1. A New Exposure Base for Vehicle Service Contracts – Miles Driven CAS Ratemaking Seminar – Atlanta 2007 March 8, 2007Slide 1 Discussion Paper Presentation “An Exposure Based Approach to Automobile Warranty Ratemaking and Reserving” Authors: John Kerper, FSA, MAAA Lee M. Bowron, ACAS, MAAA Kerper and Bowron LLC www.kerper-bowron.com

2. A New Exposure Base for Vehicle Service Contracts – Miles Driven CAS Ratemaking Seminar – Atlanta 2007 March 8, 2007Slide 2 Vehicle Service Contracts – A Different Animal Service Contracts are single premium, long term policies These require special treatment on actuarial opinions Insurance Company typically receives the premium after payment of expenses In some cases, not considered insurance Other times, only a “CLP” premium is remitted However the legal treatment, establishing the liability and pricing the book are still issues

3. A New Exposure Base for Vehicle Service Contracts – Miles Driven CAS Ratemaking Seminar – Atlanta 2007 March 8, 2007Slide 3 Typical Cash Flow of Premium

4. A New Exposure Base for Vehicle Service Contracts – Miles Driven CAS Ratemaking Seminar – Atlanta 2007 March 8, 2007Slide 4 Claims Pattern for New Car Vehicle Service Contract for example, 7 years/84,000 miles with a 3 year/36,000 mile basic and a 5 year/60,000 mile powertrain Initial period of few claims due to manufacturer’s basic (bumper-to-bumper) warranty A period of claims during the powertrain only manufacturer’s warranty An increase in claims when the manufacturer’s warranty expires A slowing of claims as the coverage “miles out”

5. A New Exposure Base for Vehicle Service Contracts – Miles Driven CAS Ratemaking Seminar – Atlanta 2007 March 8, 2007Slide 5 Earnings Curves Earnings curves are predetermined amounts of earnings for system reports Earnings curves are not the true earnings since the unearned premium reserve is subject to additional actuarial testing Rule-of-thumb curves (pro-rata, reverse rule of 78s) should be avoided in most cases.

6. A New Exposure Base for Vehicle Service Contracts – Miles Driven CAS Ratemaking Seminar – Atlanta 2007 March 8, 2007Slide 6 Current Actuarial Practice The most common method is to triangulate pure premiums at various evaluations Pure premiums are then trended to the evaluation date Tail factors are usually defaulted to earning curve assumptions.

7. A New Exposure Base for Vehicle Service Contracts – Miles Driven CAS Ratemaking Seminar – Atlanta 2007 March 8, 2007Slide 7 Pure Premium Method - Contract Count New Domestic 7/84 Term In-Force Contracts PolicyPolicy Age Year 12 24 36 48 60 72 84 2002 200 194 191 187 179 2003 600 583 557 542 2004 1,200 1,176 1,145 2005 1,500 1,455 2006 1,000 Total 4,500 3,409 1,893 729 179

8. A New Exposure Base for Vehicle Service Contracts – Miles Driven CAS Ratemaking Seminar – Atlanta 2007 March 8, 2007Slide 8 Pure Premium Method – Pure Premiums New Domestic 7/84 Term PolicyPolicy Age Year12243648607284 20022.1921.8145.89134.58160.38 20031.1647.9058.93172.62 20041.1241.2279.98 20052.3463.00 20063.00 Average1.9643.4961.60153.60160.38 Selected1.9643.4961.60153.60160.38

9. A New Exposure Base for Vehicle Service Contracts – Miles Driven CAS Ratemaking Seminar – Atlanta 2007 March 8, 2007Slide 9 Pure Premium Method – Future Pure Premiums New DomesticFuture Values Trended 2%7/84 Term Development Policy Year1224364860 20022.1921.8145.89134.58160.38 20031.1647.9058.93172.62163.59 20041.1241.2279.98156.67166.86 20052.3463.0062.83159.81170.20 20063.0044.3564.09163.00173.60

