE is independent of age of claim ULAE and losses paid at same rate and time Loss reserves are accurate Same inflation% for losses & ULAE

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Richard Bill’s Revision to Kittel’s Conclusions

Inflation distorts the "Classical" 50/50 assumption regarding the payment of ULAE.

If high inflation, then % of ULAE paid at claim closure is significantly greater than % of ULAE paid at claim opening.

In a high inflation environment, the use of the 50/50 assumption tends to understate the ULAE reserve

This effect will be more pronounced the longer the payout pattern

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Factoring in Growth

If a company is growing rapidly in a low inflation environment, the use of the "Classical" paid-to-paid method will overstate the ULAE reserve

If longer payout pattern, then larger overstatement of reserves

Kittel's revised ratio produces a better ULAE reserve

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Factoring in Growth - continued

If a company is growing rapidly in a high inflation environment, the correct ratio is somewhere between the "Classical" ratio and Kittel's ratio depending upon the relative impact of exposure growth versus inflation.

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Wendy Johnson Method

General Concept– Forecast a workload measure (“weighted open

claims”) for settling current and prior accident years

– Forecast ULAE paid per unit of work– Do the math

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Wendy Johnson - Assumptions

ULAE incurred from time of reporting to time of closure

ULAE unrelated to nature of claim (it is a maintenance cost)

Effort associated with maintaining a claim file is twice as great during 1st year compared to subsequent years

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Wendy Johnson - Assumptions

No adjustment for claims closed during 1st year

Consistent claim reporting and disposal patterns

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Wendy Johnson - Step One

Calculate ULAE per “weighted open claim” during calendar year y

Ny= # pending claims at 12/31/y ny= # claims opened during calendar year y Weighted open claims = Ny + ny

ULAEy = calendar year y paid ULAE ULAE per weighted open claim for CY y =

ULAEy / (Ny + ny)

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Wendy Johnson - Modifications to Reflect Claims Closed Avg(#claims open @12/31/y,@12/31/y-1)

– or

assume all claims open @12/31/y will continue to be open throughout year y+1– or

assume that effort associated with maintaining a claim file is twice as great in both the year in which the claim is opened and the year it is closed.

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Modified W. Johnson - Example

Calendar Year Expense Per Weighted Claim

Calendar Year

Overhead Unallocated

LAE

Number of Outstanding

Claims

Number of Claims

ReportedNumber of

Claims ClosedWeighted

Claim Counts

Expense Per Weighted

Claim1990 124,300,000 78,700 1,294,000 1,280,000 1,692,700 73.431991 135,300,000 89,800 1,358,000 1,373,000 1,791,050 75.541992 146,800,000 99,100 1,397,000 1,400,000 1,846,100 79.521993 163,600,000 118,400 1,425,000 1,524,000 1,924,400 85.011994 166,600,000 142,300 1,513,000 1,610,000 2,057,800 80.961995 189,000,000 157,400 1,588,000 1,633,000 2,153,650 87.761996 210,700,000 172,400 1,657,000 1,695,000 2,253,150 93.511997 217,000,000 182,500 1,720,000 1,710,000 2,330,000 93.131998 242,700,000 226,000 1,860,000 1,820,000 2,541,000 95.51

Count WeightsReported 1.000

Outstanding 1.000Closes 0.250

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Wendy Johnson - Step 2a

UltClms(AYt ) = Ultimate Claims estimated for accident year t

%Rd=Cumulative % reported by dev. year d

%Cd=Cumulative % closed by dev. year d

Claims outstanding(AYt,@12/31/t+i)

= Nt,t+i = UltClms(AYt ) * (%Ri+1 - %Ri)

Claims opened(AYt,during CYt+i)

= nt,t+i = UltClms(AYt ) * (%Ri+1 - %Ci+1)

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Modified W. Johnson - Example

Selected Cumulative and Incremental Ratios12 24 36 48 60 72 84 96 108 120

Cum Reported 0.91420 0.98900 0.99550 0.99800 0.99920 0.99960 0.99990 1.00000 1.00000 1.00000Incr Reported 0.07480 0.00650 0.00250 0.00120 0.00040 0.00030 0.00010 0.00000 0.00000 0.00000Cum Closed 0.81350 0.98690 0.99400 0.99700 0.99840 0.99910 0.99950 0.99970 0.99990 1.00000Incr Closed 0.17340 0.00710 0.00300 0.00140 0.00070 0.00040 0.00020 0.00020 0.00010 0.00000

