Reserve Margins and Capital CLRS – New Orleans September 11, 2001

1. Reserve Margins and CapitalCLRS – New OrleansSeptember 11, 2001 Chuck Emma, MHL/Paratus Chandu Patel, KPMG Kevin Madigan, MHL/Paratus

2. Reserve Margins Chuck Emma, MHL/Paratus Risk Modeling Application Chandu Patel, KPMG Accounting and Management Considerations Kevin Madigan, MHL/Paratus Reserve Implications in Runoff Companies

3. Risk Modeling Application Casualty Loss Reserve Seminar New Orleans September 11, 2001 Chuck Emma, FCAS, MAAA

4. Risk Modeling Application A Research Question Sample Company - background - modeling assumptions Coherent Risk Measures Conclusions

5. A Research Question Question: Does recording a reserve higher than management’s best estimate have an effect on the capital required to support the company’s operations? One Answer: Model the company’s financial risk under different reserving strategies. Calculate the level of capital required to support operations.

6. Company Example • Initial Policyholder Surplus = $70MM • Writes approximately 2 to 1 • Risk Factors • Economic Variables • Interest • Inflation • Pure Loss Variability • Loss Payout Pattern • Five Year Projections of Operating Results

7. Economic Risk Factors • Cox-Ingersoll-Ross Interest Rate Generator • Mean-reverting random walk for interest rates • Cascading dependency of inflation rates • Linear relationship with error term it =m . rt + b+ e Interest Rates Inflation

8. Reserve Variability • Reserve adequacy defined by expected inflation rate • Actual (generated) inflation rate provides hindsight reserve • For example: • 6.0% expected inflation at 12/31/00 • 6.2% generated in 2001 • Effect of unanticipated 0.2% of inflation is calculated over life of reserve. Adverse development occurs.

9. Company Reserving Policy • Three Reserving Policies Examined • Mean level reserving • 75th percentile reserving • 90th percentile reserving • Management Reserving Policy • Each year absorb any adverse reserve developments up to 50% of remaining margin • For example: $5MM prior year “hit” reduces any available margin by $2.5MM. This flows to income.

10. Simulated Financial Results Parameterized, Validated, What the actuary fusses over Decision-Making Performance measures Risk measures Consistent with financial world Coherent Risk Measures From DFA simulations to financial decisions. How do we get there? ?

11. Coherent Risk Measures Article – 1994 AFIR Colloquium • Clarkson: “The Coming Revolution in the Theory of Finance” • Van Slyke’s review 1995: “Need to consider total distribution”

12. Coherent Risk Measures • “Coherent Measures of Risk” • Philippe Artzner, Freddy Delbaen, Jean-Marc Eber and David Heath, Math. Finance 9 (1999), no. 3, 203-228 • http://www.math.ethz.ch/~delbaen/ftp/preprints/CoherentMF.pdf • Coherent Measures of Risk - An Explanation for the Lay Actuary • Glenn Meyers • http://www.casact.org/pubs/forum/00sforum/meyers/Coherent%20Measures%20of%20Risk.pdf

13. Coherent Risk Measures Swiss Paper (Artzner, et al) • Setting margin requirements on exchange • Similar to capitalization of insurer • Based on four axioms • “Coherent”: in the eyes of the beholders?

14. CRM - Survey of Risk Measures Standard Deviation Value-At-Risk Expected Policyholder Deficit

15. CRM - Standard Deviation Material departures from normal behavior can lead to problems Includes upside variation • The free lottery ticket “costs too much”

16. CRM - Value at Risk The value at a selected quantile Problems • The most extreme values are ignored • Doesn’t distinguish between tails • Can mislead when combining risks

17. Coherent Risk Measures So, What Would Make More Sense? • Guiding question: How big is “big”? • Guiding Principle: The purpose of capital is to fund prospective losses • Try “Tail Value-at-Risk”

18. Tail Value at Risk is the average of all losses above the Value at Risk

19. Results of Modeling Base Case

20. Results of Modeling Higher Economic Variability

21. Results of Modeling Higher Economic and Reserve Variability

22. Conclusions • Reserve margins can be used to stabilize income and reduce capital requirements • The reduction in reported capital can be offset to a degree by the hedge which a margin offers • Risk modeling techniques are the best way to evaluate the merits of margins • Accounting, regulatory, and other external realities limit the extent to which margins are possible and desirable

23. Reserve Margins and Capital Casualty Loss Reserve Seminar New Orleans September 11, 2001 Chandu C. Patel, FCAS, MAAA

24. Reserve Margins and Capital – The CFO Perspective Statutory • Codification requires that held reserves should correspond to Management’s best estimate. • Ideally, this would correspond to the actuarial best estimate. • Although the intent is to prevent “low” end reserves, “high” end reserves also require documentation. • Generally, on an on-going basis, statutory framework (e.g. IRIS ratios) favors high end reserves.

