Current Loss Reserving
Developments
CAS Annual Meeting
November 15, 2005
Chuck Emma, Pinnacle
Tom Ryan, Milliman
John J. Kollar, ISO
ISO Study of Loss and Loss
Adjustment Expense Reserves
A. Industry Schedule P (Net)
B. Analysis of Direct Losses
CAS Annual Meeting
November 15, 2005
John J. Kollar, ISO
A. Industry Loss Reserve Analysis
•
•
•
•
More than 900 insurer groups
Year-ended 12/31/04
Schedule P data compiled by A. M. Best
More than 95% of LLAE reserves for
studied lines
Lines studied
•
•
•
•
PP Auto Liability
HO/Farmowners
Com. Auto Liability
Other & Products Liab.
Claims-Made
• Other Liab. Occurrence
• Com. Multi-Peril
•
•
•
•
Med Mal Occurrence
Med Mal Claims-Made
Products Occurrence
Reinsurance (NonProportional Liability)
• Workers Compensation
Some Key Points
• Excludes reserves for environmental
and asbestos (E&A) claims
– Possibly $30B to $50B deficient
• Analysis assumes incurred losses from
9/11 were fully developed at year-end
2004
– Estimated direct insured losses: $20B to
$30B
– U.S. net insured losses: $6B to $9B
• Adjustments have been made for other
major catastrophes
Methodology
• Paid link-ratio technique
• Case-incurred link-ratio technique
• Consistent with ISO study of 2003 data
Factors affecting analysis
•
•
•
•
Data quality
Development factors
Tail factors
Professional judgment
Conventions
• Each deficiency/redundancy expressed
as percentage of indicated
undiscounted reserve as estimated by
ISO
– Positive percentages indicate deficiencies
– Negative percentages indicate
redundancies
Summary Preliminary Indications
of Reserve Deficiencies
Paid
• Lines Studied
• All Other Lines
• Total – all lines
+ 2%
+ 3%
+ 2%
• In Dollars
$9B
– (excluding E & A )
Case Incurred
+ 7%
+ 3%
+ 7%
$31B
Perspective
• Reserve adequacy has improved for 3
consecutive years
– Reserves were about 3 percentage points
more adequate at year-end 2004 than at
year-end 2003
– Reserves were about 11 percentage points
more adequate at year-end 2004 than at
year-end 2001
Preliminary Indications by Line
• Lines with deficiencies
Paid
•
•
•
•
Products Occurrence
Com. Multi-Peril
Workers Comp
Reinsurance (Non-Prop.)
+ 7%
+ 1%
+ 9%
+25%
Case Inc.
+12%
+ 4%
+15%
+33%
Preliminary Indications by Line
• Other Lines
•
•
•
•
•
•
•
Priv. Pass. Auto Liability
Homeowners/Farmowners
Commercial Auto Liability
Other Liability Occurrence
Claims Made Other & Prod.
Medical Malpractice – Occ.*
Medical Malpractice – C-M.*
Paid
Case Inc.
- 4%
-16%
-10%
- 3%
- 8%
- 3%
-11%
- 6%
-10%
- 1%
+ 5%
+ 1%
+12%
- 9%
*ISO still investigating whether reserve adequacy is
overstated consequent to data anomalies.
LALAE Ratios: Accident Year vs. Calendar Year
%
100
95
90
85
80
75
70
65
60
Reserve adequacy deteriorated for at least 6
years but then improved in 2002, 2003 & 2004.
1996
1997
1998
1999
Accident Year
2000
2001
2002
2003
2004
Calendar Year
Loss Reserve Changes vs. Industry
Profitability, All Lines
%
Changes in reserves are
correlated with profitability.
35
30
25
20
15
10
5
0
-5
'71
'74
'77
'80
'83
'86
'89
'92
'95
'98
Change in LLAE Reserves / Paid LLAE
GAAP Return on Average Net Worth
'01
'04
Retrospective Estimated Deficiencies &
Economic Discount, All Studied Lines
%
Discounted reserves were
inadequate from 2000 to 2003.
30
25
20
15
10
5
0
-5
-10
1996
1997
1998
1999
2000
Paid Link Ratio
Compound Discount Factor
2001
2002
2003
2004
Case-Incurred Link Ratio
B. Analysis of Direct Losses
• Segment Analysis
– State/coverage/class group/etc.
