Study Manual Review - 1a. Testing the Assumptions of the Reported Claim Development Technique
Assume that the adequacy of the case O/S has not been changing over time. However if it has, then the
fundamental assumption of the development method does not hold and the method will not produce reliable
results of ultimate claims or unpaid claims.
Approaches to determine if an insurer has sustained changes in case O/S adequacy:
1. Meet with the claims department management to discuss the claims process
2. Calculate various claim development diagnostic tests, including: the ratio of paid-to-reported claims,
average case O/S, average reported claim, and average paid claims.
In their medical malpractice example, B/S compares the annual change in the average case O/S to the
annual change in the average paid claims to determine a shift in case O/S adequacy.
Begin testing the underlying assumptions in Exhibit I, Sheet 4 with a review of the average case O/S triangle.
 Average case O/S triangle is the unadjusted case O/S divided by the open claim counts
 Look down each column, the two latest points are significantly higher than the preceding values at each
maturity age (i.e., the latest two diagonals are higher than prior diagonals).
At 24 months, the average case O/S values for the last two AYs are $22,477 and $32,160 compared to
$13,785 and $11,433 for the preceding two AYs.
Chapter 13 - Berquist-Sherman Techniques
Berq-Sher Med Mal Insurer
Development Triangle - Unadjusted Data
Accident
Year
12
24
1969
3,701
5,660
1970
7,250
10,635
1971
5,877
8,122
1972
8,324
11,433
1973
10,124
13,785
1974
8,261
22,477
1975
11,176
32,160
1976
13,028
Exhibit I
Sheet4
Unadjusted Average Case Outstanding as of (months)
36
9,262
12,960
10,613
15,499
30,223
34,402
48
10,151
14,221
14,373
25,040
33,266
60
11,745
17,067
21,706
28,019
Annual Change based on Exponential Regression Analysis of Severities and Accident Year
15.62%
29.50%
31.11%
34.17%
32.96%
Goodness of Fit Test of Exponential Regression Analysis (R-Squared)
79.96%
89.46%
85.79%
94.05%
98.88%
72
16,627
23,411
29,044
84
19,238
24,551
32.16%
27.62%
98.31%
100.00%
96
21,423
Exponential regression is used to determine the annual trend rate in the average case O/S at each age.
 The average case O/S is fit at each maturity age with the AY.
 The fitted trend rate and the R-squared test (goodness of fit) for each age is shown.
 Annual trend rates of 30% for maturity ages 24 months through 72 months with R-squared values of
85% or greater for all of these ages.
Testing the Assumptions of the Reported Claim Development Technique (continued):
Exhibit I, Sheet 5: Ratios of paid-to-reported claims and trend rates in the average paid claim triangle.
 If there has been an increase in the case O/S adequacy level, the ratios of paid-to-reported claims
should be decreasing along the latest two diagonals of the triangle.
 Some decreases are seen in this ratio triangle, but there is variability and it is hard to draw definitive
conclusions based on this diagnostic.
The test that B/S uses is to compare annual trend rates, using regression, of the average case O/S and the
average paid claims on closed counts.
The paid claim triangle can be used with the closed claim counts triangle to approximate the average paid
claims on closed counts (since partial payments are not common in Med Mal).
Mechanics of the Berquist-Sherman Paid Claim Development Adjustment
1. Determine the disposal rates by AY and maturity, where the definition of disposal rates is the same as that
used in the FS approach of Chapter 11.
