Measuring the Effect of Classification Factor Changes in Complex Rating Plans

1. Dave Schofield Measuring the Effect of Classification Factor Changes in Complex Rating Plans

2. Introduction • Outline a method for measuring the effect of classification factor changes on the overall rate; or • Partitioning your overall change into its component parts.

3. Topics of Discussion • A Few Definitions • A First Look at the Rating Plans • Two Ways of Looking at Percent Change • The Multiplicative Model • The Additive Model • Mixed Models

4. Definitions • Base Rate - The dollar amount to which classification factors are applied to obtain the final rate • Rating Plan - A mathematical model incorporating a base rate and classification factors in such a way as to produce an applicable rate

5. More Definitions • Classification - A type of characteristic of the policyholder, insured property or type or level of coverage • Classification Level - the specific value of a classification associated with a policy • Classification Factor - a numeric quantity that adjusts the otherwise applicable rate to the level associated with the policy’s particular classification level

6. A First Look at Rating Plans

7. Percent Change Perspectives • Percent Change With Respect to the Otherwise Applicable Rate • Percent Change With Respect to Current Rate

8. The Multiplicative Model • Want to find factors that satisfy both: • Natural factorization is

9. The Additive Model • Want to find factors that satisfy both: • What is the best way to factor?

10. Additive Model Example • Overall change is 13.33%; $15 change in base rate; $5 change in additive factor

11. Additive Model Example(cont.) • Author’s selected factoring method:

12. Additive Model Example(cont.) • Interesting note, if

13. The Invariance Criteria

14. The Simple Mixed Model • Contains elements of both additive and multiplicative models • Can be thought of as an additive model where each of the additive components is comprised of a multiplicative model

15. Mixed Model Example • Want to find appropriate factors for

16. Mixed Model Example (cont.)

17. Mixed Model Example (cont.)

18. Mixed Model Example (cont.) • Summary

19. The General Mixed Model • Use same techniques as the Simple Mixed Model • Effects for Classification Factors across additive components can be multiplied together to get total effect for that Class Factor • Selected Additive Factoring Method satisfies invariance criteria

20. What This Means • Help estimate the effect of changes in classification factors on average rate • Partition Overall change into percent changes by classification variable

21. Next Steps • Off Balance Issues • Utilization While Developing Classification Factors