1. RESERVING TECHNIQUES
By Lorie Darrow
Select Actuarial

2. Situational Reserving Internal/External Forces
Topics
Fundamentals
Situational Reserving
Internal/External Forces
Business Context/Pricing
The opinions expressed in this document are solely those of the presenter.

3. Fundamentals of Loss Reserving
Definitions/Terminology
Basic Reserving Techniques
Paid Loss Development Method (PLDM)
Incurred Loss Development Method (ILDM)
Expected Loss Ratio (ELR)
Bornhuetter-Ferguson (BF)
Update

4. Definitions

5. Basic Reserving Techniques Definitions
Loss Development
The financial activity on claims from the time they occur to the time they are eventually settled and paid
Triangles
Compiled to measure the changes in cumulative claim activity over time in order to estimate patterns of future activity
Loss Development Factor
The ratio of losses at successive evaluations for a defined group of claims (e.g. accident year)

6. Examples of Reserving Issues
Immature Years
Claim Department Changes
Environmental Changes
Unique Exposures

7. Basic Reserving Techniques
Compilation of Paid Loss Triangle
The losses are sorted by the year in which the accident occurred
The losses are summed at the end of each year
Losses paid to date are shown on the most recent diagonal
The data is organized in this way to highlight historical patterns

8. Basic Reserving Techniques
Calendar Year Paid Losses by Accident Year

9. Basic Reserving Techniques
Compilation of Paid Loss Triangle
The goal is to estimate the total amount that will ultimately be paid 12 24 36 48 60 72
Yr 1
3,780
6,671
8,156
9,205
9,990
10,508
???
Yr 2
4,212
7,541
9,351
10,639
11,536
Yr 3
4,901
8,864
10,987
12,458
Yr 4
5,708
10,268
12,699
Yr 5
6,093
11,172
Yr 6
6,962
Accident
Year
Cumulative Paid Losses ($000 Omitted)
Development Stage in Months
Ultimate
Total
Cost

10. Basic Reserving Techniques: Paid Loss Development Factors
Loss Development Factors (LDFs) are also known as:
Age-to-Age factors
Link Ratios

11. Basic Reserving Techniques: Paid Loss Development Factors
12-24
24-36
36-48
48-60
60-72
72 to Ultimate
Yr 1
1.765
1.223
1.129
1.085
1.052
Yr 2
1.790
1.240
1.138
1.084
Yr 3
1.809
1.134
Yr 4
1.799
1.237
Yr 5
1.834
Yr 6
Simple Average - All Years
1.800
1.235
Simple Average - Latest 3 Years
1.814
1.239
xxx
Simple Average - Excluding High & Low
Weighted Average - All Years
1.803
Selected Loss Development Factors
1.070
Accident
Year
Evaluation Interval in Months

12. Basic Reserving Techniques: Paid Loss Development Factors
12-24
24-36
36-48
48-60
60-72
72 to Ultimate
Yr 1
1.765
1.223
1.129
1.085
1.052
1.070
Yr 2
1.790
1.240
1.138
1.084
Yr 3
1.809
1.134
Yr 4
1.799
1.237
Yr 5
1.834
1.235
Yr 6
1.800
Simple Average - All Years
Simple Average - Latest 3 Years
1.814
1.239
xxx
Simple Average - Excluding High & Low
Weighted Average - All Years
1.803
Selected Loss Development Factors
Accident
Year
Evaluation Interval in Months

13. Basic Reserving Techniques: Application of Paid LDM
Evaluation Interval in Months
72 to
12-24
24-36
36-48
48-60
60-72
Ultimate
LDFs
1.800
1.235
1.134
1.085
1.052
1.070
Cumulative Paid Losses ($000 Omitted)
Accident
Development Stage in Months
Total
Year 12 24 36 48 60 72
Cost
Yr 1
3,780
6,671
8,156
9,205
9,990
10,508
11,244
Yr 2
4,212
7,541
9,351
10,639
11,536
12,136
12,985
Yr 3
4,901
8,864
10,987
12,458
13,517
14,220
15,215
Yr 4
5,708
10,268
12,699
14,401
15,625
16,437
17,588
Yr 5
6,093
11,172
13,797
15,646
16,976
17,859
19,109
Yr 6
6,962
12,532
15,477
17,550
19,042
20,032
21,435
Sample Calculations for Accident Year 2003:
At 24 Months:
12,532 = 6,962 x 1.800
At 36 Months:
15,477 = 12,532 x 1.235 or
15,477 = 6,962 x x 1.235
Cumulative Development Factors
12 to Ult
24 to Ult
36 to Ult
48 to Ult
60 to Ult
72 to Ult
3.079
1.710
1.385
1.221
1.126

