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.

2. Introduction to Experience Rating
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Introduction to Experience Rating
Agenda:
Basic Experience Rating Methodology
Diagnostics: telling the story
Credibility weighting with exposure rate
Examples
Problems & Challenges (time permitting)

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Introduction to Experience Rating Basic Experience Rating Methodology
Steps in Experience Rating:
Assemble Data
Adjust Subject Premium to Future Level
Trend and Layer Losses
Apply Loss Development

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Introduction to Experience Rating Basic 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 Losses
Experience Rate =

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Introduction to Experience Rating Basic Experience Rating Methodology
(1) Assemble Data
Second Rule: Get all the detail on historical losses
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

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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)

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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.

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Introduction to Experience Rating Basic Experience Rating Methodology
Adjust Subject Premium to Future Level

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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.

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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

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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)

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Introduction to Experience Rating Basic Experience Rating Methodology
(3) Trend Losses: Depends on Treaty Basis:
Experience Period (AY)
Losses Occurring Treaty
Experience Period (AY)
Risks Attaching Treaty

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Introduction to Experience Rating Basic Experience Rating Methodology
Trend Losses – Leveraged Effect
1,000,000
1,200,000
trend

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Introduction to Experience Rating Basic Experience Rating Methodology
(3) Trend Losses - Impact on Excess Layer
All numbers are for illustration only, and not for use in pricing.

15. Introduction to Experience Rating Basic Experience Rating Methodology
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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

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Introduction to Experience Rating Basic Experience Rating Methodology
(4) Develop Losses to Ultimate
All numbers are for illustration only, and not for use in pricing.

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Introduction to Experience Rating Basic Experience Rating Methodology
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 Solution: B-F or “Cape Cod” Methods

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Introduction to Experience Rating Basic Experience Rating Methodology
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 Rating Basic Experience Rating Methodology
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 Premium
ELR
 Ultimate Loss =

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Introduction to Experience Rating Basic Experience Rating Methodology
Develop Losses to Ultimate
“Cape Cod” ELR turns out to be calculated simply as follows:
 Premium/LDF
ELR
 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 Rating Basic Experience Rating Methodology
(4) Develop Losses to Ultimate
Key Formulas in “Cape Cod” Method:
Cumulative % of Loss Reported = 1 / LDF
Subject Premium / LDF
Subject Premium
Reported Loss × LDF
Reported Loss =

22. Introduction to Experience Rating Diagnostics: Telling the Story
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Introduction to Experience Rating Diagnostics: Telling the Story
Does the Experience-Rating make sense?
Graphical Display
Comparisons
Prior years’ Experience Rating
Exposure Rating

23. Introduction to Experience Rating Diagnostics: Telling the Story
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Introduction to Experience Rating Diagnostics: Telling the Story
Simple test of actual versus expected:
All numbers are for illustration only, and not for use in pricing.

24. Introduction to Experience Rating Diagnostics: Telling the Story
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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?

25. Introduction to Experience Rating Credibility
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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

26. Introduction to Experience Rating Credibility
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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

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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?

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Introduction to Experience Rating
EXAMPLES

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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
Inclusion of Excess or Umbrella Policies

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Introduction to Experience Rating Challenges
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 Rating Challenges
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?

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Introduction to Experience Rating Challenges
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.
Complex Simple

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Introduction to Experience Rating Challenges
(1) Changing Policy Limits Distribution
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 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.

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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

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Introduction to Experience Rating Challenges
Changing Policy Limits Distribution
All numbers are for illustration only, and not for use in pricing.

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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.

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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

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Introduction to Experience Rating Challenges
Inclusion of Excess Policies
Challenges:
Proper handling of “supported” and “unsupported” excess policies
Proper application of inflation trend

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Introduction to Experience Rating Challenges
(2) Inclusion of Excess Policies
“Supported” Excess
“Unsupported” Excess
Primary Policy
1M Limit
Excess
Policy
1M xs 1M
2M Exposed
Excess Policy
1M xs 1M
1M Exposed

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Introduction to Experience Rating Challenges
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

42. Introduction to Experience Rating Challenges
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Introduction to Experience Rating Challenges
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”