Introduction to Experience Rating Casualty Actuarial Society Reinsurance Pricing Seminar July, 2005 Dave ClarkAmerican Re-Insurance Company © Copyright.

Introduction to Introduction to Experience RatingExperience Rating

Casualty Actuarial SocietyCasualty Actuarial SocietyReinsurance Pricing SeminarReinsurance Pricing Seminar

July, 2005July, 2005

Dave ClarkDave Clark American Re-Insurance CompanyAmerican Re-Insurance Company

© Copyright 2005 American Re-Insurance Company. All rights reserved.

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.

Introduction to Experience RatingIntroduction to Experience Rating

Agenda:Agenda: Basic Experience Rating MethodologyBasic Experience Rating Methodology Diagnostics:Diagnostics: telling the story telling the story Credibility weighting with exposure Credibility weighting with exposure

raterate ExamplesExamples Problems & ChallengesProblems & Challenges (time permitting) (time permitting)

Introduction to Experience RatingIntroduction to Experience RatingBasic Experience Rating MethodologyBasic Experience Rating Methodology

Steps in Experience Rating:Steps in Experience Rating:

1.1. Assemble DataAssemble Data

2.2. Adjust Subject Premium to Future Adjust Subject Premium to Future LevelLevel

3.3. Trend and Layer LossesTrend and Layer Losses

4.4. Apply Loss DevelopmentApply Loss Development

Introduction to Experience RatingIntroduction to Experience RatingBasic Experience Rating MethodologyBasic Experience Rating Methodology

(1) Assemble Data(1) Assemble Data

First Rule: First Rule: Apples-to-Apples collection of Apples-to-Apples collection of historical subject premium and loss datahistorical subject premium and loss data

Trended OnLevel Subject Trended OnLevel Subject PremiumPremium

Trended Ultimate Layer Trended Ultimate Layer LossesLossesExperience Rate Experience Rate

==

Introduction to Experience RatingIntroduction to Experience RatingBasic Experience Rating MethodologyBasic Experience Rating Methodology

(1) Assemble Data(1) Assemble Data

Second Rule: Second Rule: Get all the detail on historical Get all the detail on historical losseslosses

1.1. Include all historical losses that would trend into Include all historical losses that would trend into the layer (rule of thumb: get all losses > half of the layer (rule of thumb: get all losses > half of your attachment point)your attachment point)

2.2. Split out ALAE for each lossSplit out ALAE for each loss3.3. Include historical policy limits (and SIR if applicable)Include historical policy limits (and SIR if applicable)4.4. Confirm that losses are assembled by occurrence, Confirm that losses are assembled by occurrence,

not by claimantnot by claimant

Introduction to Experience RatingIntroduction to Experience RatingBasic Experience Rating MethodologyBasic Experience Rating Methodology

(2) Adjust Subject Premium to Future (2) Adjust Subject Premium to Future LevelLevel

Filed [manual] rate changesFiled [manual] rate changes

““Price-level” changesPrice-level” changes Schedule-Rating, company tiers, etcSchedule-Rating, company tiers, etc

Exposure TrendExposure Trend(for inflation-sensitive exposure bases)(for inflation-sensitive exposure bases)

Introduction to Experience RatingIntroduction to Experience RatingBasic Experience Rating MethodologyBasic Experience Rating Methodology

(2) Adjust Subject Premium to Future (2) Adjust Subject Premium to Future LevelLevel

Goal is to adjust historical premium to a level Goal is to adjust historical premium to a level “as if” it has been written during the future “as if” it has been written during the future period.period.

The split between “rate” and “price” is not The split between “rate” and “price” is not always obvious (e.g., where are LCMs or always obvious (e.g., where are LCMs or package factors included?): get a full package factors included?): get a full description from the ceding company.description from the ceding company.

Introduction to Experience RatingIntroduction to Experience RatingBasic Experience Rating MethodologyBasic Experience Rating Methodology

(2)(2) Adjust Subject Premium to Future LevelAdjust Subject Premium to Future Level

Primary Loss Ratios

0.0%

20.0%

40.0%

60.0%

80.0%

100.0%

120.0%

1996 1997 1998 1999 2000 2001 2002 2003 2004 2005

Accident Year

Ult

imat

e L

oss

Rat

io

Introduction to Experience RatingIntroduction to Experience RatingBasic Experience Rating MethodologyBasic Experience Rating Methodology

(2) Adjust Subject Premium to Future (2) Adjust Subject Premium to Future LevelLevel

Note to actuaries coming from a Note to actuaries coming from a primary rate-filing background:primary rate-filing background:

In a rate filing, you typically adjust In a rate filing, you typically adjust premium to the premium to the currentcurrent rate level. rate level.