14. Basic Reserving Techniques: Paid LDM Projections & Reserves
Loss Reserve Yr 6 = $ million
Actual
Cumulative
Estimated
Paid
Development
Ultimate
Loss
Accident
Losses
Selected
Factors to
Reserves
Year
@ Yr 6
LDFs
[(2) x (4)]
[(5) - (2)]
(1)
(2)
(3)
(4)
(5)
(6)
Yr 1
10,508
1.070
11,244
736
Yr 2
11,536
1.052
1.126
12,985
1,449
Yr 3
12,458
1.085
1.221
15,215
2,757
Yr 4
12,699
1.134
1.385
17,588
4,889
Yr 5
11,172
1.235
1.710
19,109
7,937
Yr 6
6,962
1.800
3.079
21,435
14,473
Total
65,335
97,576
32,241

15. Selection of Tail Factors
How much difference does the tail factor selection make?
Effect on Estimates Given a 2% Increase in Paid Losses Tail Factor
Paid
Estimated
Unpaid
Accident
Losses
Selected LDF's
Ultimate
Earned
Year
@ Yr 6
LDF
Age to Ult.
Premium
Yr 1
10,508
1.070
1.090
11,454
18,168
946
Yr 2
11,536
1.052
1.147
13,232
21,995
1,696
Yr 3
12,458
1.085
1.244
15,498
24,173
3,040
Yr 4
12,699
1.134
1.411
17,918
25,534
5,219
Yr 5
11,172
1.235
1.743
19,473
31,341
8,301
Yr 6
6,962
1.800
3.137
21,840
38,469
14,878
Total
65,335
99,415
159,680
34,080
Estimated Unpaid Losses Based on Original PLDM
32,241
(Without the 2% Tail Factor Increase)
Increase in Estimated Unpaid Losses Due to Increased Tail Factor 6%

16. Basic Reserving Techniques: Compilation of Incurred Loss Triangle
Case Reserves ($000 Omitted)
Accident
Development Stage in Months
Year 12 24 36 48 60 72
Yr 1
5,657
4,176
2,936
1,987
1,145
742
Yr 2
6,428
4,664
3,300
2,051
1,189
Yr 3
7,074
4,968
3,251
1,955
Yr 4
7,635
5,174
3,367
Yr 5
8,376
5,604
Yr 6
9,599
Cumulative Reported Losses* ($000 Omitted)
Ultimate
Total
Cost
9,437
10,847
11,092
11,192
11,135
11,250
???
10,640
12,205
12,651
12,690
12,725
11,975
13,832
14,238
14,413
13,343
15,442
16,066
14,469
16,776
16,561
* = paid losses + case reserves

17. Basic Reserving Techniques: Selected Incurred LDFs
12-24
24-36
36-48
48-60
60-72
72 to Ultimate
Yr 1
1.149
1.023
1.009
0.995
1.010
Yr 2
1.147
1.037
1.003
Yr 3
1.155
1.029
1.012
Yr 4
1.157
1.040
Yr 5
1.159
Yr 6
Simple Average - All Years
1.153
1.032
1.008
0.999
Simple Average - Latest 3 Years
1.035
xxx
Simple Average - Excluding High & Low
1.154
1.033
Weighted Average - All Years
Selected Loss Development Factors
1.000
Selected Cumulative Development Factors to Ultimate
1.204
1.043
Accident
Year
Evaluation Interval in Months

