Retention & Conversion
Modeling
2004 CAS Ratemaking Seminar
March 11-12, 2004
Robert J. Walling, FCAS, MAAA
Objectives




Why do it?
What characteristics matter?
How do you model it?
What applications are there?
Why Do Retention Modeling?
More complete picture of your customers
and prospective customers
 More complete picture of pricing impacts on
policy retention, conversion and premium
 Better specified pricing and financial models
 Allows pricing to focus on program stability
and profitable growth

Additional Benefits of Renewal
& Conversion Analyses
Can help maximize profitability
 Can be used for target marketing &
profitable growth
 Can enhance program stability
 Facilitates consideration of market
conditions in realistic customer
responses

Rate Impacts:
The Current Problem
What’s the impact of a +25% rate change?
Current Loss Ratio = Loss/Premium
Proposed Loss Ratio = Loss/(Premium*1.25)
= Loss/Premium*(1/1.25)
= Loss/Premium*80%
= 80% of Curr. Loss Ratio
The only answer is -20% on the Loss Ratio!
The Absurdity
(If a little is good…)
What’s the impact of a 200% rate increase?
Ignoring inflation momentarily.
If Current Loss Ratio = Loss/Premium
Proposed Loss Ratio = Loss/(Premium*3)
= Loss/Premium*(1/3)
= Loss/Premium*33.3%
= 33% of Curr. Loss Ratio
More Absurdity (What Cycle?)
In 1999, PA Med Mal loss costs decreased 13.3%
Do you think the market would respond the same
way to a 10% decrease today as it did in 1999?
Problem with the Current
Pricing Analysis World

No change in response expected from
policyholders:
–
–
–
–
–
–
–
Likelihood of Renewal
Satisfaction of Policyholder
Book Churning/Adverse Selection
Mix of Business Shift
Consideration of Marketing/Underwriting
Satisfaction of Agent
Competition
Why Hasn’t Retention Modeling
Been Done?
Sensitive to many factors
 Tough parameterization issues
 New business penalty poorly understood
 More pressing product development and
pricing needs
 “New Territory” for many actuaries

The Flexible Shape of the
Retention Demand Curve
100%
Renewal
Rate (R)
R1
R = f(P)
Demand Curve
0%
P1
Price (P)
11
%
15
%
19
%
23
%
7%
3%
1.00
0.95
0.90
0.85
0.80
0.75
0.70
0.65
0.60
0.55
0.50
-2
5%
-2
1%
-1
7%
-1
3%
-9
%
-5
%
-1
%
Retention
Retention Curve Varies by Many
Characteristics
% Rate Change
Hard Mkt Class 1
Soft Mkt Class 1
Renewal Behavior Characteristics
Renewal Pricing Change (% or $)
 Competitive Position
 Customer Rating Characteristics
 Market Conditions

–
–
–
–
Inflation
U/W Cycle
Reinsurance Pricing
Market Capitalization
Renewal Behavior Characteristics

Traditional Rating Factors
–
–
–
–






Class
Territory
Limit
Industry Group
- Multiple Policy
- Limit
- Account Size
Financial Underwriting Score (Credit, D&B)
Claims/MVR/Underwriting History
Age of Youngest Additional Driver
Satisfaction with Agent/Service
Number of Years Insured
Distribution Channel
Retention Modeling Database
Risk#
Age
Sex
MS
Terr
Limit
Ren?
Comp
Score
1
25
M
S
1
2
Y
3
500
2
64
F
S
1
6
Y
2
500
3
17
M
S
2
1
Y
2
525
4
36
F
S
2
4
Y
1
500
5
44
M
S
1
4
N
5
500
6
21
F
M
1
2
N
2
600
7
55
M
M
2
5
N
2
625
8
70
F
M
2
6
Y
3
500
9
29
M
M
1
3
Y
1
500
10
40
F
M
2
4
Y
4
656
Multivariate Analysis Determines
Renewal Probability
Risk#
Age
Sex
MS
Terr
Limit
Comp
Score
P(Ren)
1
25
M
S
1
2
3
500
.85
2
64
F
S
1
6
2
500
.86
3
17
M
S
2
1
2
525
.87
4
36
F
S
2
4
1
500
.80
5
44
M
S
1
4
5
500
.70
6
21
F
M
1
2
2
600
.92
7
55
M
M
2
5
2
625
.94
8
70
F
M
2
6
3
500
.80
9
29
M
M
1
3
1
500
.85
10
40
F
M
2
4
4
656
.91
Reviewing Renewal Differences
Competitive Position
Competitive Index
7
6
5
4
3
2
1
0.66
0.77
0.88
0.88
0.90
1.02
1.03
Changing Market Conditions


Market conditions change over time in the
historical data
Historical market conditions are not
necessarily predictive of future market
dynamics
How do you reflect future market conditions in
a retention model?
Retention Modeling Database
– Market Scenario Testing
Risk# Age
Sex
MS
Terr
Limit
Ren? Market Comp
Score
1
25
M
S
1
2
Y
1
3
500
2
64
F
S
1
6
Y
3
2
500
3
17
M
S
2
1
Y
1
2
525
4
36
F
S
2
4
Y
2
1
500
5
44
M
S
1
4
N
1
5
500
6
21
F
M
1
2
N
1
2
600
7
55
M
M
2
5
N
2
2
625
8
70
F
M
2
6
Y
3
3
500
9
29
M
M
1
3
Y
1
1
500
10
40
F
M
2
4
Y
2
4
656
Conversion Issues –
Premium Quoted
Assumes the potential risk provides
accurate information
 Assumes only one quote is issued
 Assumes the point of sale contact
accurately retains all information
 Often, records not kept for risks that
don’t actually buy a policy

Conversion Issues –
Current Premium
Assumes the insured knows actual
current premium
 Assumes insured knows actual current
coverages
 May be estimated by rate comparison
engine

Conversion Issues –
Solutions?
Look to an existing resource for conversion
data
 At least one Agency Management and
Comparison Rating vendor can provide
detailed, comprehensive conversion data
with rating characteristics and competitive
rank and/or competitor premiums along
with “hit” statistics

What Applications Are There?
Retention/Conversion by class segment
 Improved premium/policy/loss ratio
impacts of rate changes
 Lifetime Customer Value
 Optimal Rate Changes/ Effective Rate
Impact

Optimal Pricing Strategy
Risk
Premium
Model
Expenses
Proposed
Rates
Renewal/
Conversion
Model
Optimization
Algorithm
Most Loyal
Most Profitable
MOST
VALUABLE
Parting Thoughts

Where there is no vision, the people perish.
–
Proverbs 29:18
The data’s ready,
The technology’s ready,
ARE YOU READY???