Robert F. Wolf, FCAS, MAAAConsultant

312-560-5228wolf1138@comcast.net

This Presentation will be available to download from CAS website at www.casact.org

AGENDACarried Reserves and Reserve Risk 101Managing Reserve Risk with respect to our

publics1. Auditors2. Regulators3. Rating Agencies4. Wall Street

Reserve Ranges Economic CapitalConclusion

Loss and Loss Adjustment Expense Reserves- What is it?Items on the balance Sheet of a property

casualty insurance companyA 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 RiskPricing

Covers Costs of ultimate loss and loss adjustment expenses and expenses

Covers profit load needed to cover cost of capitalEstimate of the resultant premiums accounted for

in the unearned premium reservesUEPR amortized over the life of the exposure

(typically 1 year)Loss/LAE portion accrues into loss/LAE reserves

The Origin- Pricing RiskPricing Risk

Uncertainty of what will happenReserving Risk

What Happened Happened, Known and Unknown

Uncertainty of How will it all play-outManaging Reserve Risk =

Managing the release of earningsManaging the release of reservesManaging 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 reasonablenessX

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

AllConsistent EarningsReasonable RangesSupporting Capital Adequacy

Balances Capital Adequacy and Capital DeploymentProfitability and Risk

Key to ERM and Reserve RiskSatisfy all Audiences and ConsiderationsKey

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 sheetAre 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

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?

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SIDETRACK-A homework Problem in College

Prove that there are infinitely many prime numbersIntuitively …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.

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A Homework Problem in CollegeProofAssume a finite number of primes p1p2p3…pn

Of course there exists a number n = p1p2p3…pn +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 p1p2p3…pn , say pi, is a factor of n. Obviously pi is a factor of p1p2p3…pn .

Then pi must be a factor of 1 …..which is impossibleTherefore, by contradiction, there are infinitely

many number of prime numbers

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Moral of the StoryIf 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.

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What is a Reasonable Range?That which is Not Unreasonable

Unreasonable Unreasonable

Reasonable

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Diagnostic TestsTake Your Apriori reasonable range and test for unreasonableness

Paid/Ultimate TrianglesIncurred/Ultimate TrianglesReported Claim Counts/Ultimate Claim Count

TrianglesClosed Claim Counts/Ultimate Claim Count

TrianglesAverage Paids, Incurred, Opens, Closed, Unpaid

TrianglesYes Yes…we are back to deterministic models…but this time starting from a proposed answer

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Paid/Ultimate DiagnosticPaid - Total Loss

Policy Year 12 24 36 48 60 72 84 96 108 120 Ultimate1996 8,478 13,975 17,610 19,363 20,844 21,780 22,435 22,652 22,942 23,215 24,048 1997 8,753 14,756 18,763 21,600 23,447 24,494 25,318 26,062 26,317 - 28,408 1998 8,985 15,867 20,155 23,980 26,543 28,720 29,787 30,580 - - 34,389 1999 10,261 18,033 22,852 26,161 28,294 29,667 30,664 - - - 33,687 2000 9,415 17,512 23,226 27,022 29,487 30,977 - - - - 35,224 2001 10,383 19,673 26,322 29,797 31,930 - - - - - 37,274 2002 9,078 17,143 22,798 26,950 - - - - - - 35,335 2003 10,255 17,587 22,781 - - - - - - - 35,486 2004 9,760 17,422 - - - - - - - - 35,023 2005 9,119 - - - - - - - - - 30,897

- - - - - - - - - -

Paid / Ultimate - Total Loss & ALAE 12 24 36 48 60 72 84 96 108 120

1996 0.353 0.581 0.732 0.805 0.867 0.906 0.933 0.942 0.954 0.965 1997 0.308 0.519 0.660 0.760 0.825 0.862 0.891 0.917 0.926 1998 0.261 0.461 0.586 0.697 0.772 0.835 0.866 0.889 1999 0.305 0.535 0.678 0.777 0.840 0.881 0.910 2000 0.267 0.497 0.659 0.767 0.837 0.879 2001 0.279 0.528 0.706 0.799 0.857 2002 0.257 0.485 0.645 0.763 2003 0.289 0.496 0.642 2004 0.279 0.497 2005 0.295

Slightly Optimistic?

