From

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From Reasonable Reserve Range to Carried
Reserve What do you Book?

• Mark R. Shapland, FCAS, ASA, MAAA
• Consulting Actuary

2007 CAS Annual MeetingChicago,
IllinoisNovember 11-14, 2007
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Overview

• Terminology
• Ranges vs. Distributions
• What is Reasonable to Book?

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Terminology

• Reserve an amount carried in the liability
  section of a risk-bearing entitys balance sheet
  for claims incurred prior to a given accounting
  date.
• Liability the actual amount that is owed and
  will ultimately be paid by a risk-bearing entity
  for claims incurred prior to a given accounting
  date.
• Loss Liability the expected value of all
  estimated future claim payments.
• Risk (from the risk-bearers point of view)
  the uncertainty (deviations from expected) in
  both timing and amount of the future claim
  payment stream.

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Terminology

• Process Risk the randomness of future outcomes
  given a known distribution of possible outcomes.
• Parameter Risk the potential error in the
  estimated parameters used to describe the
  distribution of possible outcomes, assuming the
  process generating the outcomes is known.
• Model Risk the chance that the model
  (process) used to estimate the distribution of
  possible outcomes is incorrect or incomplete.

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Terminology

• Risk unknown outcomes with quantifiable
  probabilities.
• Uncertainty unknown outcomes that cannot be
  estimated or quantified.
• All entrepreneurship involves both risk (which
  can be transferred) and uncertainty (which cannot
  be transferred).

Source Knight, Frank H. 1921. Risk,
Uncertainty, and Profit. Houghton Mifflin.
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Terminology

• Measures of Risk from Statistics

• Variance, standard deviation, kurtosis, average
  absolute deviation, Value at Risk, Tail Value at
  Risk, etc. which are measures of dispersion.
• Other measures useful in determining
  reasonableness could include mean, mode,
  median, pain function, etc.
• The choice for measure of risk will also be
  important when considering the reasonableness
  and materiality of the reserves in relation to
  the capital position.

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CAS Exams vs. Real World

• As part of your analysis of unpaid claims, the
  CEO of your company would like you to create a
  Reserve Range to discuss with the Board.
• How do you proceed?

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CAS Exams vs. Real World

• You use a variety of methods to arrive at a range
  of point estimates.
• Removing the unreasonable estimates you are
  left with the following

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CAS Exams vs. Real World

• You present the Reserve Range to the CEO and
  the Board and they ask
• How likely are these reserves to be adequate?
• How likely is it that the final result will be in
  this range?
• How much capital do we need to support our
  business?
• OOPS!!!

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Ranges vs. Distributions

• A Range is not the same as a Distribution
• A Range of Reasonable Estimates is a range of
  estimates that could be produced by appropriate
  actuarial methods or alternative sets of
  assumptions that the actuary judges to be
  reasonable.
• A Distribution is a statistical function that
  attempts to quantify probabilities of all
  possible outcomes.

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Ranges vs. Distributions

• A Range, by itself, creates problems

• A range can be misleading to the layperson it
  can give the impression that any number in that
  range is equally likely.
• A range can give the impression that as long as
  the carried reserve is within the range
  anything is reasonable.

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Ranges vs. Distributions

• A Range, by itself, creates problems

• There is currently no specific guidance on how to
  consistently determine a range within the
  actuarial community (e.g., /- X, /- X, using
  various estimates, etc.).
• A range, in and of itself, needs some other
  context to help define it (e.g., how to you
  calculate a risk margin?)

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Ranges vs. Distributions

• A Distribution provides

• Information about all possible outcomes.
• Context for defining a variety of other measures
  (e.g., risk margin, materiality, risk based
  capital, etc.)

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Methods vs. Models

• A Method is an algorithm or recipe a series of
  steps that are followed to give an estimate of
  future payments.
• The well known chain ladder (CL) and
  Bornhuetter-Ferguson (BF) methods are examples.
• The search for the best pattern.

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Methods vs. Models

• A Model specifies statistical assumptions about
  the loss process, usually leaving some parameters
  to be estimated.
• Then estimating the parameters gives an estimate
  of the ultimate losses and some statistical
  properties of that estimate.
• The search for the best model.

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What Reserve to Book?
(Point Estimates)
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What Reserve to Book?
(Distributions)
The Most Likely Outcome?
Mode
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What Reserve to Book?
(Distributions)
Equally Likely to be High / Low?
Mode
Median
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What Reserve to Book?
(Distributions)
Enough On Average?
Expected Value
Mode
Median
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What Reserve to Book?
(Distributions)
Which Risks are Included?
Expected Value
Mode
Median
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What Reserve to Book?
Aggregate Distributions
LOB A
Aggregate Distribution with 100
Correlation (Added)
LOB B
Aggregate Distribution with 0 Correlation (Indepe
ndent)
LOB C
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What Reserve to Book?
Aggregate Distributions
Aggregate Distribution with 0 Correlation (Indepe
ndent)
Aggregate Distribution with 100
Correlation (Added)
Capital 1,000M
Capital 600M
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What Reserve to Book?
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What Reserve to Book?
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What Reserve to Book?
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What Reserve to Book?
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What Reserve to Book?
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What Reserve to Book?
Reasonable Distribution
Range of Reasonable Estimates
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What Reserve to Book?
(Range of Reasonable Estimates)
Best Estimate
11M
16M
Range of Possible Estimates
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What Reserve to Book?
(Multiple Distributions)
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What Reserve to Book?
(Reasonable Distributions)
Range of Mean Estimates
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What Reserve to Book?
(Reasonable Distributions)
Best Distribution
Range of Mean Estimates
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Questions?
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CAS Exams Revisited

• Reserves as of 12/31/2006?
• One claim to be settled 1/1/2007 with immediate
  payment of 1 million times roll of fair die
• All results equally likely so some accounting
  guidance says book low end (1 million), others
  midpoint (3.5 million), still others the mode
  (1, 2, 3, 4, 5 or 6 million)
• Mean and median are 3.5 million
• What reserve to book?