1998 CASUALTY LOSS RESERVE SEMINAR
Intermediate Track III- Techniques
SEPTEMBER 28, 1998
INTRODUCTION
The Ideal Situation
Loss reserve data should contain a long stable
history of homogeneous claim experience,
where no significant operational changes
materially affect either the mix of business or
the handling of claims, and there should be
sufficient number of claims to produce
credible loss patterns.
Slide 1
INTRODUCTION
The Reality
Virtually All Elements of “The Ideal” are Periodically Violated:
1. The Mix Changes
2. Claim Handling Changes:
 Payments Accelerate / Decelerate
 Case Reserves are Strengthened / Weakened
3. The Environment Changes:
 New Causative Agents Impact Loss Costs
 Society’s Attitudes Change
 Court Decisions Change “The Rules”
 Changes in the Economy Affect Claim Inflation
Slide 2
INTRODUCTION
This Session Will Discuss
1. The potential impact of mix changes. (Slides 4-10)
2. Changes in claim closing patterns. (Slides 11-21)
3. Changes in case reserve adequacy. (Slides 22-31)
4. Tail factor selection. (Slides 32-37)
Slide 3
CHANGE IN MIX
Cumulative Paid Losses (Combined)
.
Accident
Year
1994
1995
1996
1997
Slide 4
Months of Development
12
24
36+
$2,000
$4,000
$5,000
$2,000
$4,000
$5,000
$2,000
$4,000
$2,000
CHANGE IN MIX
Cumulative Paid Losses (by Type of Claim)
Each of
1994-1996
Category A
Category B
% of
Total
(75%)
(25%)
Months of Development
12
24
36+
$1,500
$1,800
$2,000
$500
$2,200
$3,000
$2,000
$4,000
$5,000
1997
Category A
Category B
(25%)
(75%)
$500
$1,500
$2,000
Slide 5
CHANGE IN MIX
Cumulative Paid Losses (by Type of Claim)
Each of
1994-1996
Category A
Category B
Months of Development
12
24
36+
$1,500
$1,800
$2,000
$500
$2,200
$3,000
$2,000
$4,000
$5,000
1997
Category A
Category B
If Forecasting By Claim Category
$500
$600
$700
$1,500
$6,600
$9,000
$2,000
$7,200
$9,700
If Ignoring Claim Category
$2,000
$4,000
$5,000
1997
Combined
Slide 6
CHANGE IN MIX
Key Principle
Always Search for Subdivisions
of Data Related to Possible
Causes of Variable Loss
Development
Slide 7
CHANGE IN MIX
Suggested Subdivisions of Data Include
Primary:
1. Geographic: Laws Vary, Regional Office May Use Different
Claims Personnel, Degree of Litigiousness Varies
2. New Products Versus Old
3. Subline or Coverage
4. Deductibles or Policy Limits
5. Type of Loss Payment (e.g. Medical vs. Indemnity)
Reinsurance:
1. Attachment Point
2. Production Source
3. Line or Subline
Slide 8
.
CHANGE IN MIX
How Do You Decide?
Ask:
1. Underwriters
2. Claims Department
3. Agents
4. Actuaries
The Key:
Learn as Much as Possible About the Book of Business
You are Evaluating.
 What it has been historically
 What it is becoming
Slide 9
CHANGE IN MIX
What Should be Done if Mix Change Includes New Business for
Which You Have Insufficient Data?
1. Seek Alternative Sources of Data. For example, perhaps a general
liability book formerly comprised solely of “OL&T” exposures, but in
recent years began adding “M&C” risks
Possible Solution: Relate ISO development patterns for M&C to OL&T
and modify development factors for your evaluation.
.
.
2. Discuss Potential Impacts With Claims, Underwriting, and Other
Actuaries. Discuss how the change might affect:
.

Length of the tail

Frequency

Severity

Loss Ratios
Slide 10
.
CLAIM CLOSING PATTERNS
How Can Changes In Payment
Patterns Be Recognized?


Look at Settlement Rates for the Most Recent Accident Years
Ask the Claims Department About Changes in:
- Opening and Closing Practices
- The Claims Handling Environment
- Levels of Staffing, Reorganizations
- Definition of a Claim (e.g. Multiple Claimants)
Slide 11
CLAIM CLOSING PATTERNS
Data Needed

