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### Loss Adjustment Expense Reserving

Adam D. Hartman, ACAS

Casualty Loss Reserve Seminar

September 14, 1999

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

CLRS1999_ULAE.ppt

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

CLRS1999_ULAE.ppt

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

CLRS1999_ULAE.ppt

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

CLRS1999_ULAE.ppt

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

CLRS1999_ULAE.ppt

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

CLRS1999_ULAE.ppt

“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%

CLRS1999_ULAE.ppt

“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]

CLRS1999_ULAE.ppt

“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

CLRS1999_ULAE.ppt

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]

CLRS1999_ULAE.ppt

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

CLRS1999_ULAE.ppt

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

CLRS1999_ULAE.ppt

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

CLRS1999_ULAE.ppt

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.

CLRS1999_ULAE.ppt

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

CLRS1999_ULAE.ppt

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

CLRS1999_ULAE.ppt

Wendy Johnson - Assumptions

- No adjustment for claims closed during 1st year
- Consistent claim reporting and disposal patterns

CLRS1999_ULAE.ppt

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)

CLRS1999_ULAE.ppt

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.

CLRS1999_ULAE.ppt

Modified W. Johnson - Example

CLRS1999_ULAE.ppt

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)

CLRS1999_ULAE.ppt

Modified W. Johnson - Example

CLRS1999_ULAE.ppt

Modified W. Johnson - Example

CLRS1999_ULAE.ppt

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

CLRS1999_ULAE.ppt

Modified W. Johnson - Example

CLRS1999_ULAE.ppt

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 }

CLRS1999_ULAE.ppt

Modified W. Johnson - Example

CLRS1999_ULAE.ppt

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

CLRS1999_ULAE.ppt

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}

CLRS1999_ULAE.ppt

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

CLRS1999_ULAE.ppt

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).

CLRS1999_ULAE.ppt

Annual Statement Allocation of CY paid ULAE to AY

- Assumptions
- 50% of ULAE is paid when the claim is reported
- 50% of ULAE is paid when the claim is closed
- 90% of claims are reported during the calendar year when the accident occurred
- 10% of claims are reported during the following calendar year

CLRS1999_ULAE.ppt

Annual Statement Allocation of CY paid ULAE to AY

- Problems 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

CLRS1999_ULAE.ppt

Annual Statement Allocation of CY paid ULAE to AY

- Problems 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

CLRS1999_ULAE.ppt

Distributing ULAE Reserves to Accident Year

- Annual 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.

CLRS1999_ULAE.ppt

Distributing ULAE Reserves to Accident Year

- Assumptions
- 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 reported
- 50% 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

CLRS1999_ULAE.ppt

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}

CLRS1999_ULAE.ppt

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 method
- Inadequate, for the Wendy Johnson method
- In reality, the Kittel and Wendy Johnson ULAE reserves will be more accurate.

CLRS1999_ULAE.ppt

Other Considerations

- Reinsurance
- Catastrophes
- Reserves for non-year-end financial statements

CLRS1999_ULAE.ppt

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.

CLRS1999_ULAE.ppt

Appendix

CLRS1999_ULAE.ppt

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

CLRS1999_ULAE.ppt

“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”

CLRS1999_ULAE.ppt

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

CLRS1999_ULAE.ppt

(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

CLRS1999_ULAE.ppt

“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”

CLRS1999_ULAE.ppt

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

CLRS1999_ULAE.ppt

(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.

CLRS1999_ULAE.ppt

To 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]

Reserve based upon Ultimate IncurredsCLRS1999_ULAE.ppt

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

CLRS1999_ULAE.ppt

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

CLRS1999_ULAE.ppt

Annual Statement instructions unclear on distribution basis

- Argument in favor of using direct loss payments to distribute paid ULAE to AY
- ULAE are primarily related to direct loss payments
- Any 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

CLRS1999_ULAE.ppt

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