In reinsurance pricing, you want to In reinsurance pricing, you want to adjust premium to the adjust premium to the averageaverage rate rate level in the future period.level in the future period.

Introduction to Experience RatingIntroduction to Experience RatingBasic Experience Rating MethodologyBasic Experience Rating Methodology

(2) Adjust Subject Premium to Future Level(2) Adjust Subject Premium to Future Level

Obvious observation:Obvious observation:If the ceding company’s effective rates drop If the ceding company’s effective rates drop by -10% for the prospective period, but we by -10% for the prospective period, but we assume that rates are “flat,” then our assume that rates are “flat,” then our experience rating will be understated by 10%. experience rating will be understated by 10%.

Recommended Reading: Trent Vaughn’s Recommended Reading: Trent Vaughn’s Commercial Lines Price MonitoringCommercial Lines Price Monitoring; ; CAS Forum Fall 2004CAS Forum Fall 2004

Introduction to Experience RatingIntroduction to Experience RatingBasic Experience Rating MethodologyBasic Experience Rating Methodology

(3) Trend & Layer Losses(3) Trend & Layer Losses

Purpose is to bring the historical value up Purpose is to bring the historical value up to the average level in the future periodto the average level in the future period

Typically we apply trend and then cap the Typically we apply trend and then cap the trended loss at the historical policy limittrended loss at the historical policy limit

Hidden assumption:Hidden assumption: All losses trend at the All losses trend at the same percent (trend does not vary by size same percent (trend does not vary by size of loss)of loss)

Introduction to Experience RatingIntroduction to Experience RatingBasic Experience Rating MethodologyBasic Experience Rating Methodology

(3) Trend Losses:(3) Trend Losses: Depends on Treaty Basis:Depends on Treaty Basis:

Experience Period

(AY)

Risks Attaching

Treaty

Experience Period

(AY)

Losses Occurring

Treaty

Introduction to Experience RatingIntroduction to Experience RatingBasic Experience Rating MethodologyBasic Experience Rating Methodology

(3)(3) Trend Losses – Leveraged EffectTrend Losses – Leveraged Effect

1,000,000

1,200,000

trend

Introduction to Experience RatingIntroduction to Experience RatingBasic Experience Rating MethodologyBasic Experience Rating Methodology

(3) Trend Losses - Impact on Excess Layer (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.

Introduction to Experience RatingIntroduction to Experience RatingBasic Experience Rating MethodologyBasic Experience Rating Methodology

(4) Develop Losses to Ultimate(4) Develop Losses to Ultimate

Factors depend on Layer of Reinsurance Factors depend on Layer of Reinsurance being pricedbeing priced

We apply LDFs to We apply LDFs to trendedtrended layer losses so that all layer losses so that all years are on the same basis.years are on the same basis.

Development is an aggregate loss conceptDevelopment is an aggregate loss concept Includes new claims (“true IBNR”), development Includes new claims (“true IBNR”), development

on known claims, reopening of closed claims, on known claims, reopening of closed claims, etcetc

Introduction to Experience RatingIntroduction to Experience RatingBasic Experience Rating MethodologyBasic Experience Rating Methodology

(4) Develop Losses to Ultimate(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.

Introduction to Experience RatingIntroduction to Experience RatingBasic Experience Rating MethodologyBasic Experience Rating Methodology

(4)(4) Develop Losses to UltimateDevelop Losses to Ultimate

Problem:Problem: Most recent periods are very Most recent periods are very green and may have zero losses reported green and may have zero losses reported to date. Should they be included? to date. Should they be included? Alternatively, if there are losses, then they Alternatively, if there are losses, then they are hit with huge LDF.are hit with huge LDF.

