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

3. 5/19/20153 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 5/19/20154

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 5/19/20155

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” 5/19/20156

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. 5/19/20157

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 5/19/20158

9. A Look At “Reasonable” Consider the following triangle: 5/19/20159 Year1224364860728496108120 19971,0001,0101,1111,1221,2341,3581,3711,3851,3991,413 19981,0001,0101,0201,0301,0411,0511,0621,0721,083 19991,0001,0101,0201,0301,0411,0511,0621,072 20001,0001,0101,0201,0301,0411,0511,062 20011,0001,0101,0201,0301,0411,051 20021,0001,1001,1111,1221,133 20031,0001,0101,0201,030 20041,0001,0101,020 20051,0001,010 20061,000

10. A Look at “Reasonable” The triangle was generated randomly by the following development at each age: – 1.01090% of the time – 1.10010% 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? 5/19/201510

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 = 0.90 9 ) 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 5/19/201511

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 5/19/201512

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 5/19/201513

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 5/19/201514

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 5/19/201515

16. ERM Focus Actuary needs to be clear what “estimates” mean – The result of reasonable methods with reasonable assumptions (the 38 th 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? 5/19/201516

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 5/19/201517

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 5/19/201518

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. 5/19/201519

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 5/19/201520

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 5/19/201521

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 5/19/201522

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 5/19/201523

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 5/19/201524

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 5/19/201525