Transcript Distribution

From “Reasonable Reserve Range” to
“Carried Reserve” – What do you Book?
Mark R. Shapland, FCAS, ASA, MAAA
Consulting Actuary
2007 CAS Annual Meeting
Chicago, Illinois
November 11-14, 2007
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 entity’s 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:
$11M
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$16M
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)
$11M
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$16M
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?
Mode
Median
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Expected Value
What Reserve to Book?
(Distributions)
Which Risks are Included?
Mode
Median
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Expected Value
What Reserve to Book?
Aggregate Distributions
LOB “A”
Aggregate Distribution with 100% Correlation
(Added)
LOB “B”
Aggregate Distribution with 0% Correlation
(Independent)
LOB “C”
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What Reserve to Book?
Aggregate Distributions
Aggregate Distribution with 100% Correlation
(Added)
Aggregate Distribution with 0% Correlation
(Independent)
Expected Value
Expected Value
99th Percentile
Capital = 1,000M
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99th Percentile
Capital = 600M
What Reserve to Book?
$11M
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$16M
What Reserve to Book?
50th Percentile
75th Percentile
$16M
$11M
Mode
Median
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Expected Value
What Reserve to Book?
50th Percentile
75th Percentile
$11M
$16M
Mode
Median
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Expected Value
What Reserve to Book?
50th Percentile
75th Percentile
$16M
$11M
Mode
Median
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Expected Value
What Reserve to Book?
50th Percentile
75th Percentile
$11M
Mode
Median
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$16M
Expected Value
What Reserve to Book?
Range of Reasonable Estimates
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Reasonable Distribution
What Reserve to Book?
(Range of “Reasonable” Estimates)
“Best” Estimate
$11M
$16M
Range of Possible Estimates
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What Reserve to Book?
Probability
(Multiple Distributions)
Liability Estimates
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What Reserve to Book?
(Reasonable Distributions)
Probability
Range of Mean Estimates
Unpaid Estimates
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What Reserve to Book?
(Reasonable Distributions)
“Best” Distribution
Probability
Range of Mean Estimates
Unpaid 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?
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