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Incurred/Ultimate Diagnostic

Incurred / Ultimate - Total Loss & ALAE accident year 12 24 36 48 60 72 84 96 108 120

1996 0.701 0.849 0.905 0.929 0.944 0.940 0.950 0.957 0.972 0.984 1997 0.658 0.777 0.835 0.881 0.891 0.923 0.958 0.956 0.968 1998 0.589 0.710 0.996 0.823 0.886 0.905 0.948 0.964 1999 0.667 0.761 0.801 0.865 0.910 0.937 0.961 2000 0.541 0.681 0.825 0.879 0.927 0.946 2001 0.495 0.743 0.851 0.887 0.924 2002 0.443 0.692 0.806 0.884 2003 0.565 0.713 0.831 2004 0.556 0.738 2005 0.603

Incurred - Total Loss & ALAE (net of recovery) ($000s)

accident year 12 24 36 48 60 72 84 96 108 120 Ultimate

1996 16,850 20,420 21,759 22,337 22,712 22,604 22,849 23,025 23,386 23,657 24,048 1997 18,679 22,060 23,720 25,032 25,318 26,227 27,207 27,159 27,509 - 28,408 1998 20,262 24,410 34,262 28,292 30,455 31,105 32,595 33,158 - - 34,389 1999 22,459 25,626 26,991 29,128 30,646 31,548 32,381 - - - 33,687 2000 19,062 23,977 29,071 30,954 32,646 33,306 - - - - 35,224 2001 18,456 27,681 31,731 33,066 34,436 - - - - - 37,274 2002 15,660 24,436 28,467 31,240 - - - - - - 35,335 2003 20,049 25,317 29,473 - - - - - - - 35,486 2004 19,463 25,857 - - - - - - - - 35,023 2005 18,640 - - - - - - - - - 30,897

Bias Low?

Inquire

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Similarly – Look at Claim count EmergenceClosed Counts / Ultimate Counts

AY 15 27 39 51 63 75 87 99 111 123

1996 0.720 0.894 0.942 0.967 0.980 0.990 0.994 0.996 0.997 0.998 1997 0.691 0.876 0.932 0.959 0.982 0.989 0.993 0.995 0.996 1998 0.677 0.875 0.921 0.964 0.980 0.987 0.991 0.992 1999 0.655 0.881 0.949 0.976 0.985 0.990 0.993 2000 0.693 0.899 0.954 0.971 0.980 0.988 2001 0.694 0.914 0.952 0.971 0.982 2002 0.781 0.913 0.947 0.968 2003 0.815 0.911 0.947 2004 0.788 0.900 2005 0.805

Reported Counts / Ultimate Counts AY 15 27 39 51 63 75 87 99 111 123

1996 0.992 0.998 0.999 0.999 1.000 1.000 1.000 1.000 1.000 1.000 1997 0.989 0.998 0.999 0.999 1.000 1.000 1.000 1.000 1.000 1998 0.986 0.996 0.998 0.999 1.000 1.000 1.000 1.000 1999 0.984 0.998 1.000 1.000 1.000 1.000 1.000 2000 0.986 0.999 0.999 0.999 1.000 1.000 2001 0.993 0.998 0.998 0.999 1.000 2002 0.997 0.998 0.999 0.999 2003 0.994 0.997 0.999 2004 0.990 0.998 2005 0.992

Shift in Settlement Rates 4 years ago

Consistent Reporting Rate

Faster Maturity may validate the optimistic projections

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Severities- Average Paid, Average OpenAverage Paid (Paid / Closed Counts) -Total Loss

AY 12 24 36 48 60 72 84 96 108 120

1996 1,814 2,411 2,881 3,086 3,279 3,390 3,478 3,507 3,547 3,586 1997 2,049 2,726 3,259 3,646 3,865 4,007 4,126 4,237 4,276 1998 2,184 2,985 3,602 4,096 4,462 4,790 4,950 5,075 1999 2,518 3,291 3,873 4,312 4,622 4,819 4,968 2000 2,273 3,257 4,072 4,653 5,031 5,241 2001 2,767 3,985 5,114 5,676 6,019 2002 2,506 4,048 5,191 6,006 2003 3,049 4,680 5,829 2004 3,795 5,936 2005 3,822

Average Open (Case Reserve / Open Counts)

AY 12 24 36 48 60 72 84 96 108 120

1996 4,743 9,534 11,212 14,163 14,588 13,504 11,826 14,891 23,384 31,527 1997 5,398 9,713 11,858 13,675 16,704 26,269 43,940 39,181 49,671 1998 6,021 11,623 30,272 20,148 32,331 32,227 52,007 54,849 1999 5,968 10,459 13,100 19,917 25,023 31,348 38,172 2000 5,506 10,847 21,491 23,265 27,004 33,765 2001 5,002 17,561 21,899 22,387 25,572 2002 6,582 18,557 23,819 29,182 2003 13,271 21,713 31,273 2004 14,769 26,361 2005 17,247

Case Reserve Strengthening Keeping up with apparent severity Trends

Again the last 4 years stand out

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Severity Trends and Maturity ShiftsBecause 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)

Closed Counts / Ultimate Counts AY 15 27 39 51 63 75 87 99 111 123

1996 0.720 0.894 0.942 0.967 0.980 0.990 0.994 0.996 0.997 0.998 1997 0.691 0.876 0.932 0.959 0.982 0.989 0.993 0.995 0.996 1998 0.677 0.875 0.921 0.964 0.980 0.987 0.991 0.992 1999 0.655 0.881 0.949 0.976 0.985 0.990 0.993 2000 0.693 0.899 0.954 0.971 0.980 0.988 2001 0.694 0.914 0.952 0.971 0.982 2002 0.781 0.913 0.947 0.968 2003 0.815 0.911 0.947 2004 0.788 0.900 2005 0.805

