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Basic Track II
1998 CLRS
September 28, 1998
Philadelphia, Pennsylvania
CLRS Basic Track II
1
Introduction

Topics Covered
»
»
Comparison of Results from Paid
and Incurred LDMs
Reasonableness Checks
–
–
»
Current Year Sensitivity Analysis
–
–
–
–
»
Historical Ratios
Ultimate Levels
Rate Level Adequacy
Claim Frequency & Severity
Claim Closure Rate
Adequacy of Case Reserves
Importance of Tail Factors
CLRS Basic Track II
2
Comparison of LDM
Projections
Accident
Year
1992
1993
1994
1995
1996
1997
Estimated Ultimate Losses Based on:
Paid
Incurred
Average =
LDM
LDM
Selected
Paid Method
Incurred Method
Average
11,244
11,250
11,247
12,990
12,738
12,864
15,224
14,471
14,848
17,601
16,307
16,954
19,126
17,531
18,329
21,457
20,105
20,781
Total
97,642
92,402
95,023
Ultimate Loss Projections
19
92
19
93
19
94
19
95
19
96
19
97
25,000
20,000
15,000
10,000
5,000
-
CLRS Basic Track II
Paid
Method
Incurred
Method
Average
3
Comparison of Loss
Development
Methods
Underlying
Assumptions
Pro
PLDM: No changes in the payment pattern
ILDM: No changes in case reserve adequacy
PLDM: “Hard” data; no estimates involved
ILDM: Uses all the available information
PLDM: May generate large, volatile loss
development factors & take longer to
develop to ultimate
Con
CLRS Basic Track II
ILDM: Uses case reserves, which are
estimates, to develop estimates of
ultimate losses
4
Key Assumptions &
Potential Problems
Assumptions
Sample Problems
Claims settlement patterns unchanging
Increasing delays in claim closing rates
Case reserving practices & philosophies
unchanging
Conscious effort to improve case reserve
adequacy;
Introduction of new case reserving
procedures
No claim processing changes
Change in data processing;
Revised claim payment recording
procedures
Policy limits have no impact on loss
development
Increasing frequency of full policy limits
claims;
Changing policy limits
Loss development unaffected by
changing
loss cost trends
Surges in inflation;
Increased litigation;
Diminished policy defenses
No change in mix of business
Changes in reinsurance coverages;
Increased long-tail exposures;
Introduction of new or revised coverages
No cyclical loss development
No data anomalies
CLRS Basic Track II
Claims settlement or reserving impacted
by business underwriting cycles
Catastrophic or unusual losses reflected in
loss experience;
Unusual claim settlement/reporting delays
5
Comparison of
Estimated Reserves
Estimated Loss Reserves Based on:
Paid
Incurred
Average =
LDM
LDM
Selected
Paid Method Incurred Method
Average
736
742
739
1,454
1,202
1,328
2,766
2,013
2,390
4,902
3,608
4,255
7,954
6,359
7,157
14,495
13,143
13,819
Accident
Year
1992
1993
1994
1995
1996
1997
Total
32,307
27,067
Accident Y
1992
1993
1994
1995
1996
1997
29,688
Components of Selected
Reserve @ 12/31/97
16,000
14,000
12,000
10,000
IBNR
Case
8,000
6,000
4,000
2,000
97
19
96
19
95
19
94
19
93
19
19
92
-
Accident Year
CLRS Basic Track II
6
Formulas to Derive
IBNR Reserves

Once an estimate of ultimate
loss has been obtained, the
arithmetic of IBNR is simple.
Ultimate Losses
Ultimate Losses
Unpaid Losses
Minus
Minus
Minus
Paid Losses
Reported
Losses
Case Reserves
Minus
Case Reserves
CLRS Basic Track II
7
Other Reserving
Methods Tested

Discussed in subsequent CLRS
sessions
»
»
»
»