25. A DFA Approach to Valuing a Run Off Operation • ABC Insurance Companies wants to put a book(s) of business into run-off • Reasons for such action include: • A management decision to exit a market • A need to segregate a collection of policies from ongoing operations (asbestos, construction defects, etc.) • Let’s assume ABC wants to sell this run-off operation (possibly to a subsidiary)

26. Reserve Margins and Capital – The CFO Perspective GAAP • Typically reserves are many multiples of earnings • As a result, any movement within the actuarial range has a significant impact on earnings; this can be construed as earnings management • To maintain a consistent reserving philosophy, this would suggest that held reserves should be based on the actuarial range and at a consistent percentile of the range • In fact if a high percentile is targeted, this may lead to greater variability in results – need model to evaluate

27. Reserve Margins and Capital – The CFO Perspective IRS • Generally, IRS is not sympathetic to conservative reserves. However actuarial range may provide adequate justification for high end reserves • Utah Medical – actuarial range accepted • Minnesota Lawyers – actuarial range not considered • No clear case history

28. Reserve Margins and Capital – The CFO Perspective Risk Based Capital • Formulaic approach considers held reserves as “best estimate” even though there may be a margin in the reserves • Hence Company is penalized in terms of lower statutory surplus and higher RBC • Offsetting effect is favorable loss development

29. Reserve Margins and Capital – The CFO Perspective TVAR adjusted for reserve margin • Based on model output, it is clear that the higher the percentile of held reserves, the lower the TVAR. However, when adjusted for the reserve margin, there is a point of optimality. • Could be due to…..

30. Reserve Margins and Capital – The CFO Perspective CV of Return On Surplus • High margin implies lower surplus leading to a higher return; however this also increases volatility due to a lower base surplus • Vice-versa for low margins • CV = (Mean ROS / Std Dev of ROS) is a good measure • Once again, based on the graph, there is a point of optimality • This is also a function of loss variability

31. Reserve Margins and Capital – The CFO Perspective Earnings Per Share (EPS) • Important measure for public companies • Measured standard deviation of EPS • Based on the model, one can see that the higher the reserve margin, the lower the variability in EPS

32. Reserve Margins and Capital – The CFO Perspective Summary • External Factors – Statutory Surplus/RBC, SEC, IRS • Internal Factors – Goal for earnings stability, “cost” of capital • Other – If pricing is based on conservative reserves, implications of future profits

33. A DFA Approach to Valuing a Run Off OperationCAS CLRS September 11, 2001 Kevin Madigan MHL/Paratus

34. A DFA Approach to Valuing a Run Off Operation We are assuming that ABC is selling the run-off operation to a buyer who will set it up as an insurance company or companies. However, most of the following applies if ABC is setting up a run-off business unit.

35. A DFA Approach to Valuing a Run Off Operation Why would anyone want to buy it? To take cash out of it! Sound, aggressive, focused approaches to • Claims settlement • Commutations • Investments Should allow for significant annual “dividends” & an extraordinary one “at the end of the day”.

36. A DFA Approach to Valuing a Run Off Operation What’s a good price?

37. What’s A Good Price? The only appropriate actuarial answer is:

38. What’s A Good Price? Well ... ...that depends.

39. What’s A Good Price? What does it depend on? • The liabilities Gross, net, and ceded loss & LAE, and the adequacy of the reserves • Payment patterns (and how many more years?) • “Bad debt” – i.e. how collectable is/will be the cessions? When and how will this be recognized? Schedule F issues? • What has been commuted, and for how much?

40. What’s A Good Price? What does it depend on? • Investment Income • RBC • General Expenses • Income and Other Taxes • Paid-in Capital • Additional Reinsurance • etc.

41. What’s A Good Price? Probably the most important factors are • The parties’ risk appetites • The perceived adequacy of the reserves These factors cannot be modeled But all is not lost

42. What’s A Good Price? One can build a DFA style model under the assumption that there will be yearly dividends. There is no way to definitively determine a “good price” for all possible players. That is determined by the parties to the transaction. One can produce distributions of the NPV of future dividends using various term structures, and let them decide.

43. What’s A Good Price? For example

44. What’s A Good Price? For example, continued If the model’s assumptions are reasonable, then the table says that a $16M price provides the buyer with • An 80% prob of a return of 4% or better • A 40% prob of a return of 16% or better, etc. Whereas a $21M price provides the buyer with • A 50% prob of a return of 4% or better • A 20% prob of a return of 20% or better, etc.

45. What’s A Good Price? For example, continued Alternatively, if one requires, say a 14% ROR, then the table can be used to evaluate possible purchase prices (e.g. $15M gives only a 50% probability of meeting the required ROR; $10M gives an 80% probability, etc.).

46. Other Issues At the time of purchase, the buyer gets more than just the reserves. There has to be some associated capital to support the operations. The amount of this paid in capital will greatly affect the surplus of the new run-off entity, and will have an impact on the size of the yearly dividends.

47. Other Issues Too little capital  Low purchase price Very little inv. income Small or zero dividends Surplus and RBC issues Too much capital  High purchase price Drain on seller’s assets

48. Other Issues If the parties’ perceptions of reserve adequacy are not similar, the deal could be doomed from the start - even if they agree on everything else. For example if the seller thinks the reserves are at the 65th percentile of the distribution, and the buyer thinks they are at the 50th percentile, we could have a deal breaker..

49. Other Issues An obvious way around this is for the seller to increase the reserves, or the amount of paid in capital. But, this “solution” is very unattractive to the seller.

50. Other Issues Another way around this is for the seller to provide a cover for adverse development. If the seller is correct regarding reserve adequacy, this will cost them nothing. Such a cover will alter the risk to the buyer, and will effect the distribution of future dividends. However, the “price” will increase, but by less than the cost of the reinsurance.