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