Reserve Margins and Capital CLRS – New Orleans September 11, 2001 Chuck Emma, MHL/Paratus Chandu Patel, KPMG LLP Kevin Madigan, MHL/Paratus

Reserve Margins and Capital

CLRS – New OrleansSeptember 11, 2001

Chuck Emma, MHL/Paratus

Chandu Patel, KPMG LLP

Kevin Madigan, MHL/Paratus

Reserve Margins

Chuck Emma, MHL/ParatusRisk Modeling Application

Chandu Patel, KPMG LLPAccounting and Management Considerations

Kevin Madigan, MHL/ParatusReserve Implications in Runoff Companies

Risk Modeling Application

Casualty Loss Reserve Seminar

New Orleans

September 11, 2001

Chuck Emma, FCAS, MAAA

Risk Modeling Application

A Research Question

Sample Company

- background

- modeling assumptions

Coherent Risk Measures

Conclusions

A Research Question

Question: Does recording a reserve higher than management’s best estimate have an effect on the capital required to support the company’s operations?

One Answer: Model the company’s financial risk under different reserving strategies. Calculate the level of capital required to support operations.

Company Example

• Initial Policyholder Surplus = $70MM• Writes approximately 2 to 1 • Modest Business Growth (3-6%)• Risk Factors

– Economic Variables• Interest• Inflation

– Pure Loss Variability

• Five Year Projections of Operating Results

Economic Risk Factors

• Cox-Ingersoll-Ross Interest Rate Generator– Mean-reverting random walk for interest rates

• Cascading dependency of inflation rates– Linear relationship with error term

Interest Rates

Inflationit = m . rt + b + e

Reserve Variability

• Reserve adequacy defined by expected inflation rate

• Actual (generated) inflation rate provides hindsight reserve

• For example:– 6.0% expected inflation at 12/31/00

– 6.2% generated in 2001

– Effect of unanticipated 0.2% of inflation is calculated over life of reserve. Adverse development occurs.

Company Reserving Policy

• Three Reserving Practices Examined– Mean level reserving– 75th percentile reserving– 90th percentile reserving

• Management Reserving Practice: Eroding Margin– Each year absorb any adverse reserve developments up

to 50% of remaining margin– For example: $5MM prior year “hit” reduces any

available margin by $2.5MM. The other $2.5MM flows to income.


Simulated Financial Results

– Parameterized,– Validated,– What the actuary

fusses over

Decision-Making

– Performance measures

– Risk measures

– Consistent with financial world

From DFA simulations to financial decisions. How do we get there?

?


Article – 1994 AFIR Colloquium

– Clarkson: “The Coming Revolution in the Theory of Finance”

– Van Slyke’s review 1995: “Need to consider total distribution”


• “Coherent Measures of Risk”

– Philippe Artzner, Freddy Delbaen, Jean-Marc Eber and David Heath, Math. Finance 9 (1999), no. 3, 203-228

– http://www.math.ethz.ch/~delbaen/ftp/preprints/CoherentMF.pdf

• Coherent Measures of Risk - An Explanation for the Lay Actuary

– Glenn Meyers– http://www.casact.org/pubs/forum/00sforum/meyers/Coherent%20Measures%20of%20Risk.pdf


Swiss Paper (Artzner, et al)

– Setting margin requirements on exchange– Similar to capitalization of insurer– Based on four axioms– “Coherent”: in the eyes of the beholders?

CRM - Survey of Risk Measures

Standard Deviation

Value-At-Risk

Expected Policyholder Deficit

CRM - Standard Deviation

Material departures from normal behavior can lead to problems

Includes upside variation– The free lottery ticket “costs too much”

CRM - Value at Risk

The value at a selected quantile

Problems– The most extreme values are ignored– Doesn’t distinguish between tails– Can mislead when combining risks


So, What Would Make More Sense?

– Guiding question: How big is “big”?

