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Version 10/1/11 Cutting Edge Tools for Pricing and Underwriting Seminar Integrating External Data into the Decision Making / Predictive Modeling Process Casualty Actuarial Society Ron Zaleski, Jr., FCAS, MAAA Fall 2011 1 Version 10/1/11

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Cutting Edge Tools for Pricing and Underwriting Seminar

Integrating External Data into the Decision Making / Predictive Modeling Process

Casualty Actuarial Society Ron Zaleski, Jr., FCAS, MAAA Fall 2011

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CAS Anti-Trust Notice

  • The Casualty Actuarial Society is committed to adhering strictly to the letter and

spirit of the antitrust laws. Seminars conducted under the auspices of the CAS are designed solely to provide a forum for the expression of various points of view

  • n topics described in the programs or agendas for such meetings.
  • Under no circumstances shall CAS seminars be used as a means for competing

companies or firms to reach any understanding – expressed or implied – that restricts competition or in any way impairs the ability of members to exercise independent business judgment regarding matters affecting competition.

  • It is the responsibility of all seminar participants to be aware of antitrust

regulations, to prevent any written or verbal discussions that appear to violate these laws, and to adhere in every respect to the CAS antitrust compliance policy.

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The Hanover: About Us

  • Property and Casualty Insurance Company
  • Founded over 150 years ago
  • Among the largest property and casualty companies with

revenues of $2.8+ billion

  • Best of both national and regional companies
  • The Boston Globe named us the #1 publicly traded financial

services business in Massachusetts

  • Both The Boston Globe and Business Insurance named us to

their list of 2010 Best Places to Work

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AGENDA

  • Background
  • Case Study: Territory Definitions & Factors
  • Selecting & Handling External Data
  • Incorporating Competitor Data
  • Supplementing with Industry Data
  • Summary
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Reminder

  • Modeling is an iterative process
  • How does the analyst decide

which factors are most valuable?

  • Parameters/standard errors
  • Consistency of patterns over time
  • r random data sets
  • Type III statistical tests

(e.g., chi-square tests)

  • Judgment (e.g., do the trends

make sense)

  • Focus of the section is on

gathering data NOT analysis

Complicate Simplify Review Model

This presentation will focus on ways to select external data for modeling and evaluation of a territory project

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  • Select analytical basis and approach
  • Geographic Unit:

i.e. Census Tract

  • Target Variable:

i.e. Loss Ratio ex. Territory Factors

  • Modeling Approach:

i.e. GLM w. Spatial Smoothing

  • Develop internal data
  • Experience data (exposures, premiums, losses)
  • Existing rating plan variables and derivations
  • Identify and incorporate any external data, if needed
  • Measures that describe geographic unit to be used in the model
  • Supporting data to guide modeling effort and inform final decision

process, especially where internal data is thin

Case Study:

PL Auto Territory Development

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Questions Addressed

Location Proxy Data

What types of data can we use to represent geographic units in a model framework?

Credibility

How can we utilize external information to provide ballast when our internal data is thin or non-existent?

Competitor Analytics

How can we indentify the appropriate competitor data to use in the decision-making process?

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AGENDA

  • Background
  • Case Study: Territory Definitions & Factors
  • Selecting & Handling External Data
  • Incorporating Competitor Data
  • Supplementing with Industry Data
  • Summary
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External Data:

Location

Attributes & Attitudes Policyholder Characteristics

Location

Goal: Append external data that represents similarity between geographic units beyond proximity Location-Proxy Variables

  • U.S. Census Data (Demographics)
  • Traffic Statistics (NHTSA)
  • Other data providers, such as EASI

Competitor Information

  • Rate Filing Research
  • Competitor Rate Engines(InsurQuote / Quadrant)

Industry Data

  • ISO Data Cubes
  • IIHS/HLDI Data
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  • After appending external data, spend time with exploratory

analyses to understand relationships between variables

  • Correlation Tests, such as Cramer’s V
  • X-by-X plots (Unsupervised), such as Scatter Plots, Box-Whisker and

2-Way Plots to detect patterns

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External Data:

Variable Inspection

Box-Whisker X-X Scatterplot Two-Way Plot

Software Snapshots: JMP, SAS, and EMBLEM

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External Data:

Dealing with Correlation

  • Principal Components Analysis
  • Unsupervised learning technique that seeks to explain the variance

in the X’s

  • Reduces a large number of continuous variables into a manageable

smaller set that are a linearly independent, linear combination of the underlying larger set set

  • Partial Least Squares
  • Similar to PCA, except the technique is supervised learning, seeking

to maximize the covariance between the X’s and the dependent Y

  • The advantage is that the PLS variables are extracted in order of

importance based on relationship to the target (not each other)

  • The disadvantage is that it is supervised and therefore the outcome

depends on the target variable.

