CAS Spring Meeting 2006 Reserve Variability Session 1 Where Are We Today? Rodney Kreps

1. CAS Spring Meeting 2006Reserve Variability Session 1Where Are We Today?Rodney Kreps

2. A Fundamental Truth In order to be meaningful and useful, any measurement or estimate must also have a sense of the size of its uncertainty. 15 feet 5 yards 180 inches

3. We know this We use this automatically, often without doing a conscious calculation. It is so automatic we don’t even think about it having done it, for example in crossing the street. Why are we not explicit about this in our work?

4. Corollaries The statement of the estimate frequently implies the size of the uncertainty, correctly or not. When the uncertainty gets too big, the estimate loses all meaning. The size of the desired uncertainty depends on the situation.

5. Confusion Sourceon Reserve Uncertainty and Range • The term “reserve” is used in many contexts: As the • information actually booked. • estimate of the dollars still to be paid for claims. • actual outcome of paying off claims. • distribution of possible outcomes of paying off claims. • Each of these has its own notion of uncertainty. • The only meaning relevant to the actual underlying current economic value of the company is the last, even though analysts and stockholders react strongly to the first. • Wouldn’t it be nice if the first reflected the last, even if it required sophisticated interpretation?

6. Uncertainty in Booked • The number, as booked, is known (at least to the nearest thousand) • The range of numbers all of which were possible management estimates and could have been booked is known to management, and usually not elsewhere. • The choice from this range of estimates depends on many factors, such as what they think competitors will do, what the current cash flows may look like, what reserve changes they have taken recently, and so on.

7. Uncertainty in the Actuarial Estimate • Usually there are several ways to get the estimate. • The Actuarial Standards of Practice are meant to provide guidance, and ASOP 36 speaks only to this uncertainty, not that of the outcomes. • The guidance suggests strongly that the several ways should all be different ways of calculating a mean value. • This may suggest a range of possible permissible estimates, but says nothing about the variability in what you are going to pay. • It does, at least, allow possible other statistics. See, for example, “Management’s Best Estimate” for a discussion of an economically rational way to choose a statistic.

8. ASOP 36 Definition 2.6 • “Expected Value Estimate - An estimate of the mean value of an unknown quantity where the mean value represents a probability-weighted average of the quantity over the range of all possible values.” • Please note for later reference the use of the phrases “all possible values” and “probability-weighted.”

9. ASOP 36, 3.6.3 Expected Value Estimate – In evaluating the reasonableness of reserves, the actuary should consider one or more expected value estimates of the reserves, except when such estimates cannot be made based on available data and reasonable assumptions. Other statistical values such as the mode (most likely value) or the median (50th percentile) may not be appropriate measures for evaluating loss and loss adjustment expense reserves, such as when the expected value estimates can be significantly greater than these other estimates. Translation: use the mean. We don’t want low reserves. Err on the high side. We know these are skewed distributions.

10. ASOP 36, 3.6.3 (cont.) The actuary may use various methods or assumptions to arrive at expected valueestimates. In arriving at such expected value estimates, it is not necessary to estimate or determine the rangeof all possible values, nor the probabilities associated with any particular values. Wait a minute – what happened to the definition? Question: So, if I don’t need a distribution, what is my expected value? What I expect to happen? Question: If I have a distribution, why should I not use my judgment as to the appropriate statistic? Why is the mean enshrined?

11. Uncertainty in Actual Outcome Why can’t you actuaries get the reserves right? Feel like a target?

12. Uncertainty in Actual Outcome= Distribution of Outcomes • Now we are acknowledging there is a distribution of possible outcomes. • There is always some underlying sense of the distribution of outcomes. • Although, formulation of a formal statistical distribution may be difficult or impossible. The standards of practice go out of their way not to require one. • Nevertheless, the practitioner should and usually does have some sense for it. • “Well, I estimated 100 million and would be surprised if it ended up being over 115 million or under 95 million.” • This is not a statement that all values in the range are equally good.

13. Uncertainty in the Distribution • Some techniques such as predictive modeling and some classes of models will give actual distributions. • Chain ladder estimates have actual underlying statistical models, but they are seldom invoked. • In fact, the data is seldom systematically tested for the applicability of the underlying models in using a technique. • Even when there is distribution, there is usually considerable parameter uncertainty in it. • Nevertheless, one can arrive at one’s best estimate of the predictive distribution. • This is the fundamental basis for actuarial estimates, whether explicitly or implicitly – and more often the latter.

14. Where Are We Now? • ASB Exposure Draft • Property/Casualty Unpaid Claim and Claim Adjustment Expense Estimates • Comment Deadline June 30, 2006. There is still time to comment. • The essential element is the notion of Actuarial Central Estimate, which replaces the old mean estimate.

