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Transcript of Introduction to Experience Rating Casualty Actuarial Society Reinsurance Pricing Seminar Dave Clark,...
Introduction to Experience RatingCasualty Actuarial SocietyReinsurance Pricing Seminar
Dave Clark, Actuary and VPMunich Reinsurance America, Inc.
2
Introduction to Experience Rating
Agenda:
Basic Experience Rating Methodology
Diagnostics: telling the story
Credibility weighting with exposure rate
Examples
Problems & Challenges (time permitting)
3
Introduction to Experience RatingBasic 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
4
Introduction to Experience RatingBasic Experience Rating Methodology
(1) Assemble Data
First Rule: Apples-to-Apples collection of
historical subject premium and loss data
Trended OnLevel Subject Premium
Trended Ultimate Layer LossesExperience Rate =
5
Introduction to Experience RatingBasic Experience Rating Methodology
(1) Assemble Data
Second Rule: Get all the detail on historical losses
1. Include all historical losses that would trend into the layer (rule of thumb: get all losses > half of your attachment point)
2. Split out ALAE for each loss
3. Include historical policy limits (and SIR if applicable)
4. Confirm that losses are assembled by occurrence, not by claimant
6
Introduction to Experience RatingBasic Experience Rating Methodology
(2) Adjust Subject Premium to Future Level
Filed [manual] rate changes
“Price-level” changes
Schedule-Rating, company tiers, etc
Also include “soft” changes such as terms & conditions, changes in
underwriting standards, etc
Exposure Trend
(for inflation-sensitive exposure bases)
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Introduction to Experience RatingBasic 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.
8
Introduction to Experience RatingBasic Experience Rating Methodology
(2) Adjust Subject Premium to Future Level
Primary Loss Ratios
0%10%
20%30%40%50%
60%70%80%
90%100%
1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008
Accident Year
Ult
imat
e L
oss
Rat
io
Trend and Onlevel
9
Introduction to Experience RatingBasic 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.
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Introduction to Experience RatingBasic 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
Handouts from Chris Nyce and Brian Hughes at the 2007 CAS Ratemaking Seminar (www.casact.org)
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Introduction to Experience RatingBasic Experience Rating Methodology
(2) Adjust Subject Premium to Future Level
Change in Net Written Premium (Detrended by GDP)Industrywide, All Lines
-6.00%
-4.00%
-2.00%
0.00%
2.00%
4.00%
6.00%
8.00%
10.00%
12.00%
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
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Introduction to Experience RatingBasic Experience Rating Methodology
(2) Adjust Subject Premium to Future Level
Nonproportional Casualty Reinsurance (Schedule P)Industrywide
0%
20%
40%
60%
80%
100%
120%
140%
160%
180%
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
13
Introduction to Experience RatingBasic 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)
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Introduction to Experience RatingBasic Experience Rating Methodology
(3) Trend Losses: Depends on Treaty Basis:
Experience Period (AY)
Risks Attaching
Treaty
Experience Period (AY)
Losses Occurring
Treaty
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Introduction to Experience RatingBasic Experience Rating Methodology
(3) Trend Losses – Leveraged Effect
1,000,000
1,200,000
trend
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Introduction to Experience RatingBasic Experience Rating Methodology
(3) Trend Losses - Impact on Excess Layer
Layer: 500,000 excess of 500,000
Untrended Trended Trend %Total # of Claims 100 100
Pareto B 125,000 135,000Pareto Q 1.55 1.55Overall Severity 227,273 245,455 8.0%
Layer Counts 8.3 9.1 9.9%Layer Severity 313,899 315,687 0.6%Layer Loss Cost 2,590,513 2,864,008 10.6%
All numbers are for illustration only, and not for use in pricing.
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Introduction to Experience RatingBasic 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
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Introduction to Experience RatingBasic Experience Rating Methodology
(4) Develop Losses to Ultimate
Cumulative Reporting Pattern
0.0%10.0%20.0%30.0%40.0%50.0%60.0%70.0%80.0%90.0%
100.0%
0 12 24 36 48 60 72 84 96 108 120 132 144 156 168 180 192 204 216 228 240
% R
epo
rted
as
of
Eva
luat
ion
Ag
e
Primary 400 xs 100 1M xs 1M
All numbers are for illustration only, and not for use in pricing.
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Introduction to Experience RatingBasic Experience Rating Methodology
(4) Develop Losses to Ultimate
Problem:
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.
Possible Solutions: B-F or “Cape Cod” Methods
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Introduction to Experience RatingBasic 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?
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Introduction to Experience RatingBasic 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.
