Transcript The “Modified Bornhuetter-Ferguson” Approach to IBNR Allocation Trent Vaughn, Republic Insurance Phoebe Tinney, Towers Perrin.

The “Modified Bornhuetter-Ferguson” Approach
to IBNR Allocation
Trent Vaughn, Republic Insurance
Phoebe Tinney, Towers Perrin
What makes a good IBNR
allocation procedure?
•
•
•
•
Provide reasonable and stable results
Easy to automate
Explainable in “intuitive terms”
No need for “off-balance adjustment
factor”
• Allows for differences in a priori loss ratios
Why allocate IBNR?
• Annual Statement requirements
• Management reports
• Reinsurance Accounting
Potential Pitfalls of IBNR Allocation
• May imply degree of precision that does
not exist
• May be occasions when full reserve study
is required instead of allocation
Two Common Methods for
Allocating IBNR
• Earned Premium Method
– Weakness: Ignores differences in claim
frequency and loss ratio by program
• Case-Incurred Loss Method
– Weakness: Often results in very unstable and
unreliable allocations
“Modified BF Method”
• Compromise between earned premium
and case-incurred loss allocations
– Relative weights assigned to each method
vary by accident year
– Immature Accident Years: Most of the weight
goes to EP allocation
– Older Accident Years: Most of the weight goes
to Case Incurred Allocation
• Numeric Example
Loss Projections & Earned Premium
Calendar/
Accident Year
2000
2001
2002
Calendar/
Accident Year
Cumulative
Case Incurred
Losses
Earned
Premium
1,200
1,200
1,200
700
650
200
Earned
Premium
Program
Projected
Ultimate
Losses
900
900
900
Cumulative
Case Incurred
Losses
2000
2000
2000
A
B
C
500
400
300
400
200
100
2001
2001
2001
A
B
C
500
400
300
350
200
100
2002
2002
2002
A
B
C
500
400
300
185
10
5
Loss IBNR
200
250
700
Projected
Ultimate
Loss Ratio
75.00%
75.00%
75.00%
Step 1: Earned Premium Method
Calendar/
Accident Year
2000
2001
2002
Calendar/
Accident Year
Cumulative
Case Incurred
Losses
Earned
Premium
1,200
1,200
1,200
700
650
200
Earned
Premium
Program
Projected
Ultimate
Losses
900
900
900
Cumulative
Case Incurred
Losses
Loss IBNR
200
250
700
Pro-rata
Earned
Premium
Projected
Ultimate
Loss Ratio
75.00%
75.00%
75.00%
Premium
Based
Allocation
2000
2000
2000
A
B
C
500
400
300
400
200
100
41.67%
33.33%
25.00%
83.33
66.67
50.00
2001
2001
2001
A
B
C
500
400
300
350
200
100
41.67%
33.33%
25.00%
104.17
83.33
62.50
2002
2002
2002
A
B
C
500
400
300
185
10
5
41.67%
33.33%
25.00%
291.67
233.33
175.00
Earned Premium for
Program / Total
Earned Premium for
the Year
Pro-rata Earned
Premium x IBNR for
the Year
Step 2: Case Incurred Loss Method
Calendar/
Accident Year
2000
2001
2002
Calendar/
Accident Year
Cumulative
Case Incurred
Losses
Earned
Premium
1,200
1,200
1,200
700
650
200
Earned
Premium
Program
Projected
Ultimate
Losses
900
900
900
Cumulative
Case Incurred
Losses
2000
2000
2000
A
B
C
500
400
300
400
200
100
2001
2001
2001
A
B
C
500
400
300
350
200
100
2002
2002
2002
A
B
C
500
400
300
185
10
5
Loss IBNR
200
250
700
Pro-rata
Earned
Premium
Projected
Ultimate
Loss Ratio
75.00%
75.00%
75.00%
Premium
Based
Allocation
41.67%
83.33
Case
Incurred Losses
33.33%
66.67
for the Program / Total
25.00%
50.00
Case Incurred Losses
for the Year
41.67%
104.17
33.33%
83.33
25.00%
62.50
Pro-rata Case
Incurred Losses x
41.67%
291.67
IBNR for the Year
33.33%
233.33
25.00%
175.00
Pro-rata
Case Incurred
Case Incurred
Based
Losses
Allocation
57.14%
28.57%
14.29%
114.29
57.14
28.57
53.85%
30.77%
15.38%
134.62
76.92
38.46
92.50%
5.00%
2.50%
647.50
35.00
17.50
Step 3: Calculating Weights
Calendar/
Accident Year
2000
2001
2002
Calendar/
Accident Year
Cumulative
Case Incurred
Losses
Earned
Premium
1,200
