1. Considerations in P&C Pricing Segmentation February 25, 2015 Bob Weishaar, Ph.D., FCAS, MAAA

2.  Introduction to personal lines auto pricing considerations  Insurance supply and demand  Statistical modeling of insurance metrics  Simulation and optimization  Modern pricing platforms Agenda

3.  Bodily Injury premium =  Base rate (e.g., $341)  * territory factor (e.g., 1.7 for urban versus 1.0 for rural)  * age factor (e.g., 3.2 for 18 year old versus 1.0 for 50)  * gender factor (e.g., 0.95 for female)  * credit factor (e.g., 0.70 for good credit)  * increased BI limit factor (e.g., 1.5 for $300,000)  * prior BI limit factor (e.g., 0.8 for $300,000) Simplified auto pricing rating algorithm

4. There are several factors to consider when pricing for a characteristic Driver Age Cost or Price 15 20 25 30 35 40 45 50 55 What happens if we don’t use age in pricing? Young drivers have higher loss costs than mature drivers. What might happen if a competitor comes along and prices like this?

5.  Costs  Losses  Expenses  Retention rate: acceptance of renewal offers  Quote volumes  Conversion rate: acceptance of new business offer  Transition rates  Deterministic: Driver and vehicle aging  Random: Increasing limits, buying a new car, adding other products  Competitive position  Price elasticity (aka sensitivity) Metrics that influence pricing decisions

6. Economics of Insurance Product Pricing Policies in Force (PIF) Price Supply Demand

7. Supply is a function of losses and expenses Policies in force (PIF) Price Supply

8.  Aggregate pricing  Premium components  Loss  Expenses  Investment income  Risk margin  Future rate need  Loss development  Loss and premium trends  Segmentation – Predictive models  Geography  Coverage/asset attributes: car type, car age, deductible…  Owner attributes: age, number of drivers, credit score… Cost-based pricing

9. Demand curves are derived by elasticity modeling Price +x% -y% Demand Policies in Force (PIF) Elasticity = sensitivity of policy volume with respect to price = y/x Elasticity varies significantly by segment

10. Price elasticity measures how demand varies with price Price Percent of offers accepted Demand 100%

11.  Consumer behavior  Brand value  Number of competitors shopped  Intermediaries  Agency involvement: number competitors shopped; shopping at renewal  Use of comparative raters  Market forces  Number of competitors in market  Spread in competitor rates Determinates of demand (price elasticity)

12. Price elasticity varies significantly by segment Price Percent of offers accepted Reasons for differences Shopping behavior Brand affinity Competitor behavior

13.  Strike rate: Percent of offers accepted  Conversion rate for new business  Retention for renewals  Premium differential: Relevant price comparison  Competitive position for new business  Typically premium change for renewals Elasticity modeling terminology

14. Elasticity modeling New business responds to differences in competitive position Renewal business responds primarily to rate change = Percent change in PIF divided by percent change in price Elasticity is the sensitivity of policy volume with respect to price Company premium over average competitor premium New premium over old premium Conversion Rate Retention Rate 25% 0% 100% 70%

15. Regression modeling is often used to predict metric values x y 60 62 64 66 68 70 72 74 76 62 64 66 68 70 72 74 Father’s Height Son’s Height “Best fit line”

16. Link functions allow a variety of metrics to be modeled Link functions determine the range of predictions Linear Exponential Logistic 1.0 x y

17.  Loss  Frequency: Log link with Poisson error  Incidence: Logit link with binomial error  Severity: Log link with gamma error  Pure premium: Log link with Tweedie error  Strike rate: Logit link with binomial error  Marketing response: Logit link with binomial error  Elasticity: Nonlinear form needed:  Need strike rate between 0 and 1  Need coefficient of premium differential to be negative (higher price  lower volume)  Elasticity is related to coefficient of the premium differential Strike rate=(conversion rate predictors)+(prem diff)*(elasticity predictors) Examples of regression models in insurance

18. Elasticity modeling Percent of offers accepted Price Demand This slope is very difficult to compute in insurance

19.  Target is unknown  Contrasted with loss or strike rate modeling  Cannot offer same customer two different prices at same point in time  Price tests: only way to get truly unbiased estimates of elasticity  Other methods introduce bias  Over time – competitor prices and marketing programs change  Between segments – Segment behavior might cause differences  One of the predictors, price, is changing, so coefficient is very important. In many models, only the prediction is important. Elasticity modeling is a difficult business problem

20. Simulation and optimization to meet financial objectives Policies-in- Force Market Acquisition Retention Profit, growth and risk metrics 1. Loss, expense, and risk modeling: How much does it cost to insure customers? 2. Elasticity modeling: How do consumers respond to prices? 3. Price selections: How should products be priced? Simulation

21. Techniques have evolved to derive prices that meet objectives Profit/Growth CreditInteractions Household composition Vehicle scores New Rating Elements and Structures (examples for illustration only) Enhanced symbolsTelematics Cost Based: Diminishing or even negative returns due to disruption and the new business penalty Competitive Intelligence + Judgment: Significant lift available through consideration of market forces Pricing strategies Portfolio Simulation: Deeper understanding of consumer behavior ensures that sophisticated rating elements yield profit and growth

22. Portfolio simulation can be used to shift the demand curve Policies in Force (PIF) Demand B: Elasticity 0.5 A: Elasticity 2.0 $100 2000 1000 (100,2000)

23. Portfolio simulation can be used to shift the demand curve Policies in Force (PIF) Demand B: Elasticity 0.5 A: Elasticity 2.0 $90 2000 1000 (100,2000) $110

24. Portfolio simulation can be used to shift the demand curve Policies in Force (PIF) Demand B: Elasticity 0.5 A: Elasticity 2.0 $90 2000 1000 (100,2000) (98.84,2150) $110

25. Portfolio simulation can be used to shift the demand curve Policies in Force (PIF) Price 2. Derive demand curves using elasticity modeling 3. Increase demand using granular simulation Demand Increase volume with no loss of profit Increase profit with no loss of volume

26. Segment level pricing is a balancing act Age Price 15 20 25 30 35 40 45 50 55 Ignoring a rating variable can lead to adverse selection and unprofitable growth Pricing to segment level indications will protect against adverse selection Final pricing selections will depend on business objectives and segment metrics

27.  Regression modeling capabilities  Approach to avoid/handle “negative elasticities”  Methods to incorporate customer transitions: deterministic, simple stochastic, and major changes  Simulation using integration of all relevant metrics  Optimization:  Objective functions  Constraint specification  Policy versus segment level prices  End-user interface for business decisions  Rate change specification: percents and/or rating tables  Marketing/Sales/UW applications (e.g., quote volumes) Modern pricing platforms