Reinsurance and the Homeowners Indication

1. Reinsurance and the Homeowners Indication CAS Ratemaking Seminar March 10-11, 2005

2. Agenda • Brief Review of the Basics • Catastrophe Excess Reinsurance • Justification for Including Cost in Rates • Components of the Reinsurance Premium • Two Methods to Include the Cost of Reinsurance into the Rate • An Example of the “Net Cost of Reinsurance Method” • Miscellaneous/Related Topics

3. The Basics of Reinsurance • Reinsurance is simply insurance for insurance companies • In exchange for a premium, the reinsurer agrees to assume all or part of some risk that had previously been assumed by the primary insurer.

4. The Basics of Reinsurance • Primary insurers purchase reinsurance for a variety of reasons, including: • To increase capacity • To stabilize underwriting results • To provide catastrophe protection • To obtain surplus relief

5. Catastrophe Excess Reinsurance • Under a catastrophe excess agreement, the reinsurer indemnifies the primary insurer for aggregate losses in excess of a given amount, called the retention, arising from a catastrophic event • The reinsurer’s risk is generally limited to some amount • A reinsurer may only indemnity the primary company for a percentage of loss in excess of the retention

6. Catastrophe Excess Reinsurance - Example • Assume a reinsurance contract provides coverage for 50% of $600MM of loss in excess of $400MM per catastrophic event • If no event causes loss in excess of $400MM, the reinsurer pays nothing

7. Catastrophe Excess Reinsurance - Example • Assume a reinsurance contract provides coverage for 50% of $600MM of loss in excess of $400MM per catastrophic event • If an event causes loss in excess of $1 billion, the reinsurer pays $300MM (= $600MM limit x 50%)

8. Catastrophe Excess Reinsurance - Example • Assume a reinsurance contract provides coverage for 50% of $600MM of loss in excess of $400MM per catastrophic event • If an event causes loss between $400MM and $1 billion, the reinsurer pays 50% of the amount in excess of $400MM.

9. Catastrophe Excess Reinsurance - Example

10. Catastrophe Excess Reinsurance • Reasons to purchase catastrophe excess reinsurance • Catastrophic events may cause an unacceptable drain on company surplus • Company is unable to achieve the required return on the capital it must hold because of the risk of catastrophic events

11. Alternatives to Catastrophe Excess Reinsurance • Possible Alternatives to Catastrophe Excess Reinsurance • Non-renewal of existing policies • Restrictions on new business

12. Justifying Including Reinsurance in the Rate • Catastrophe Excess Reinsurance • contributes to the availability of insurance • is a legitimate business expense that benefits both the insurer, and the market as a whole

13. Catastrophe Excess Reinsurance • A rate should provide for “all costs associated with the transfer of risk” • “Consideration should be given to the effect of reinsurance agreements in the development of the rate” - Statement of Principles Regarding Property and Casualty Ratemaking

14. Components of the Reinsurance Premium • Expected Loss and Loss Adjustment Expenses • Reinsurer Expenses • Reinsurer Profit

15. Components of the Reinsurance Premium • Expected Loss and Loss Adjustment Expenses – “Reinsurance Benefit” • Reinsurer Expenses • Reinsurer Profit • Terminology from Reflecting Reinsurance Costs in Rate Indications for Homeowners by Mark J. Homan “Transaction Costs”

16. Components of the Reinsurance Premium • Only the transaction costs represent incremental, or “net,” costs to the primary insurer • This is because the premium for the reinsurance benefit is offset by a corresponding reduction in the primary company’s losses

17. Including the Cost of Reinsurance in the Indication • Two possible methods • Distinct, but theoretically equivalent • Arise from the separation of the reinsurance premium into its transaction cost on reinsurance benefit components

18. Including the Cost of Reinsurance in the Indication • First Possible Method • “Net Cost of Reinsurance” method • Include only the transaction costs, or net cost, of the contract as an expense • Leave expected losses unadjusted

19. Including the Cost of Reinsurance in the Indication • Second Possible Method • “Net Loss Plus Reinsurance” method • Include the entire reinsurance premium as an expense • Reduce expected losses by the amount of the expected reinsurance benefit

20. Net Cost of Reinsurance vs.Net Loss Plus Reinsurance • Which is preferable? • Theoretically, they are identical • Reduction in losses under the Net Loss Plus Reinsurance method is offset exactly by the inclusion of the additional portion of the reinsurance premium as an expense • No preference on theoretical grounds

21. Net Cost of Reinsurance vs.Net Loss Plus Reinsurance • Which is preferable? • Preference given to the method that best conveys the pertinent information within. • If the total effect of the reinsurance agreement on the indication is of interest, the Net Cost of Reinsurance method is preferred.