Possible Solution: Possible Solution: B-FB-F or or “Cape Cod” Methods“Cape Cod” Methods

Introduction to Experience RatingIntroduction to Experience RatingBasic Experience Rating MethodologyBasic Experience Rating Methodology

(4)(4) Develop Losses to UltimateDevelop Losses to Ultimate

LDF Method:LDF Method:Ultimate = Reported × LDFUltimate = Reported × LDF

Bornhuetter-Ferguson (B-F) Method:Bornhuetter-Ferguson (B-F) Method:Ultimate = Reported + Prem×ELR×(1-1/ Ultimate = Reported + Prem×ELR×(1-1/

LDF)LDF)

But what But what ELRELR do we use? do we use?

Introduction to Experience RatingIntroduction to Experience RatingBasic Experience Rating MethodologyBasic Experience Rating Methodology

(4)(4) Develop Losses to UltimateDevelop Losses to Ultimate

““Cape Cod” method is a special case of the Cape Cod” method is a special case of the B-F method.B-F method.

The ELR is selected to be equal to the final The ELR is selected to be equal to the final value of the all-year average loss ratio.value of the all-year average loss ratio.

Subject PremiumSubject PremiumELRELR

Ultimate Ultimate LossLoss==

Introduction to Experience RatingIntroduction to Experience RatingBasic Experience Rating MethodologyBasic Experience Rating Methodology

(4)(4) Develop Losses to UltimateDevelop Losses to Ultimate

““Cape Cod” ELR turns out to be calculated Cape Cod” ELR turns out to be calculated simply as follows:simply as follows:

Premium/LDFPremium/LDFELRELR

Reported Reported LossLoss==

Where Premium/LDF is the “exposed premium” Where Premium/LDF is the “exposed premium” corresponding to the loss that we would expect corresponding to the loss that we would expect to have been reported to date.to have been reported to date.

Introduction to Experience RatingIntroduction to Experience RatingBasic Experience Rating MethodologyBasic Experience Rating Methodology

(4) (4) Develop Losses to UltimateDevelop Losses to UltimateKey Formulas in “Cape Cod” Method:Key Formulas in “Cape Cod” Method:

Subject Premium / Subject Premium / LDFLDF

Subject Subject PremiumPremium

Reported Loss Reported Loss ×× LDFLDF

Reported Reported LossLoss==

Cumulative % of Loss Reported = 1 / Cumulative % of Loss Reported = 1 / LDFLDF

Introduction to Experience RatingIntroduction to Experience RatingDiagnostics: Diagnostics: Telling the StoryTelling the Story

Does the Experience-Rating make Does the Experience-Rating make sense?sense?

Graphical DisplayGraphical Display

ComparisonsComparisons Prior years’ Experience RatingPrior years’ Experience Rating Exposure RatingExposure Rating

Introduction to Experience RatingIntroduction to Experience RatingDiagnostics: Diagnostics: Telling the StoryTelling the Story

Simple test of actual versus expected:Simple test of actual versus expected:

Actual versus Expected Analysis

Accident Evaluated Evaluated Expected Expected ActualYear 09/30/2004 LDF 09/30/2005 LDF Link Ratio Dvlpmnt Dvlpmnt

1996 571,093 1.103 599,683 1.077 1.024 13,787 28,5901997 492,265 1.141 559,165 1.103 1.034 16,959 66,9001998 319,707 1.195 219,653 1.141 1.047 15,131 -100,0541999 1,762,534 1.277 1,831,330 1.195 1.069 120,944 68,7962000 250,563 1.407 285,397 1.277 1.102 25,508 34,8342001 577,569 1.633 969,391 1.407 1.161 92,772 391,8222002 362,216 2.087 854,699 1.633 1.278 100,702 492,4832003 333,336 3.376 712,321 2.087 1.618 205,879 378,9852004 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.

Introduction to Experience RatingIntroduction to Experience RatingDiagnostics: Diagnostics: Telling the StoryTelling the Story

Some questions to ask when reconciling Some questions to ask when reconciling with prior rating or exposure rating:with prior rating or exposure rating:

Is the experience rating distorted by large Is the experience rating distorted by large losses?losses?

Is the ELR used in exposure rating Is the ELR used in exposure rating consistent with the ceding company’s consistent with the ceding company’s experience?experience?

How has the business changed? Is the How has the business changed? Is the experience even relevant?experience even relevant?

