1. 1999 CASUALTY LOSS RESERVE SEMINAR Intermediate Track II - Techniques
SEPTEMBER 1999

2. RESERVE MODELS Average Hindsight Reserve Method (Slides 2 - 12)
Average Incremental Paid Method (Slides )
Bornhuetter-Ferguson Method (Slides )
Slide 1

3. AVERAGE HINDSIGHT RESERVE METHOD
Goal:
Estimate The Average Future Settlement Value Per Claim For Recent Accident Years, Both For Claims Already Reported and Future Claim Reports
Based On:
Projected Ultimate Losses and Hindsight Average Values For More Mature Accident Years
Hindsight (Current Ultimate-Historical Payments) is the Implied Unpaid Amount
Slide 2

4. AVERAGE HINDSIGHT RESERVE METHOD Data Needed
Cumulative Paid Loss Triangle
Cumulative Closed (Paid) Claim Count Triangle
Estimated Ultimate Number of Claims for All Accident Years
Estimated Ultimate Losses For Several Mature Accident Years
Slide 3

5. AVERAGE HINDSIGHT RESERVE METHOD XYZ Auto Insurance Company Cumulative Paid Losses ($000)
Accident Months Of Development
Year Ultimate
$ $ $ $ $ $ $ $119.7 * * *
*To be estimated
Slide 4

6. AVERAGE HINDSIGHT RESERVE METHOD XYZ Auto Insurance Company Cumulative Number Of Closed Claims
Accident Months Of Development
Year Ultimate*
*Estimated using claim count development factors.
Slide 5

7. Slide 6 (1) (2) (3) (4) (5) (6) (7) (8)
AVERAGE HINDSIGHT RESERVE METHOD XYZ Auto Insurance Company Calculation Of Average Outstanding Losses At 36 Months Purpose: Project Future Settlement Dollars For 1996
Number
Estimated Estimated Number of to Settle Average
Estimated Paid Future Ultimate Closed Beyond Future
Accident Ultimate Losses at Payments Number Claims at Mos* Payment Year Losses Months = (2)-(3) of Claims Months =(5)-(6) =(4)/(7)
(1) (2) (3) (4) (5) (6) (7) (8)
$119, $98, $21, $1,792
, , , ,946
, , , ,113
, , , ,347
*Includes IBNR Claims Fitted forecasted value for AY = $2,549
Slide 6

8. AVERAGE HINDSIGHT RESERVE METHOD XYZ Auto Insurance Company Estimated Ultimate Losses: Accident Year 1996
(1) Forecasted Average Future Payment [Slide 6] = $2,549
(2) Number of Future Claims to Settle [Slide 5]
(Ultimate - Closed Claims) = =
(3) Estimated Future Loss Payments [(1) x (2)] = $ 48,431
(4) Paid Losses to Date [Slide 4] = $226,400
(5) Estimated Ultimate Losses [(3) + (4)] = $274,831
Slide 7

9. Slide 8 (1) (2) (3) (4) (5) (6) (7) (8)
AVERAGE HINDSIGHT RESERVE METHOD XYZ Auto Insurance Company Calculation Of Average Outstanding Losses At 24 Months Purpose: Project Future Settlement Dollars For 1997
Number
Estimated Estimated Number of to Settle Average
Estimated Paid Future Ultimate Closed Beyond Future
Accident Ultimate Losses at Payments Number Claims at Mos* Payment Year Losses Months = (2)-(3) of Claims Months =(5)-(6) =(4)/(7)
(1) (2) (3) (4) (5) (6) (7) (8)
$143, $97, $46, $1,733
, , , ,890
, , , ,086
, , , ,268
*Includes IBNR Claims Fitted forecasted value for AY = $2,484
Slide 8

10. AVERAGE HINDSIGHT RESERVE METHOD XYZ Auto Insurance Company Estimated Ultimate Losses: Accident Year 1997
(1) Forecasted Average Future Payment [Slide 8] = $2,484
(2) Number of Future Claims to Settle [Slide 5]
(Ultimate - Closed Claims) = =
(3) Estimated Future Loss Payments [(1) x (2)] = $ 114,264
(4) Paid Losses to Date [Slide 4] = $233,400
(5) Estimated Ultimate Losses [(3) + (4)] = $347,664
Slide 9

