Practical Application of Retention Modeling Chuck Boucek, FCAS e

Page 2 Retention Modeling  Goal: 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

Page 3 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

Page 4 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?

Page 5 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

Page 6 ABM Applied to Retention Company (Rates, Profit) Customers (Age, Gender, Marital Status, etc.) Competitors (Rates) Shopping Function Switching Function

Page 7 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

Page 8 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

Page 9 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

Page 10 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

Page 11 Practical Issues in Model Development  Output – 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

Page 12 Output Scatter Plot of Retention and Loss Ratio

Page 13 Output Retention by amount of rate change WowSweet Spot Slippery Slope Realignment

Page 14 Output Summary of different rate scenarios Rate Change Premium (000’s) Modeled Retention Modeled Loss Ratio Op. Result (000’s) 2%97, %70.2%$815 4%99, %68.0%$2,956 6%101, %67.6%$3,463 8%102, %65.2%$5,911 10%104, %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

Page 15 Output Summary of different rate scenarios Scenario Rate Change Premium (000’s) Modeled Retention Modeled Loss Ratio Op. Result (000’s) 1+6%$102, %67.3%$3, %$100, %66.8%$4, %$101, %67.4%$3, %$103, %66.7%$4, %$100, %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