Introduction To
Reinsurance Reserving
Atlanta, Georgia
September 11, 2006
Anita Sathe, ACAS, ASA – Deloitte Consulting LLP
Christopher Bozman, FCAS, MAAA – Towers Perrin Tillinghast
Michael Angelina, ACAS, MAAA – Endurance Specialty Holdings
Agenda
• Reinsurance Contract Types
• Data Grouping Dimensions
• Differences Between Reinsurance and Primary that
affect Loss Reserving
• Other Considerations & Development Methods
• Other Reserving Methods
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An Introduction to Reinsurance Reserving
Agenda
• Reinsurance Contract Types
• Data Grouping Dimensions
• Differences Between Reinsurance and Primary that
affect Loss Reserving
• Other Considerations & Development Methods
• Other Reserving Methods
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An Introduction to Reinsurance Reserving
Reinsurance Contract Types
• Type of policies
• Mechanics of cession
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An Introduction to Reinsurance Reserving
Reinsurance Contract Types – Type of Policies
• Treaty Reinsurance
– Covers a book or class of business
– Automatic reinsurance
– Insured/policies are unknown at inception but become known
subsequently
– Typical Uses:
• Provide stability
• Increase aggregate capacity
• Facultative Reinsurance
–
–
–
–
Covers a specific individual risk
The reinsurer retains the right to accept or reject each risk
The one insured/policy is known to the reinsurer at inception
Typical uses:
• Unique exposures
• Hazardous exposures
• Provide line capacity
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An Introduction to Reinsurance Reserving
Reinsurance Contract Types – Type of Policies
• Finite Reinsurance
–
–
–
–
Non-traditional treaty reinsurance
Transfers a limited amount of risk
Involves profit sharing elements
Typical uses
• Surplus relief
• “Smoothing” results
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An Introduction to Reinsurance Reserving
Reinsurance Contract Types – Mechanics of cession
• Two mechanics of cession:
– Pro Rata reinsurance
• Proportional sharing of premiums and losses
– Excess of loss reinsurance
• Losses in excess of a given dollar retention are covered
• Applicable to both treaty and facultative reinsurance
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An Introduction to Reinsurance Reserving
Reinsurance Contract Types – Mechanics of cession
• Pro Rata reinsurance
– Quota Share
• Fixed percentage of premium & losses shared
• Dollar amount ceded varies by size of risk
• E.g. QS Reinsurance with 25% retention.
Total Premiums = $1,000,000
Total Losses = $700,000
25%
Retained
Total
Premiums
Losses
Loss Ratio
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75%
Ceded
1,000,000
250,000
750,000
700,000
175,000
525,000
70%
8
70%
70%
An Introduction to Reinsurance Reserving
Reinsurance Contract Types – Mechanics of cession
• Pro Rata reinsurance
– Surplus Share
• Fixed amount (line) of losses ceded
• Percentage shared varies by size of risk
• E.g. Surplus share $200,000 xs of $150,000
% Sharing of Risk
Policy
Size of
Risk
%
Retained
Share of Losses
%
Ceded
Loss
Amount
Retained
Ceded
A
100,000
100%
0%
100,000
100,000
0
B
200,000
75%
25%
200,000
150,000
50,000
C
500,000
60%
40%
400,000
240,000
160,000
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An Introduction to Reinsurance Reserving
Reinsurance Contract Types – Mechanics of cession
• Excess Reinsurance
– Per risk
• Applies to property risks
• Limit applies separately to each risk (e.g. building)
– Per occurrence
• Typically applies to liability covers
• Limit applies to total loss for an occurrence regardless of
number of risks or policies involved
– Aggregate excess
• Can apply to both property and liability covers
• Limits and retentions stated in terms of loss ratio bands
– Reinsurer’s relative participation is NOT pre-determined,
but depends on the size of the loss or loss ratio
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An Introduction to Reinsurance Reserving
Reinsurance Contract Types – Mechanics of cession
• Excess Reinsurance
– E.g. XOL $3,000,000 xs of $400,000
Policy
Loss
Amount
Retained
Ceded
PER RISK
X
500,000
400,000
100,000
Y
1,200,000
400,000
800,000
Z
400,000
400,000
2,100,000
1,200,000
900,000
400,000
1,700,000
Total
-
PER OCCURRENCE
A
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2,100,000
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An Introduction to Reinsurance Reserving
Agenda
• Reinsurance Contract Types
• Data Grouping Dimensions
• Differences Between Reinsurance and Primary that
affect Loss Reserving
• Other Considerations & Development Methods
• Other Reserving Methods
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An Introduction to Reinsurance Reserving
Data Grouping Dimensions
• Accident Year vs. Underwriting Year
– or “Losses Occurring” vs. “Risks Attaching”
• Casualty vs. Property
• Treaty vs. Facultative
• Excess of Loss vs. Proportional
• Broker vs. Direct
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An Introduction to Reinsurance Reserving
Data Grouping Dimensions
• Accident Year vs. Underwriting Year
– AY allows for easiest application of standard techniques
• Premium fixed as of December 31
• Population of claims fixed at December 31 as well, though
many may be unknown
• May not always be an option for reinsurance
– Underwriting year includes experience on all treaties
written during the year
– Underwriting Year is often used in reinsurance, especially
for proportional contracts
– UY can cover two policy years and three calendar years for
losses. Current UY as of 12 months is “incomplete”
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An Introduction to Reinsurance Reserving
“Incomplete Underwriting Year”
• UY 2001 includes all treaties written by the
reinsurer in 2001
– “Risks Attaching” and/or “Policies Incepting”
– UY 2001 can span two years and three accident years
• At 12/31/2001, UY 2001 is “incomplete”
– Standard development methods derived from the past UYs
will overstate the development of UY 2001.
