2012®

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“Predictive Modeling: Pricing Service Contracts in a Competitive

Environment”

Mike Paczolt, FCAS, MAAA

Consulting ActuaryMilliman

®About Milliman• Actuaries and other consultants

• Independent – Not broker or insurance carrier

• Over 2,100 Employees

• Offices in most major cities globally

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Adverse Selection – Year 1

PRICE

Low Risk High Risk

Company A $25 $75

Company B $50 $50

# of Policies

Low Risk High Risk

Company A 1,000 1,000

Company B 1,000 1,000

Company B – Profit Summary

Low Risk High Risk

Profit Per Policy +$25 -$25

# Policies x 1,000 x 1,000

Total Profit +$25,000 -$25,000

®Econ 101

Price

Demand

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Adverse Selection – Year 2

PRICE

Low Risk High Risk

Company A $25 $75

Company B $50 $50

# of Policies

Low Risk High Risk

Company A 1,500 500

Company B 500 1,500

Company B – Profit Summary

Low Risk High Risk

Profit Per Policy +$25 -$25

# Policies x 500 x 1,500

Total Profit +$12,500 -$37,500

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Adverse Selection – Year 3

PRICE

Low Risk High Risk

Company A $25 $75

Company B $50 $50

# of Policies

Low Risk High Risk

Company A 2,000 0

Company B 0 2,000

Company B – Profit Summary

Low Risk High Risk

Profit Per Policy +$25 -$25

# Policies x 0 x 2,000

Total Profit $0 -$50,000

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2 Types of Pricing Analysis

Cost Per Exposure

• High level analysis

• Average historical cost per policy

• Often segmented by product type

Predictive Modeling

• Identifies patterns in data

• Captures relationship between claims and policy characteristics

• Accounts for correlation between policy characteristics

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Why use Predictive Modeling?

Pricing Develop accurate rates to maintain profitability and competitiveness

Underwriting Prioritize business for underwriting scrutinySales Target profitable customer base for new

and renewal businessLoss Control Identify root causes of product failures for

quality controlClaims Management

Set thresholds for determining acceptable claim severities

Customer Management

Target highly profitable business for renewals based on lapse rates

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Probability is a function of…

• Predictive modeling attempts to convert these tendencies into a mathematical formula

Family History Age Lifestyle Disease

On-base % ERA Slugging

%Baseball

Wins

Product Age Supplier Dealer

Extended Warranty Claims

®Predictive Models• One-Way Linear Regression

• Multivariate Linear Regression

• Market Segmentation

• Other advanced techniques are becoming more popular (e.g. machine learning, price optimization, etc.)

®Variables

• Location – Zip Code• Brand/Product Type• Dealer/Salesman• Factory• Product Age/Usage• Manufacturer/Supplier• Parts/Components• Customer Demographics• Service Level

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One-Way Regression Example

0 1 2 3 4 5 6 7 8$0

$20

$40

$60

$80

$100

$120

$140

$160

Cost Per Unit by Product Age

Product Age (Years)

Cost

Per

Un

it

®Inter-Dependencies

Supplier X

Sold in ILCustomerCredit Score <300

75%85%

55%

85%45%

125%

90%

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Multivariate Linear RegressionExample

0 1 2 3 4 5 6 7 8

$0

$20

$40

$60

$80

$100

$120

$140

$160

$180

A

C

Cost Per Unit byProduct Age & Supplier

ABCD

Product Age (Years)

Supplier

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Market SegmentationHow does it work?

Initial Population10,000 Policies

Brand A7,500 Policies

Dealer 1Brand A

4,000 Policies

Dealer 2Brand A

3,500 Policies

Brand B2,500 Policies

Dealer 1Brand B

1,500 Policies

Dealer 2Brand B

1,000 Policies

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Market SegmentationExample of Results

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Building a Predictive Model

Data• Gather Data• Prepare Data

Model• Create Model• Validate Model

Implementation• Pricing• Underwriting

Decisions

®Data Gathering• Sales / Policy Database

• Location, supplier, product type, etc…

• Claims Database• Number of claims by type, claim values amounts

labor/parts, etc…

• External Database• Credit score, customer purchase history, etc…

®Data Prep• Clean data is crucial

• May exclude suspect data

• Not uncommon to eliminate 10% to 25% of records

• Data can be held back to validate model

®Create Model• Decide purpose of model

• Claim Frequency• Claim Severity• Loss Ratios• CPU

• Iterative process

• Use one-way analysis to identify important variables

• Group variables together

®Model Validation• Monitor “best fit” based on stats

• Correlation vs. Causality

• Back-testing on holdout sample

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Predictive Modeling Results• Sophisticated statistical model identifying key traits of

claims that answers:• What segments of my portfolio am I making

money?• What is my price floor?• Are certain dealers/salesman underperforming

peers?• What is causing my warranty claims?• Should I reduce or expand coverage?• Which customers should my sales team target?

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Sample ResultsUnderwriting Purpose

1 2 3 4 5 6 7 8 9 1025%

50%

75%

100%

125%

150%Loss Ratio by Segment

Segment

Loss R

ati

o

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Sample ResultsRating Plan

Base RatingProduct Wholesale Price Rate Policy Length Factor

<$1,000 $200 1 Year 1.00$1,001 to $10,000 $300 2 Year 1.90

>$10,000 $1,000

Rating     RatingProduct Age Factor Renewal   Factor

< 1 Year 1.00   No 1.001 Year to 5 Years 1.20   Yes 0.95

> 5 Years 2.00

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Sample ResultsSales Purpose

-10% -8% -6% -4% -2% 0% 2% 4% 6% 8% 10%25%

50%

75%

100%

125%

150%

Loss Ratio vs.Relative SC Revenue Growth

Relative Service Contract Revenue Growth

Loss R

ati

o

Questions

®Contact Info

• Email: michael.paczolt@milliman.com• Phone: 312-499-5720