Introduction to Experience RatingIntroduction to Experience RatingCredibilityCredibility

Credibility:Credibility:Experience Rating = Experience Rating = Projection of losses Projection of losses

based only on what took place for this based only on what took place for this specific accountspecific account

Exposure Rating = Exposure Rating = A PrioriA Priori estimate of estimate of losses based on information other than losses based on information other than the specific account’s experiencethe specific account’s experience

Introduction to Experience RatingIntroduction to Experience RatingCredibilityCredibility

Credibility:Credibility:Separating claim counts is useful for Separating claim counts is useful for

comparing experience and exposure comparing experience and exposure ratings, and also for gauging credibility.ratings, and also for gauging credibility.

A good credibility standard is: A good credibility standard is: the number of the number of claims that we would have expected to claims that we would have expected to observe in the historical periods.observe in the historical periods.

Z =Z =nn

n + kn + k

Introduction to Experience RatingIntroduction to Experience RatingCredibilityCredibility

Credibility:Credibility: Other ConsiderationsOther Considerations Stability of Experience: How much would Stability of Experience: How much would

experience rate change if we remove the experience rate change if we remove the largest claim or add an additional full limit largest claim or add an additional full limit loss?loss?

Are pricing factors (LDFs, rate changes, etc) Are pricing factors (LDFs, rate changes, etc) from the account or are they default values?from the account or are they default values?

Do the characteristics of the ceding company Do the characteristics of the ceding company match the business in the exposure rating match the business in the exposure rating curves?curves?

Introduction to Experience RatingIntroduction to Experience Rating

EXAMPLESEXAMPLES

Introduction to Experience RatingIntroduction to Experience RatingChallengesChallenges

We will look at two challenges that We will look at two challenges that require some variation on the require some variation on the experience-rating:experience-rating:

(1) Changing Mix of Business or Policy (1) Changing Mix of Business or Policy Limits DistributionLimits Distribution

(2)(2) Inclusion of Excess or Umbrella Inclusion of Excess or Umbrella PoliciesPolicies

Introduction to Experience RatingIntroduction to Experience RatingChallengesChallenges

(1)(1) Changing Mix of BusinessChanging Mix of Business

Wherever possible, we want the experience Wherever possible, we want the experience rating performed on homogeneous rating performed on homogeneous experience. That is, each historical experience. That is, each historical period writes the same business as will period writes the same business as will be in the future period.be in the future period.

A changing mix by line of business means A changing mix by line of business means that separate experience ratings are that separate experience ratings are needed by line.needed by line.

Introduction to Experience RatingIntroduction to Experience RatingChallengesChallenges

(1)(1) Changing Policy Limits DistributionChanging Policy Limits Distribution

Suppose we are pricing a 500,000 Suppose we are pricing a 500,000 excess of 500,000 layer, but the excess of 500,000 layer, but the ceding company has only recently ceding company has only recently begun writing high limit policies.begun writing high limit policies.

How can the historical experience be How can the historical experience be used?used?

Introduction to Experience RatingIntroduction to Experience RatingChallengesChallenges

(1)(1) Changing Policy Limits DistributionChanging Policy Limits Distribution

(a) Trend past historical policy limits.(a) Trend past historical policy limits.

(b) Price lower “fully exposed” layer and then (b) Price lower “fully exposed” layer and then use exposure-rating model relativities.use exposure-rating model relativities.

(c) Adjust each historical period to the future (c) Adjust each historical period to the future period’s level of exposure.period’s level of exposure.

(d) Use curve-fitting model to historical losses.(d) Use curve-fitting model to historical losses.

C

om

ple

x S

imple

Introduction to Experience RatingIntroduction to Experience RatingChallengesChallenges

(1) Changing Policy Limits Distribution(1) Changing Policy Limits Distribution(a)(a) Trend past historical policy limits.Trend past historical policy limits.

Advantage:Advantage: Very simpleVery simpleDisadvantage:Disadvantage: Only works if the reason that policy limits Only works if the reason that policy limits

have changed is that they have drifted have changed is that they have drifted up with inflation.up with inflation.

Introduction to Experience RatingIntroduction to Experience RatingChallengesChallenges

(1) Changing Policy Limits Distribution(1) Changing Policy Limits Distribution(b) Experience rate “fully exposed layer”(b) Experience rate “fully exposed layer”

Advantage:Advantage: Relatively simpleRelatively simpleDisadvantages:Disadvantages: Subject premium still needs to be adjusted Subject premium still needs to be adjusted

to the average policy limit profile of future to the average policy limit profile of future period.period.

Does not make use of the loss experience Does not make use of the loss experience in the layer that we are actually pricing.in the layer that we are actually pricing.

