Retention Modeling

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Retention Modeling

• 2003 CAS Ratemaking Seminar
• March 27-28, 2003
• Robert J. Walling, FCAS, MAAA

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Objectives

• Why do it?
• What characteristics matter?
• How do you model it?
• What applications are there?

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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

4
Rate Impacts The Current Problem

• Whats the impact of a 25 rate change?
• Current Loss Ratio Loss/Premium
• Proposed Loss Ratio Loss/(Premium1.25)
• 
  Loss/Premium(1/1.25)
• 
  Loss/Premium80
• 80 of Curr.
  Loss Ratio
• The only answer is -20 on the Loss Ratio!

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The Absurdity (If a little is good)

• Whats the impact of a 200 rate increase?
• Ignoring inflation momentarily.
• If Current Loss Ratio Loss/Premium
• Proposed Loss Ratio Loss/(Premium3)
• 
  Loss/Premium(1/3)
• 
  Loss/Premium33.3
• 33 of Curr.
  Loss Ratio

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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?

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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

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Why Hasnt Retention Modeling Been Done?

• Sensitive to many factors
• Tough parameterization issues
• New business penalty poorly understood
• Not the Coolest area of research

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Renewal Behavior Characteristics

• Renewal Pricing Change ( or )
• Competitive Position
• Customer Rating Characteristics
• Market Conditions (Inflation, U/W Cycle, etc.)

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The Flexible Shape of the Retention Demand Curve
Renewal Rate (R)
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Renewal Behavior Rating Factor Characteristics

• Traditional Rating Factors
• Class - Multiple Line
• Territory - Limit
• Limit - Account Size
• Industry Group
• Financial Underwriting Score (Credit, DB)
• Claims/MVR/Underwriting History
• Age of Youngest Additional Driver
• Satisfaction with Agent/Service
• Number of Years Insured
• Distribution Channel

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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
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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
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Reviewing Renewal Differences
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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?

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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
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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
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Modeling Retention Market Differences
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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

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Optimal Pricing Strategy