Retention: A New Focus Lee Bowron CAS Ratemaking Seminar March 7 – 8, 2002 Tampa, FL

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

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)

Impact of Retention on Calendar Year Results

Same Example but 50 additional Renewals

Same Example but 50 additional New Business

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

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

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

The Real World: Policyholder Personalities In-Betweeners: –In the middle ground between the categories above Each category requires it’s own retention strategy, both operational and pricing.

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

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.

Renewal Discount Strategies

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.”

Preferred Auto Product – Loss Ratios by Number of Renewals

Accident Year Results for New Preferred Auto Product

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.

Modeling Retention & Effective Rate Impact Rob Walling CAS Ratemaking Seminar March 8 –9, 2002 Tampa, FL

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

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

Renewal Rate (R) Price (P) 100% 0% Demand Curve R = f(P) The Flexible Shape of the Retention Demand Curve

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

Premium Retention can be modeled as: where: P 1 = Proposed Rate Level P 0 = Current Rate Level P M = Market Level i i m i i P P P P 1 1 r                  Modeling Retention

Premium Retention using: where: P 1 = 110  =.3 P 0 = 100  = 2r = 69.5% P M = 100  = 2 Modeling Retention - Example i i m i i P P P P 1 1 r                 

Modeling Retention - Graphically

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

Factors to Consider in a Retention Analysis Change Over Last Year’s Premium Market Competitiveness Traditional Rating Factors Age of Youngest Additional Driver Satisfaction with Agent/Service Number of Years Insured Etc.

Retention Modeling Database Risk#AgeSexMSTerrLimitRen?CompScore 125MS12 Y FS16 Y MS21 Y FS24 Y MS14 N FM12 N MM25 N FM26 Y MM13 Y FM24 Y4656

Multivariate Analysis Determines Renewal Probability Risk#AgeSexMSTerrLimitCompScoreP(Ren) 125MS FS MS FS MS FM MM FM MM FM

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

Rate Impacts: The Current Problem What’s the impact on loss ratio of a 25% rate increase? Ignoring inflation momentarily. If Current Loss Ratio = Loss/Premium Proposed Loss Ratio = Loss/(Premium*1.25) = Loss/Premium*(1/1.25) = Loss/Premium*80% = 80% of Current Loss Ratio The only answer is a 20% reduction in the Loss Ratio!

Editorial Comment

The Absurdity (If a little is good…) What’s the impact on loss ratio 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 Current Loss Ratio

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

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 = E[Loss Ratio without rate change] E[Loss Ratio reflecting rate change]

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 = = +10% 0.54

Effective Rate Impact 1)Assume: a.Expected Number of Quotes b.Expected Loss Ratio prior to change -Use rate level indications -Use assumptions underlying loss model -Simulate using same assumptions 2)Model Current Conversion/Retention Parameters 3)Model Current Loss Parameters a.Frequency & Severity or Loss Ratio b.New vs. Renewal c.Some Class Plan Detail is Preferable

Effective Rate Impact 4)Model/Select Proposed Rating Plan Factors a.May come from Loss Model b.May be state mandated approach (CA Sequential) c.May be rate bureau or competitive benchmarks 5)Simulate Number of Policies Retained/Converted 6)Calculate Premiums (Policies x Rate Levels) 7)Simulate Losses 8)Calculate Modeled Loss Ratio 9)Calculate ERI Note: This approach can be stochastic or deterministic.

Effective Rate Impact - Example

Why Hasn’t 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

Why Hasn’t 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?!

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?

LCV - Definitions Pr = ProfitP = Premium L = LossesE = Expenses I = Investment Incomet = time P(Ren) = probability of renewal thru time t P(Con) = probability of conversion thru time t d = discount rate E(Pr t ) = P t + I t – E(L t ) - E t

LCV – Renewal Component Lifetime Customer Value (t): Expected profit at time t+1, t+2, etc. times the probability of realizing that profit in year t+1, t+2, etc. (retention ratio) adjusted for the time value of money E(Pr t ) E(Pr t+1 ) x P(Ren t+1 ) E(Pr t+2 ) x P(Ren t+2 ) ….. (1+d) (1+d) 2 (1+d) 3

LCV – New Business Component Lifetime Customer Value (t): Expected profit at time t+1, t+2, etc. times the probability of realizing that profit in year t+1, t+2, etc. (renewal ratio) adjusted for the time value of money adjusted for the probability of writing the risk (conversion ratio) ) ( x P(Con t ) E(Pr t ) E(Pr t+1 ) x P(Ren t+1 ) E(Pr t+2 ) x P(Ren t+2 ) … (1+d) (1+d) 2 (1+d) 3