Ultimate CountsAccident Yr Ultimates

1984 228,7001985 263,2001986 296,8001987 321,3001988 332,3001989 339,1001990 334,2001991 331,6001992 337,4501993 355,3001994 362,7001995 347,6001996 357,2501997 349,1001998 355,300

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Modified W. Johnson - ExampleFuture Claims Reported

Accident Yr 12/1999 12/2000 12/2001 12/2002 12/2003 12/2004 12/2005 12/2006 12/20071990 0 0 0 0 0 0 01991 0 0 0 0 0 0 0 01992 50 0 0 0 0 0 0 0 01993 150 50 0 0 0 0 0 0 01994 250 187 62 0 0 0 0 0 01995 720 240 180 60 0 0 0 0 01996 1,139 547 182 137 46 0 0 0 01997 2,009 773 371 124 93 31 0 0 01998 27,549 2,394 921 442 147 110 37 0 0

Forecasted Claim counts adjusted for actuals, ergo, sum of forecasted + actuals to date = ultimate for each accident year

Future Claims ClosedAccident Yr 12/1999 12/2000 12/2001 12/2002 12/2003 12/2004 12/2005 12/2006 12/2007

1990 10 0 0 0 0 0 01991 20 10 0 0 0 0 0 01992 20 20 10 0 0 0 0 0 01993 133 67 67 33 0 0 0 0 01994 263 150 75 75 37 0 0 0 01995 607 303 173 87 87 43 0 0 01996 1,100 513 257 147 73 73 37 0 01997 2,222 939 438 219 125 63 63 31 01998 64,804 2,653 1,121 523 262 149 75 75 37

Forecasted Claim counts adjusted for actuals, ergo, sum of forecasted + actuals to date = ultimate for each accident year

Future Claims OutstandingAccident Yr 12/1999 12/2000 12/2001 12/2002 12/2003 12/2004 12/2005 12/2006 12/2007

1990 0 0 0 0 0 0 01991 10 0 0 0 0 0 0 01992 30 10 0 0 0 0 0 0 01993 117 100 33 0 0 0 0 0 01994 88 125 113 38 0 0 0 0 01995 213 150 157 130 43 0 0 0 01996 189 222 148 138 110 37 0 0 01997 487 321 253 158 126 94 31 0 01998 845 585 385 303 189 150 112 37 0

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Wendy Johnson - Step 2b

Projected Weighted Open Claims for CYy

WOCy= Sumt=all AY thru current{Nt,CYy + nt, CYy}

Fit historical ULAE per WOC through the current calendar year, x. a = annual trend

Project fitted values of ULAE per WOC for calendar year x+i

FVx+i = FVx * (1+a)i

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Modified W. Johnson - Example

Fitted Expense

Calendar Year

Adjusted Natural

LogarithmAdjusted Fitted

Expense Trend Factors1990 4.29637 73.85 Fitted 1.03451991 4.32469 76.40 Selected 1.0500

1992 4.37600 79.041993 4.44281 81.761994 4.39396 84.591995 4.47458 87.501996 4.53811 90.521997 4.53403 93.651998 4.55927 96.88

Trended ExpenseCalendar

YearTrended

Expenses12/1999 101.7212/2000 106.8112/2001 112.1512/2002 117.7612/2003 123.6412/2004 129.8312/2005 136.3212/2006 143.1312/2007 150.2912/2008 157.81

Future Weighted Claim CountsAccident Yr 12/1999 12/2000 12/2001 12/2002 12/2003 12/2004 12/2005 12/2006 12/2007

1990 2 0 0 0 0 0 01991 15 2 0 0 0 0 0 01992 85 15 2 0 0 0 0 0 01993 300 167 50 8 0 0 0 0 01994 403 350 194 56 9 0 0 0 01995 1,085 466 380 212 65 11 0 0 01996 1,603 897 394 311 174 55 9 0 01997 3,052 1,328 734 336 250 140 47 8 01998 44,594 3,642 1,586 876 402 298 168 56 9

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Wendy Johnson - Step 3

Projected ULAE paid in calendar year x+i on claims from accident years x and prior

