Retention: A New Focus

1
Retention A New Focus

• Lee Bowron
• CAS Ratemaking Seminar
• March 7 8, 2002
• Tampa, FL

2
Retention Defining the Problem

• Retention Data is Not Publicly Available
• Retention is Not Always a Rating Variable
• Several Definitions of Retention, including
• Ratio Method (Percent of Policies-in-Force /
  Original Policies-in-Force)
• Expected Policy Life

3
Retention A Simple Example

• Acme Auto Insurance Company writes 2,000 New
  Business and 8,000 Renewal Polices a Year
• Currently, Acme renews 80 of their policies and
  policies-in-force are steady
• Management wants to increase PIF to 10,500 this
  year
• This will require a 25 increase in new business
  (2,500) or a 6.25 increase in renewals (8,500)

4
Impact of Retention on Calendar Year Results
5
Same Example but 50 additional Renewals
6
Same Example but 50 additional New Business
7
Factors Impacting Retention

• Retention can differ based on many factors,
  including
• Product Type
• Rating Variable
• Customer Demographics
• Competitive Considerations
• Softness of Market

8
The Real World Policyholder Personalities

• Auto Insurance is sold to a wide demographic
  market
• Short-term defectors
• Buy to renew a tag
• Low priority of continuous insurance
• High propensity to price insurance
• Have more violations or accidents, which causes
  large price swings
• They are transient

9
The Real World Policyholder Personalities

• Loyal Policyholders
• Personal relationship with agent
• Not likely to shop due to price increase
• Low cost of auto insurance in relation to budget
• Multiple products with the same company or agency
• Long-term residents of community

10
The Real World Policyholder Personalities

• In-Betweeners
• In the middle ground between the categories above
• Each category requires its own retention
  strategy, both operational and pricing.

11
Operational Strategies to Improve Retention

• Retention issues may be better addressed through
  operational changes than pricing strategies.
  Such strategies include
• Improved Service
• Clearer Correspondence
• Payment Options

12
Pricing Strategies - Renewal Discounts

• Most companies do not give the full indicated
  discount
• If companies gave the indicated discount, there
  would be no difference in loss ratios between new
  and renewal business
• In order to maximize profitability, any discount
  should pay for itself to be justified.

13
Renewal Discount Strategies
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A New Product

• It is very important that you know the retention
  characteristics of a new product that you
  introduce.
• Retention characteristics will impact calendar
  year results until the product matures.

15
Preferred Auto Product Loss Ratios by Number of
Renewals
16
Accident Year Results for New Preferred Auto
Product
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Retention is Important!

• Retention issues are important in operational and
  pricing decisions.
• Successful firms make retention considerations a
  part of both existing and new market strategies.

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Modeling Retention Effective Rate Impact

• Rob Walling
• CAS Ratemaking Seminar
• March 8 9, 2002
• Tampa, FL

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Objectives

• Characteristics of Retention
• Approach to Modeling Retention
• Effective Rate Impact (ERI)
• A Stochastic Approach to ERI
• Extensions and Considerations

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What Characteristics Should a Retention Model
Have?

• Has Flexible Shape
• Simplified Parameterization
• Creates Actuarially Intuitive Scenarios
• Decreasing Incremental Changes for larger rate
  actions
• Asymptotic Behaviors at Extremes
• Allows Different Retention Behavior for Different
  Rating Characteristics

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The Flexible Shape of the Retention Demand Curve
Renewal Rate (R)
23
Retention Behavior Depends on Characteristics
Like

• Change in Pricing on Renewal
• Competitive Positioning
• Market Conditions (Inflation, U/W Cycle, etc.)
• Customer Rating Characteristics
• Age
• Territory
• Policy Size
• Years on Risk

24
Modeling Retention

• Premium Retention can be modeled as
• where
• P1 Proposed Rate Level
• P0 Current Rate Level
• PM Market Level

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Modeling Retention - Example

• Premium Retention using
• where
• P1 110 a .3
• P0 100 b 2 r 69.5
• PM 100 g 2

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Modeling Retention - Graphically
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Retention Analysis Goal

• Based on the characteristics of a particular
  current policyholder, how likely is it that the
  policyholder will renew with me?

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Factors to Consider in a Retention Analysis

• Change Over Last Years Premium
• Market Competitiveness
• Traditional Rating Factors
• Age of Youngest Additional Driver
• Satisfaction with Agent/Service
• Number of Years Insured
• Etc.