18. Basic Reserving Techniques: Incurred LDM Projections & Reserves
Actual
Estimated
Reported
Development
Ultimate
Paid
Loss
Accident
Losses
Factors to
Reserves
Year
@ Yr 6
[(2) x (3)]
[(4) - (5)]
(1)
(2)
(3)
(4)
(5)
(6)
Yr 1
11,250
1.000
10,508
742
Yr 2
12,725
11,536
1,189
Yr 3
14,413
12,458
1,955
Yr 4
16,066
1.008
16,195
12,699
3,496
Yr 5
16,776
1.043
17,502
11,172
6,330
Yr 6
16,561
1.204
19,939
6,962
12,977
Total
87,791
92,023
65,335
26,688

19. Basic Reserving Techniques: Issues to Consider for LDM
Have there been any changes which might make the older years irrelevant?
Are the more recent years better predictors of the future?
Are there outlier points that need to be ignored or adjusted?
Examples
There are more motorcycle
losses in the oldest years; Typical
P&C no longer insures
motorcycles.
Typical P&C has begun writing
more business in state X.
In one year, there were bad ice
storms at the end of December.
late reporting caused unusually
high development in the next
year

20. Comparison of Loss Development Methods
Underlying Assumptions
PLDM: No changes in the payment pattern
ILDM: No changes in case reserve adequacy
Disadvantages
Advantages
PLDM: “Hard” data; no
estimates involved
ILDM: Uses all available
information
PLDM: May generate large,
volatile loss development factors &
take longer to develop to ultimate
ILDM: Uses case reserves, which
are estimates, to develop
estimates of ultimate losses

21. Expected Loss Ratio Method
Expected Loss Ratio (ELR)
The anticipated ratio of projected ultimate losses to
earned premiums
Sources:
Pricing assumptions
Historical data such as Schedule P
Industry data
Issue 1 immature years

22. Expected Loss Ratio Method
Use when you have no history such as:
New product lines
Radical changes in product lines
Immature accident years for long tailed lines
Can generate negative reserves or negative IBNR if
Ultimate Losses<Paid Losses-MOST LIKELY
ILLOGICAL!!!
Ultimate Losses<Incurred Losses
Issue 1 immature years

23. Expected Loss Ratio

24. Expected Loss Ratio Advantages Disadvantages Straight forward Not pure
Relies on pricing Relies on pricing

25. Bornhuetter-Ferguson Method
Reserves Base on ELR and Actual Loss
(EP x ELR) x (IBNR Factor) = (IBNR Reserves)
Where IBNR Factor = ( /CDF)
Actual + IBNR Reserve = Ultimate Losses
Case Reserves + IBNR Reserve = Total Reserve
The IBNR Factor is the percent of the expected losses
unreported.
Issue 1 immature years

26. Paid Bornhuetter-Ferguson
Need Exhibit

27. Incurred Bornhuetter-Ferguson
Need Exhibit

28. Bornhuetter-Ferguson Method
Advantages
Compromise between loss
development and expected loss
ratio methods
Avoids overreaction to unexpected
incurred losses to date
Suitable for new or volatile line of
business
Can be used with no internal loss
history
Easy to use
Disadvantages
Assumes that case
development is unrelated to
reported losses
Relies on accuracy of expected
loss ratio
Less responsive to losses incurred
to date
Relies on accuracy of earned premium
Issue 1 immature years

29. Comparison of all Methods
Need Exhibit

30. Comparison of all Methods
Need Exhibit

31. Situation Claim Department Changes
Paid to Incurred relationship changes – Munich Chain
Reserve strengthening or weakening - Berquist - Sherman
Review with Lorie

32. Situation Exposure Change Frequency and severity
Rate per unit of exposure
Mergers - mix change (state, line, segment)
Contractors - seasonality (summer vs. winter)
Review with Lorie

33. Situation Environment Small claims go away - type of claim (mix shift)
Frequency Severity will change
the development pattern
Review with Lorie

34. Unique Exposures : Methodology in estimating Unique liabilities
Asbestos – Science/no claims
-Ground up analysis
Credit Crunch – D&O and E&O
Construction Defect
Review with Lorie