Reported Claims Development Triangle

Closed Claims Development Triangle

Projected Ultimate Claims

Paid Loss Development Triangle
Slide 12
CLAIM CLOSING PATTERNS
Unadjusted Paid Loss Development Method
Accident
Year
1995
1996
1997
Age - Age
Age - Ultimate
Slide 13
Months of Development
12
24
36
$1,000
$1,000
$750
$4,000
$3,500
$6,000
12-24
3.75
5.63
24-36
1.50
1.50
36-Ult
1.00
1.00
Ultimate
$6,000
$5,250
$4,223
CLAIM CLOSING PATTERNS
Accident
Year
12
1995
1996
1997
500
480
450
Accident
Reported Claims
24
900
880
36
1,000
Closed Claims
Year
12
24
36
1995
1996
1997
250
240
180
810
704
1,000
Slide 14
Ultimate
1,000
980
900
CLAIM CLOSING PATTERNS
Accident
Year
12
1995
1996
1997
50.0%
50.0%
40.0%
Accident
Closed / Reported
24
90.0%
80.0%
36
100.0%
Closed / Ultimate
Year
12
24
36
1995
1996
1997
25.0%
24.5%
20.0%
81.0%
71.8%
100.0%
Slide 15
CLAIM CLOSING PATTERNS
Accident
Year
1995
1996
1997
12
20.0%
20.0%
20.0%
Accident
Year
71.8%
71.8%
36
100.0%
Adjusted Closed Claims
12
1995
200
1996
196
1997
180
* 718 = 71.8% x 1,000
Slide 16
Closing Percent
24
24
36
718*
704
1,000
CLAIM CLOSING PATTERNS - AY 1995
Age
Actual
Closed
Claims
Adjusted
Closed
Claims
Actual
Paid
Losses
Adjusted
Paid
Losses
0
0
0
$0
$0
12
250
200
$1,000
?
24
810
718
$4,000
?
36
1,000
1,000
$6,000
?
Slide 17
CLAIM CLOSING PATTERNS
Linear Interpolation of Adjusted Paid Losses
AY = 1995
@ 12 Months
200 - 0
250 - 0
x (1,000 - 0) + 0 = 800
AY = 1995
@ 24 Months
718 - 250
810 - 250 x (4,000 - 1,000) + 1,000 = 3,507
AY = 1996
@ 12 Months
196 - 0
240 - 0 x (1,000 - 0) + 0 = 817
Slide 18
CLAIM CLOSING PATTERNS
Adjusted Paid Loss Development Method
Accident
Year
1995
1996
1997
Age - Age
Age - Ultimate
Slide 19
Months of Development
12
24
36
$800
817
750
12-24
4.33
7.40
$3,507
3,500
24-36
1.71
1.71
$6,000
36-Ult
1.00
1.00
Ultimate
$6,000
5,985
5,550
CLAIM CLOSING PATTERNS
Impact of Adjustment
Accident
Year
Revised
Forecast
Original
Forecast
1995
$6,000
$6,000
$0
1996
5,985
5,250
735
1997
5,550
4,223
1,327
Total
$17,535
$15,473
$2,062
Slide 20
Difference
CLAIM CLOSING PATTERNS
Step 1: Review Closing Rates to Determine Whether
There Has Been a Change
Step 2: Seek Independent Confirmation That Change
Occurred
Step 3: Restate Historical Closed Claims Using Current
Closing Rates
Step 4: Restate Historical Paid Losses Using Restated
Closed Claims
Step 5: Apply Standard Loss Development Method To
Restated Paid Losses
Slide 21
CASE RESERVE ADEQUACY
Claim Data
Accident
Year
12
1995
1996
1997
5,000
5,000
5,000
Accident
8,000
8,000
36
Ultimate
10,000
10,000
10,000
10,000
24
36
Ultimate
6,000
6,000
10,000
10,000
10,000
10,000
Closed Claims
Year
12
1995
1996
1997
1,000
1,000
1,000
Slide 22
Reported Claims
24
CASE RESERVE ADEQUACY
Loss Data
Accident
Year
Incurred Losses ($000)
12
24
36
1995
1996
$10,000
$10,000
1997
$10,417
Accident
Year
12
1995
1996
1997
$2,000
$2,500
$3,125
$40,000
$45,000
$50,000
$56,250
$55,340
Paid Losses ($000)
24
36
$24,000
$30,000
The Issue: What Is Driving The Divergence?
Slide 23
$50,000
Projected
Ultimate
$50,000
Projected
Ultimate
$50,000
$62,500
$78,125
CASE RESERVE ADEQUACY
STEP 1:
Review Paid-To-Incurred Triangles:
Accident
Year
Months of Development
24
12
1995
20%
60%
1996
25%
67%
1997
30%
36
.
100%
Does the Change in These Ratios Portray a Speed-Up in
Payments, a Decrease in Case Reserve Adequacy, or Both?
Slide 24
CASE RESERVE ADEQUACY
STEP 2:
Review Settlement Rates (No. Closed/No. Reported)
Accident
Year
12
Settlement Rate
24
36
1995
20%
75%
100%
1996
20%
75%
1997
20%
Observation: The settlement rates appear to be consistent.
Slide 25
.
CASE RESERVE ADEQUACY
STEP 3:
Review Trends in Average Paid Claims Versus Trends in
Average Case Reserves
Accident
Year
1995
1996
1997
Trend
Average Paid
12
24
$2,000
$4,000
$2,500
$5,000
$3,125
25%
25%
Average Case Reserves
12
24
$2,000
$8,000
$1,875
$7,500
$1,823
-4.5%
-6.3%
Observations: Case reserve trend is much lower than paid trend.
Slide 26
.
CASE RESERVE ADEQUACY
STEP 4:

Review Potential Reasons For Observed Trends
Is the book shifting to a lower severity mix?

Have policy limits and/or reinsurance retentions kept pace
with claims inflation?