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Retention Modeling Database
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Multivariate Analysis Determines Renewal
Probability
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Modeling Rate Competitiveness

• Competitive Analysis Tools
• Average Income Analysis to Market Company(ies)
• Competitive Analysis Batch Rater
• Comparison to Benchmark Rates/Loss Costs
• Historical Variances off of Benchmarks
• Empirical Data from Quotes
• Qualitative Information from Marketing/Agents

32
Rate Impacts The Current Problem

• Whats the impact on loss ratio of a 25 rate
  increase?
• Ignoring inflation momentarily.
• If Current Loss Ratio Loss/Premium
• Proposed Loss Ratio Loss/(Premium1.25)
• 
  Loss/Premium(1/1.25)
• 
  Loss/Premium80
• 80 of
  Current Loss Ratio
• The only answer is a 20 reduction in the Loss
  Ratio!

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Editorial Comment
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The Absurdity (If a little is good)

• Whats the impact on loss ratio 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
  Current Loss Ratio

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Problems with the Current Pricing World

• Current actuarial assumptions presuppose a static
  book of business.
• This assumption does not respond to the impact of
  shifts in mix of business
• Maturity/Seasoning (New Business Penalty)
• Class
• Territory
• Caused by
• Retention/Conversion Differences
• Policyholder Response Differences
• Agent Satisfaction
• Changes in Growth Strategies
• Competition

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Effective Rate Impact

• For actuarial purposes, the effective rate impact
  is
• the inverse of the percent change in expected
  loss ratios created by the proposed rate change.
• ERI ELoss Ratio without rate change -
  1.00
• ELoss Ratio reflecting rate change

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Effective Rate Impact - Example

• Suppose current trended expected loss ratio is
  60 and a proposed class plan is expected to
  result in a loss ratio of 54
• ERI 0.60 - 1.00 10
• 0.54

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Effective Rate Impact

• Assume
• Expected Number of Quotes
• Expected Loss Ratio prior to change
• Use rate level indications
• Use assumptions underlying loss model
• Simulate using same assumptions
• Model Current Conversion/Retention Parameters
• Model Current Loss Parameters
• Frequency Severity or Loss Ratio
• New vs. Renewal
• Some Class Plan Detail is Preferable

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Effective Rate Impact

• Model/Select Proposed Rating Plan Factors
• May come from Loss Model
• May be state mandated approach (CA Sequential)
• May be rate bureau or competitive benchmarks
• Simulate Number of Policies Retained/Converted
• Calculate Premiums (Policies x Rate Levels)
• Simulate Losses
• Calculate Modeled Loss Ratio
• Calculate ERI
• Note This approach can be stochastic or
  deterministic.

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Effective Rate Impact - Example
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Why Hasnt Retention Modeling Been Used for
Ratemaking?

• Established ratemaking techniques are path of
  least resistance
• Parameterization issues
• Macro view of pricing
• Micro considerations (class plan, territory,
  etc.) are typically very simplified
• Sensitive to many factors
• Black Box mentality

42
Why Hasnt Retention Modeling Been Used for
Ratemaking?

• New business penalty impact poorly understood
• Different Growth Strategies indicate different
  indicated rate changes to achieve the same
  efffective rate change
• Point Estimate mentality
• Have you ever tried convincing 50 different
  regulators about a selection within a range of
  reasonable estimates?!

43
Another Way of Looking at Things

• Have you ever tried to sell your underwriters,
  marketing reps and agents on a huge increase that
  makes no competitive sense?
• or dreaded a big decrease presented as capable
  of doubling retention or hit ratios?

44
LCV - Definitions

• Pr Profit P Premium
• L Losses E Expenses
• I Investment Income t time
• P(Ren) probability of renewal thru time t
• P(Con) probability of conversion thru time t
• d discount rate
• E(Prt) Pt It E(Lt) - Et

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LCV Renewal Component

• Lifetime Customer Value (t) Expected profit at
  time t1, t2, etc. times the probability of
  realizing that profit in year t1, t2, etc.
  (retention ratio) adjusted for the time value of
  money

E(Prt) E(Prt1) x P(Rent1) E(Prt2) x
P(Rent2)
------- -----------------------
----------------------- ..
(1d) (1d)2
(1d)3
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LCV New Business Component

• Lifetime Customer Value (t) Expected profit at
  time t1, t2, etc. times the probability of
  realizing that profit in year t1, t2, etc.
  (renewal ratio) adjusted for the time value of
  money adjusted for the probability of writing the
  risk (conversion ratio)

)
(
E(Prt) E(Prt1) x P(Rent1) E(Prt2) x
P(Rent2)
x P(Cont)
------- -----------------------
----------------------
(1d) (1d)2
(1d)3