Expected Loss Technique
Bornhuetter-Ferguson Method
Severity/Frequency Method
Many, many others
Note that development method
may also be applied to claim
counts.
CLRS Basic Track II
8
Development Method
on Claim Counts
Accident
Year
1992
1993
1994
1995
1996
1997
Cumulative Number of Claims Reported *
Development Stage in Months
12
24
36
48
60
72
1,428
1,710
1,358
1,510
1,488
1,604
2,772
3,032
2,780
2,588
2,604
2,850
3,086
2,990
2,656
2,866
3,094
3,000
2,870
3,110
2,888
Final
Total
Cost
???
???
???
???
???
???
'* The definition of a "reported claim" varies from
company to company. Some companies count claims as
one per claimant when more than one claim is involved
in an incident. Some companies remove claims that close
without payment. We assume that Typical P&C Insurance
Company counts on a per claimant basis and includes
closed claims without payment.
CLRS Basic Track II
9
Reported Counts DM:
RTR Factors Selected
Evaluation Interval in Months
Accident
Year
12-24
24-36
36-48
48-60
60-72
1992
1.941
1.028
1.006
1.001
1.006
1993
1.773
1.018
1.003
1.005
1994
2.047
1.076
1.003
1995
1.714
1.026
1996
1.750
1997
Simple Average - All Years
1.845
1.037
1.004
1.003
1.006
Simple Average - Latest 3 Years
1.837
1.040
1.004
Simple Average - Excluding High & Low
1.821
1.027
1.004
Selected RTR Development Factors
1.821
1.037
1.006
Selected Development Factors to Ultimate
1.919
1.054
1.016
CLRS Basic Track II
XXX
XXX
XXX
XXX
1.004
1.006
1.010
1.006
72 to
Ultimate
???
1.000
1.000
10
Reported Counts DM:
Projection
Actual
Estimated Estimated
Claims Development Ultimate Unreported
Accident Reported
Factors to
Claims
Claims
Year @ 12/31/97
Ultimate
[(2) x (3)]
(4) - (2)
(1)
(2)
(3)
(4)
(5)
1992
1993
1994
1995
1996
1997
2,888
3,110
3,000
2,656
2,604
1,604
Total
15,862
CLRS Basic Track II
1.000
1.006
1.010
1.016
1.054
1.919
2,888
3,129
3,030
2,699
2,744
3,078
0
19
30
43
140
1,474
17,568
1,706
11
Reasonableness

Ultimate losses should be
measured for reasonableness
against relevant indicators:
»
premium
–
»
exposures or number of policies
–
»
frequency, pure premium
claim counts
–