11. Slide 10 (1) (2) (3) (4) (5) (6) (7) (8)
AVERAGE HINDSIGHT RESERVE METHOD XYZ Auto Insurance Company Calculation Of Average Outstanding Losses At 12 Months Purpose: Project Future Settlement Dollars For 1998
Number
Estimated Estimated Number of to Settle Average
Estimated Paid Future Ultimate Closed Beyond Future
Accident Ultimate Losses at Payments Number Claims at Mos* Payment Year Losses Months = (2)-(3) of Claims Months =(5)-(6) =(4)/(7)
(1) (2) (3) (4) (5) (6) (7) (8)
$178, $75, $103, $1,665
, , , ,831
, , , ,998
, , , ,187
*Includes IBNR Claims Fitted forecasted value for AY = $2,397
Slide 10

12. AVERAGE HINDSIGHT RESERVE METHOD XYZ Auto Insurance Company Estimated Ultimate Losses: Accident Year 1998
(1) Forecasted Average Future Payment [Slide 10] = $2,397
(2) Number of Future Claims to Settle [Slide 5]
(Ultimate - Closed Claims) = =
(3) Estimated Future Loss Payments [(1) x (2)] = $ 251,385
(4) Paid Losses to Date [Slide 4] = $181,100
(5) Estimated Ultimate Losses [(3) + (4)] = $432,785
Slide 11

13. AVERAGE HINDSIGHT RESERVE METHOD ADVANTAGES
Relatively Unaffected by Changes in Case Reserving Practices
Can Easily Adjust Trend Assumption
Allows Separate Analysis of Frequency and Severity
DISADVANTAGES
Sensitive to Payment Pattern Shifts
Averages Highly Variable When Only a Few Claims
May be Insufficient if Business has Significantly Changed (Example: Retentions Dramatically Increase)
Too “Formula” Driven
Slide 12

14. AVERAGE INCREMENTAL PAID METHOD Incremental Paid Losses per Ultimate Claim (Actual)
Accident Months Of Development
Year *
* 335 = (97,000-60,200) / 110
(Slide 24 months -Slide 12 months) / Slide 5 Ultimate
Slide 13

15. AVERAGE INCREMENTAL PAID METHOD Trend Factors
Accident Months Of Development
Year
1993/ % % % % % %
1994/ % %* % % %
1995/ % % % %
1996/ % % %
1997/ % %
1998/ %
Select % % % % % % %
* 6.6% = 357 /
Slide 13 (1994) / Slide 13 (1993) - 1
Slide 14

16. AVERAGE INCREMENTAL PAID METHOD Incremental Paid Losses per Ultimate Claim (On-level)
Accident Months Of Development
Year *
Select N/A
* 515 = 335 x (1.09 ^ 5)
Slide 13 x (Slide 14 ^ number of years) Slide 15

17. AVERAGE INCREMENTAL PAID METHOD Incremental Paid Losses per Ultimate Claim (Projected)
Accident Months Of Development
Year Total *
,179
* 83 = 70 x (1.09 ^ 2)
= 1994 value x (Slide 14 ^ number of years)
Slide 16

18. AVERAGE INCREMENTAL PAID METHOD Projected Ultimate Losses
(1) (2) (3) (4) (5)
Paid Loss Projected Projected Projected Projected
Per Ult. Claim Future Ultimate Ultimate Ultimate
Accident as of Severity Severity Claims Losses ($000)
. Year /31/ (Slide 16) (1) + (2) (Slide 5) (3) x (4)
$1, $ $1, $119.7
, ,
, ,
, ,
, ,
, ,
, ,
(1) = Slide 13, summed across row Slide 17

19. AVERAGE INCREMENTAL PAID METHOD Summary
Step 1: Project Ultimate Claims
Step 2: Calculate Historical Severities
Step 3: Select Trend Factor
Step 4: Calculate On-level Severities
Step 5: Select On-level Severities
Step 6: Project Future Severities
Step 7: Multiply Total Severities by Ultimate Claims
Slide 18

20. AVERAGE INCREMENTAL PAID METHOD
ADVANTAGES
Allows separate analysis of frequency and severity trends.
Can be modified to account for changes affecting accident year severity (e.g deductibles, benefit changes).
Model can accommodate different trends by accident year, calendar year, or development age.
DISADVANTAGES
Very dependent upon estimate of future inflation rates.
Less accurate for low frequency lines of business.
Could be distorted if payout patterns change.
Slide 19

21. BORNHEUTTER-FERGUSON METHOD Data Needed
Earned Premium or Exposure By Year
A priori Expected Loss Ratio or Pure Premium For Each Year
An Estimate of the Percent of Dollars Unreported, Usually Based on Loss Development Factors (LDFs)
Slide 20