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AGENDA

  • Background
  • Case Study: Territory Definitions & Factors
  • Selecting & Handling External Data
  • Incorporating Competitor Data
  • Supplementing with Industry Data
  • Summary
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Competitor Territory Models

  • At other companies, actuaries are selecting territory

definitions and factors, too…

  • They’re performing similar analyses on the same metrics…
  • They’re working on another sample of the population…
  • So let’s view these territories as competing models to ours!

This section will cover the following:

  • How can we identify the best competitor model for comparison?
  • How can we use the competitors’ territories directly in our analysis to

strengthen predictions?

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Competitor Evaluation:

Lift Charts

0% 2% 4% 6% 8% 10% 12% 14% 16% 18% 20% 0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80 2.00 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Exposure Distribtion Loss Ratio Relativity (ex. Territory Factors) Ventile (5% Groups)

Lift Chart: Territory Based on Competitor X

Exposure Distribution Expected (Based on Competitor X) Actual (Based on Internal Data)

Using a traditional model evaluation technique, such as a lift chart, you can judge the appropriateness of a competitor’s territory on your own data.

Actual performance using Competitor X matches Expected very well

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0% 2% 4% 6% 8% 10% 12% 14% 16% 18% 20% 0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80 2.00 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Exposure Distribtion Loss Ratio Relativity (ex. Territory Factors) Ventile (5% Groups)

Lift Chart: Territory Based on Competitor Y

Exposure Distribution Expected (Based on Competitor Y) Actual (Based on Internal Data)

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Actual performance using Competitor Y matches Expected very well, too!!

But what happens when a second competitor looks just as good?

Competitor Evaluation:

Comparing Lift Charts

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0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

Cumulative % of Losses Explained Cumulative % of Exposures Earned

Gini / Lorenz Curve: Territory Based on Competitor X

GINI INDEX = 0.202

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Competitor Evaluation:

Lorenz/Gini Curve

An alternative view is to use a Lorenz curve and calculate a Gini Index to provide a quantitative measure to compare two models

Higher Gini Index implies a greater degree of loss segmentation based on the selected model

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Competitor Evaluation:

Ranking by Gini

Ranking the performance of each of the Competitor Models by Gini Index will help guide your selection.

Takeaway: Using quantitative measures, such as the Gini Index, makes determining the “best” model easier

Competitor Name Gini Index Competitor X 0.202 Competitor Y 0.160 Competitor Z 0.084 Competitor W 0.080 Competitor U 0.064 Competitor V 0.056

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0% 2% 4% 6% 8% 10% 12% 14% 16% 18% 20% 0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80 2.00

Exposure Distribtion Loss Ratio Relativity (ex. Territory Factors) Average Discrepancy Factor (= X Factor/ Y Factor)

Discrepancy Graph: Competitor X vs. Competitor Y

Exposure Distribution Expected (Based on Competitor X) Expected (Based on Competitor Y) Actual (Based on Internal Data)

Actual loss performance tracks better with Competitor X than Y.

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Another alternative visual comparison is the discrepancy or “X” graph that compares models against each other.

Competitor Evaluation:

The “Playoffs”

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Competitor Territories:

Integration into Decision-Making

So Competitor X seems to perform best… now what?

  • Incorporate factors directly as variables in model
  • Perform correlation analysis to identify other potential

predictive variables

Model Development

  • Consider Competitor X statistics, such as Gini, as

minimum performance standards

  • Compare models using Discrepancy “X” graphs

Benchmarks

  • Competitor X is determined to be the best competitor

complement

  • Integrate discrepancy in spatial/residual smoothing

Credibility Complements

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AGENDA

  • Background
  • Case Study: Territory Definitions & Factors
  • Selecting & Handling External Data
  • Incorporating Competitor Data
  • Supplementing with Industry Data
  • Summary
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Industry Data

  • In dealing with the common problem of low data volume, we

constantly look for ways to supplement analysis to deal with the credibility in separating the signal form the noise

  • A data source, such as HLDI, can provide both an early

indication of which external variables are important as well as helping to detect the underlying signal in a noisy process

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Identifying Signal:

Bring on the Noise…

Detection of signal is especially difficult where the data is thin. Consider the analysis of Principal Component below.