loss ratios
severity
Assumptions & methods should
be documented and subjected to
sensitivity analysis.
CLRS Basic Track II
12
Reasonableness
Checks:
Ultimate Loss Ratios
Accident
Year
Earned
Premium
Est. Ultimate Losses ($000)
Using:
PLDM
ILDM
Selected
Indicated Loss Ratio
Using:
PLDM
ILDM Selected
1992
1993
1994
1995
1996
1997
18,168
21,995
24,173
25,534
31,341
38,469
11,244
12,990
15,224
17,601
19,126
21,457
11,250
12,738
14,471
16,307
17,531
20,105
11,247
12,864
14,848
16,954
18,329
20,781
0.619
0.591
0.630
0.689
0.610
0.558
0.619
0.579
0.599
0.639
0.559
0.523
0.619
0.585
0.614
0.664
0.585
0.540
Total
159,680
97,642
92,402
95,023
0.611
0.579
0.595
Ultimate Loss Ratio
0.700
0.650
0.600
Paid LDM
0.550
Incurred LDM
0.500
Selected
1992
1993
1994
1995
1996
1997
Accident Year
CLRS Basic Track II
13
Reasonableness
Checks:
Frequency & Severity
Ultimate
Claim
Accident
Claim
Earned
Frequency
Year
Count
Exposures*
(2) / (3)
(1)
(2)
(3)
(4)
1992
2,888
102
28.314
1993
3,129
98
31.929
1994
3,030
103
29.417
1995
2,699
105
25.705
1996
2,744
109
25.174
1997
3,078
118
26.085
* Earned exposures are used to measure the underlying
volume or units covered by insurance in each year. For
automobile liability, exposures are typically measured by
the number of cars insured for the year.
Accident
Year
(1)
1992
1993
1994
1995
1996
1997
Ultimate
Claim
Count
(2)
2,888
3,129
3,030
2,699
2,744
3,078
CLRS Basic Track II
Est. Ultimate Losses ($000)
Using:
PLDM
ILDM
Selected
(3)
(4)
(5)
11,244
12,990
15,224
17,601
19,126
21,457
11,250
12,738
14,471
16,307
17,531
20,105
11,247
12,864
14,848
16,954
18,329
20,781
Indicated Severity
Using:
PLDM
ILDM
Selected
(6)
(7)
(8)
3,893
4,151
5,024
6,521
6,970
6,971
3,895
4,071
4,776
6,042
6,389
6,532
3,894
4,111
4,900
6,282
6,680
6,751
14
Reasonableness
Checks: Pure
Premium
Values at 12 Months
Earned
Pure
Accident Exposures Reported Premium Percentage
Year
('000's)
Losses
[(2)/(1)]
Change
1992
1993
1994
1995
1996
1997
102
98
103
105
109
118
9,337
10,540
11,875
13,343
14,469
16,561
91.5
107.6
115.3
127.1
132.7
140.3
17%
7%
10%
4%
6%
1992
1993
1994
1995
1996
1997
At 12 Months
91.5
107.6
115.3
127.1
132.7
140.3
Estimated Ultimate Values
Earned
Pure
Accident Exposures Incurred Premium Percentage
Year
('000's)
LDM
[(2)/(1)]
Change
1992
1993
1994
1995
1996
1997
102
98
103
105
109
118
11,250
12,738
14,471
16,307
17,531
20,105
110.3
130.0
140.5
155.3
160.8
170.4
18%
8%
11%
4%
6%
Ultim ate Pure
Prem ium
Pure Premium Trends
200.0
150.0
100.0
50.0
1992 1993 1994
A t 12 M o nths
CLRS Basic Track II
1995 1996 1997
A dditio nal to Ultimate
15
Sensitivity Analysis:
Current Year Analysis

Improvements in results may
stem from:
»
»
»

Higher rates
Lower claim frequency
Lower claim severity
Better results would appear to
be present if:
»
»
»
Claims were being processed or
paid more slowly
Case reserves were less adequate
Mix of business is different
CLRS Basic Track II
16
Sensitivity Analysis:
Ratios

