Robert F. Wolf, FCAS, MAAA Consultant This Presentation will be available to download from CAS website at

AGENDA Carried Reserves and Reserve Risk 101 Managing Reserve Risk with respect to our publics 1. Auditors 2. Regulators 3. Rating Agencies 4. Wall Street Reserve Ranges Economic Capital Conclusion

Loss and Loss Adjustment Expense Reserves- What is it? Items on the balance Sheet of a property casualty insurance company A snapshot, an estimate of the unpaid liabilities of things that have occurred known or unknown as of a specific date A provision, a debt owed to the policyholders on the promises implied in P&C insurance contracts An unknown that needs to be estimated

The Origin- Pricing Risk Pricing Covers Costs of ultimate loss and loss adjustment expenses and expenses Covers profit load needed to cover cost of capital Estimate of the resultant premiums accounted for in the unearned premium reserves UEPR amortized over the life of the exposure (typically 1 year) Loss/LAE portion accrues into loss/LAE reserves

The Origin- Pricing Risk Pricing Risk Uncertainty of what will happen Reserving Risk What Happened Happened, Known and Unknown Uncertainty of How will it all play-out Managing Reserve Risk = Managing the release of earnings Managing the release of reserves Managing the release of capital support

Loss Reserve Distribution Characteristics Carried Reserves Carried Reserves with Risk Load Assets Needed to Support Reserve Risk

Auditors say they want… Carried Reserves Carried Reserves with Risk Load Assets Needed to Support Reserve Risk ….consistency in the position of the range from year-end to year-end Range of reasonableness X

Regulators say they want… Carried Reserves Carried Reserves with Risk Load Assets Needed to Support Reserve Risk ….to make sure reserves are adequate (whatever that means) …but what they really want is to make sure policyholders are protected So why are we only opining on carried reserves???

Wall Street wants… Carried Reserves Carried Reserves with Risk Load Assets Needed to Support Reserve Risk …Consistent earnings …. Using different points in the range to smooth calendar year earnings is ok Profit recognition relative to the risks change in profile. Range of reasonableness

Rating Agencies want… Carried Reserves Carried Reserves with Risk Load Assets Needed to Support Reserve Risk All Consistent Earnings Reasonable Ranges Supporting Capital Adequacy Balances Capital Adequacy and Capital Deployment Profitability and Risk

Key to ERM and Reserve Risk Satisfy all Audiences and Considerations Key How much assets do you need to support reserve risk? What is a range of reasonable estimates? What Number do you book (i.e. carry) on your balance sheet Are published earnings reasonable given the risk profile of the company? Enterprise Risk and Return Management

Assets Needed to Support Reserve Risk Stochastic Reserving (modeling) Roger’s Three Uncertainties Process Parameter Model Assets Needed to Support Reserve Risk

Bear in Mind that we may have 5 or more assessments of this from the various audiences …but a more general consensus can be achieved as realizing a range of probable maximum events are more readily agreeable than a range of the most likely outcomes ????????? ???

What is a Range of reasonable estimates? Ok, we have 5 actuaries stochastically modeling reserve risk We are still arguing what to book?

15 SIDETRACK- A homework Problem in College Prove that there are infinitely many prime numbers Intuitively …no problem..but how to prove formally Direct Proof, Induction… Couldn’t do it.. Then I decided…heck..there can’t be a finite number… Hence, my 5-hour ordeal turned into a 5-minute, 5-line Proof.

16 A Homework Problem in College Proof Assume a finite number of primes p 1 p 2 p 3… p n Of course there exists a number n = p 1 p 2 p 3… p n +1. Since every integer can be reduced to a product of prime numbers, I know that one of the primes in the list of finite primes p 1 p 2 p 3… p n, say p i, is a factor of n. Obviously p i is a factor of p 1 p 2 p 3… p n. Then p i must be a factor of 1 …..which is impossible Therefore, by contradiction, there are infinitely many number of prime numbers

17 Moral of the Story If you have trouble demonstrating or reasoning a point ……. Assume the opposite position Sometimes it’s easier to work with Get the contradiction (s) You proved whatever point you were trying to make.