Exhibit II, Sheets 3 and 4: Projected number of ultimate claims based on reported claim counts
Exhibit II
Sheet 3
Chapter 13 - Berquist-Sherman Techniques
Berq-Sher Auto BI Insurer
Reported Claim Counts
PART 1 - Data Triangle
Accident
Year
12
1969
6,553
1970
7,277
1971
8,259
1972
7,858
1973
7,808
1974
6,278
1975
6,446
1976
6,115
24
7,696
8,537
9,765
9,474
9,376
7,614
7,884
PART 2 - Age-to-Age Factors
Accident
Year
12 - 24
24 - 36
1969
1.174
1.010
1970
1.173
1.009
1971
1.182
1.012
1972
1.206
1.015
1973
1.201
1.015
1974
1.213
1.017
1975
1.223
Reported Claim Counts as of (Months)
36
48
60
72
7,770
7,799
7,814
7,819
8,615
8,661
8,675
8,679
9,884
9,926
9,940
9,945
9,615
9,664
9,680
9,513
9,562
7,741
Age-to-Age Factors
36 - 48
48 - 60
1.004
1.002
1.005
1.002
1.004
1.001
1.005
1.002
1.005
60 - 72
1.001
1.000
1.001
72 - 84
1.000
1.000
84
7,820
8,682
84 - 96
1.000
96
7,821
To Ult
PART 3 - Average Age-to-Age Factors
12 - 24
Simple Average
All Years
1.196
24 - 36
Averages
36 - 48
48 - 60
1.013
1.005
1.002
60 - 72
72 - 84
1.001
1.000
84 - 96
To Ult
1.000
PART 4 - Selected Age-to-Age Factors
12 - 24
Selected
1.196
CDF to Ultimate
1.221
Percent Reported
81.9%
24 - 36
1.013
1.021
97.9%
Development Factor Selection
36 - 48
48 - 60
60 - 72
1.005
1.002
1.001
1.008
1.003
1.001
99.2%
99.7%
99.9%
Exhibit II
Sheet 3
Chapter 13 - Berquist-Sherman Techniques
Berq-Sher Auto BI Insurer
Reported Claim Counts
Accident
Year
(1)
1969
1970
1971
1972
1973
1974
1975
1976
Total
Age of
Accident Year
at 12/31/76
(2)
96
84
72
60
48
36
24
12
Reported
Claim Counts
at 12/31/76
(3)
7,821
8,682
9,945
9,680
9,562
7,741
7,884
6,115
67,430
72 - 84
84 - 96
96- 108
1.000
1.000
1.000
1.000
1.000
1.000
100.0%
100.0%
100.0%
CDF
to Ultimate
(4)
1.000
1.000
1.000
1.001
1.003
1.008
1.021
1.221
Projected
Ultimate
Claim Counts
(5) = [(3) x (4)]
7,821
8,682
9,945
9,690
9,591
7,803
8,051
7,468
69,050
Column Notes:
(2) Age of accident year in (1) at December 31, 1976.
(3) Based on data from Berq-Sher Auto BI Insurer.
(4) Based on CDF from Exhibit II, Sheet 3.
Exhibit II, Sheet 5: Disposal Rate and Development of Adjusted Closed Claim Counts
Exhibit II
Sheet 5
Chapter 13 - Berquist-Sherman Techniques
Berq-Sher Auto BI Insurer
Disposal Rate and Development of Adjusted Closed Claim Counts
Accident
Year
1969
1970
1971
1972
1973
1974
1975
1976
12
0.522
0.510
0.494
0.464
0.461
0.447
0.437
0.433
24
0.846
0.833
0.822
0.809
0.799
0.796
0.773
36
0.920
0.910
0.912
0.903
0.903
0.886
Selected Disposal Rate by Maturity Age
0.433
0.773
0.886
Accident
Year
1969
1970
1971
1972
1973
1974
1975
1976
12
3,383
3,755
4,301
4,191
4,148
3,375
3,482
3,230
Disposal Rate as of (months)
48
60
72
0.958
0.981
0.991
0.955
0.978
0.991
0.957
0.981
0.991
0.955
0.977
0.948
0.948
0.977
0.991
Adjusted Closed Claim Counts as of (months)
24
36
48
60
72
6,048
6,932
7,415
7,643
7,750
6,714
7,695
8,231
8,484
8,603
7,691
8,814
9,429
9,719
9,855
7,494
8,588
9,187
9,469
7,417
8,500
9,093
6,035
6,916
6,226
84
0.996
0.996
96
0.998
0.996
0.998
84
7,789
8,647
96
7,806
Projected
Ultimate
Claim Counts
7,821
8,682
9,945
9,690
9,591
7,803
8,051
7,468
Disposal rate equals cumulative closed claim counts for each AY-maturity age cell/ultimate claim counts
for a given accident year.
The disposal rates show a decrease in the rate of claims settlement.
B/S select the claims disposal rate along the latest diagonal as the basis for adjusting the closed claim
count triangle, since the latest diagonal of the adjusted paid claim triangle will not change from the
unadjusted paid claim triangle.