Reserve Margins and Capital
CLRS – New Orleans
September 11, 2001
Chuck Emma, MHL/Paratus
Chandu Patel, KPMG LLP
Kevin Madigan, MHL/Paratus
Reserve Margins
Chuck Emma, MHL/Paratus
Risk Modeling Application
Chandu Patel, KPMG LLP
Accounting and Management Considerations
Kevin Madigan, MHL/Paratus
Reserve 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
it = m . rt + b + e
Inflation
Rates
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
From DFA simulations to financial
decisions. How do we get there?
Simulated Decision-Making
Financial
Results ? – Performance
measures
– Parameterized, – Risk measures
– Validated, – Consistent with
– What the actuary financial world
fusses over
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)
1.00
0.90
0.80
Cumulative Probability
0.70
0.60 Tail Value at Risk is
0.50 the average of all
0.40
losses above the
0.30
Value at Risk
0.20
0.10
0.00
Value At Risk
Subject Loss
Results of Modeling
Base Case with Constant Percentage Margin
Average Average
Beginning Terminal Rate of CV Net Capital
Surplus Surplus Return Income 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
Average Average
Beginning Terminal Rate of CV Net Capital
Surplus Surplus Return Income 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
Average Average
Beginning Terminal Rate of CV Net Capital
Surplus Surplus Return Income 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)
A DFA Approach to Valuing a Run Off
Operation
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?
What’s A Good Price?
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.
Interest Rate
Percentile 4% 6% 8% 10% 12% 14% 16% 18% 20%
10th $15M $14M $13M $11M $10M $9M $8M $6M $5M
20th $16M $15M $14M $12M $11M $10M $9M $7M $6M
30th $18M $17M $16M $14M $13M $12M $11M $9M $8M
40th $20M $19M $18M $16M $15M $14M $13M $11M $10M
50th $21M $20M $19M $17M $16M $15M $14M $12M $11M
60th $23M $22M $21M $19M $18M $17M $16M $14M $13M
70th $27M $26M $25M $23M $22M $21M $20M $18M $17M
80th $31M $30M $29M $27M $26M $25M $24M $22M $21M
90th $36M $35M $34M $32M $31M $30M $29M $27M $26M
95th $44M $43M $42M $40M $39M $38M $37M $35M $34M
What’s A Good Price?
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.).
Other Issues
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 price
Drain 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.