22. Net Cost of Reinsurance vs.Net Loss Plus Reinsurance • An example…. • Reference Exhibit 1

23. Net Cost of Reinsurance vs.Net Loss Plus Reinsurance

24. Net Cost of Reinsurance vs.Net Loss Plus Reinsurance

25. Net Cost of Reinsurance vs.Net Loss Plus Reinsurance

26. Net Cost of Reinsurance vs.Net Loss Plus Reinsurance

27. A Complete Example • Flannel Insurance Company (FIC) • State of Armstrongland • Current rates appear to be perfectly adequate • Reference Exhibit 2

28. A Complete Example

29. A Complete Example • Subsequently, FIC enters into the following reinsurance agreement • Reference Exhibit 3

30. A Complete Example

31. A Complete Example • A few assumptions: • The exposure base for the development of the hurricane catastrophe provision is the AIY, where 1 AIY = $1000 of Dwelling Coverage insured for 1 year • A model is used to simulate a sufficient number of years of experience from which to develop an expected hurricane loss per AIY • Only hurricane events will trigger a reinsurance recovery

32. Quantifying the Reinsurance Benefit • Quantifying the Reinsurance Benefit • Reinsurer’s Estimate • Internal Estimate

33. Quantifying the Reinsurance Benefit • The Reinsurer’s Estimate • Advantages • Saves the primary company the work of developing its own estimate • Disadvantages • May be difficult to obtain • May not be compatible with the primary company’s estimate of expected hurricane losses

34. Quantifying the Reinsurance Benefit • Problems with using the Reinsurer’s Estimate: • Insurer expects $10 million in hurricane loss/year • Cedes all hurricane risk to reinsurer • Reinsurer estimates loss at $12 million/year • This implies negative net losses!

35. Quantifying the Reinsurance Benefit • Problems with using the Reinsurer’s Estimate: • Same may arise within any individual layer or portion of loss that might be reinsured • When possible, internally generated estimate should be used

36. Quantifying the Reinsurance Benefit • Developing an Internal Estimate • Obtain modeled loss for each simulated event, and the AIYs underlying those losses • Determine AIYs to be insured during the reinsurance contract period • Adjusted modeled losses to future exposure level • Apply contract terms to each adjusted modeled loss • Determine average annual reinsurance benefit as average annual simulated reinsured loss • Reference Exhibits 4 and 5

37. Quantifying the Reinsurance Benefit • Consider Event 4 from Year 5 • Model simulates $97,275,005 in loss • Model assumes 13,248,231 AIYs • We expect 15,891,785 AIYs will actually be insured over the reinsurance contract period.

38. Quantifying the Reinsurance Benefit • Consider Event 4 from Year 5 cont. • Adjust the expected loss by multiplying it by the ratio of expected AIYs to modeled AIYs • $97,275,005 x (15,891,785 / 13,248,231) = $116,685,274

39. Quantifying the Reinsurance Benefit • Consider Event 4 from Year 5 cont.. • We then apply the contract terms to the $116,685,274 loss • 8,342,637 of the loss is reinsured

40. Quantifying the Reinsurance Benefit • We follow this process for each modeled loss • Losses under $100 million do not trigger coverage • Losses over $500 million trigger maximum coverage of $200 million • Losses between $100 million and $500 million trigger coverage of 50% of the loss excess of $100 million

41. Quantifying the Reinsurance Benefit • Then sum up the reinsured losses and divide by 100,000 years (or however many have been modeled) to determine an expected annual reinsurance benefit of $4,767,536

42. Determining the Net Cost of Reinsurance • The net cost of reinsurance equals: $11,000,000 reinsurance premium - $ 4,767,536 reinsurance benefit $ 6,232,464 net cost of reinsurance

43. Incorporating the Net Cost of Reinsurance into the Indication • Now must adjust for difference in reinsurance period and ratemaking period

44. Incorporating the Net Cost of Reinsurance into the Indication • If the company believes the terms of the contract will be similar in the remaining years, it may be easiest to relate the net cost to some base, and assume a constant net cost relative to that base over time

45. Incorporating the Net Cost of Reinsurance into the Indication • In this instance we’ll assume the net cost of reinsurance is proportional to AIYs. • This assumption is not quite true, since expected losses within a layer are not exactly proportional to exposure, even if total losses are • However, it is a reasonable, and easy to calculate, approximation

46. Incorporating the Net Cost of Reinsurance into the Indication • Net cost of reinsurance per AIY = $6,232,464 / 15,891,785 = $.39/AIY • Reference Exhibit 6

47. Incorporating the Net Cost of Reinsurance into the Indication • Once net cost per AIY is determined, incorporate it as an expense into the indication • (Reference Exhibit 7)

48. Incorporating the Net Cost of Reinsurance into the Indication

49. Incorporating the Net Cost of Reinsurance into the Indication

50. Incorporating the Net Cost of Reinsurance into the Indication • Indication increased 12.2% • Indicated premium increased $60.94 • In return for the additional premium, policyholders are more assured that coverage will remain available, both before and after a catastrophic event, and, in the case of such an event, that their own losses will be paid.