UCYx+i,AY x&prior = WOCCYx+i,AY x&prior * FVx+i

Total ULAE reserve at 12/31/x

= Sumi=1 to end of tail{UCYx+i,AY x&prior }

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Modified W. Johnson - ExampleULAE Reserve

Accident Yr 12/1999 12/2000 12/2001 12/2002 12/2003 12/2004 12/2005 12/2006 12/20071990 254 0 0 0 0 0 01991 1,526 267 0 0 0 0 0 01992 8,646 1,602 280 0 0 0 0 0 01993 30,517 17,802 5,607 981 0 0 0 0 01994 41,007 37,383 21,729 6,624 1,159 0 0 0 01995 110,369 49,755 42,617 24,925 8,037 1,406 0 0 01996 163,039 95,832 44,206 36,636 21,500 7,140 1,250 0 01997 310,416 141,865 82,311 39,619 30,862 18,234 6,400 1,120 01998 4,536,265 389,033 177,827 103,165 49,675 38,675 22,852 8,024 1,404

Total 5,202,040 733,539 374,578 211,951 111,234 65,456 30,501 9,144 1,404

ULAE Totals

Accident YrAll Report

Years Total1984 01985 01986 01987 01988 01989 01990 2541991 1,7931992 10,5291993 54,9071994 107,9021995 237,1101996 369,6031997 630,8281998 5,326,920Total 6,739,846

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Estimating ULAE Reserve when Overhead Levels are Fixed Projected CYy paid ULAE for all AY

Uy,all AY=[CYx Paid ULAEall AY] * (1+alpha)y-x

where x = current CY, alpha = fixed growth%

CYx Paid ULAE may be fitted or actual

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Estimating ULAE Reserve when Overhead Levels are Fixed Projected CYy paid ULAE for AY x & prior

Uy,x&prior= Uy,all AY * WOCy,x&prior / WOCy,all AY

ULAE Reserve at 12/31/x

= Sumi=1 to end of tail{UCY x+i,AY x&prior}

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Advantages - W Johnson method

Flexibility: explicitly adjusts for change in– claims reporting and closure patterns– exposure growth– expense cost trends

Can be modified to assume ULAE payments in future years are fixed

Straightforward Uses relevant, readily available data

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Annual Statement Allocation of CY paid ULAE to AY

ULAE paid during the most recent calendar year are distributed to accident year as follows:

– (a) 45% to the most recent year

– (b) 5% to the next most recent year

– (c) the balance to all years, including the most recent, in proportion to the amount of loss payments (net of reinsurance) paid for each accident year during the most recent calendar year

– Exception: if the distribution in (a) or (b) produce an accumulated distribution to accident year > 10% of earned premium (net) for that year, excluding all distributions made under (c), such accumulated distribution should be limited to 10% of earned premiums and the balance distributed based on (c).

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Annual Statement Allocation of CY paid ULAE to AYAssumptions

50% of ULAE is paid when the claim is reported

50% of ULAE is paid when the claim is closed90% of claims are reported during the calendar

year when the accident occurred– 10% of claims are reported during the

following calendar year

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Annual Statement Allocation of CY paid ULAE to AYProblems with these Assumptions

Products Liability claims are often not reported until years after the accident date, and insurers spend significant time negotiating settlements and handling the claims. Statutory distribution assigns too much ULAE to

most recent years

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Annual Statement Allocation of CY paid ULAE to AYProblems with these Assumptions

Workers Comp permanent disability cases may have weekly indemnity payments extending over the disabled worker's lifetime.Statutory distribution assigns too little ULAE to

most recent years

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Distributing ULAE Reserves to Accident YearAnnual Statement contains no instructions

for distributing ULAE reserves to accident year.

If ULAE reserve can be distributed in same proportion as the quantity

Case Reserves + 2*IBNR Reserves

Then the reserves will have the advantage of anticipating future annual statement allocations of paid ULAE.

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Distributing ULAE Reserves to Accident YearAssumptions

IBNR claims are paid in the year they are reported"Bulk + IBNR" reserves consist of pure IBNR (no

provision for development on known claims is made in the IBNR reserves)

50% of ULAE is paid when the claim is reported50% of ULAE is paid when the claim is closed

These assumptions are generally not appropriate, but they are consistent with the Annual Statement allocation of paid ULAE

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Allocation of ULAE reserve to Accident Year - Wendy Johnson WOCx+i,t=Projected weighted open claims for

calendar year x+i, from accident year t

where x is current year and t < or = x

Indicated ULAE paid in CYx+i from AYt

UCY x+i,AY t=UCYx+i,AY x&prior * WOCCYx+i, AY t

WOCCYx+i,AY x&prior

ULAE Reserve at 12/31/x for AY t

= Sumi=1 to end of tail{UCY x+i,AY t}

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Distributing ULAE Reserves to Accident Year In a rapid growth / low inflation environment,

subsequent Annual Statement development will indicate that the ULAE reserve is...