– Historical development after 12 months includes exposures
yet to be earned
– Provision for these losses should not be included in reserves
at the 12/31/2001 accounting date.
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An Introduction to Reinsurance Reserving
“Incomplete Underwriting Year”
Underwriting Year 2001
Covers Losses Occurring
During this Period
Underwriting Year
2001 Covers Policies
Incepting During this
Period
Accident
Year 2001
1/1/2001
Accident
Year 2002
1/1/2002
Accident
Year 2003
1/1/2003
1/1/2004
Sample Time Line
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An Introduction to Reinsurance Reserving
Data Grouping Dimensions
• Casualty vs. Property
– Casualty business generally has a longer development tail
– Line of business (LOB) detail is often not available to the
reinsurer, but if it is you might want to further subdivide by
LOB as different LOBs may develop differently
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An Introduction to Reinsurance Reserving
Data Grouping Dimensions
• Treaty vs. Facultative
– These display different development patterns, all else equal
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An Introduction to Reinsurance Reserving
Data Grouping Dimensions
• Excess of Loss vs. Proportional
– Can be more important to split than line of business
– Different development patterns
– Possible reserve adequacy mix
• Excess of Loss - Case reserves generally reviewed by reinsurer
claim dept and “ACRs” established
• Proportional - Case reserves booked as reported by ceding
company without reinsurer review
– Split Excess by layer - low, high, catastrophe
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An Introduction to Reinsurance Reserving
Data Grouping Dimensions
• Broker vs. Direct
– Reinsurers obtain business either directly from cedant or
through broker (or both)
– Data flowing through broker may create additional
reporting lag and result in different development patterns
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An Introduction to Reinsurance Reserving
Agenda
• Reinsurance Contract Types
• Data Grouping Dimensions
• Differences Between Reinsurance and Primary
that affect Loss Reserving
• Other Considerations & Development Methods
• Other Reserving Methods
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An Introduction to Reinsurance Reserving
Differences Between Primary and Reinsurance
• Reporting Lag/Development Lag
• Data
• Increased Variability
• Tailor-Made or Atypical Contracts or Features
• “Accumulation of Issues”
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An Introduction to Reinsurance Reserving
Differences Between Primary and Reinsurance
• Reporting Lag/Development Lag
– Primary losses develop faster than reinsurance losses due
to time lag for data to reach reinsurer
– Proportional business: Accounts not due to reinsurer until
30-90 days after quarter close
• It is possible that losses booked by ceding company in
calendar year “X” will be realized and booked by reinsurer in
calendar year “X+1”
– Excess business: Reporting lag compounds with
development lag
• Reinsurer not notified immediately of the loss
• The losses do not “hit” the reinsurer’s data until they exceed
the threshold established in the Excess reinsurance contract
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An Introduction to Reinsurance Reserving
Differences Between Primary and Reinsurance
• Reporting Lag/Development Lag
– Excess business: Reporting lag compounds with
development lag
• Example:
– $400,000 excess of $100,000 per risk cover
– Loss occurs in Year 1, reserved for $25,000
– Year 3 - reserve increased to $50,000, reinsurer verbally notified
that loss MAY eventually reach their contract
– Year 5, reserve increased to $150,000, reinsurer incurs loss 4
years after the primary company
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An Introduction to Reinsurance Reserving
Primary vs. Reinsurer
Percentage of Ultimate
Historical Loss Development
Workers Compensation
100%
90%
80%
70%
60%
50%
40%
30%
20%
10%
0%
Primary
Reinsurer
1
2
3
4
5
6
7
8
9
10
Report Period (Year)
Reproduction of RAA 2001 Historical Loss Development Study Graph
Primary Company Data Source: A.M. Best Company
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An Introduction to Reinsurance Reserving
Differences Between Primary and Reinsurance
• Reporting Lag/Development Lag
– Premium Estimates
• Needed in reinsurance more than for primary insurance
• Reserves must be set against premium earned as of the
accounting date
• Reporting lag can cause large earned premium amounts to be
unreported to the reinsurer as of the accounting date
• Creates a need to estimate premium and losses associated
with this premium
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An Introduction to Reinsurance Reserving
Differences Between Primary and Reinsurance
• Data
– Quantity
• The “infinite” detail of primary company data is often lost when
reported to reinsurers as data gets “collapsed” along several
dimensions
– Accident dates not reported
– Lines of business not reported
• Industry benchmarks by line of business or accident year can
thus be difficult to use
– Quality – affected by “varied quantity”
• Some ceding companies report more detail to reinsurers than
do others
• As reinsurance data for reserving is organized at the level of
common detail in terms of reported data fields, this has an
impact on the quality of the analysis
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An Introduction to Reinsurance Reserving
Differences Between Primary and Reinsurance
• Increased Variability
– Primary insurers purchase reinsurance (among other