22. BORNHUETTER-FERGUSON METHOD “IBNR” RESERVES
As of the evaluation date, there are four categories of future claims activity that may not be reflected in either claim payments or case reserves.
1. Losses Not Yet Reported To The Company
2. Claims In Transit (Reported But Not Recorded)
3. Future Development On Known Open Claims
4. Reopenings on Claims Currently Closed
The Bornhuetter-Ferguson method and most accident year methods estimate “broad” IBNR which includes all four categories.
NOTE: The sum of (1) and (2) is termed “True” or “Pure” IBNR.
Slide 21

23. BORNHUETTER-FERGUSON METHOD Basic Formulas
Expected Losses = Loss Ratio x Earned Premium
= Pure Premium x Exposure
= Frequency x Severity
IBNR Reserve = IBNR Factor x Expected Losses
Slide 22

24. BORNHUETTER-FERGUSON METHOD XYZ Auto Insurance Company
Accident Year
(1) Earned Premium $1, $1, $2,000
(2) Expected Loss Ratio % % %
(3) Initial Expected Losses (1) x (2) $ $1, $1,500
(4) Development Factor
(5) IBNR Factor [1 - [1 / (4)] % % %
(6) IBNR Reserve (3) x (5) $ $ $750
(7) Reported Losses at 12/31/ $ $ $1,000
(8) Estimated Ultimate Losses (6) + (7) $ $1, $1,750
Slide 23

25. BORNHUETTER-FERGUSON METHOD IBNR Factor Derivation
IBNR Factor = IBNR / Ultimate Losses
= Ultimate - Incurred to Date
Ultimate
= (Incurred to Date/Ultimate)
= [1.000/(LDF-to-Ultimate)]
= Percent Unreported
= Percent Unreported
Slide 24

26. BORNHUETTER-FERGUSON METHOD XYZ Auto Insurance Company
Accident Year
(1) Ultimate Losses
a. Expected (Slide 23, Line 3) , ,500
b. Estimated (Slide 23, Line 8) , ,750
(2) Reported Losses at 12/31/98
a. Expected (Slide 23, Line 3 - Line 6)
b. Actual ,000
(3) Loss Ratio
a. Expected (Slide 23, Line 2) % % %
b. Estimated (Slide 23, Line 8/Line 1) % % %
Slide 25

27. BORNHEUTTER-FERGUSON METHOD Considerations
Premium Adequacy and Expected Loss Ratios
- Sources: pricing assumptions, historical data such as Schedule P, industry data
Changes in Operations:
- Reinsurance
- Longer-Tailed Lines (LDF selection more critical)
- Underlying Limits, Deductibles
- Claims Made versus Occurrence
- Claims Handling
Changes in Mix of Business That May Impact Either Loss Ratios, and/or Development Patterns
Slide 26

28. BORNHUETTER-FERGUSON METHOD Advantages
Easy to Use
Compromises Between Loss Development and Expected Loss Ratio Methods
Avoids Overreaction: Doesn’t apply Development Factors to an Unusual Claim Occurrence
Suitable for New or Volatile Lines of Business
Can be Used with No Internal Loss History
Can also be Used with Paid Data
Disadvantages
Depends on Expected Loss Ratio or A Priori Pure Premium
Requires Development Factors
Slide 27

29. BORNHUETTER-FERGUSON METHOD XYZ Auto Insurance Company Illustration Of Tempering Effect
One Extra
Large Claim
Expected of $150
EXPECTED LOSS RATIO METHOD
(1) Earned Premium $2, $2,000
(2) Expected Loss Ratio % %
(3) Projected Ultimate Losses (1) x (2) $1, $1,500
LOSS DEVELOPMENT METHOD
(4) Actual Reported to Date $ $900
(5) Development Factor
(6) Projected Ultimate Losses (4) x (5) $1, $1,800
Slide 28

30. BORNHUETTER-FERGUSON METHOD XYZ Auto Insurance Company Illustration Of Tempering Effect
One Extra
Large Claim
Expected of $150
BORNHUETTER-FERGUSON METHOD
(1) Earned Premium $2, $2,000
(2) Expected Loss Ratio % %
(3) Expected Ultimate Losses (1) x (2) $1, $1,500
(4) Actual Reported to Date $ $900
(5) Development Factor
(6) IBNR Factor [1 / (5)] % %
(7) Projected Ultimate Losses $1, $1,650
(4) + [(3) x (6)]
Slide 29

31. Slide 30 (2) Loss Development $1,500 $1,800
BORNHUETTER-FERGUSON METHOD XYZ Auto Insurance Company Illustration Of “Tempering” Effect
One Extra
Large Claim
Method Expected of $150
(1) Expected Loss Ratio Method $1, $1,500
(2) Loss Development $1, $1,800
(3) Bornhuetter-Ferguson $1, $1,650
Slide 30