Practical Application of Retention Modeling

Chuck Boucek, FCAS

e

Page 2

Retention ModelingGoal: Develop a model of policyholder

behavior that will estimate the impact that a rate change will have on Retention (Volume) Profitability Analyze relationships between retention,

growth and loss ratio for major class groupings

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Retention Modeling Techniques A modeling technique called Agent Based

Modeling (ABM) was used to to build a retention model

Elements of an agent based model Economic Agents – discrete decision making

entities Parameters – descriptive information regarding

agents Rules that govern how the agents interact

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Applications of ABM ABM has been applied to analyze diverse

behavior such as Retirement ages in response to law changes Stock Market reaction to decimalization Crime Rates

While modeling is performed at the individual level, the focus is group behavior

If ABM can be used to analyze these behaviors, can it also be used to analyze a customers reaction to a rate change?

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ABM Applied to Retention Agents and Parameters

Company Rates Profitability results

Competitors Rates

Customers Age, gender, marital status, etc.

Rules Shopping function that estimates probability that an insured

will seek alternative quotes in response to a rate change Switching function that estimates the probability that an

insured that shops will switch companies

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ABM Applied to Retention

Company(Rates, Profit)

Customers(Age, Gender,

Marital Status, etc.)

Competitors(Rates)

Shopping Function Switching Functio

n

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Model in Operation Generate Virtual Policyholders (the virtual market) Let policyholders “see” a rate change Individual policyholders “decide” whether to shop Those that shop, “decide” whether to switch Competitor policyholders will also switch Let policyholders generate claims based on their loss

propensity Aggregate premium and losses of insured

policyholders for a given rate scenario Compare results under different scenarios

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Practical Issues in Model Development Complexity of Rate Structures – Company

rate structures have become very complex making the modeling of their rates difficult

Options Detailed modeling including tiering, credit scoring,

as well as standard rating elements Simplified rate structures Use commercially available rating software

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Practical Issues in Model Development Developing the shopping and switching

functions – these are the real brains of the model and are thus critical to sound results

Sources of Information Publicly available information – III Analysis of data from actual rate changes Surveys

Own customer base Random Sample in US

Reverse testing of model Would only be reflective of specific company experience

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Practical Issues in Model Development Shopping and switching functions – continued Classifications of Information

Amount of Rate Change Competitive position Driver Age Multi Car/Single Car Multi Line Number of Times Renewed Channel

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Practical Issues in Model DevelopmentOutput – Proper summary of model

results is critical to reasonability testing of results Graphs of results by key classifications Retention vs. rate change High level profit and retention summaries

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OutputScatter Plot of Retention and Loss Ratio

Retention vs. Loss Ratio by Driver Age

70%

75%

80%

85%

90%

95%

100%

50% 60% 70% 80% 90% 100%

Loss Ratio

Ret

enti

on

16-18

60-64

50-54

30-34

55-59

45-49

65+

40-44

25-29

21-24

35-39

19-20

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OutputRetention by amount of rate change

Rate Change

Ret

enti

on

Rate Change

Ret

enti

on

Wow Sweet Spot

Slippery Slope

Realignment

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OutputSummary of different rate scenarios

Rate Change

Premium (000’s)

Modeled Retention

Modeled Loss Ratio

Op. Result (000’s)

2% 97,427 91.0% 70.2% $815

4% 99,226 90.8% 68.0% $2,956

6% 101,195 90.3% 67.6% $3,463

8% 102,602 89.8% 65.2% $5,911

10% 104,559 89.2% 63.6% $7,714

As long as rates are not out of line with competition, more rate is better than less in the short term

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OutputSummary of different rate scenarios

ScenarioRate

ChangePremium (000’s)

Modeled Retention

Modeled Loss Ratio

Op. Result (000’s)

1 +6% $102,309 89.8% 67.3% $3,823

2 +6% $100,456 90.0% 66.8% $4,198

3 +6% $101,449 90.0% 67.4% $3,652

4 +6% $103,242 89.9% 66.7% $4,399

5 +6% $100,024 89.7% 66.4% $4,601

The value in retention modeling lies in exploring different ways of taking a given rate increase. 30% differential in operating result Distribution of rate change should not be based on tribal

wisdom or simple one-dimensional analyses