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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.
Coherent Risk Measures
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?
?
Coherent Risk Measures
Article – 1994 AFIR Colloquium
– Clarkson: “The Coming Revolution in the Theory of Finance”
– Van Slyke’s review 1995: “Need to consider total distribution”
Coherent Risk Measures
• “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
Coherent Risk Measures
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
Coherent Risk Measures
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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0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
1.00
Subject Loss
Cu
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ve P
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abil
ity
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
Average Terminal Surplus
Average Rate of Return
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
Average Terminal Surplus
Average Rate of Return
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.
Reserve Margins and Capital – The CFO Perspective
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
Reserve Margins and Capital – The CFO Perspective
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
Reserve Margins and Capital – The CFO Perspective
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
Reserve Margins and Capital – The CFO Perspective
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
Reserve Margins and Capital – The CFO Perspective
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.
Reserve Margins and Capital – The CFO Perspective
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.
Reserve Margins and Capital – The CFO Perspective
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
A DFA Approach to Valuing a Run Off Operation
• 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.
A DFA Approach to Valuing a Run Off Operation
Q: Why buy it?
A: To take cash out of it
A DFA Approach to Valuing a Run Off Operation
Sound, aggressive, focused approaches to• Claims settlement• Commutations• Investments
Allow for significant annual “dividends”
& an extraordinary one “at the end of the day”.
A DFA Approach to Valuing a Run Off Operation
What’s a good price?
A DFA Approach to Valuing a Run Off Operation
The only appropriate actuarial answer is:
What’s A Good Price?
Well ...
What’s A Good Price?
Well ...
...that depends.
What’s A Good Price?
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’s A Good Price?
What else does it depend on?• Investment Income• RBC• General Expenses• Income and Other Taxes• Paid-in Capital• Additional Reinsurance• etc.
What’s A Good Price?
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
What’s A Good Price?
• 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.
What’s A Good Price?
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.
What’s A Good Price?
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.).
What’s A Good Price?
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