Introduction to Experience RatingIntroduction to Experience RatingChallengesChallenges

(1) Changing Policy Limits Distribution(1) Changing Policy Limits Distribution(c) Adjust years based on exposure (c) Adjust years based on exposure

rating each historical periodrating each historical period

Advantage:Advantage: This is the most accurate method.This is the most accurate method.Disadvantage(s):Disadvantage(s): Requires full policy limit profile for each Requires full policy limit profile for each

historical periodhistorical period Difficulty in explaining adjustment Difficulty in explaining adjustment

factorsfactors

Introduction to Experience RatingIntroduction to Experience RatingChallengesChallenges

(1)(1) Changing Policy Limits DistributionChanging 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

1996 75.00% 20.00% 5.00% 14.71% 3.09%1997 75.00% 20.00% 5.00% 14.71% 3.09%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 50.00% 20.00% 30.00% 14.24% 6.18%2002 25.00% 20.00% 55.00% 13.77% 9.27%2003 10.00% 20.00% 70.00% 13.49% 11.13%2004 10.00% 20.00% 70.00% 13.49% 11.13%2005 10.00% 20.00% 70.00% 13.49% 11.13%2006 10.00% 20.00% 70.00% 13.49% 11.13%

All numbers are for illustration only, and not for use in pricing.

Introduction to Experience RatingIntroduction to Experience RatingChallengesChallenges

(1) Changing Policy Limits Distribution(1) Changing Policy Limits Distribution(c) Adjust years based on exposure rating (c) Adjust years based on exposure rating

each historical periodeach historical period

The exposure rates from this table are used to The exposure rates from this table are used to “layer” the subject premium to find the “layer” the subject premium to find the portion of premium corresponding to the portion of premium corresponding to the losses in the layer; the layered premium losses in the layer; the layered premium becomes the new “adjusted subject becomes the new “adjusted subject premium.”premium.”

Note: this is a variation on the exposure adjustment described by Mata & Note: this is a variation on the exposure adjustment described by Mata & Verheyen in their Spring 2005 CAS Forum article.Verheyen in their Spring 2005 CAS Forum article.

Introduction to Experience RatingIntroduction to Experience RatingChallengesChallenges

(1) Changing Policy Limits Distribution(1) Changing Policy Limits Distribution(d) Fit curve to historical data(d) Fit curve to historical data

Advantage:Advantage: Makes use of all the loss informationMakes use of all the loss information

Disadvantage(s):Disadvantage(s): Does not properly include developmentDoes not properly include development Significant increase in complexitySignificant increase in complexity Temptation to extrapolate beyond dataTemptation to extrapolate beyond data

Introduction to Experience RatingIntroduction to Experience RatingChallengesChallenges

(2)(2) Inclusion of Excess PoliciesInclusion of Excess Policies

Challenges:Challenges: Proper handling of “supported” and Proper handling of “supported” and

“unsupported” excess policies“unsupported” excess policies Proper application of inflation trendProper application of inflation trend

Introduction to Experience RatingIntroduction to Experience RatingChallengesChallenges

(2) Inclusion of Excess Policies(2) Inclusion of Excess Policies

Primary Policy

1M Limit

Excess

Policy

1M xs 1M2M Exposed

Excess Policy

1M xs 1M

1M Exposed

““Supported” Supported” ExcessExcess

““Unsupported” Unsupported” ExcessExcess

Introduction to Experience RatingIntroduction to Experience RatingChallengesChallenges

(2)(2) Inclusion of Excess PoliciesInclusion of Excess Policies““supported” and “unsupported” excess policiessupported” and “unsupported” excess policies

(a) Combine primary and excess portions of (a) Combine primary and excess portions of large losseslarge losses

• This is the right answer, but requires the ability to This is the right answer, but requires the ability to match loss records from the two types of policiesmatch loss records from the two types of policies

(b) Price excess layer on a “responds ground-(b) Price excess layer on a “responds ground-up” basisup” basis

Introduction to Experience RatingIntroduction to Experience RatingChallengesChallenges

(2)(2) Inclusion of Excess PoliciesInclusion of Excess PoliciesProper application of inflation trendProper application of inflation trend

(a) Add SIR to loss amount before trending(a) Add SIR to loss amount before trending

(b) Use a higher trend percent to reflect (b) Use a higher trend percent to reflect “leverage”“leverage”