18 What is a Reasonable Range? That which is Not Unreasonable Unreasonable Reasonable

19 Diagnostic Tests Take Your Apriori reasonable range and test for unreasonableness Paid/Ultimate Triangles Incurred/Ultimate Triangles Reported Claim Counts/Ultimate Claim Count Triangles Closed Claim Counts/Ultimate Claim Count Triangles Average Paids, Incurred, Opens, Closed, Unpaid Triangles Yes Yes…we are back to deterministic models…but this time starting from a proposed answer

20 Paid/Ultimate Diagnostic Slightly Optimistic?

21 Incurred/Ultimate Diagnostic Bias Low? Inquire

22 Similarly – Look at Claim count Emergence Shift in Settlement Rates 4 years ago Consistent Reporting Rate Faster Maturity may validate the optimistic projections

23 Severities- Average Paid, Average Open Case Reserve Strengthening Keeping up with apparent severity Trends Again the last 4 years stand out

24 Severity Trends and Maturity Shifts Because settlement rates have increased in the last 4 years, the maturity of the accident year experience increased Leaving less claims open Average opens higher because smaller claims settle earlier than larger claims Therefore, not as much an inflation effect as it is a shift in maturity of the accident year (faster realization of ultimate average costs)

25 Incurred/Ultimate Diagnostic Bias Low? Inquire

26 Gauging and Explaining Bias This insight allays some concerns that actuary’s estimates are optimistically biased Reasonable to conclude that Incurred Emergence Should increase

27 Reserving is a Holistic Process Traditional Approach Holistic Approach 10 Methods 10 Answers One Selection Diagnostic Testing Reasonableness checks Best Estimate range

28 What is Best Estimate Range? That which is Not Unreasonable Unreasonable Reasonable

29 What is the Number to Book? Unreasonable Reasonable Any number in the range as it is management’s estimate

…..But be able to support having adequate capital to support reserve risk and that what’s carried on the books is not unreasonable Carried Reserves with Risk Load Assets Needed to Support Reserve Risk

Are published earnings reasonable given the risk profile of the company? If the carried reserves are reasonably carried and the company has sufficient economic capital, the answer to this question takes care of itself over time Management Carried the Burdon of Proof of providing evidence of reasonableness of carried reserves and the sufficiency of capital

We Need to Educate Our Publics of what we Do Our Publics expects and perceives this process as Deductive Reasoning Therefore the Reserve has to be the final answer. If not…we’re not doing our jobs It is really Inductive Reasoning 32

33 Reserving is “Inductive Reasoning” When we disclose reasonable ranges of reserves, we should be using communication (as in typical inductive logic). Based upon our information (history, trend measurement, variations, the likelihood of contingent events, it is reasonable to assume a range of $X to $Y as a reasonable provision for the unpaid liabilities as of xx/xx/xx. ▪ God knows the real reserve needed At time 0, Based upon analysis and synthesis of all information available, we provide a vector of premises (Θ 0 ) we determine a range estimate. ( ) Reserves ultimately run- off to the number God Knows at time We may have been close..maybe not…but our estimates were still reasonable if Θ 0 was reasonable at time 0. Initial Reserve Estimate/ Θ 0 R

34 Reserving is “Inductive Reasoning” At time one, we get an additional vector of experience (X 1 ) Which may or may not make us reasonable assume a revised vector of premises (Θ 1 ) Which then may produce an updated range estimate (R 1 Range /Θ 1 ) …again based on updated information and corresponding updated premises, it is reasonable to assume……………… ▪ ( ) R 0 Range/ Θ 0 R (R 1 Range /Θ 1 ) ( ) Process Continues… (R 2 Range /Θ 2 ) (R 3 Range /Θ 3 ) …………….. ……………. (Ultimate Range /Θ done ) ……Looks Bayesian to me.

35 In Conclusion…My Opinions Only A Reasonable Range is that which is not Unreasonable Booking High/Low is ok as long as high/low is reasonable and enough capital supports the risks Use Holistic Techniques not a bunch of myopic techniques Consideration of who your audience is. Our Statement of opinion should reflect accounting number reasonable reserve range and…..economic capital needed to support reserve risk. Education of the Public as to the Inductive Reasoning of the Reserving Process…… ……not unlike your favorite TV weatherman

36 Thank You Very Much !!