0% 2% 4% 6% 8% 10% 12% 0.00 0.50 1.00 1.50 2.00 2.50 3.00

  • 3.08
  • 2.81
  • 2.58
  • 2.32
  • 2.14
  • 1.91
  • 1.71
  • 1.5
  • 1.31
  • 1.12
  • 0.93
  • 0.76
  • 0.59
  • 0.42
  • 0.25
  • 0.09

0.06 0.23 0.38 0.54 0.69 0.84 0.99 1.15 1.32 1.48 1.66 1.84 2.02 2.19 2.39 2.62 2.85 3.08

Exposure Distribtion Pure Premium Relative to Average Principal Component #1

Pure Premium Relativity: Internal Data Only

Exposure Distribution Internal Pure Premium Relativity

There appears to be a decreasing trend across the variable, but are the spikes with low volume just noise?

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Identifying Signal:

The Advantage of Large Data…

More data helps to flatten “noisy” spikes and reveal the true signal, especially where internal data is thin. It is also a good sign when trends are consistent.

0% 2% 4% 6% 8% 10% 12% 0.00 0.50 1.00 1.50 2.00 2.50 3.00

  • 3.08
  • 2.81
  • 2.58
  • 2.32
  • 2.14
  • 1.91
  • 1.71
  • 1.5
  • 1.31
  • 1.12
  • 0.93
  • 0.76
  • 0.59
  • 0.42
  • 0.25
  • 0.09

0.06 0.23 0.38 0.54 0.69 0.84 0.99 1.15 1.32 1.48 1.66 1.84 2.02 2.19 2.39 2.62 2.85 3.08

Exposure Distribtion Pure Premium Relative to Average Principal Component #1

Pure Premium Relativity: Internal vs. Industry

Exposure Distribution Internal Pure Premium Relativity Industry Pure Premium Relativity

The absence of more credible data may have resulted in a poor decision

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  • Append external variables and transformations onto the

industry data and build (partial) predictive models

  • Advantages:
  • More data (rows) = clearer signal; reduced noise pollution
  • Allows you to test sampling variance on a larger population
  • Disadvantages:
  • Less data (columns) = Difficult to reflect other class plan variables not

available on the industry data to avoid OVB (Omitted Variable Bias)

  • Could be considering “cheating” from a sampling perspective since

your data/signal may be included in the dataset

Identifying Signal:

Suggested Approach

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Final Result

  • Industry Territory model that can be included in modeling

dataset

  • Modeling “Guide” -- Lists of variables with an importance

measure for each coverage analyzed:

Parameter Estimates on Industry Data Variable Coverage A Coverage B Coverage C Coverage D Principle Component 1 0.140 0.410 0.230 Principle Component 2 0.840 0.590 0.320 0.690 Principle Component 3 0.680 0.400 Principle Component 4 1.370 0.070 1.170 3.860 Principle Component 5 1.060 0.160 0.740 Principle Component 6 0.270 0.380

Remember! The results on industry data could suffer from OVB, capturing signal that your underlying class plan would have already accounted for

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AGENDA

  • Background
  • Case Study: Territory Definitions & Factors
  • Selecting & Handling External Data
  • Incorporating Competitor Data
  • Supplementing with Industry Data
  • Summary
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  • The foundation of every modeling project is developing the

right data for the task

  • External data is readily available and provides not only useful

predictors, but also validation and benchmarks

  • Creatively using competitor and industry data can strengthen

the final decision by lending additional credibility to underlying data and providing another modeler’s opinion.

SUMMARY

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Contact Details

Ronald Zaleski, Jr., FCAS, MAAA The Hanover Insurance Group AVP – Actuary Personal Lines Research & Development 440 Lincoln Street Worcester, MA 01653 (508) 855-8121 rzaleski@hanover.com

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Census Data: http://www.census.gov/ NHTSA: http://www.nhtsa.gov/ EASI: http://www.easidemographics.com/ IIHS-HLDI: http://www.iihs.org/ ISO: http://www.iso.com/

Useful Links