reasons) to make their results less variable (i.e. from
catastrophes)
– Reinsurer data is subject to this reinsured variation
– Depending on the type of reinsurance cover, reinsurer data
may BE this variation
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An Introduction to Reinsurance Reserving
Primary Experience Gross of Reinsurance
180
160
140
120
100
80
60
40
20
0
1998
1999
2000
2001
2002
Losses (in $ millions)
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An Introduction to Reinsurance Reserving
Primary Experience Net of Reinsurance
180
160
140
120
100
80
60
40
20
0
1998
1999
2000
2001
2002
Losses (in $ millions)
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An Introduction to Reinsurance Reserving
Reinsurance Experience
180
160
140
120
100
80
60
40
20
0
1998
1999
2000
2001
2002
Losses (in $ millions)
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An Introduction to Reinsurance Reserving
Differences Between Primary and Reinsurance
• Tailor-made or Atypical Contracts or Features
– Many (possibly large) reinsurance contracts have features
that affect the way their experience will develop relative to
other contracts with which they would otherwise be
grouped
• Examples: Stop loss arrangements, loss corridors, sunset
clauses, etc
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An Introduction to Reinsurance Reserving
Differences Between Primary and Reinsurance
• “Accumulation of Issues”
– Each primary insurer faces issues (e.g. changes in reserve
adequacy, settlement patterns, etc.)
– Issues affect company’s loss reserving data, and reserving
analyst has tools to neutralize the effects
– Reinsurance loss reserving data is an accumulation of
primary data each of which may have these issues
– Adds a further complication to the reinsurance loss
reserving process
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An Introduction to Reinsurance Reserving
Agenda
• Reinsurance Contract Types
• Data Grouping Dimensions
• Differences Between Reinsurance and Primary that
affect Loss Reserving
• Other Considerations & Development Methods
• Other Reserving Methods
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An Introduction to Reinsurance Reserving
Applications, Complications, and Considerations
• Application of Projection Methods
–
–
–
–
Loss Development Method
Loss Ratio Method
Bornhuetter-Ferguson Method
Other Methods
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An Introduction to Reinsurance Reserving
Applications, Complications and Considerations
• Complications
– parameter uncertainty
•
•
•
•
Volatility in report-to-report (RTR) factors
Result can be very leveraged by tail factor selection
Loss trend factors
Expected loss ratios
– data constraints
•
•
Line of business definition
Claim count information often lacking
• Other considerations
– qualitative information
•
Often lack information on claims and underwriting changes at
cedant level
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An Introduction to Reinsurance Reserving
Loss Development Method – Assumptions
• Assumes the relative change in a given year’s
reported loss & ALAE from one evaluation to the
next will be similar to the relative change in prior
years’ reported loss & ALAE at similar evaluation
points
•
•
RTR factors measure change in reported loss & ALAE at
successive evaluations
tail factor allows for development beyond the observed
experience
• Assumes the relative adequacy of the company’s
case reserves has been consistent over time
• Assumes no material changes in the rate claims
are paid or reported
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An Introduction to Reinsurance Reserving
Loss Development Method Suggestions for Tail
Factors
• Industry benchmarks
– RAA for excess
•
•
Reinsurance industry data going back 40+ years
Available for treaty vs. facultative and by attachment range
– Primary sources lagged for pro-rata
•
•
•
ISO
A.M. Best
NCCI
• Curve fitting
– Compare to benchmarks for reasonability
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An Introduction to Reinsurance Reserving
Loss Development Method
How to deal with variability in Historical Development
• Refine data
– Line of business mix
•
At the very least need to split property vs. casualty & pro-rata
vs. excess
– Treaty vs. facultative
•
Development patterns may differ
– Attachment points/limits
•
•
Need to understand attachment points on from ground up
(FGU) basis
How are attachment points/limits changing over time
– Assess whether or not data is still credible after making
refinements
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An Introduction to Reinsurance Reserving
Loss Development Method
How to deal with variability in Historical Development
• Adjust for unique situations and claims
– Commutations
•
Remove from analysis, otherwise projections will be distorted
– Treat any finite contracts separately
•
•
E.g. aggregate stop loss covers – will not develop similarly to
per occurrence excess
Be watchful of traditional contracts with “finite” features
–
Annual aggregate deductibles, loss corridors
– Asbestos, pollution, mass tort claims should be subdivided
and reviewed separately
•
If these claims are included in development data, the tail factor
will be overstated for more recent periods
– Segregate cats, 9/11 losses, other large/unusual losses
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An Introduction to Reinsurance Reserving
Loss Development Method
How to deal with variability in Historical Development
• Supplement with benchmarks
– Utilize benchmark (or weighting of benchmarks) that is
most appropriate for the book of business being analyzed.
