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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:
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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)
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.
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.”
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
100% R = f(P) Demand Curve 0% Price (P) The Flexible Shape of the Retention Demand Curve Renewal Rate (R)
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
Modeling Retention • Premium Retention can be modeled as: • where: • P1 = Proposed Rate Level • P0 = Current Rate Level • PM = Market Level 1 r = i b g P P i i æ ö æ ö 1 1 1 + a ç ÷ ç ÷ P P i è ø è ø m 0
Modeling Retention - Example • Premium Retention using: • where: • P1 = 110 a = .3 • P0 = 100 b = 2 r = 69.5% • PM = 100 g = 2 1 r = i b g P P i i æ ö æ ö 1 1 1 + a ç ÷ ç ÷ P P i è ø è ø m 0
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.
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!
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] - 1.00 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 = 0.60 - 1.00 = +10% 0.54
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
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.
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 = 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
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(Prt) E(Prt+1) x P(Rent+1) E(Prt+2) x P(Rent+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) ) ( E(Prt) E(Prt+1) x P(Rent+1) E(Prt+2) x P(Rent+2) x P(Cont) ------- + ----------------------- + ---------------------- +… (1+d) (1+d)2 (1+d)3