Transcript Download Handout 1

Introduction to Experience
Rating
Casualty Actuarial Society
Reinsurance Pricing Seminar
July, 2005
Dave Clark
American Re-Insurance Company
This material is being provided to you for information only, and is not permitted to be further
distributed without the express written permission of American Re. This material is not
intended to be legal, underwriting, financial or any other type of professional advice. Examples
given are for illustrative purposes only.
© Copyright 2005 American Re-Insurance Company. All rights reserved.
1234
Introduction to Experience Rating
Agenda:
 Basic Experience Rating Methodology
 Diagnostics: telling the story
 Credibility weighting with exposure rate
 Examples
 Problems & Challenges (time permitting)
1234
Introduction to Experience Rating
Basic Experience Rating Methodology
Steps in Experience Rating:
1. Assemble Data
2. Adjust Subject Premium to Future Level
3. Trend and Layer Losses
4. Apply Loss Development
1234
Introduction to Experience Rating
Basic Experience Rating Methodology
(1) Assemble Data
First Rule: Apples-to-Apples collection of
historical subject premium and loss data
Experience Rate =
Trended Ultimate Layer Losses
Trended OnLevel Subject Premium
1234
Introduction to Experience Rating
Basic Experience Rating Methodology
(1) Assemble Data
Second Rule: Get all the detail on historical losses
1.
2.
3.
4.
Include all historical losses that would trend into the
layer (rule of thumb: get all losses > half of your
attachment point)
Split out ALAE for each loss
Include historical policy limits (and SIR if applicable)
Confirm that losses are assembled by occurrence, not
by claimant
1234
Introduction to Experience Rating
Basic Experience Rating Methodology
(2) Adjust Subject Premium to Future Level

Filed [manual] rate changes

“Price-level” changes


Schedule-Rating, company tiers, etc
Exposure Trend
(for inflation-sensitive exposure bases)
1234
Introduction to Experience Rating
Basic Experience Rating Methodology
(2) Adjust Subject Premium to Future Level
Goal is to adjust historical premium to a level “as
if” it has been written during the future period.
The split between “rate” and “price” is not always
obvious (e.g., where are LCMs or package
factors included?): get a full description from the
ceding company.
1234
Introduction to Experience Rating
Basic Experience Rating Methodology
(2) Adjust Subject Premium to Future Level
Primary Loss Ratios
Ultimate Loss Ratio
120.0%
100.0%
80.0%
60.0%
40.0%
20.0%
0.0%
1996
1997
1998
1999
2000
2001
Accident Year
2002
2003
2004
2005
1234
Introduction to Experience Rating
Basic Experience Rating Methodology
(2) Adjust Subject Premium to Future Level
Note to actuaries coming from a primary
rate-filing background:
In a rate filing, you typically adjust
premium to the current rate level.
In reinsurance pricing, you want to adjust
premium to the average rate level in
the future period.
1234
Introduction to Experience Rating
Basic Experience Rating Methodology
(2) Adjust Subject Premium to Future Level
Obvious observation:
If the ceding company’s effective rates drop by
-10% for the prospective period, but we
assume that rates are “flat,” then our
experience rating will be understated by 10%.
Recommended Reading: Trent Vaughn’s Commercial Lines Price Monitoring;
CAS Forum Fall 2004
1234
Introduction to Experience Rating
Basic Experience Rating Methodology
(3) Trend & Layer Losses



Purpose is to bring the historical value up to the
average level in the future period
Typically we apply trend and then cap the
trended loss at the historical policy limit
Hidden assumption: All losses trend at the same
percent (trend does not vary by size of loss)
1234
Introduction to Experience Rating
Basic Experience Rating Methodology
(3) Trend Losses:
Experience
Period (AY)
Experience
Period (AY)
Depends on Treaty Basis:
Losses
Occurring
Treaty
Risks
Attaching
Treaty
1234
Introduction to Experience Rating
Basic Experience Rating Methodology
(3) Trend Losses – Leveraged Effect
1,200,000
1,000,000
trend
1234
Introduction to Experience Rating
Basic Experience Rating Methodology
(3) Trend Losses - Impact on Excess Layer
Layer:
500,000
excess of
Untrended
100
Trended
100
Pareto B
Pareto Q
Overall Severity
125,000
1.55
227,273
135,000
1.55
245,455
8.0%
Layer Counts
Layer Severity
Layer Loss Cost
8.3
313,899
2,590,513
9.1
315,687
2,864,008
9.9%
0.6%
10.6%
Total # of Claims
500,000
Trend %
All numbers are for illustration only, and not for use in pricing.
1234
Introduction to Experience Rating
Basic Experience Rating Methodology
(4) Develop Losses to Ultimate
Factors depend on Layer of Reinsurance being
priced