– Guiding Principle: The purpose of capital is to fund prospective losses

– Try “Tail Value-at-Risk”

Tail Value at Risk - (TVaR)

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0.20

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0.40

0.50

0.60

0.70

0.80

0.90

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Subject Loss

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Value At Risk

Tail Value at Risk is the average of all losses above the Value at Risk

Results of Modeling

Base Case with Constant Percentage Margin

Beginning Surplus

Average Terminal Surplus

Average Rate of Return

CV Net Income

Capital TVAR10

Mean Reserving 70,000 99,705 6.84% 1.731 24,366 10% Margin 60,000 79,311 5.74% 2.430 32,553 20% Margin 50,000 62,413 4.54% 3.220 48,551

Results of Modeling

Base Case – Eroding Margin

Beginning Surplus



CV Net Income

Capital TVAR10

Mean Reserving 70,000 99,705 7.33% 1.731 24,366 75th Percentile 63,588 99,357 9.34% 1.464 22,467 90th Percentile 56,927 97,493 11.36% 1.293 20,962

Results of Modeling

Higher Economic and Reserve Variability

Beginning Surplus



CV Net Income

Capital TVAR10

Mean Reserving 70,000 97,489 6.84% 4.133 65,355 75th Percentile 57,361 96,695 11.01% 2.925 61,837 90th Percentile 44,379 92,897 15.92% 2.353 59,243

Other Tests Under Examination

• Longer Reserve Durations

– Under best estimate reserving, the company needs more capital

– Using greater margins, capital requirements are eventually reduced

Conclusions

• Reserve margins can be used to stabilize income and reduce capital requirements

• The reduction in reported capital is offset by lower requirements due to the hedge which a margin can offer

• Accounting, regulatory, and other external realities limit the extent to which margins are possible and desirable

Reserve Margins and Capital

Casualty Loss Reserve Seminar

New Orleans

September 11, 2001

Chandu C. Patel, FCAS, MAAA

Reserve Margins and Capital – The CFO Perspective

Statutory considerations for reserve margins• Codification requires that held reserves should correspond

to Management’s best estimate.

• Ideally, this would correspond to the actuarial best estimate.

• Although the intent is to prevent “low” end reserves, “high” end reserves also require documentation.

• Generally, on an on-going basis, statutory framework (e.g. IRIS ratios) favors high end reserves.


GAAP considerations for reserve margins• Typically reserves are many multiples of earnings• As a result, any movement within the actuarial range has a

significant impact on earnings; this can be construed as earnings management

• To maintain a consistent reserving philosophy, this would suggest that held reserves should be based on the actuarial range and at a consistent percentile of the range

• In fact if a high percentile is targeted, this may lead to greater variability in results – need model to evaluate


IRS considerations for reserve margins• Generally, IRS is not sympathetic to conservative reserves.

However actuarial range may provide adequate justification for high end reserves

• Utah Medical – actuarial range accepted

• Minnesota Lawyers – actuarial range not considered

• No clear case history


AM Best and Other Ratings considerations for reserve margins

• Reserve adequacy has a significant impact on BCAR

• Rating agencies place a lot of emphasis on reserve adequacy

• Consistent, favorable development of past estimates will lead to higher rating


Risk Based Capital considerations• Formulaic approach considers held reserves as “best

estimate” even though there may be a margin in the reserves

• Hence Company is penalized in terms of lower statutory surplus and higher RBC

• Offsetting effect is favorable loss development


TVAR adjusted for reserve margin• Based on model output, given the ability to release

reserves per the model assumptions, it is clear that the higher the percentile of held reserves, the lower the TVAR.

• Release of reserve margins leads to reduced variability as the margin provides a cushion for adverse scenarios.

• This would suggest that a high reserve margin is desirable form a TVAR perspective.

• However, end position reflects an erosion in the margin and this has to be “replenished” if the original reserve margin is to be maintained.


Average ROR and CV of Net Income• High margin implies lower surplus leading to a higher return;

the reverse is true for lower margins• In addition, reserve release increases the average net income as

well. This leads to a higher numerator and a higher average return

• Reserve release also reduces the variability of net income since adverse outcomes are cushioned.

• All indicators point to a strategy of holding a high a reserve margin, based on the model assumptions

• Once again erosion of reserve margin and perception of “earnings management’ have to be considered as well.


Summary of considerations• External Factors – Statutory guidelines, Statutory

Surplus/RBC, SEC, IRS, AM Best• Internal Factors – TVAR, Goal for earnings stability,

“cost” of capital• Other – If pricing is based on conservative reserves,

implications of future profits• Other – If investment decisions are based on whether

funds are considered “reserves” or “surplus”, impact on investment income

A DFA Approach to Valuing a Run Off Operation

CAS CLRS September 11, 2001

Kevin Madigan

MHL/Paratus


• ABC Insurance Companies wants to put a book(s) of business into run-off– Reasons for such action include:

• A management decision to exit a market• A need to segregate a collection of policies

from ongoing operations (asbestos, construction defects, etc.)