Adequate, for the "Classical" paid-to-paid method (this is true regardless of environment)

Inadequate, for the Kittel adjustment methodInadequate, for the Wendy Johnson method

In reality, the Kittel and Wendy Johnson ULAE reserves will be more accurate.

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Other Considerations

Reinsurance Catastrophes Reserves for non-year-end financial

statements

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Conclusion: It bears repeating...

What’s Really Important– Identifying the components of LAE– Understanding the way in which the components are

incurred– Understanding the timing of the corresponding expense

payments

Additional reading– “Two Alternative Methods for Calculating the ULAE

Reserve”, Donald Mango & Craig Allen, CAS Forum, Fall 1999.

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Appendix

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Defining Terms An “LAE Reserve” should provide for the

ultimate expense required to settle outstanding claims as of the reserve date. (CAS Statement of Principles)

Loss Adjustment Expenses have been segregated into “Allocated” LAE and “Unallocated” LAE

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“Allocated” LAE For the 1996 Annual Statement and prior, NAIC

defined as all LAE that could be tied to a claim file.

External legal plus external adjuster and appraiser expenses

From the 1998 AS forward (‘97 optional), redefined: legal + medical cost containment

Renamed in 1999 AS, “Defense and Cost Containment”

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Defense & Cost Containment All litigation and medical cost containment

expenses, including…– surveillance expenses– fixed amounts for medical cost containment– litigation management expenses– LAE for participation in voluntary and

involuntary market pools if reported by accident year

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(more) Defense & Cost Containment Fees or salaries for appraisers, private

investigators, hearing representatives, reinspectors, & fraud investigators, if working in defense of a claim

Fees or salaries for rehab nurses, if not included in losses

Atty. Fees incurred owing to duty to defend Cost of engaging experts

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“Unallocated” LAE

For the 1996 AS and prior, NAIC defined as all LAE that could not be tied to a claim file.

Was company legal plus all other “non-allocated” LAE

From the 1998 AS forward (‘97 optional), ULAE excludes company legal expenses and includes external adj & appr

Renamed in 1999 AS, “Adjusting & Other”

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Adjusting & Other

LAE not within “Defense & Cost Containment”, including…– Fees of adjusters/settling agents– LAE for participation in voluntary and

involuntary market pools if reported by calendar year

– Atty. Fees incurred in determination of coverage, including litigation between insurer and policyholder

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(more) Adjusting & Other

– Fees/salaries of appraisers, private investigators, hearing representatives, reinspectors, and fraud investigators if working in the capacity of an adjuster

– “Standard unallocated” expenses such as salaries of Claims personnel and Loss Reserving staff, Claims’ share of rent and other overhead, etc.

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Reserve based upon Ultimate IncurredsTo reflect work on

Opening claims

Closing claims

Maintaining open claim files

Distribute CY(x) Paid ULAE to accident years in proportion to

Opening factor*[CY(x) Incd

Loss by AY]Closing factor*[CY(x) Paid

Loss by AY]

Open factor*[Average Loss Rsv by AY]

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Advantages of Reserve Based on Ultimate Incurred

Accounts for work on open files in a systematic manner

Self-adjusting (ultimate reflect changing factors, persistence)

Inflation-sensitive Reduces the effect of change in work

handled by independent and staff adj One method for ALAE and ULAE

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Disadvantages of Reserve Based on Ultimate Incurred

Requires some work to determine– percentage to assign each factor– percentage of LAE to distribute to Casualty

field adjusters and operations

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Annual Statement instructions unclear on distribution basisArgument in favor of using direct loss

payments to distribute paid ULAE to AYULAE are primarily related to direct loss paymentsAny reinsurance compensation for the ceding

insurer's ULAE is booked as offset to commissions, not to LAE

Argument in favor of using net loss payments to distribute paid ULAE to AY– It is common practice to use net loss payments