Reserve Risk Within ERM

1. Reserve Risk Within ERM Presented by Roger M. Hayne, FCAS, MAAA CLRS, San Diego, CA September 10-11, 2007

3. Why is There Reserve Risk? • First an observation: • Given knowledge available at a valuation date there is usually a range of potential outcomes relating to a specific set future uncertain events. Given that knowledge, some of those outcomes may be more likely than others. The potential outcomes along with their relative likelihoods is often called a distribution of outcomes. • Key aspects: • Future uncertain events • With financial implications • Can only use current information

4. Actuarial Analysis • An actuary usually uses past history relating to the specific set of uncertain future events to develop an understanding of the related future outcomes and their relative likelihood. • Assessment can be subjective • Assessment can be based on one or more underlying methods or models, often with statistical underpinnings • Traditional methods deterministic • Stochastic models have underlying distributions

5. What You Don’t Know Can Hurt • In an ERM analysis it is crucial that the ERM professional knows what the actuary means, even if they are the same person! • Notice focus in first slide on distribution of outcomes • Actuaries often talk in terms of “ranges of reasonable reserves” • “An actuarially sound loss reserve … is a provision, based on estimates derived from reasonable assumptions and appropriate actuarial methods for the unpaid amount required to settle all claims …” • Not outcome

6. Methods and Models • Traditional actuarial reserve techniques • Are deterministic • Do not directly provide information regarding the distribution of outcomes • Are examples of “methods” or techniques amenable to cook-book descriptions • Stochastic methods begin with assumptions regarding the underlying statistical process • Directly provide some information regarding uncertainty • Are examples of “models” or mathematical descriptions of “reality”

7. A Simple Example – Chain Ladder • A “method” • Look at triangle of link ratios • Use the triangle to formulate an assumptions about development from one age to the next • Multiply factors and amounts to date to get “forecasts” of ultimate values • The result: • If losses move from 12 to 24 months exactly equal to our selected factor, and if • If losses move from 24 to 36 months, etc. • Then ultimate losses for the most recent year will be $XXX.

8. What Do We Have? • At the end we have a set of forecasts if each and every assumption fits what will happen in the future • No direct information about potential alternative possible (probable) outcomes • One approach is to make alternative selections for age to age factors and see the results • No direct information as to the likelihood of either original or alternate selections • Does give some read of sensitivity

9. A Look At “Reasonable” • Consider the following triangle:

10. A Look at “Reasonable” • The triangle was generated randomly by the following development at each age: • 1.010 90% of the time • 1.100 10% of the time • What is a “reasonable” pick for an age-to-age factor? • Average (1.019)? • Mode or Median (1.01)? • Something else? • How would you assess the volatility of the chain ladder here?

11. A Look at “Reasonable” • Hard to argue that 1.01 is not a “reasonable” selection for each age-to-age factor, after all, it happens 9 times out of 10. • Given the true underlying model, doing this will give you a forecast with a 38.7% chance of occurring (0.387 = 0.909) and all other outcomes would be above this amount. • Actually picking the mean each time is no better, also giving a forecast below 61.3% of outcomes • Underlines the fundamental weakness of deterministic methods

12. A Look At “Reasonable” • Traditional chain ladder method gives no direct assessment of uncertainty • Usually actuary develops a “gut feel” for uncertainty by viewing the historical development factors compared to his/her selections • History may not be long enough to be appropriately representative of “rare” events In this example there is a 27.1% chance of at least 1.10 factor showing at an age with 3 observations, but the average of the observations would far exceed the expected

13. A Look At “Reasonable” • So making “reasonable” selections of age-to-age factors may not be enough • Traditionally the reserving actuary will get his/her assessment of uncertainty from looking at both the volatility of link ratios for the chain ladder as well as looking at other approaches including • Chain ladder applied to other data sets • Different forecast methods • Based on these the actuary often develops a “gut feel” for the volatility of his/her estimates