Average Open (Case Reserve / Open Counts)

AY 12 24 36 48 60 72 84 96 108 120

1996 4,743 9,534 11,212 14,163 14,588 13,504 11,826 14,891 23,384 31,527 1997 5,398 9,713 11,858 13,675 16,704 26,269 43,940 39,181 49,671 1998 6,021 11,623 30,272 20,148 32,331 32,227 52,007 54,849 1999 5,968 10,459 13,100 19,917 25,023 31,348 38,172 2000 5,506 10,847 21,491 23,265 27,004 33,765 2001 5,002 17,561 21,899 22,387 25,572 2002 6,582 18,557 23,819 29,182 2003 13,271 21,713 31,273 2004 14,769 26,361 2005 17,247

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Incurred/Ultimate Diagnostic

Incurred / Ultimate - Total Loss & ALAE accident year 12 24 36 48 60 72 84 96 108 120

1996 0.701 0.849 0.905 0.929 0.944 0.940 0.950 0.957 0.972 0.984 1997 0.658 0.777 0.835 0.881 0.891 0.923 0.958 0.956 0.968 1998 0.589 0.710 0.996 0.823 0.886 0.905 0.948 0.964 1999 0.667 0.761 0.801 0.865 0.910 0.937 0.961 2000 0.541 0.681 0.825 0.879 0.927 0.946 2001 0.495 0.743 0.851 0.887 0.924 2002 0.443 0.692 0.806 0.884 2003 0.565 0.713 0.831 2004 0.556 0.738 2005 0.603

Incurred - Total Loss & ALAE (net of recovery) ($000s)

accident year 12 24 36 48 60 72 84 96 108 120 Ultimate

1996 16,850 20,420 21,759 22,337 22,712 22,604 22,849 23,025 23,386 23,657 24,048 1997 18,679 22,060 23,720 25,032 25,318 26,227 27,207 27,159 27,509 - 28,408 1998 20,262 24,410 34,262 28,292 30,455 31,105 32,595 33,158 - - 34,389 1999 22,459 25,626 26,991 29,128 30,646 31,548 32,381 - - - 33,687 2000 19,062 23,977 29,071 30,954 32,646 33,306 - - - - 35,224 2001 18,456 27,681 31,731 33,066 34,436 - - - - - 37,274 2002 15,660 24,436 28,467 31,240 - - - - - - 35,335 2003 20,049 25,317 29,473 - - - - - - - 35,486 2004 19,463 25,857 - - - - - - - - 35,023 2005 18,640 - - - - - - - - - 30,897

Bias Low?

Inquire

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Gauging and Explaining BiasThis insight allays some concerns that

actuary’s estimates are optimistically biasedReasonable to conclude that Incurred

Emergence Should increaseIncurred / Ultimate - Total Loss & ALAE

accident year 12 24 36 48 60 72 84 96 108 120

1996 0.701 0.849 0.905 0.929 0.944 0.940 0.950 0.957 0.972 0.984 1997 0.658 0.777 0.835 0.881 0.891 0.923 0.958 0.956 0.968 1998 0.589 0.710 0.996 0.823 0.886 0.905 0.948 0.964 1999 0.667 0.761 0.801 0.865 0.910 0.937 0.961 2000 0.541 0.681 0.825 0.879 0.927 0.946 2001 0.495 0.743 0.851 0.887 0.924 2002 0.443 0.692 0.806 0.884 2003 0.565 0.713 0.831 2004 0.556 0.738 2005 0.603

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Reserving is a Holistic ProcessTraditional Approach

Holistic Approach

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What is Best Estimate Range?That which is Not Unreasonable

Unreasonable Unreasonable

Reasonable

29

What is the Number to Book?

Unreasonable 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 DoOur 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

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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 (Θ0) 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 Θ0 was reasonable at time 0.

Initial Reserve Estimate/ Θ0R

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Reserving is “Inductive Reasoning”At time one, we get an

additional vector of experience (X1)

Which may or may not make us reasonable assume a revised vector of premises (Θ1)

Which then may produce an updated range estimate (R1 Range /Θ1)…again based on

updated information and corresponding updated premises, it is reasonable to assume………………

▪( )

R0 Range/ Θ0

R

(R1 Range /Θ1)

( )

Process Continues… (R2 Range /Θ2) (R3 Range /Θ3) …………….. ……………. (Ultimate Range /Θdone)

……Looks Bayesian to me.

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In Conclusion…My Opinions OnlyA Reasonable Range is that which is not

UnreasonableBooking High/Low is ok as long as high/low is

reasonable and enough capital supports the risksUse Holistic Techniques not a bunch of myopic

techniquesConsideration 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

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Thank You Very Much !!