15. ASB Exposure DraftBackground Section • “The subcommittee discussed whether or not the proposed standard should specify the measurement the actuary should produce when estimating unpaid claims, such as specifying that the estimate must be a mean or median. In the end, the subcommittee decided the proposed standard should instruct the actuary to describe the estimate produced, without mandating the specifics of that estimate. “ • “The intent of using the term actuarial central estimate is to allow the actuary to make an estimate without determining the complete probability distributionor using a more sophisticated statistical analysis. “ The intent is good: we don’t have to use the mean, and we don’t have to have a formal distribution. Let’s see what came out of it.

16. ASB Exposure DraftDefinition Section • “Actuarial Central Estimate—An estimate that represents a meanexcluding remote or speculative outcomes that, in the actuary’s professional judgment, is neither optimistic nor pessimistic. An actuarial central estimate may or may not be the result of the use of a probability distribution or a statistical analysis. This definition is intended to clarify the concept rather than assign a precise statistical measure, as commonly used actuarial methods typically do not result in a statistical mean.“ So if I have a distribution, use the mean but throw away parts of the distribution? How remote, how speculative? And if I don’t, make up what I thought the mean would be if I had one? And what happened to those other statistical estimates?

17. ASB Exposure DraftDefinition Section • “Actuarial Central Estimate—An estimate that represents a mean excluding remote or speculative outcomes that, in the actuary’s professional judgment, is neither optimistic nor pessimistic. An actuarial central estimate may or may not be the result of the use of a probability distribution or a statistical analysis. “ Optimistic and pessimistic mean what? That I have been unprofessionally bending numbers in the process to lean some direction? If I feel guilty, I should re-think my estimate? Or, that there is too small a chance of the estimate being close to the outcome? And I evaluate that how, without a distribution? With what criteria?

18. ASB Exposure DraftDefinition Section • “Process Risk - Risk associated with the projection of future contingencies, which are inherently variable. For example, even if the mean frequency and the mean severity are properly evaluated, the actual observed results will generally vary from the underlying means.“ Hey, good. We are talking outcomes. But, not only generally vary, but almost surely. Never play dice with someone who can tell you exactly how they will come up. However, it would be nice to know on average how far away they will be, or some other measure of variability.

19. ASB Exposure DraftDefinition Section • “Parameter Risk - The risk that the parameters within the models are misestimated.“ Well, sort of. It may well be not a problem in the estimation but that that there is intrinsic variability in the parameters themselves and we are looking at a mixed process.

20. ASB Exposure DraftAnalysis of Issues and Recommended Practices • “Methods—The actuary should consider methods for estimating unpaid claims that, in the actuary’s professional judgment, are appropriate. …For any particular component of the unpaid claim estimate, the actuary should use multiple applicable methods, unless, in the actuary’s professional judgment, a particular method is clearly superior to other methods. ” Are we back to “how many ways can we find a mean, without even a distribution?” And is using multiple methods supposed to be a surrogate for having a more real estimate of the actual variability of the outcomes?

21. ASB Exposure DraftAnalysis of Issues and Recommended Practices • “Uncertainty - The actuary is not required to measure uncertainty, but if the actuary is measuring uncertainty, the actuary should consider the types and sources of uncertainty being measured and choose the methods and assumptions that, in the actuary’s professional judgment, are appropriate for the measurement of such uncertainty. Such types and sources of uncertainty surrounding unpaid claim estimates may include uncertainty due to model risk, parameter risk, and process risk. ” It would be nice if there were SOME estimate of the uncertainty of the outcomes were present. In fact, for meaningfulness it is really ESSENTIAL. See original soapbox.

22. A Glimmer of Hope ASB Exposure Draft Section 4.2 – Additional Disclosures 4.2.a says “in the case when the actuary specifies a range of estimates, the actuary should disclose the basis of the range provided, for example, a range of actuarial central estimates; a range representing a confidence interval within the range of outcomes produced by a particular model or models; or a range representing a confidence interval reflecting certain risks, such as process risk and parameter risk ..” At least an estimate of the uncertainty of the outcomes is allowed.

23. Summary • Historically, we started with ad-hoc methods to estimate a reserve. Originally the focus was on getting a number for the annual statement. • Then came the realization that variability in the outcomes which that number represented could be quite significant, and not necessarily a tiny fraction of the current cash flow. • This encourages the statement of a range, preferably with probabilities but at least with some sense of what would be surprising. The estimate is really not meaningful without it. • And now, with all good intentions and sophisticated recognition of the random nature of the claims process and parameter estimation, we seem to have gone back to only thinking of a number. And that from a modified mean. • I do hope I am wrong.