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Determination of Statistically Optimal
Geographical Territory Boundaries
Casualty Actuaries of the Southeast
Klayton N. Southwood
October 10, 2005
© 2005 Towers Perrin
Risk Classification
Definition — A grouping of risks with similar risk characteristics
so that differences in costs may be recognized
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Purpose —
Means by which data can be gathered so as to
measure and quantify a specific risk
characteristic’s relation to the propensity for loss
Example — Territory classes are a means to gather data so as
to measure and quantify geographic risk factors
relative to the propensity for loss
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Homogeneity
Definition — A risk classification is homogeneous if all risks in the
class have the same or a similar degree of risk with
respect to the specific risk factor being measured
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Purpose — Homogeneity of the class increases the credibility of
the loss data generated by the class
Example — A territory is considered homogeneous if all risks in
the territory represent the same, or approximately
the same, level of geographical risk
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Statistical Test of Homogeneity
Within Variance: Based on the squared difference between
each zip code pure premium in the cluster and the average pure
premium for the specific cluster being tested
Between Variance: Based on the squared difference between
each cluster’s pure premium and the statewide average pure
premium
Total Variance = Within Variance + Between Variance
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Within Variance Percentage = Within Variance divided by Total
Variance
Goals: Low Percentage of Total Variance Within
High Percentage of Total Variance Between
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Building Blocks
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Territory Risk Classes
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Basis to Group Areas
County
 Largely stable over time
 Broad area
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ZIP Code
 Narrowly defined may be beneficial to define territories
 Useful for online rating
 Main disadvantage is need to deal with change over time
Geo Coding
 Finest detail
 Static over time
 No predefined grouping
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Loss Indice Normalized Pure Premium
Normalized Zip Code Pure Premium
EQUALS
Actual Zip Code Pure Premium
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TIMES
State Ave. Prem.
State Ave. Base
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Zip Ave. Prem.
Zip Base
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Loss Indice Econometric Model
 Population Density
 Vehicle Density
 Accidents per Vehicle
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 Injuries per Accident
 Thefts per Vehicle
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Credibility
 3000 Claims
 Complement
 Neighborhood Pure Premium
 Within Two Miles
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 One Mile Extension
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Clustering
 Contiguous v. Non-Contiguous
 Absolute Dollar Difference
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 Absolute Percentage Difference
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Homeowners Fire (Contiguous)
Texas
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COVERAGES
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Homeowners Fire (Non-Contiguous)
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Texas
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ISO Public Protection Classifications
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Texas
©ISO Properties, Inc., 2003
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Within Territory Variance as a Percentage
of Total Variance — Fire (Contiguous)
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Texas
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Within Territory Variance as a Percentage
of Total Variance — Fire (Non-Contiguous)
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Texas
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Homeowners Liability (Contiguous)
Texas
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COVERAGES
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Within Territory Variance as a Percentage
of Total Variance — Liability (Contiguous)
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Texas
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Homeowners Theft/Vandalism (Contiguous)
Texas
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COVERAGES
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Within Territory Variance as a Percentage
of Total Variance — Theft/Vandalism (Contiguous)
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Texas
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Homeowners Wind and Water (Contiguous)
Texas
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COVERAGES
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Texas Auto Benchmark
Texas
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AUTO BENCHMARK
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Indicated Auto Territories —
All Coverages (Contiguous)
Texas
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ALL COVERAGES
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Within Territory Variance as a Percentage
of Total Variance — All Coverages (Contiguous)
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Texas
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Indicated Auto Territories —
All Coverages (Non-Contiguous)
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Texas
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Within Territory Variance as a Percentage of
Total Variance — All Coverages (Non-Contiguous)
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Texas
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Current Auto Territories — All Coverages
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North Carolina
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1997 – 1999 Indicated Auto Territories —
All Coverages (Contiguous)
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North Carolina
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Within Territory Variance as a Percentage
of Total Variance — All Coverages (Contiguous)
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North Carolina
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1997 – 1999* Indicated Auto Territories —
All Coverages (Non-Contiguous)
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North Carolina
* 1993 – 1999 for Comprehensive
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Within Territory Variance as a Percentage of
Total Variance — All Coverages (Non-Contiguous)
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North Carolina
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1997 – 1999 Indicated Auto Territories —
Bodily Injury (Contiguous)
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North Carolina
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Within Territory Variance as a Percentage
of Total Variance — Bodily Injury (Contiguous)
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North Carolina
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1997 – 1999 Indicated Auto Territories —
Property Damage (Contiguous)
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North Carolina
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Within Territory Variance as a Percentage
of Total Variance — Property Damage
(Contiguous)
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North Carolina
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1997 – 1999 Indicated Auto Territories —
Comprehensive (Contiguous)
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North Carolina
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Within Territory Variance as a Percentage
of Total Variance — Comprehensive (Contiguous)
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North Carolina
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1997 – 1999 Indicated Auto Territories —
Collision (Contiguous)
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North Carolina
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Within Territory Variance as a Percentage
of Total Variance — Collision (Contiguous)
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North Carolina
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Stability
Predictive stability
 Choice of perils included in data
 Number of years of data
Rating stability
 Limit movement between zones
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 Use of capping
 Use of confidence intervals to help analyze changes
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Predictive Power and Stability
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Predictive Power – Test #1
 1993/1994 v. 1995/1996
 Correlation Coefficient
 Current = New Contiguous
 Non-Contiguous Better
Predictive Power – Test #2
 1993/1995 v. 1994/1996
 Tested Boundaries Based on 1994/1996
 Within Variance Only Marginally Better for 1994/1996 Data
Stability
 1993/1995 Clusters v. 1994/1996 Clusters
 Compared Indicated Boundaries and Relativities
 Little Dislocation
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Determination of Statistically Optimal
Geographical Territory Boundaries
2005 CAS Predictive Modeling Seminar
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Klayton N. Southwood
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