We apply LDFs to trended layer losses so that all
years are on the same basis.
Development is an aggregate loss concept


Includes new claims (“true IBNR”), development on
known claims, reopening of closed claims, etc
1234
Introduction to Experience Rating
Basic Experience Rating Methodology
(4) Develop Losses to Ultimate
% Reported as of Evaluation Age
Cumulative Reporting Pattern
100.0%
90.0%
80.0%
70.0%
60.0%
50.0%
40.0%
30.0%
20.0%
10.0%
0.0%
0
12 24 36 48
60 72 84 96 108 120 132 144 156 168 180 192 204 216 228 240
Primary
400 xs 100
1M xs 1M
All numbers are for illustration only, and not for use in pricing.
1234
Introduction to Experience Rating
Basic Experience Rating Methodology
(4) Develop Losses to Ultimate
Most recent periods are very green and
may have zero losses reported to date. Should
they be included? Alternatively, if there are
losses, then they are hit with huge LDF.
Problem:
Possible Solution: B-F or “Cape Cod” Methods
1234
Introduction to Experience Rating
Basic Experience Rating Methodology
(4)Develop Losses to Ultimate
LDF Method:
Ultimate = Reported × LDF
Bornhuetter-Ferguson (B-F) Method:
Ultimate = Reported + Prem×ELR×(1-1/ LDF)
But what ELR do we use?
1234
Introduction to Experience Rating
Basic Experience Rating Methodology
(4)Develop Losses to Ultimate
“Cape Cod” method is a special case of the B-F
method.
The ELR is selected to be equal to the final value
of the all-year average loss ratio.
ELR
=
 Ultimate Loss
 Subject Premium
1234
Introduction to Experience Rating
Basic Experience Rating Methodology
(4)Develop Losses to Ultimate
“Cape Cod” ELR turns out to be calculated simply
as follows:
ELR
=
 Reported Loss
 Premium/LDF
Where Premium/LDF is the “exposed premium”
corresponding to the loss that we would expect to
have been reported to date.
1234
Introduction to Experience Rating
Basic Experience Rating Methodology
(4) Develop Losses to Ultimate
Key Formulas in “Cape Cod” Method:
Cumulative % of Loss Reported = 1 / LDF
Reported Loss
×
LDF
Subject Premium
=
Reported Loss
Subject Premium / LDF
1234
Introduction to Experience Rating
Diagnostics: Telling the Story
Does the Experience-Rating make
sense?

Graphical Display

Comparisons


Prior years’ Experience Rating
Exposure Rating
1234
Introduction to Experience Rating
Diagnostics: Telling the Story
Simple test of actual versus expected:
Actual versus Expected Analysis
Accident
Year
Evaluated
09/30/2004
LDF
Evaluated
09/30/2005
1996
1997
1998
1999
2000
2001
2002
2003
2004
571,093
492,265
319,707
1,762,534
250,563
577,569
362,216
333,336
110,169
1.103
1.141
1.195
1.277
1.407
1.633
2.087
3.376
14.169
599,683
559,165
219,653
1,831,330
285,397
969,391
854,699
712,321
408,968
Total
4,779,452
Expected
LDF Link Ratio
1.077
1.103
1.141
1.195
1.277
1.407
1.633
2.087
3.376
Expected
Dvlpmnt
Actual
Dvlpmnt
13,787
16,959
15,131
120,944
25,508
92,772
100,702
205,879
352,220
28,590
66,900
-100,054
68,796
34,834
391,822
492,483
378,985
298,799
1.024
1.034
1.047
1.069
1.102
1.161
1.278
1.618
4.197
6,440,607
All numbers are for illustration only, and not for use in pricing.
943,902 1,661,155
1234
Introduction to Experience Rating
Diagnostics: Telling the Story
Some questions to ask when reconciling
with prior rating or exposure rating:



Is the experience rating distorted by large
losses?
Is the ELR used in exposure rating consistent
with the ceding company’s experience?
How has the business changed? Is the
experience even relevant?
1234
Introduction to Experience Rating
Credibility
Credibility:
Experience Rating = Projection of losses
based only on what took place for this specific
account
Exposure Rating = A Priori estimate of losses
based on information other than the specific
account’s experience
1234
Introduction to Experience Rating
Credibility
Credibility:
Separating claim counts is useful for comparing
experience and exposure ratings, and also for
gauging credibility.
A good credibility standard is: the number of
claims that we would have expected to
observe in the historical periods.
Z=
n
n+k
1234
Introduction to Experience Rating
Credibility
Credibility:



Other Considerations
Stability of Experience: How much would
experience rate change if we remove the largest
claim or add an additional full limit loss?
Are pricing factors (LDFs, rate changes, etc) from
the account or are they default values?
Do the characteristics of the ceding company match
the business in the exposure rating curves?
1234
Introduction to Experience Rating
EXAMPLES
1234
Introduction to Experience Rating
Challenges
We will look at two challenges that require
some variation on the experience-rating:
(1) Changing Mix of Business or Policy
Limits Distribution
(2) Inclusion of Excess or Umbrella Policies
1234
Introduction to Experience Rating
Challenges
(1) Changing Mix of Business
Wherever possible, we want the experience rating
performed on homogeneous experience. That
is, each historical period writes the same
business as will be in the future period.
A changing mix by line of business means that
separate experience ratings are needed by
line.
1234
Introduction to Experience Rating
Challenges
(1) Changing Policy Limits Distribution
Suppose we are pricing a 500,000 excess of
500,000 layer, but the ceding company
has only recently begun writing high limit
policies.
How can the historical experience be used?
1234
Introduction to Experience Rating
Challenges
Complex
Simple
(1) Changing Policy Limits Distribution
(a) Trend past historical policy limits.
(b) Price lower “fully exposed” layer and then use
exposure-rating model relativities.
(c) Adjust each historical period to the future
period’s level of exposure.
(d) Use curve-fitting model to historical losses.
1234
Introduction to Experience Rating
Challenges
(1) Changing Policy Limits Distribution
(a)Trend past historical policy limits.
Advantage:

Very simple
Disadvantage:

Only works if the reason that policy limits have
changed is that they have drifted up with
inflation.
1234
Introduction to Experience Rating
Challenges
(1) Changing Policy Limits Distribution
(b) Experience rate “fully exposed layer”
Advantage:

Relatively simple
Disadvantages:

Subject premium still needs to be adjusted to
the average policy limit profile of future period.

Does not make use of the loss experience in
the layer that we are actually pricing.
1234
Introduction to Experience Rating
Challenges
(1) Changing Policy Limits Distribution
(c) Adjust years based on exposure rating
each historical period
Advantage:

This is the most accurate method.
Disadvantage(s):

Requires full policy limit profile for each
historical period

Difficulty in explaining adjustment factors
1234
Introduction to Experience Rating
Challenges
(1) Changing Policy Limits Distribution
AY
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
Policy Limit Distribution
500,000
1,000,000
5,000,000
75.00%
75.00%
75.00%
75.00%
75.00%
50.00%
25.00%
10.00%
10.00%
10.00%
10.00%
20.00%
20.00%
20.00%
20.00%
20.00%
20.00%
20.00%
20.00%
20.00%
20.00%
20.00%
5.00%
5.00%
5.00%
5.00%
5.00%
30.00%
55.00%
70.00%
70.00%
70.00%
70.00%
Exposure Rate
250,000
500,000
excess of excess of
250,000
500,000
14.71%
14.71%
14.71%
14.71%
14.71%
14.24%
13.77%
13.49%
13.49%
13.49%
13.49%
All numbers are for illustration only, and not for use in pricing.
3.09%
3.09%
3.09%
3.09%
3.09%
6.18%
9.27%
11.13%
11.13%
11.13%
11.13%
1234
Introduction to Experience Rating
Challenges
(1) Changing Policy Limits Distribution
(c) Adjust years based on exposure rating
each historical period
The exposure rates from this table are used to
“layer” the subject premium to find the portion
of premium corresponding to the losses in the
layer; the layered premium becomes the new
“adjusted subject premium.”
Note: this is a variation on the exposure adjustment described by Mata &
Verheyen in their Spring 2005 CAS Forum article.
1234
Introduction to Experience Rating
Challenges
(1) Changing Policy Limits Distribution
(d) Fit curve to historical data
Advantage:

Makes use of all the loss information
Disadvantage(s):

Does not properly include development

Significant increase in complexity

Temptation to extrapolate beyond data
1234
Introduction to Experience Rating
Challenges
(2) Inclusion of Excess Policies
Challenges:

Proper handling of “supported” and
“unsupported” excess policies

Proper application of inflation trend
1234
Introduction to Experience Rating
Challenges
(2) Inclusion of Excess Policies
“Supported” Excess
Excess
“Unsupported” Excess
Policy
Excess
Policy
1M xs 1M
1M xs 1M
2M Exposed
Primary
Policy
1M Limit
1M Exposed
1234
Introduction to Experience Rating
Challenges
(2) Inclusion of Excess Policies
“supported” and “unsupported” excess policies
(a) Combine primary and excess portions of large
losses
•
This is the right answer, but requires the ability to
match loss records from the two types of policies
(b) Price excess layer on a “responds ground-up”
basis
1234
Introduction to Experience Rating
Challenges
(2) Inclusion of Excess Policies
Proper application of inflation trend
(a) Add SIR to loss amount before trending
(b) Use a higher trend percent to reflect “leverage”