Review historical relationships
» Losses
– Reported losses to paid
» Claim counts
– Settlement rate
– Ratio of CNP claims to total closed
claims
» Losses and Claim Counts
– Severities or average values
CLRS Basic Track II
17
Sensitivity Analysis:
Ratios - Examples
Accident
Year
1992
1993
1994
1995
1996
1997
Ratio of Paid Losses to Reported Losses
Development Stage in Months
12
24
36
48
60
72
0.405
0.400
0.413
0.428
0.421
0.420
Accident
Year
12
1992
1993
1994
1995
1996
1997
6,539
6,164
8,744
8,836
9,724
10,325
CLRS Basic Track II
0.615
0.618
0.641
0.661
0.666
0.735
0.745
0.772
0.790
0.822
0.838
0.864
0.889
0.907
Average Reported Loss
Development Stage in Months
24
36
48
60
3,913
4,025
4,976
6,005
6,442
3,892
4,067
4,762
6,049
3,905
4,101
4,804
3,915
4,092
0.934
72
3,895
18
Sensitivity Analysis:
Rate Level Adequacy
Accident
Year
1992
1993
1994
1995
1996
1997
Earned
Premium
18,168
21,995
24,173
25,534
31,341
38,469
Earned
Exposures
102
98
103
105
109
118
Average
Premium
178.1
224.4
234.7
243.2
287.5
326.0
Change from
Prior Year
26%
5%
4%
18%
13%
Increases in average premium are primarily due to:
Changes in the mix of business.
Rate increases.
If the changes in average premium in the latest two years are due
to rate increases, then that would explain much of the improvement
in loss ratios.
If the changes are due to shifts in the mix of business, then the improvement
in the loss ratios may or may not be real. Further investigation would be
needed to understand what the shift was and whether the different business
types have varying loss development characteristics.
CLRS Basic Track II
19
Sensitivity Analysis:
Claim Severity
Accident
Year
(1)
1992
1993
1994
1995
1996
1997
Est. Ultimate Severity
Using:
PLDM
ILDM
Selected
(3)
(4)
(5)
3,893
4,151
5,024
6,521
6,970
6,971
3,895
4,071
4,776
6,042
6,389
6,532
3,894
4,111
4,900
6,282
6,680
6,751
Est. Change in Severity
Using:
PLDM
ILDM
Selected
(6)
(7)
(8)
7%
21%
30%
7%
0%
5%
17%
27%
6%
2%
6%
19%
28%
6%
1%
There is no consistent pattern in severity, except that it has
generally increased over the years. This is typical, as we expect
severity to increase due to inflation.
The very small increase in severity that is forecast for the current
year is unusual. In the same year, claim frequency has increased.
Perhaps there is an increase in the number of small dollar claims?
This would be a good question to ask the Claim Department.
CLRS Basic Track II
20
Sensivitity Analysis:
Claim Closure Rate
Accident
Year
1992
1993
1994
1995
1996
1997
Accident
Year
1992
1993
1994
1995
1996
1997
Number of Closed Claims by Development Age
12
24
36
48
60
72
826
2,131
2,559
2,706
2,795
782
2,308
2,738
2,957
3,049
780
2,146
2,665
2,832
917
1,980
2,368
911
1,978
Ultimate
Claims
2,845
2,888
3,129
3,030
2,699
2,744
1,106
3,078
Percentage Closed to Est. Ultimate Number
12
24
36
48
60
72
29%
74%
89%
94%
97%
25%
74%
88%
95%
97%
26%
71%
88%
93%
34%
73%
88%
33%
72%
99%
36%
Example: 29% = 826 / 2,888
In the past few years, claims have been closing more rapidly. This
would imply that claims are being paid more rapidly and that the paid
loss development factor is probably too high. One of the major
assumptions of the PLDM (consistent payment patterns) has been
violated.
CLRS Basic Track II
21
Sensitivity Analysis:
Case Reserve
Adequacy
Accident
Year
1992
1993
1994
1995
1996
1997
Accident
Year
1992
1993
1994
1995
1996
1997
Accident
Year
1992
1993
1994
1995
1996
1997
CLRS Basic Track II
12
Case Reserves ($000)
24
36
48
60
5,557
4,176
2,936
1,987
1,245
6,328
4,664
3,200
2,051
1,189
6,974
4,968
3,251
1,955
7,635
5,274
3,367
8,376
5,604
72
742
9,599
12
Number of Open Claims
24
36
48
60
72
602
641
291
160
75
928
724
348
137
61
578
634
325
168
593
608
288
577
626
43
498
12
Average Case Reserve
24
36
48
60
9,231
6,515
10,089
12,419
16,600
6,819
6,442
9,195
14,971
19,492
12,066
7,836
10,003
11,637
12,875
8,674
11,691
14,516
8,952
72
17,256
19,275
22
Sensitivity Analysis:
Case Reserve
Adequacy
In general, we expect increasing numbers:
1. Across the rows because smaller claims settle more
quickly; and
2. Down the columns due to inflation.
It is important to understand the company’s case
reserving philosophy and procedures to be able to
interpret trends in the data. Many changes in case reserve
procedures can be monitored by talking to the Claims
Department.
Changes in case reserve adequacy affect incurred loss
development patterns. For example, if case reserves were
less adequate in the current accident year, greater future
development would be expected for those accidents that
was typical in the past. Use of historical loss development
factors in this situation would underestimate future
development and lead to inadequate overall reserve
estimates.
CLRS Basic Track II
23
Sensitivity Analysis:
Case Reserve
Adequacy
25000
Average Case Reserve
@ 12 Months
20000
15000
10000
5000
0
1992
1993
1994
1995
1996
1997
Actual
Accident Year Fitted-exp
The fit of the average case reserves @ 12 months
implies an annualized trend rate of 19%! This rate is
substantially higher than industry trend rates for
private passenger automobile liability, which are in
the range of 8% to 10%.
CLRS Basic Track II
24
Frequency/Severity
Projection Method
Accident
Year
1992
1993
1994
1995
1996
1997
Estimated Ultimate Frequency
Linear Exponential
Actual
Fit
Fit
28.3
31.9
29.4
25.7
25.2
??
R-squared
Selected for 1997
30.6
29.4
28.1
26.9
25.6
24.4
30.6
29.3
28.0
26.8
25.6
24.4
0.491
0.509
24.4
Estimated Ultimate Severity
Linear Exponential
Actual
Fit
Fit
3,894
4,111
4,900
6,282
6,680
??
3,741
4,347
5,052
5,872
6,824
7,931
3,625
4,399
5,173
5,948
6,722
7,496
0.954
0.946
7,496
A line or another curve can be fitted through actual
values for accident years 1992 through 1996. The fitted
points for the current year can be used as estimates for
the ultimate frequency and severity.
R-squared is a measure of how well a fitted curve
matches the data. The value can range from 0 to 1.00,
where 1.00 indicates a perfect fit.
CLRS Basic Track II
25
Frequency/Severity
Projection Method
Accident
Year
Earned
Exposures
Ultimate
Frequency
1992
1993
1994
1995
1996
1997
102
98
103
105
109
118
Total
635
Ultimate
Severity
28.3
31.9
29.4
25.7
25.2
24.4
3,894
4,111
4,900
6,282
6,680
7,496
Losses
Losses
Estimated @ 12/31/97
11,247
12,864
14,848
16,954
18,329
21,626
11,247
2,356
3,312
4,496
5,630
10,454
95,868
37,495
Comparison of Projected Loss Ratios for 1997
Paid Loss Development Method
55.8%
Incurred Loss Development Method
52.3%
Frequency and Severity Method
56.2%
CLRS Basic Track II
26
Selection of Tail
Factors