• Let’s assume ABC wants to sell this run-off operation (possibly to a subsidiary)

We are assuming that ABC is selling the run-off operation to a buyer who will set it up as an insurance company or companies. However, most of the following applies if ABC is setting up a run-off business unit.


Q: Why buy it?

A: To take cash out of it


Sound, aggressive, focused approaches to• Claims settlement• Commutations• Investments

Allow for significant annual “dividends”

& an extraordinary one “at the end of the day”.


What’s a good price?


The only appropriate actuarial answer is:

What’s A Good Price?

Well ...


Well ...

...that depends.


What does it depend on?• The liabilities

Gross, net, and ceded loss & LAE, and the adequacy of the reserves

• Payment patterns (and how many more years?)• “Bad debt” – i.e. how collectable is/will be the

cessions? When and how will this be recognized? Schedule F issues?

• What has been commuted, and for how much?


What else does it depend on?• Investment Income• RBC• General Expenses• Income and Other Taxes• Paid-in Capital• Additional Reinsurance• etc.


Probably the most important factors are

• The parties’ risk appetites

• The perceived adequacy of the reserves

These factors cannot be modeled

But all is not lost


• Build stochastic model assuming yearly dividends.

• No way to definitively determine a “good price” for all possible players.

• Produce distributions of the NPV of future dividends using various term structures.


Interest RatePercentile 4% 6% 8% 10% 12% 14% 16% 18% 20%10th $15M $14M $13M $11M $10M $9M $8M $6M $5M20th $16M $15M $14M $12M $11M $10M $9M $7M $6M30th $18M $17M $16M $14M $13M $12M $11M $9M $8M40th $20M $19M $18M $16M $15M $14M $13M $11M $10M50th $21M $20M $19M $17M $16M $15M $14M $12M $11M60th $23M $22M $21M $19M $18M $17M $16M $14M $13M70th $27M $26M $25M $23M $22M $21M $20M $18M $17M80th $31M $30M $29M $27M $26M $25M $24M $22M $21M90th $36M $35M $34M $32M $31M $30M $29M $27M $26M95th $44M $43M $42M $40M $39M $38M $37M $35M $34M

If the model’s assumptions are reasonable, then the table says that a $16M price provides the buyer with

• An 80% prob of a return of 4% or better• A 40% prob of a return of 16% or better, etc.

Whereas a $21M price provides the buyer with• A 50% prob of a return of 4% or better• A 20% prob of a return of 20% or better, etc.


Alternatively, if one requires, say a 14% ROR, then the table can be used to evaluate possible purchase prices (e.g. $15M gives only a 50% probability of meeting the required ROR; $10M gives an 80% probability, etc.).


At the time of purchase, the buyer gets more than just the reserves. There has to be some associated capital to support the operations. The amount of this paid in capital will greatly affect the surplus of the new run-off entity, and will have an impact on the size of the yearly dividends.

Other Issues

Too little capital Low purchase price Very little inv. income Small or zero dividends Surplus and RBC issues

Too much capital High purchase priceDrain on seller’s assets

Other Issues

If the parties’ perceptions of reserve adequacy are not similar, the deal could be doomed from the start - even if they agree on everything else.

For example if the seller thinks the reserves are at the 65th percentile of the distribution, and the buyer thinks they are at the 50th percentile, we could have a deal breaker..

Other Issues

An obvious way around this is for the seller to increase the reserves, or the amount of paid in capital.

But, this “solution” is very unattractive to the seller.

Other Issues

Another way around this is for the seller to provide a cover for adverse development. If the seller is correct regarding reserve adequacy, this will cost them nothing (other than the theoretical cost of the embedded option).Such a cover will alter the risk to the buyer, and will effect the distribution of future dividends.However, the “price” will increase, but by less than the cost of the reinsurance.

Other Issues

• Run-off Business Unit– Segregate “problems” from other business units– Initial capital infusion with anticipated yearly

“dividends” and eventual release of remaining capital

– The approach discussed here can help determine the initial capital

– More leeway in setting reserves

Other Issues

What we have been discussing illustrates the importance of providing useful ranges to decision makers.

Other Issues

What we have been discussing illustrates the importance of providing useful ranges to decision makers.

This is another example of where point estimates are useless, and where actuarial modeling can provide real value to decision makers.

Other Issues

Documents

Reserve Margins and Capital CLRS – New Orleans September 11, 2001 Chuck Emma, MHL/Paratus Chandu Patel, KPMG LLP Kevin Madigan, MHL/Paratus