14. A Look At “Reasonable” • Notice the focus is on “reasonable projections” • Traditionally assessed by considering • Alternate “reasonable” selections • The forecasts of alternative methods • Subjective assessment • A combination of the above • Not focused on a distribution of outcomes, but rather a sense of the “range of reasonable estimates” • Not much help in ERM

15. ERM Focus • What is useful to ERM is not only a reasonable estimate of what can happen but also an estimate of what can reasonably happen • Increased need for estimates of the distribution of outcomes, rather than simply a range of reasonable estimates • Need for a common language to communicate between the ERM professional and actuary, even if they are same person

16. ERM Focus • Actuary needs to be clear what “estimates” mean • The result of reasonable methods with reasonable assumptions (the 38th percentile from our example)? • A statistic based on a distribution of outcomes • Mean? • Mode? • Median? • Percentile? • Least Pain? • Other? • A rough statistic based on a subjectively estimated distribution of outcomes • Other?

17. Some Quantitative Terms • Looking at our previous example we have assumed we know everything about the process, only chain ladder with known distributions of factors • Even knowing everything about the underlying model there is uncertainty, called Process Uncertainty • Nearly always present • Statistics (mean, median, mode, percentile, least pain, etc.) distill a distribution to a single number eliminating process uncertainty

18. Other Sources of Uncertainty • Typically a statistical model specifies a distribution and then requires estimates of parameters of that distribution. Uncertainty arising from estimating those parameters, even if underlying model is exactly known is Parameter Uncertainty • Seldom are we certain about the underlying model, so on top of process and parameter uncertainty we also have Model/Specification Uncertainty • These combine to give distribution of outcomes

19. Distributions “Light” • ERM Professional should be aware of what is considered in the distribution of outcomes • Most stochastic forecasting methods focus on a single model, applied to a single data set, e.g. chain ladder applied to paid losses, Bornhuetter-Ferguson applied to incurred losses, etc. • Little in literature on combining the indications of different models to better assess distribution of outcomes • There are a few exceptions, Keatinge, Munich Chain Ladder, etc.

20. Distributions “Light” • An approach being used more often now is a two-stage approach: • Use traditional methods to derive “best estimate” • Use the distribution of outcomes implied by a bootstrap method based on the chain ladder model to impute a distribution of outcomes given the “best estimate” • Sometimes the bootstrap is later “adjusted” to “better” reflect the actuary’s subjective assessment of uncertainty • May not be consistent

21. Distributions “Light” • In some cases future contingencies not amenable to analysis by usual actuarial models • Asbestos & environmental • Property catastrophes near valuation date • Impact of significant court cases • Etc. • May need judgmental assessment of contribution to distribution of outcomes • Again user should be clear what the “distribution of outcomes” means

22. 0 Calorie Distributions • Sometimes specific distributions of outcomes are not estimated • All is not lost for the ERM professional • “Scenario testing” can give insight regarding the range of potential outcomes • With statistical methods you get distribution of outcomes without specific “reasonable” events that result in those outcomes • Scenario testing can give “comfort” being able to say “you can get that outcome if such and such happens

23. Distributions “Light” • Analysis often conducted at a line of business level • Need to consider correlations • Among forecast methods/models • Among various lines of business • Again, key to usefulness is understanding

24. Distributions and ERM • Focus of ERM the identification of risks and opportunities facing the organization • Types of uncertainty in future outcomes helps point to ways to manage • Process uncertainty is usually diversifiable, law of large numbers • Parameter and model/specification uncertainty might not be diversifiable since they may affect all parties in the same market similarly implying other ways to manage • Again, knowledge is power

25. Conclusion • Reserve liabilities usually largest on an insurer’s balance sheet and may not be insignificant for other enterprises • A key concern for ERM is the distribution of outcomes not just a “range of reasonable outcomes” • Need to understand key contributors • Process • Parameter • Model/Specification • Understand what you are looking at