1,200
1,200
700
650
200
Earned
Premium
Program
Projected
Ultimate
Losses
900
900
900
Loss IBNR
200
250
700
Projected Ultimate
Losses / Cumulative
Case Incurred Losses
Cumulative
Pro-rata
Case Incurred
Earned
Losses
Premium
Projected
Ultimate
Loss Ratio
Implied
LDF
75.00%
75.00%
75.00%
1.286
1.385
4.500
Weight to
Case Incurred
Method
0.778
0.722
0.222
1 - Weight to
Case Incurred
Pro-rata
Case
Incurred
Method
Case Incurred
Based
Losses
Allocation
1 / Implied LDF
Premium
Based
Allocation
2000
2000
2000
A
B
C
500
400
300
400
200
100
41.67%
33.33%
25.00%
83.33
66.67
50.00
57.14%
28.57%
14.29%
114.29
57.14
28.57
2001
2001
2001
A
B
C
500
400
300
350
200
100
41.67%
33.33%
25.00%
104.17
83.33
62.50
53.85%
30.77%
15.38%
134.62
76.92
38.46
2002
2002
2002
A
B
C
500
400
300
185
10
5
41.67%
33.33%
25.00%
291.67
233.33
175.00
92.50%
5.00%
2.50%
647.50
35.00
17.50
Weight to
Premium
Method
0.222
0.278
0.778
Step 4: Weighted Average Allocation
Calendar/
Accident Year
2000
2001
2002
Calendar/
Accident Year
Cumulative
Case Incurred
Losses
Earned
Premium
1,200
1,200
1,200
700
650
200
Earned
Premium
Program
Projected
Ultimate
Losses
Loss IBNR
Projected
Ultimate
Loss Ratio
Case
*
900Incurred Based
200Allocation75.00%
Weight
Method
900 to Case Incurred
250
75.00%
+900
Premium Based
Allocation * 75.00%
700
Weight to Premium Method for
Year
Cumulative
Case Incurred
Losses
Pro-rata
Earned
Premium
Premium
Based
Allocation
Implied
LDF
1.286
1.385
4.500
Weight to
Case Incurred
Method
0.778
0.722
0.222
Pro-rata
Case Incurred
Case Incurred
Based
Losses
Allocation
Weight to
Premium
Method
0.222
0.278
0.778
Weighted
Average
Allocation
2000
2000
2000
A
B
C
500
400
300
400
200
100
41.67%
33.33%
25.00%
83.33
66.67
50.00
57.14%
28.57%
14.29%
114.29
57.14
28.57
107.41
59.26
33.33
2001
2001
2001
A
B
C
500
400
300
350
200
100
41.67%
33.33%
25.00%
104.17
83.33
62.50
53.85%
30.77%
15.38%
134.62
76.92
38.46
126.16
78.70
45.14
2002
2002
2002
A
B
C
500
400
300
185
10
5
41.67%
33.33%
25.00%
291.67
233.33
175.00
92.50%
5.00%
2.50%
647.50
35.00
17.50
370.74
189.26
140.00
Alternative: Expected Loss Method
Calendar/
Accident Year
2000
2001
2002
Calendar/
Accident Year
Cumulative
Case Incurred
Losses
Earned
Premium
1,200
1,200
1,200
700
650
200
Earned
Premium
Program
Projected
Ultimate
Losses
900
900
900
Expected
Loss
Ratio
Loss IBNR
Projected
Ultimate
Loss Ratio
200
75.0%
250
75.0%
Allocation
Pro700 based on75.0%
rata Expected Losses
Expected
Ultimate
Losses
Pro-rata
Expected
Losses
Implied
LDF
1.286
1.385
4.500
Weight to
Case Incurred
Method
0.778
0.722
0.222
Expected Loss Case Incurred
Based
Based
Allocation
Allocation
Weight to
Premium
Method
0.222
0.278
0.778
Weighted
Average
Allocation
2000
2000
2000
A
B
C
400
400
400
85.0%
75.0%
65.0%
340
300
260
37.78%
33.33%
28.89%
75.56
66.67
57.78
114.29
57.14
28.57
105.68
59.26
35.06
2001
2001
2001
A
B
C
400
400
400
85.0%
75.0%
65.0%
340
300
260
37.78%
33.33%
28.89%
94.44
83.33
72.22
134.62
76.92
38.46
123.46
78.70
47.84
2002
2002
2002
A
B
C
400
400
400
85.0%
75.0%
65.0%
340
300
260
37.78%
33.33%
28.89%
264.44
233.33
202.22
647.50
35.00
17.50
349.57
189.26
161.17
Mature Accident Years
• Modified BF Procedure may not work as
well as simpler methods
– Will allocate largely in accordance with caseincurred loss
– May be more appropriate to allocate in
proportion to open claims or case reserves
Negative IBNR amounts
• “Implied LDF” in Modified BF weighting
procedure will be less than unity
– Thus, weight given to case-incurred allocation
is greater than 1, weight given to EP
allocation is negative
• For negative IBNR, straight case-incurred
allocation may be more appropriate