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Modeling Retention & Effective Rate Impact

Modeling Retention & Effective Rate Impact. Robert J. Walling, FCAS, MAAA MHL/Paratus Ltd. 2002 CAS Risk & Capital Mgmt. Seminar. Objectives. Why do it? What characteristics matter? How do you model it? What applications are there?. Why Do Retention Modeling?.

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Modeling Retention & Effective Rate Impact

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  1. Modeling Retention & Effective Rate Impact Robert J. Walling, FCAS, MAAA MHL/Paratus Ltd. 2002 CAS Risk & Capital Mgmt. Seminar

  2. Objectives • Why do it? • What characteristics matter? • How do you model it? • What applications are there?

  3. Why Do Retention Modeling? • Incomplete picture of your customers and prospective customers • Incomplete picture of pricing impacts on policy retention and premium • Underspecified financial models

  4. 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!

  5. 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

  6. Problem with the Current Pricing World No 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

  7. Why Hasn’t Retention Modeling Done? • Sensitive to many factors • Tough parameterization issues • New business penalty poorly understood • Not the “Coolest” area of research

  8. What Characteristics Matter? • Flexible Shape • Parameterization • Actuarially Intuitive Scenarios • Decreasing Incremental Changes for larger rate actions • Asymptotic Behaviors at Extremes • Different Retention Behavior for Different Rating Characteristics

  9. 100% R = f(P) Demand Curve 0% Price (P) The Flexible Shape of the Retention Demand Curve Renewal Rate (R)

  10. Renewal Behavior Characteristics • Renewal Pricing Change (% or $) • Competitive Position • Market Conditions (Inflation, U/W Cycle, etc.) • Customer Rating Characteristics

  11. Renewal Behavior Rating Factors Characteristics • Traditional Rating Factors • Age/Sex/Marital Status • Territory • Amount of Insurance • Premium Size (CML) • Industry Group • Claims/MVR/Underwriting History • Age of Youngest Additional Driver • Satisfaction with Agent/Service • Number of Years Insured • Distribution Channel

  12. How Do You Model Retention? • Premium Retention can be modeled as: where: P1 = Proposed Rate Level P0 = Current Rate Level PM = Market Level i = a segment of the rating plan

  13. Modeling Retention - Example • Premium Retention using: where: P1 = 110 a = .3 P0 = 100 b = 2 r = 69.5% PM = 100 g = 2

  14. Modeling Retention

  15. Retention Modeling Database

  16. Multivariate Analysis Determines Renewal Probability

  17. Stochastic Approach to Retention Modeling • Model “Market Rate Level” • Model/Assume Company Rate Actions • Model Retention

  18. 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

  19. Reviewing Renewal Differences

  20. LCV Definitions • Pr = Profit P = Premium • L = Losses E = Expenses • I = Investment Income t = time • P(Ren) = probability of renewal • P(Con) = probability of conversion • d = discount rate • E(Prt) = Pt + It – E(Lt) - Et

  21. E(Prt) E(Prt+1) x P(Rent+1) E(Prt+2) x P(Rent+2) ------- + ----------------------- + ----------------------- + ….. (1+d) (1+d)2 (1+d)3 Lifetime Customer Value 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

  22. Effective Rate Impact 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]

  23. 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

  24. Effective Rate Impact - Example

  25. Optimal Pricing Strategy Risk Premium Model Expenses Renewal Model PRICE Optimisation Algorithm Most Loyal Most Profitable MOST VALUABLE

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