10. A New Exposure Base for Vehicle Service Contracts – Miles Driven CAS Ratemaking Seminar – Atlanta 2007 March 8, 2007Slide 10 Estimating the Total Costs New DomesticFuture Values Trended 2% 7/84 Term FutureEarningsTotal PolicyReportedLossesFactorEstimatedFuture YearLossesContracts@60months Losses 2002 67,389 17900.78 86,396 19,007 2003 154,921 542 88,5890.78 312,191 157,271 2004 141,418 1,145 370,4470.78 656,237 514,819 2005 95,195 1,455 571,6390.78 854,915 759,720 2006 3,004 1,000 663,3180.78 854,259 851,255 461,926 1,693,992 2,763,998 2,302,072

11. A New Exposure Base for Vehicle Service Contracts – Miles Driven CAS Ratemaking Seminar – Atlanta 2007 March 8, 2007Slide 11 Issues with Pure Premium Method Data may not be available in the tail Older data may not be appropriate Subdividing data will likely decrease credibility Sensitive to outlier data points

12. A New Exposure Base for Vehicle Service Contracts – Miles Driven CAS Ratemaking Seminar – Atlanta 2007 March 8, 2007Slide 12 An Alternative Approach Instead of claims as a function of time, claims as a function of miles driven Claims = Miles Driven * Cost per mile * trend factor

13. A New Exposure Base for Vehicle Service Contracts – Miles Driven CAS Ratemaking Seminar – Atlanta 2007 March 8, 2007Slide 13 Estimating Miles Driven Miles driven during a vehicle service contract can be modeled from observed events Claims Cancellations Distributional approach to model the variability in the book Segment observations into quintiles by average miles driven per month triangulate the data and project to ultimate the average miles driven per year

14. A New Exposure Base for Vehicle Service Contracts – Miles Driven CAS Ratemaking Seminar – Atlanta 2007 March 8, 2007Slide 14 An Example - Assumptions Coverage term – 6 years / 72,000 miles Manufacturer warranty – 3 years / 36,000 miles Basic and powertrain Average miles driven per month by quintile 8,400 12,000 14,400 18,000 22,800 3% of claims during manufacturer warranty

15. A New Exposure Base for Vehicle Service Contracts – Miles Driven CAS Ratemaking Seminar – Atlanta 2007 March 8, 2007Slide 15 An Example

16. A New Exposure Base for Vehicle Service Contracts – Miles Driven CAS Ratemaking Seminar – Atlanta 2007 March 8, 2007Slide 16 Calculating the Cost per Mile Calculate average historical rate Develop relativities to adjust for contract / vehicle factors Type and term of coverage Deductible Initial mileage of vehicle when contract purchased Classification of vehicle (should reflect expected claims) Type of business

17. A New Exposure Base for Vehicle Service Contracts – Miles Driven CAS Ratemaking Seminar – Atlanta 2007 March 8, 2007Slide 17 Calculating the Cost per Mile Techniques Minimum bias Iterative approach starting with all relativities at 1, adjusting factors for variable with greatest variance (to expedite convergence) (mostly) independent variables required GLM Tweedie distribution with parameter at or near 1 (1 is same as minimum bias)

18. A New Exposure Base for Vehicle Service Contracts – Miles Driven CAS Ratemaking Seminar – Atlanta 2007 March 8, 2007Slide 18 Trending the Miles Miles should be trended for the increase in costs due to inflation and “wear-and-tear” There is also a negative trend factor for: preexisting conditions (typically on used cars) decreasing claims consciousness or unreported disposition of vehicle Apply the trend factor to the estimate of miles driven

19. A New Exposure Base for Vehicle Service Contracts – Miles Driven CAS Ratemaking Seminar – Atlanta 2007 March 8, 2007Slide 19 Calculating the Claim Rate Impact of Cancellations Claims Administration Pricing the Book