Retention Modeling
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Transcript of Retention Modeling
Retention Modeling
2003 CAS Ratemaking Seminar
March 27-28, 2003
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?
Incomplete picture of your customers and prospective customers
Incomplete picture of pricing impacts on policy retention and premium
Underspecified pricing and financial models
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 25% increase today as 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 Not the “Coolest” area of research
Renewal Behavior Characteristics
Renewal Pricing Change (% or $) Competitive Position Customer Rating Characteristics Market Conditions (Inflation, U/W Cycle, etc.)
Renewal Rate (R)
Price (P)
100%
0%
Demand Curve
1P
1RR = f(P)
The Flexible Shape of the Retention Demand Curve
Renewal Behavior Rating Factor Characteristics
Traditional Rating Factors– Class - Multiple Line– Territory - Limit– Limit - Account Size– Industry Group
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
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
Renewal Probability – Market Scenario Testing
Risk# Age Sex MS Terr Limit Comp Market Score P(Ren)
1 25 M S 1 2 3 1 500 .87
2 64 F S 1 6 2 3 500 .84
3 17 M S 2 1 2 1 525 .89
4 36 F S 2 4 1 2 500 .80
5 44 M S 1 4 5 1 500 .75
6 21 F M 1 2 2 1 600 .93
7 55 M M 2 5 2 2 625 .94
8 70 F M 2 6 3 3 500 .85
9 29 M M 1 3 1 1 500 .88
10 40 F M 2 4 4 2 656 .91
Modeling Retention – Market Differences
0.500.550.600.650.700.750.800.850.900.951.00
% Rate Change
Ret
enti
on
Hard Mkt Class 1 Soft Mkt Class 1
What Applications Are There?
Retention by class segment Improved premium/policy/loss ratio impacts
of rate changes Lifetime Customer Value Optimal Rate Changes/ Effective Rate
Impact
Risk Premium
Model
Expenses
Renewal Model PRICE
Most LoyalMost Profitable
MOST VALUABLE
Optimisation Algorithm
Optimal Pricing Strategy