Consider:
•
•
•
•
Nature of underlying exposure (e.g. products versus premises)
Attachment points/limits
Actual historical development
Ceding company profile
–
Insolvent ceding companies will cause reporting delays
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An Introduction to Reinsurance Reserving
Development by Line of Business
Exhibit A - 1
Excess Reinsurance
Historical Loss Development
Case Incurred Losses
100%
90%
80%
Percentage of Ultimate
70%
60%
50%
Automobile Liability
40%
General Liability
Excluding Mass Torts
30%
Workers Compensation
20%
Medical Malpractice
10%
0%
1
3
5
7
9
11 13 15 17 19 21 23 25 27 29 31 33 35 37 39
Maturity (Years)
Based on combined treaty and facultative data 5 year averages; all patterns
assume no development beyond oldest evaluation age in triangles.
Source: RAA Historical Loss Development Study, 2005 Edition.
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An Introduction to Reinsurance Reserving
Treaty vs. Facultative – General Liability
Exhibit E-2
Treaty vs. Facultative
Historical Loss Development
General Liability Excluding Mass Torts
Case Incurred Losses
100%
90%
80%
Percentage of Ultimate
70%
60%
50%
40%
Treaty
30%
Facultative
20%
Based on:
Treaty - 20 Companies
Facultative - 16 Companies
10%
0%
1
3
5
7
9
11
13
15
17
19
21
23
25
27
29
31
33
Maturity (Years)
Based on 5 year averages; assumes the same development pattern as Exhibit A-1
beyond 33 years.
Source: RAA Historical Loss Development Study, 2005 Edition.
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An Introduction to Reinsurance Reserving
Impact of Attachment Points – General Liability
Exhibit F-2
Impact of Attachment Points
on Historical Loss Development
General Liability
Case Incurred Losses
100%
90%
80%
Percentage of Ultimate
70%
60%
50%
40%
Current Range 1 - $1 -$180,000
Current Range 2 - $180,001 -$425,000
30%
Current Range 3 - $425,001 -$1,800,000
20%
Current Range 4 - $1,800,001 $4,750,000
10%
Current Range 5 - Greater than
$4,750,000
0%
1
3
5
7
9
11
13
15
17
19
21
Maturity (Years)
Based on 15 year averages; assumes the same development pattern as Exhibit A-1
beyond 21 years.
Source: RAA Historical Loss Development Study, 2005 Edition.
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An Introduction to Reinsurance Reserving
Loss Development Method
• Application same as for primary business
Layer
Accident
Year
Excess
Loss & ALAE
@ 12/ 31/ 2001
LDF
(1)
(2)
(3)
(4)
800 x 200
1996
$1,543
1.355
$ 2,091
800 x 200
1997
1,255
1.488
1,868
800 x 200
1998
1,988
1.755
3,488
750 x 250
1999
1,868
2.336
4,364
750 x 250
2000
863
3.473
2,997
700 x 300
2001
0
8.196
0
Total
$7,517
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Ultimate
Loss & ALAE
(3) x (4)
(5)
$14,808
An Introduction to Reinsurance Reserving
Loss Development Method
• Paid Loss Development Method not very common
for reinsurance reserving
– Payment pattern is often extremely slow and erratic
– may be appropriate for property or low limit proportional
business (e.g. nonstandard auto liability)
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An Introduction to Reinsurance Reserving
Loss Ratio Method
• Useful for new business or immature years
• Need premium base and a priori expectation
regarding loss ratio
• Advantage: stability
– ultimate loss estimate does not change unless the premium
or loss ratio are revised
• Potential problem: lack of responsiveness
– ignores actual loss experience as it emerges
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An Introduction to Reinsurance Reserving
Loss Ratio Method
Ultimate Loss = Earned Premium x ELR
Accident Year
Earned
Premium
Expected
Loss Ratio
(1)
(2)
(3)
Ultimate
Loss & ALAE
(2) x (3)
(4)
1996
$ 3,994
66.5%
$ 2,656
1997
3,577
70.0%
2,504
1998
4,161
73.5%
3,058
1999
2,564
76.5%
1,961
2000
2,769
78.8%
2,182
2001
2,654
85.4%
2,267
$19,719
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$14,628
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An Introduction to Reinsurance Reserving