How much difference does the tail
factor selection make?
Effect on Estimates Given a 2% Increase in Reported Losses Tail Factor
Reported
Accident
Losses
Year
@ 12/31/97
1992
1993
1994
1995
1996
1997
11,250
12,725
14,413
16,066
16,776
16,561
Total
87,791
Estimated
Selected LDF's
Ultimate Earned
RTR
Age to Ult. Losses Premium
1.020
1.001
1.003
1.011
1.030
1.162
1.020
1.021
1.024
1.035
1.066
1.239
11,475
12,992
14,759
16,628
17,883
20,519
18,168
21,995
24,173
25,534
31,341
38,469
63%
59%
61%
65%
57%
53%
967
1,456
2,301
3,929
6,711
13,557
94,256
159,680
59%
28,921
Estimated Unpiad Losses Based on Original ILDM
(Without the 2% Tail Factor Increase)
Increase in Estimated Unpaid Losses Due to Increased Tail Factor
CLRS Basic Track II
Revised
Unpaid
Loss
Losses
Ratio @ 12/31/97
27,067
7%
27
Selection of Tail
Factors
Ultimate losses increase by 2%
or $1.8 million.
 Loss reserves also increase by
$1.8 million; however, the 2%
increase in the tail factor
represents a 7% increase in
overall reserve levels!
 IBNR reserves are increased by
an even higher percentage as a
result of an increase of 2% in
the tail factor

CLRS Basic Track II
28