Considerations in P&C Pricing Segmentation

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

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

3. Simplified auto pricing rating algorithm • 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)

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

5. Metrics that influence pricing decisions • 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)

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

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

8. Cost-based pricing • 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…

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

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

11. Determinates of demand (price elasticity) • 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

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

13. Elasticity modeling terminology • 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

14. Elasticity modeling Elasticity is the sensitivity of policy volume with respect to price 25% 100% Conversion Rate Retention Rate 0% 70% Company premium over average competitor premium New premium over old premium 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

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

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

17. Examples of regression models in insurance • 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)

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

19. Elasticity modeling is a difficult business problem • 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.

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

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

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

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

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

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

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

27. Modern pricing platforms • 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: percentsand/or rating tables • Marketing/Sales/UW applications (e.g., quote volumes)