Loss Ratio Method
• Selecting the loss ratio:
– historical experience
•
•
•
paid and incurred loss experience
LDF projection
adjusted to appropriate year
–
–
–
rate changes
trends
coverage changes
– underwriting considerations
•
•
•
underwriting files
actuarial pricing
market considerations
– benchmarks (industry results)
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An Introduction to Reinsurance Reserving
Adjustment for Incomplete Years
• Recent underwriting or policy years may not be fully
earned as of the evaluation date
– may need to scale back loss development projections
– apply ultimate loss ratio to earned premium as of evaluation
date
•
Ensure that resulting IBNR is reasonable
• Ultimate Loss Ratio = Ultimate Loss / Ultimate
Premium
• Ultimate premium
– project development
– seek underwriter input
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An Introduction to Reinsurance Reserving
Agenda
• Reinsurance Contract Types
• Data Grouping Dimensions
• Differences Between Reinsurance and Primary that
affect Loss Reserving
• Other Considerations & Development Methods
• Other Reserving Methods
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An Introduction to Reinsurance Reserving
Reserving Methods - Bornhuetter-Ferguson
• Essentially a blend of LDF method and Expected Loss
method
– begins with an a-priori estimate of expected losses
• IELR (Initial Expected Loss Ratio) x Earned Premium
– splits a-priori estimate into two pieces
• expected reported losses = (IEL x % reported)
• expected unreported losses(IBNR) = (IEL x % unreported)
– replaces expected reported losses with actual reported (case
incurred) losses
• Restated ultimate loss estimate equals
– expected unreported(IBNR) plus actual reported (case incurred)
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An Introduction to Reinsurance Reserving
Bornhuetter-Ferguson Method - an Example
(1)
Layer
800 xs 200
800 xs 200
800 xs 200
750 xs 250
750 xs 250
700 xs 300
Total
(2)
(3)
(4)
(2) x (3)
Initial
Initial
Accident Earned Expected
Expected
Year
Premium
L/R
Loss&ALAE
2000
2001
2002
2003
2004
2005
3,994
3,577
4,161
2,564
2,769
2,654
19,719
66.5%
70.0%
73.5%
76.5%
78.8%
85.4%
2,656
2,504
3,058
1,961
2,182
2,267
14,628
(5)
(6)
(4) x (5)
(7)
(4) - (6)
Expected Expected
Expected
Percent
Reported
Unreported
Reported Loss&ALAE Loss&ALAE
73.8%
67.2%
57.0%
42.8%
28.8%
12.2%
1,960
1,683
1,743
840
628
277
696
821
1,315
1,122
1,553
1,990
7,130
7,498
Notes:
(3) Based on analysis of historical accident year results adjusted for changes in retention.
(5) Expected percent reported based on excess loss development patterns.
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An Introduction to Reinsurance Reserving
Bornhuetter-Ferguson Method - an Example (Con’t)
Layer
800 xs
800 xs
800 xs
750 xs
750 xs
700 xs
(11)
(9) - (10)
(12)
Initial
Accident Expected
Year Loss&ALAE
Expected
Reported
Loss&ALAE
Expected
Unreported
Loss&ALAE
Actual
Case Inc'd
Loss&ALAE
Ultimate
Loss&ALAE
2,656
2,504
3,058
1,961
2,182
2,267
1,960
1,683
1,743
840
628
277
696
821
1,315
1,121
1,554
1,990
1,543
1,255
1,988
1,868
863
0
2,239
2,076
3,303
2,989
2,417
1,990
14,628
7,131
7,497
7,517
15,014
200
200
200
250
250
300
Total
(13)
(11) + (12)
(10)
(8)
(9)
2000
2001
2002
2003
2004
2005
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Bornhuetter-Ferguson Method - Advantages
• Allows for smoothing of results
– LDF method understates when case incurred losses are small
• overstates if losses large (ELR may understate in this instance)
• Incorporates changes in the environment
– attachment point, coverage changes, layer restructuring, price
strengthening/deterioration
• Balances stability and actual loss emergence
• Estimates IBNR when loss activity is sparse
– ideal for long tailed lines (umbrella, xs casualty)
– redundant for short tailed lines (approximates LDF method)
• Reflects potential information found in underwriting files
– underlying limits profile
