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
2
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
3
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
4
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
5
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
6
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
7
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%
8
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]
9
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
10
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]
11
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
12
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
13
CLRS1999_ULAE.ppt
Factoring in Growth
If a company is growing rapidly in a low inflation
environment, the use of the "Classical" paid-topaid method will overstate the ULAE reserve
If longer payout pattern, then larger overstatement
of reserves
Kittel's revised ratio produces a better ULAE
reserve
14
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.
15
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
16
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
17
CLRS1999_ULAE.ppt
Wendy Johnson - Assumptions
 No adjustment for claims closed during 1st
year
 Consistent claim reporting and disposal
patterns
18
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)
19
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.
20
CLRS1999_ULAE.ppt
Modified W. Johnson - Example
Calendar Year Expense Per Weighted Claim
Calendar
Year
1990
1991
1992
1993
1994
1995
1996
1997
1998
Overhead
Unallocated
LAE
124,300,000
135,300,000
146,800,000
163,600,000
166,600,000
189,000,000
210,700,000
217,000,000
242,700,000
Number of
Outstanding
Claims
78,700
89,800
99,100
118,400
142,300
157,400
172,400
182,500
226,000
Number of
Expense Per
Claims
Number of
Weighted
Weighted
Reported
Claims Closed Claim Counts
Claim
1,294,000
1,280,000
1,692,700
73.43
1,358,000
1,373,000
1,791,050
75.54
1,397,000
1,400,000
1,846,100
79.52
1,425,000
1,524,000
1,924,400
85.01
1,513,000
1,610,000
2,057,800
80.96
1,588,000
1,633,000
2,153,650
87.76
1,657,000
1,695,000
2,253,150
93.51
1,720,000
1,710,000
2,330,000
93.13
1,860,000
1,820,000
2,541,000
95.51
Count Weights
Reported
Outstanding
Closes
1.000
1.000
0.250
21
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)
22
CLRS1999_ULAE.ppt
Modified W. Johnson - Example
Selected Cumulative and Incremental Ratios
12
0.91420
0.07480
0.81350
0.17340
Cum Reported
Incr Reported
Cum Closed
Incr Closed
24
0.98900
0.00650
0.98690
0.00710
36
0.99550
0.00250
0.99400
0.00300
48
0.99800
0.00120
0.99700
0.00140
60
0.99920
0.00040
0.99840
0.00070
72
0.99960
0.00030
0.99910
0.00040
84
0.99990
0.00010
0.99950
0.00020
96
1.00000
0.00000
0.99970
0.00020
108
1.00000
0.00000
0.99990
0.00010
120
1.00000
0.00000
1.00000
0.00000
Ultimate Counts
Accident Yr
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
Ultimates
228,700
263,200
296,800
321,300
332,300
339,100
334,200
331,600
337,450
355,300
362,700
347,600
357,250
349,100
355,300
23
CLRS1999_ULAE.ppt
Modified W. Johnson - Example
Future Claims Reported
Accident Yr
12/1999
12/2000
12/2001
12/2002
12/2003
12/2004
12/2005
12/2006
1990
0
0
0
0
0
0
0
1991
0
0
0
0
0
0
0
1992
50
0
0
0
0
0
0
1993
150
50
0
0
0
0
0
1994
250
187
62
0
0
0
0
1995
720
240
180
60
0
0
0
1996
1,139
547
182
137
46
0
0
1997
2,009
773
371
124
93
31
0
1998
27,549
2,394
921
442
147
110
37
Forecasted Claim counts adjusted for actuals, ergo, sum of forecasted + actuals to date = ultimate for each accident year
12/2007
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Future Claims Closed
Accident Yr
12/1999
12/2000
12/2001
12/2002
12/2003
12/2004
12/2005
12/2006
1990
10
0
0
0
0
0
0
1991
20
10
0
0
0
0
0
0
1992
20
20
10
0
0
0
0
0
1993
133
67
67
33
0
0
0
0
1994
263
150
75
75
37
0
0
0
1995
607
303
173
87
87
43
0
0
1996
1,100
513
257
147
73
73
37
0
1997
2,222
939
438
219
125
63
63
31
1998
64,804
2,653
1,121
523
262
149
75
75
Forecasted Claim counts adjusted for actuals, ergo, sum of forecasted + actuals to date = ultimate for each accident year
12/2007
0
0
0
0
0
0
37
Future Claims Outstanding
Accident Yr
1990
1991
1992
1993
1994
