1. Loss Adjustment Expense Reserving
Adam D. Hartman, ACAS
Casualty Loss Reserve Seminar
September 14, 1999

2. 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

3. 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

4. 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

5. 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

6. 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

7. 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

8. “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

9. “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

10. “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

11. 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

12. 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

13. 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

14. 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

15. 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

16. 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

17. 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

18. Wendy Johnson - Assumptions
No adjustment for claims closed during 1st year
Consistent claim reporting and disposal patterns
CLRS1999_ULAE.ppt

19. 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

20. Wendy Johnson - Modifications to Reflect Claims Closed
Avg(#claims open or
assume all claims will continue to be open throughout year y+1
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

21. Modified W. Johnson - Example
CLRS1999_ULAE.ppt

22. 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
= 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

23. Modified W. Johnson - Example
CLRS1999_ULAE.ppt

24. Modified W. Johnson - Example
CLRS1999_ULAE.ppt

25. 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

26. Modified W. Johnson - Example
CLRS1999_ULAE.ppt

27. 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

28. Modified W. Johnson - Example
CLRS1999_ULAE.ppt

29. 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

30. 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

31. 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

32. 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

33. 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

34. 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

35. 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

36. 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

37. 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

38. 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

39. 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

40. Other Considerations Reinsurance Catastrophes
Reserves for non-year-end financial statements
CLRS1999_ULAE.ppt

41. 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

42. Appendix
CLRS1999_ULAE.ppt

43. 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

44. “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

45. 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

46. (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

47. “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

48. 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

49. (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

50. Reserve based upon Ultimate Incurreds
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]
CLRS1999_ULAE.ppt

51. 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

52. 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

53. 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