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An Introduction to Reinsurance Reserving
Bornhuetter-Ferguson Method - Disadvantages
• Reporting pattern
– expected percentage reported = 1 / LDF
– difficulty in estimating pattern for LDF method also applies here
• Initial expected losses
– IBNR is directly related to a-priori estimate
• double the expected losses ----> double the IBNR
– importance of IELR may be lost in the analysis
• need to step back and determine % of total IBNR that is loss ratio driven
• Ultimate Premium
– most recent year may be difficult to estimate
• booked premium is probably under-reported due to timing lags
• seek underwriting estimate
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An Introduction to Reinsurance Reserving
Bornhuetter-Ferguson Method -
Alternative Sources of Initial Expected Losses
• Loss Ratio Method (incorporates pricing indices)
• Underwriting estimate from pricing study
– by definition it is the a-priori estimate
• verify that parameters for pricing and reserving are consistent
• Increased limits factors and direct premium
– may be used if you feel primary company’s higher limits pricing is
inadequate
• should have been incorporated in pricing study
– may also be used for changes in layer and/or attachment point
• Stanard-Buhlman estimates
• Frequency/Severity estimates
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An Introduction to Reinsurance Reserving
Example of change in layer structuring
Effect on IELR
(1)
(2)
Accident
Year
Ultimate
Loss&ALAE
Ratio
1999
2000
2001
2002
2003
2004
2005
Notes:
63.5%
66.5%
70.0%
73.5%
72.7%
74.8%
77.1%
(3)
Layer
(4)
Limits
Adj Factor
800 xs 200
800 xs 200
800 xs 200
800 xs 200
800 xs 200
800 xs 200
800 xs 200
1.00
1.00
1.00
1.00
1.05
1.05
1.11
(5)
(6)
Layer
Restated
Loss&ALAE
Ratio
800 xs 200
800 xs 200
800 xs 200
800 xs 200
750 xs 250
750 xs 250
700 xs 300
63.5%
66.5%
70.0%
73.5%
76.5%
78.8%
85.4%
(4) assumes that loss ratio increases 5% due to change in retention.
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An Introduction to Reinsurance Reserving
Stanard-Buhlman Estimate
• Essentially the Bornhuetter-Ferguson estimate with
“on average” perfect information
• Uses actual loss ratio indices multiplied by average
loss ratio
– incorporating loss trend and pricing changes
• Balances the expected average loss ratio so that:
– expected reported losses = actual reported losses
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An Introduction to Reinsurance Reserving
Stanard-Buhlman - an Example
(1)
Acc
Year
2000
2001
2002
2003
2004
2005
(2)
(3)
Earned
Premium
Average
Ultimate
L/R
3,994
3,577
4,161
2,564
2,769
2,654
2006 CASUALTY LOSS RESERVE SEMINAR
70.0%
70.0%
70.0%
70.0%
70.0%
70.0%
(4)
(5)
(6)
Pricing
Index
Adjusted
Ultimate
L/R
(3 x 4)
Expected
Ultimate
Loss&ALAE
(2 x 5)
0.95
1.00
1.05
1.17
1.23
1.39
66.5%
70.0%
73.5%
81.8%
86.2%
97.2%
60
2,656
2,504
3,058
2,097
2,387
2,580
An Introduction to Reinsurance Reserving
Stanard-Buhlman - an Example (continued)
(1)
Acc
Year
(2)
(6)
Earned
Premium
Expected
Ultimate
Loss&ALAE
(2 x 5)
2000
2001
2002
2003
2004
2005
3,994
3,577
4,161
2,564
2,769
2,654
2,656
2,504
3,058
2,097
2,387
2,580
Total
19,719
15,283
2006 CASUALTY LOSS RESERVE SEMINAR
(7)
(8)
(9)
Percent
Reported
Expected
Reported
Loss&ALAE
(6 x 7)
Actual
Case Inc'd
Loss&ALAE
73.8%
67.2%
57.0%
42.8%
28.8%
12.2%
1,960
1,683
1,743
898
688
315
1,543
1,255
1,988
1,868
863
0
7,286
7,517
Ratio of actual to expected:
1.032
Restated Loss Ratio:
72.2%
61
An Introduction to Reinsurance Reserving
Stanard-Buhlman - an Example (continued)
(1)
(2)
(3)
Acc
Year
Earned
Premium
Average
Ultimate
L/R
2000
2001
2002
2003
2004
2005
3,994
3,577
4,161
2,564
2,769
2,654
Total
19,719
72.2%
72.2%
72.2%
72.2%
72.2%
72.2%
2006 CASUALTY LOSS RESERVE SEMINAR
(4)
(5)
(6)
Adjusted Expected
Pricing Ultimate
Ultimate
Index
L/R
Loss&ALAE
(3 x 4)
(2 x 5)
0.95
1.00
1.05
1.17
1.23
1.39
68.6%
72.2%
75.8%
84.4%
88.9%
100.3%
2,739
2,583
3,154
2,163
2,462
2,661
15,763
62
(7)
(8)
(9)
Expected
Actual