• Reserving/Benchmarking
– Comparable mix of business
• Tail Factors
• Confidence Intervals
Schedule P Lines with
ISO Distributions
• Homeowners/Farmowners
- Homeowners
• Private Passenger Auto Liability/Medical
• Commercial Auto/Truck Liability/Medical
• Commercial Multiple Peril
- Commercial Multiple Peril Liability
- Commercial Multiple Peril Property
Schedule P Lines with
ISO Distributions (Cont’d)
• Medical Malpractice - Occurrence
- Hospitals
- Physicians
- Surgeons
• Other Liability - Occurrence
• Products Liability - Occurrence
• Auto Physical Damage
- Commercial Auto Physical Damage
- Private Passenger Auto Physical Damage
Schedule P Lines with
ISO Distributions (Cont’d)
• Special Property
- Fire
- Allied Lines
- Inland Marine
Segment Analysis – Link Ratios
14
Period 1 To Ultimate
Chain Ladder Link Ratios
12
Ratio
10
8
6
4
2
0
Sch. P
Oth. Liab.
Occ.
ISO
Prem Ops
All Tables
W. CRR
ISO
Prem Ops
Table 1
ISO
Prem Ops
Table 2
ISO
Prem Ops
Table 3
ISO
Prem Ops
Tables
1, 2, & 3
The Schedule P data is net, includes Composite Rated Risks (CRR), and is evaluated as of 12, 24, etc.
months. The ISO data is direct, excludes CRR (except as noted), and is evaluated as of 15, 27, etc. months.
Reserving/Benchmarking
• Used aggregate direct data by segment
– State/coverage/class/etc.
– Paid/incurred/losses/claim counts/LAE
• Weighted aggregate direct data by each
insurer’s unique mix of business
– Losses rather than link ratios
– Separately for each accident year
• Applied link ratios based on aggregate
data to an insurer’s data to calculate an
indicated reserve
Triangles, Link Ratios, Averages
Triangle of
developing
losses
Link
Ratio
Factors
Link
Ratio
Averages
Benchmarking of Reserves
Tail Factors
• Modified Bondy Method
The ultimate factor (UF) determined using the first prior
factor (FF) and the second prior factor (SF) as follows:
If SF > 1 and [ 0.8 * LN(SF) >= LN(FF) >= 0 ] or
SF < 1 and [ 0.8 * LN(SF) <= LN(FF) <= 0 ] then
UF = FF ^ { LN(FF) / [ LN(SF) – LN(FF) ] }
Otherwise, UF = FF ^ 4
• Development beyond 10 years – up to 20
years using direct data
Development 10 vs. 20 Years
Relative Volatility of Tail Factors
Development of Parameters for
Confidence Intervals
Estimated parameters for claim severity
and frequency separately
•
•
•
•
By line
By settlement lag (valuation)
Industry for severity
By insurer size for frequency
Reserve Risk:
Average size and volatility of
open claims increases over time
Claim Amount
Big Claims Settle Slowly
95th %
Mean
0
1
2
3
Open After n Years
4
5
6
Development of an Insurer’s
Confidence Intervals
• An insurer’s loss and loss adjustment
expense reserves
- By line
- By accident year (latest valuation)
• Reinsurance arrangements
- Retention
- Coinsurance
- Per claim limit
• Scale factors to reflect differences in average
severity
Measures of Variability
Frequency/Severity/Reserves
Measure of variability
in aggregate reserves
Measure of variability
in frequencies
Measure of variability
in severities
Measure of
variability
in reserves by
line and period
Confidence Interval and Aggregate
Loss Reserve Distribution
Cumulative Probability
Aggregate Loss Reserve Distribution
1.0
0.9
0.8
Expected Loss
0.7
0.6
0.5
0.4
50% Confidence Interval
0.3
0.2
0.1
0.0
1,000
1,100
1,200
1,300
1,400
1,500
Loss Reserves ($Millions)
1,600
1,700
1,800
Confidence Intervals for Loss
Reserves – Effect of Reinsurance
Intervals for Small Products Liability Writer
45,000,000
Without Reinsurance
With Reinsurance
35,000,000
25,000,000
15,000,000
5,000,000
70%
75%
80%
85%
90%
70%
75%
Confidence Intervals
80%
85%
90%
Confidence Intervals for Loss
Reserves – Effect of Size
Confidence Intervals for General Liability*
(Relative to the Aggregate Mean)
1.8
Smaller Insurer
1.6
Larger Insurer
1.4
1.2
1.0
0.8
Aggregate Mean = 604,383,911
0.6
Aggregate Mean = 40,292,261
(15 times the smaller insurer's volume)
0.4
70%
75%
80%
85% 90% 70% 75%
Confidence Intervals
* A mix of Other Liability and Products Liability.
80%
85%
90%
Applications
• Reserving triangles
– Combine segments using each insurer’s
unique mix of business
• Individual segment analysis
• Tail factors
• Confidence intervals (ranges around
expected)
• Benchmarking for CEO/CFO, Board,
investors, rating agencies, regulators,
etc.
Future Plans
• Explore ways of improving reserve
estimates
– Credibility weighing an insurer’s data
with larger data sets
– Generation of more refined confidence
intervals
– Additional tail factor treatments
– Correlations between
lines/dependencies
• What else would be valuable for loss
reserving?