1995
1996
1997
1998
12/1999
0
10
30
117
88
213
189
487
845
12/2000
0
0
10
100
125
150
222
321
585
12/2001
0
0
0
33
113
157
148
253
385
12/2002
0
0
0
0
38
130
138
158
303
12/2003
0
0
0
0
0
43
110
126
189
12/2004
0
0
0
0
0
0
37
94
150
12/2005
0
0
0
0
0
0
0
31
112
12/2006
0
0
0
0
0
0
0
37
12/2007
0
0
0
0
0
0
0
24
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
25
CLRS1999_ULAE.ppt
Modified W. Johnson - Example
Future Weighted Claim Counts
Accident Yr
1990
1991
1992
1993
1994
1995
1996
1997
1998
12/1999
2
15
85
300
403
1,085
1,603
3,052
44,594
12/2000
0
2
15
167
350
466
897
1,328
3,642
12/2001
12/2002
0
0
2
50
194
380
394
734
1,586
0
0
0
8
56
212
311
336
876
Calendar
Year
1990
1991
1992
1993
1994
1995
1996
1997
1998
4.29637
4.32469
4.37600
4.44281
4.39396
4.47458
4.53811
4.53403
4.55927
0
0
0
0
9
65
174
250
402
12/2004
12/2005
0
0
0
0
0
11
55
140
298
12/2006
0
0
0
0
0
0
9
47
168
0
0
0
0
0
0
8
56
12/2007
0
0
0
0
0
0
9
Trended Expense
Fitted Expense
Adjusted
Natural
Logarithm
12/2003
Adjusted Fitted
Expense
73.85
76.40
79.04
81.76
84.59
87.50
90.52
93.65
96.88
Trend Factors
Fitted
Selected
1.0345
1.0500
Calendar
Year
12/1999
12/2000
12/2001
12/2002
12/2003
12/2004
12/2005
12/2006
12/2007
12/2008
Trended
Expenses
101.72
106.81
112.15
117.76
123.64
129.83
136.32
143.13
150.29
157.81
26
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 }
27
CLRS1999_ULAE.ppt
Modified W. Johnson - Example
ULAE Reserve
Accident Yr
1990
1991
1992
1993
1994
1995
1996
1997
1998
Total
12/1999
254
1,526
8,646
30,517
41,007
110,369
163,039
310,416
4,536,265
5,202,040
12/2000
0
267
1,602
17,802
37,383
49,755
95,832
141,865
389,033
733,539
12/2001
0
0
280
5,607
21,729
42,617
44,206
82,311
177,827
374,578
12/2002
0
0
0
981
6,624
24,925
36,636
39,619
103,165
211,951
12/2003
0
0
0
0
1,159
8,037
21,500
30,862
49,675
111,234
12/2004
0
0
0
0
0
1,406
7,140
18,234
38,675
65,456
12/2005
0
0
0
0
0
0
1,250
6,400
22,852
30,501
12/2006
0
0
0
0
0
0
1,120
8,024
9,144
12/2007
0
0
0
0
0
0
1,404
1,404
ULAE Totals
Accident Yr
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
Total
All Report
Years Total
0
0
0
0
0
0
254
1,793
10,529
54,907
107,902
237,110
369,603
630,828
5,326,920
6,739,846
28
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
29
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}
30
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
31
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 32
CLRS1999_ULAE.ppt
and the balance distributed based on (c).
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
33
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
34
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
35
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.
36
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
37
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}
38
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.
39
CLRS1999_ULAE.ppt
Other Considerations
 Reinsurance
 Catastrophes
 Reserves for non-year-end financial
statements
40
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.
41
CLRS1999_ULAE.ppt
Appendix
42
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
43
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”
44
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
45
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
46
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 “nonallocated” LAE
 From the 1998 AS forward (‘97 optional),
ULAE excludes company legal expenses and
includes external adj & appr
 Renamed in 1999 AS, “Adjusting & Other”
47
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
48
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.
49
CLRS1999_ULAE.ppt
Reserve based upon Ultimate
Incurreds
To reflect work on Distribute CY(x) Paid ULAE to
accident years in proportion to
Opening claims
Closing claims
Maintaining open
claim files
Opening factor*[CY(x) Incd
Loss by AY]
Closing factor*[CY(x) Paid
Loss by AY]
Open factor*[Average Loss Rsv
by AY]
50
CLRS1999_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
51
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
52
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
53
CLRS1999_ULAE.ppt