Reported
Reported
Loss&ALAE Loss&ALAE
(6 x 7)
Percent
Reported
73.8%
67.2%
57.0%
42.8%
28.8%
12.2%
2,022
1,736
1,798
926
709
325
1,543
1,255
1,988
1,868
863
0
7,515
7,517
Ratio of actual to expected:
1.000
Restated Loss Ratio:
72.2%
An Introduction to Reinsurance Reserving
Stanard-Buhlman -
Bornhuetter-Ferguson Method (continued)
(1)
(2)
(3)
Acc
Year
Initial
Expected
Loss&ALAE
1996
1997
1998
1999
2000
2001
Expected
Reported
Loss&ALAE
(4)
(2) - (3)
Expected
Unreported
Loss&ALAE
Actual
Reported
Loss&ALAE
Ultimate
Loss&ALAE
2,739
2,583
3,154
2,163
2,462
2,661
2,021
1,736
1,798
926
709
325
718
847
1,356
1,237
1,753
2,336
1,543
1,255
1,988
1,868
863
0
2,261
2,102
3,344
3,105
2,616
2,336
15,762
7,514
8,248
7,517
15,765
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63
(5)
(6)
(4) + (5)
An Introduction to Reinsurance Reserving
Frequency Based Method -
Basic Steps - Including Policy Limit Impact
• Estimate the annual number of claims above the data limit
– 37.5 claims greater than $150,000
• Use size of loss curves to project the number of claims above
the reinsurance retention
– 11.3 (of 37.5 claims) greater than $300,000
• Use size-of-loss curves to project average severity of claims in
reinsurance layer
– $239,751 average severity of claims in $700,000 excess of $300,000 layer
• Multiply the frequency and the severity projections to estimate
the total ultimate losses
• Incorporate frequency/severity estimate into BornhuetterFerguson method
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An Introduction to Reinsurance Reserving
Frequency/Severity Estimate of claim counts above data limit
(1)
Accident
Year
2001
2002
2003
2004
2005
(2)
Detrended
Data
Limit
6.0%
118,814
125,943
133,499
141,509
150,000
Total
2006 CASUALTY LOSS RESERVE SEMINAR
(3)
(4)
(5)
Act #>
Detrended
Data
Limit
Claim
Count
Develpoment
Factors
Individual
Total
Excess
Counts
(3 x 4)
34
25
31
22
11
123
65
1.282
1.408
1.555
1.927
2.618
43.6
35.2
48.2
42.4
28.8
198.2
An Introduction to Reinsurance Reserving
Frequency/Severity -
Estimate of claim counts above data limit (Con’t)
(1)
(2)
(3)
(5)
(6)
(7)
Selected
# of
On-Level Indicated Selected
Excess
SEP
Frequency Frequency Claim s
(2 / 4)
Acc.
Year
Projected
# of claim s
> Data Lim it
2001
2002
2003
2004
2005
43.6
35.2
48.2
42.4
28.8
50,000
55,000
60,000
55,000
50,000
63,550
63,525
63,000
55,000
50,000
0.686
0.554
0.765
0.771
0.576
Total
198.2
270,000
295,075
0.672
2006 CASUALTY LOSS RESERVE SEMINAR
Subject
Earned
Prem ium
(4)
66
0.750
0.750
43.6
35.2
48.2
41.3
37.5
205.8
An Introduction to Reinsurance Reserving
Frequency/Severity - Estimation of excess losses
using pareto distribution
(1)
Accident
Year
2001
2002
2003
2004
2005
(2)
(3)
Layer
Limit XS Retention
800,000
800,000
750,000
750,000
700,000
200,000
200,000
250,000
250,000
300,000
Total
(4)
Projected #
> $150,000
> Retention
43.6
35.2
48.2
41.3
37.5
14.8
13.7
16.6
14.2
11.3
205.8
70.7
(5)
(6)
Average
Severity
in Layer
Ultimate
Loss&ALAE
in Layer
(4 x 5)
178,667
178,724
206,971
207,030
239,751
2,644,272
2,455,668
3,433,649
2,942,194
2,720,579
14,196,361
Notes: (4) from pareto size-of-loss curve frequency formula; Nx[(DL+B)/(R+B)]^Q
(5) from pareto size-of-loss curve severity formula; [(R+B)/(Q-1)]x{1-[(R+B)/(R+L+B)] ^ (Q-1)}^Q
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An Introduction to Reinsurance Reserving
Frequency/Severity Bornhuetter-Ferguson Method
(1)
Layer
800 xs
800 xs
800 xs
750 xs
750 xs
700 xs
200
200
200
250
250
300
Acc
Year
(2)
(3)
(4)
(5)
(6)
(4) + (5)
Initial
Expected
Expected
Actual
Expected
Reported
Unreported Reported
Ultimate
Loss&ALAE Loss&ALAE Loss&ALAE Loss&ALAE Loss&ALAE
2000
2001
2002
2003
2004
2005
Total
2006 CASUALTY LOSS RESERVE SEMINAR
2,550
2,644
2,456
3,434
2,942
2,721
1,882
1,777
1,400
1,470
847
332
668
867
1,056
1,964
2,095
2,389
1,543
1,255
1,988
1,868
863
0
2,211
2,122
3,044
3,832
2,958
2,389
16,747
7,708
9,039
7,517
16,556
68
An Introduction to Reinsurance Reserving
Recap of Methods Ultimate Loss and ALAE
Acc.