Subject PremiumELR
Ultimate Loss==
22
Introduction to Experience RatingBasic Experience Rating Methodology
(4) Develop Losses to Ultimate
“Cape Cod” ELR turns out to be calculated simply as follows:
Premium/LDFELR
Reported Loss==
Where Premium/LDF is the “exposed premium” corresponding to the
loss that we would expect to have been reported to date.
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Introduction to Experience RatingBasic Experience Rating Methodology
(4) Develop Losses to Ultimate
Key Formulas in “Cape Cod” Method:
Subject Premium / LDFSubject Premium
Reported Loss × LDF Reported Loss==
Cumulative % of Loss Reported = 1 / LDF
24
Introduction to Experience RatingDiagnostics: Telling the Story
Does the Experience-Rating make sense?
Graphical Display
Comparisons
Prior years’ Experience Rating
Exposure Rating
25
Introduction to Experience RatingDiagnostics: Telling the Story
Simple test of actual versus expected:
Actual versus Expected Analysis
Accident Evaluated Evaluated Expected Expected ActualYear 06/30/2006 LDF 06/30/2007 LDF Link Ratio Dvlpmnt Dvlpmnt
1998 571,093 1.103 599,683 1.077 1.024 13,787 28,5901999 492,265 1.141 559,165 1.103 1.034 16,959 66,9002000 319,707 1.195 219,653 1.141 1.047 15,131 -100,0542001 1,762,534 1.277 1,831,330 1.195 1.069 120,944 68,7962002 250,563 1.407 285,397 1.277 1.102 25,508 34,8342003 577,569 1.633 969,391 1.407 1.161 92,772 391,8222004 362,216 2.087 854,699 1.633 1.278 100,702 492,4832005 333,336 3.376 712,321 2.087 1.618 205,879 378,9852006 110,169 14.169 408,968 3.376 4.197 352,220 298,799
Total 4,779,452 6,440,607 943,902 1,661,155
All numbers are for illustration only, and not for use in pricing.
26
Introduction to Experience RatingDiagnostics: 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? Is the ALAE the same?
How has the business changed? Is the experience even relevant?
27
Introduction to Experience RatingCredibility
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 in the layer
28
Introduction to Experience RatingCredibility
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
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Introduction to Experience RatingCredibility
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?
30
Introduction to Experience Rating
EXAMPLES
31
Introduction to Experience RatingChallenges
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
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Introduction to Experience RatingChallenges
(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.
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Introduction to Experience RatingChallenges
(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?
34
Introduction to Experience RatingChallenges
(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.
Com
plex
S
impl
e
35
Introduction to Experience RatingChallenges
(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.
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Introduction to Experience RatingChallenges
(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.
37
Introduction to Experience RatingChallenges
(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
38
Introduction to Experience RatingChallenges
(1) Changing Policy Limits Distribution
Exposure Rate250,000 500,000
Policy Limit Distribution excess of excess ofAY 500,000 1,000,000 5,000,000 250,000 500,000
1998 75.00% 20.00% 5.00% 14.71% 3.09%1999 75.00% 20.00% 5.00% 14.71% 3.09%2000 75.00% 20.00% 5.00% 14.71% 3.09%2001 75.00% 20.00% 5.00% 14.71% 3.09%2002 75.00% 20.00% 5.00% 14.71% 3.09%2003 50.00% 20.00% 30.00% 14.24% 6.18%2004 25.00% 20.00% 55.00% 13.77% 9.27%2005 10.00% 20.00% 70.00% 13.49% 11.13%2006 10.00% 20.00% 70.00% 13.49% 11.13%2007 10.00% 20.00% 70.00% 13.49% 11.13%2008 10.00% 20.00% 70.00% 13.49% 11.13%
All numbers are for illustration only, and not for use in pricing.
39
Introduction to Experience RatingChallenges
(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.
40
Introduction to Experience RatingChallenges
(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
41
Introduction to Experience RatingChallenges
(2) Inclusion of Excess Policies
Challenges:
Proper handling of “supported” and “unsupported” excess policies
Proper application of inflation trend
42
Introduction to Experience RatingChallenges
(2) Inclusion of Excess Policies
Primary Policy
1M Limit
Excess
Policy
1M xs 1M2M Exposed
Excess Policy
1M xs 1M1M Exposed
“Supported” Excess “Unsupported” Excess
43
Introduction to Experience RatingChallenges
(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
44
Introduction to Experience RatingChallenges
(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”
Thank you very much for your attention.
Dave Clark, Actuary and VPMunich Reinsurance America, Inc.
© Copyright 2007 Munich Reinsurance America, Inc. All rights reserved. The Munich Re America name is a mark owned by Munich Reinsurance America, Inc.
The material in this presentation is provided for your information only, and is not permitted to be further distributed without the express written permission of Munich Reinsurance America. This material is not intended to be legal, underwriting, financial, or any other type of professional advice. Examples given are for illustrative purposes only.