Has anything material changed in the handling of claims?
- Turnover in claim department staff
- Changes in philosophy
.
.
If you conclude there has been case reserve weakening (or
strengthening), the data should be adjusted. Slides 28-30 give
one approach.
Slide 27
CASE RESERVE ADEQUACY
STEP 5: Adjust Historical Case Reserves to Current Adequacy Levels
Accident
Year
Adjusted Average Case Reserves
12
24
36
1995
$1,166
$6,000
1996
$1,458
$7,500
1997
$1,823
.
$0
Examples: $6,000 = $7,500 / 1.25
$1,116 = $1,823 / (1.25 ^ 2)
ASSUME: 25% is the Actual Rate of Claim Inflation
Slide 28
CASE RESERVE ADEQUACY
Formula
Adjust
Paid to
Number
Incurred = Date +
of
x
Losses
Losses
Open
AY = 95
@ 12 Months 6,664
2,000
+
(4,000
x
1.166)
AY = 95
@ 24 Months 36,000 = 24,000
+
(2,000
x
6.000)
2,500 +
(4,000
x
1.458)
AY = 96
@ 12 Months
=
Adjusted
Average
Case Reserves
8,332 =
Note: All dollar amounts are in thousands.
Slide 29
CASE RESERVE ADEQUACY
STEP 6:
Accident
Year
Project Ultimate Losses Using Adjusted Incurred
Losses and Standard Loss Development Method
Adjusted Incurred Losses ($000)
12
24
36
1995
$6,664
$36,000
1996
$8,332
$45,000
1997
$10,417
Slide 30
$50,000
Ultimate
.
$50,000
$62,500
$78,125
CASE RESERVE ADJUSTMENT
Comparison of Estimates
Original
Incurred
Estimate
Original
Paid
Estimate
Revised
Incurred
Estimate
1995
$50,000
$50,000
$50,000
1996
$56,250
$62,500
$62,500
1997
$55,340
$78,125
$78,125
Accident
Year
Slide 31
TAIL FACTORS
The Need For Tail Factors
Accident
Year
1986
1987
Accident
Year
1986
1987
Accident
Year
1986
1987
96
243
250
96
55
60
96
341,500
366,200
108
247
256
108
45
53
Reported Claims
120
132
250
252
261
264
Open Claims
120
35
44
.
144
253
.
132
25
31
Incurred Losses
108
120
132
413,200
462,800
495,200
443,100
496,300
531,000
144
15
.
144
515,000
IT APPEARS LOSS DEVELOPMENT WILL CONTINUE BEYOND THE ENDPOINT OF THE DATA.
Slide 32
.
TAIL FACTOR SELECTION METHODS
Techniques To Derive Tail Factors
1. Examine broader data sources: e.g. ISO, NCCI, RAA, Best’s (Caution: Learn
the limitations of such data.)
.
2. Curve Fitting
3. “Generalized Bondy Method” which assumes that the age-to-age factors are
decaying at a constant rate over time.
.
Example: Determine a tail factor based on the following observed age-to-age
factors (LDFs).
96-108
LDF
108-120
LDF
120-132
LDF
132-144
LDF
1.210
1.120
1.070
1.040
Slide 33
TAIL FACTOR SELECTION
Using Generalized Bondy Method To Calculate Tail Factors
(1)
Actual LDFs
Months
(2)=Ln(1)
Ln(Actual)
(3)=(2)/(2 prior)
Decay Ratio
96-108
1.210
0.191
108-120
1.120
0.113
0.595
120-132
1.070
0.068
0.597
132-144
1.040
0.039
0.580
(4)
Predicted LDFs
144-156
1.024=(1.040)0.600
156-168
1.014=(1.024) 0.600
168-180
1.008=(1.014) 0.600
Selected Decay Ratio
Tail Factor (144 months to Ultimate)
Notes:
0.600
1.061=(1.040)1.500
1. This method can be misleading when decay rates are unstable.
2. The tail factor is very sensitive to the last selected age-to-age factor.
Slide 34
TAIL FACTORS
When To Use These Different Approaches To Tail Factors
Situation
Source
Reinsurance lines
RAA Data
Standard Workers Compensation line
NCCI
Unusual line where industry data is
difficult to obtain, e.g. aviation
Curve fitting or Bondy
Company’s own data is unstable or not
credible, or a start-up line
Slide 35
Industry Data
TAIL FACTORS
How Much Tail Can There Be In Development In Reinsured Layers?
Line of
Business
Selected Cumulative Age to Ultimate Factors*
15 Years to Ult.
25 Years to Ult.
W.C. Treaty
1.582
1.149
G.L. Treaty
1.234
1.030
A.L. Treaty
1.021
1.000
* Based on RAA Data.
Slide 36
.
TAIL FACTORS
Some Examples Of When Development Occurs Beyond 10 Years
LINE
REASONS
Products and
Pollution/Environmental
Issues complex (Who’s liable? How to prove the
injury was caused by the product? Date of loss?)
Workers Compensation
Occupational Disease
Life pension cases, with escalation clauses in
some states
Medical Malpractice
Slide 37
Delayed manifestation, with subsequent
complex issues