Year
LDF
Loss
Ratio
Bornhuetter
Ferguson
(w/ IELR)
StanardBuhlman
Bornhuetter
Frequency/ Ferguson
Severity
(w/ F/S)
2000
2001
2002
2003
2004
2005
2,091
1,868
3,488
4,364
2,997
0
2,656
2,504
3,058
1,961
2,182
2,267
2,239
2,076
3,303
2,989
2,417
1,990
2,261
2,102
3,344
3,105
2,616
2,336
2,550
2,644
2,456
3,434
2,942
2,721
2,211
2,122
3,044
3,832
2,958
2,389
Total
14,808
14,628
15,014
15,764
16,747
16,556
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An Introduction to Reinsurance Reserving
Recap of Methods Ultimate Loss and ALAE Ratios
(1)
(2)
(3)
(4)
Bornhuetter
Ferguson
(w/ IELR)
StanardBuhlman
56.1%
58.0%
79.4%
116.6%
87.3%
75.0%
56.6%
58.8%
80.4%
121.1%
94.5%
88.0%
Acc.
Year
LDF
Loss
Ratio
2000
2001
2002
2003
2004
2005
52.4%
52.2%
83.8%
170.2%
108.2%
0.0%
66.5%
70.0%
73.5%
76.5%
78.8%
85.4%
2006 CASUALTY LOSS RESERVE SEMINAR
(5)
70
(6)
(7)
Bornhuetter
Frequency/ Ferguson
Severity
(w/ F/S)
63.8%
73.9%
59.0%
133.9%
106.2%
102.5%
55.4%
59.3%
73.2%
149.5%
106.8%
90.0%
An Introduction to Reinsurance Reserving
Final Selection of Ultimates
Rules of Thumb
• LDF methods for older, more mature accident/policy periods
– look at LDF/ percentage reported to determine maturity
• umbrella versus auto physical damage
• Expected Loss techniques for newer, less mature
accident/policy periods
– most recent or two most recent accident years
• Bornhuetter-Ferguson/ Stanard Buhlman, anywhere in between
– requires judgment: (GL, umbrella, excess casualty)
• Frequency/Severity: similar to expected loss techniques
– better estimate when loss ratio is unstable/unreliable
• high layers, single treaties
• Benchmarks
– IBNR to case O/S ratios; loss ratios
2006 CASUALTY LOSS RESERVE SEMINAR
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An Introduction to Reinsurance Reserving
Other Thoughts
• Look for trends, stability, shocks
– are they reasonable ?
• Communicate with the underwriting and claims departments
–
good fodder for next underwriting audit or pricing season
• Gather knowledge on reserving philosophy (level of ACRs)
– make adjustments where necessary to benchmarks
• How to handle new lines of business with no history
– benchmarks, underwriting files, actuarial pricing analysis
• Incomplete underwriting year
– ultimate loss & ALAE ratio using ultimate premium
• apply to estimated earned premium; look at actual case incurred
• Difficult Coverages (Agg XS, deductibles, reinstatements)
– requires modeling of underlying exposures
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An Introduction to Reinsurance Reserving
Other Approaches (Con’t)
• Asbestos, Pollution, Other Health Hazards
– Need to handle separately
• Cedant information, industry data, benchmarks
• Results of exposure based modeling techniques
• Large Events / Market Losses (WTC losses)
– Seek input from claims department
– Utilize market information / knowledge
• Property Catastrophes
– Results of models (may need to adjust)
– Underwriter estimates
– Traditional top-down techniques
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An Introduction to Reinsurance Reserving
Contact Information
• Anita Sathe, ACAS, ASA
Deloitte Consulting LLP
Phone: (860) 725-3093
ansathe@deloitte.com
• Christopher Bozman, FCAS, MAAA
Towers Perrin Tillinghast
Phone: (215) 246-7405
Christopher.Bozman@towersperrin.com
• Michael Angelina, ACAS, MAAA
Endurance Specialty Holdings, Ltd
Phone: (441) 278-0987
mangelina@endurance.bm
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An Introduction to Reinsurance Reserving