Download Estimating Reserve Ranges: Practical Suggestions

Estimating Reserve Ranges:
Practical Suggestions
Richard E. Sherman,
FCAS, MAAA
Richard E. Sherman & Associates, Inc.
A Range of Reasonable Estimates
ASOP 36 defines it as “a range of
estimates that could be
produced by appropriate
actuarial methods or alternative
sets of assumptions that the
actuary judges to be
reasonable.” P&C Practice Note, p. 33
1) A Comfortable Range
Paid projection
$9 M
Incurred projection
$11 M
Born Ferg projection
$10 M
Selected range
%-age range
$9 M - $11 M
+/- 10%
2) A Range with 2 Adjusted Projections
Paid projection
Incurred projection
Born Ferg projection
Berq Sher adj paid
Berq Sher adj inc’d
Selected range
%-age range
$7 M
$14 M
$11 M
$9 M
$11 M
$9M - $11 M
+/- 10%
3) All Projections Much Too Low
Paid projection
Incurred projection
Born Ferg projection
Adjusted paid proj.
Adjusted inc’d proj.
Adj. Born Ferg proj.
Selected range
Should range be:
$6 M
$7 M
$6 M
$8 M
$7 M
$7 M
$6M - $8M
$9M - $11M ???
4) Too Large a Range?
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Paid projection: $4 M
Incurred projection: $16 M
Adjusted paid proj.: $6 M
Adjusted incurred proj.: $14 M
Born Ferg proj.: $10 M
Selected range: $6 M - $ 14 M
Disturbing +/- 40% range
“Can’t you do better than that?”
5) Too Good to Be True
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Paid projection: $10 M
Incurred projection: $10 M
BornFerg projection: $10 M
FreqSev projection: $10 M
No changes in settlement rates or
adequacy level of reserves
HELP!!!!
Ranges & Actuarial Opinions: A
Regulatory Perspective
Nicole Elliott, ACAS,
MAAA
Texas Dept of
Insurance
Type of AOS Review
Point
467
54%
Range
145
17%
Point & Range
248
29%
Total
859
What Types of Ranges are
Regulators Seeing?
Not discussed in Report
 Methods considered proprietary
 Used actuarial judgment - common
 % +/- a point estimate - common
 Scenario testing
 Statistical distributions - rare
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Possible Help
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Use PLDFs to derive projections of future
incremental paids. Assume 6% underlying
inflation & derive alternative projections of
incremental paids based on 3% & 9%
inflation.
Run a simulation based on mean LDFs and
std dev of LDFs, reflecting correlation
between the LDFs in successive DYs.
Cold Showers
for Confident Actuaries
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Review your own track record of past
estimates & how they have developed.
Cover up the latest 2 diagonals and
estimate LDFs based on prior factors.
Then compare your projections with actual
LDFs.
Dig up an old rate filing you did 3-5 years
ago & compare the projected rates/pure
premiums with the ultimates in your latest
filing.
More Cold Showers
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Review Schedule P—Parts 2 & 3 by
AY and calculate %-age favorable/
adverse development of previously
carried reserves.
Run a Monte Carlo simulation (using
@RISK or Crystal Ball software) to
get a feel for the probability
distribution of future payments.
Become a High Roller
at Monte Carlo Simulation
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Level 1—Poisson for # of claims; lognormal or
pareto for claim size [Process Risk]
Level 2—Add a probability distribution for the
uncertainty of lambda for Poisson and for the
mean & std dev for lognormal [Parameter Risk]
Level 3—Dream up models from an alternative
universe and assign each model a probability of
representing reality. Simulate at all 3 levels.
[Model Risk]
Encountering Reality:
Industry Runoff Statistics
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2,500 P/C Insurers
Schedule P – Parts 2 & 3
Focus on distribution of individual
company results
Findings never presented on 9/11/01
at CLRS by Kevin Wick of PwC.
5 Year Hindsight Comparisons
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Use latest ultimates less cumulative
paid from 5 years ago.
Compile %-age of insurers where
hindsight reserve was within +/- 5%,
etc.
All Lines of Business
5 Year Hindsight
Reserve:
Within 5%
%-age of
Insurers
Between 5% & 10%
14%
Between 10% & 25%
37%
More than 25%
29%
20%
Private Passenger Auto Liability
5 Year Hindsight
Reserve:
Within 5%
%-age of
Insurers
Between 5% & 10%
19%
Between 10% & 25%
44%
More than 25%
22%
15%
Workers Compensation or CMP
5 Year Hindsight
Reserve:
Within 5%
%-age of
Insurers
Between 5% & 10%
14%
Between 10% & 25%
37%
More than 25%
31%
18%
Other Liability Occurrence
5 Year Hindsight
Reserve:
Within 5%
%-age of
Insurers
Between 5% & 10%
10%
Between 10% & 25%
29%
More than 25%
49%
12%
Med Mal Claims Made
5 Year Hindsight
Reserve:
Within 5%
%-age of
Insurers
Between 5% & 10%
6%
Between 10% & 25%
15%
More than 25%
68%
11%
By Size of All Lines Reserves
Total
Reserve
<$1M
12%
$10-50 M
> $500 M
17%
30%
Between
5% & 10%
5%
16%
15%
Between
10% & 25%
20%
37%
45%
More than
25%
63%
30%
10%
5 Year
Hindsight
Reserve:
Within 5%
Total
Reserve
Total
Reserve
Consult Hindsight Deviation
Profiles for the Reserve Size and
LOBs Being Analyzed
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May cause you to widen your
judgmental feel for the size of the
range from your analysis.
Suppose a new part were added to
Schedule P to display the %-age
hindsight error in stated reserves? A
downside: It would make it easier for
outsiders to derive quick and dirty
estimates of future development.
Future Payments Can Be Fickle
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Even if the chosen model explains past
development well, it may not explain
much of future development.
Industry runoff results show disturbingly
high %-age of insurers with reserve
development %-ages greater than 10%
and greater than 25%. Unanticipated
major influences can cause dramatic
movements in ultimates.
Edgy Reasonableness
Is a reserve estimate still reasonable
if every one of numerous key
assumptions are chosen at the low
end of the range of reasonable
values for each assumption? At the
high end?
Trend, Cycle or Noise?
AY
DY 2
DY 3
DY 4
2003
1.374
1.062
1.031
2004
1.424
1.055
1.029
2005
1.456
1.049
2006
1.474
Trend, Cycle or Noise?
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Usually not possible to determine whether
data is following a trend, a cyclical
pattern, or just fluctuating randomly in a
column.
Simulation exercise. Start with a given
mean LDF and std dev and generate a
series of four LDFs for DY 2. Compile
simulation results of what %-age of the
time the data will show a clear trend, even
though there is no real trend.
Trend, Cycle or Noise?
Choose a series of four underlying
distributions for the four LDFs for DY
2, where the means are dropping
steadily. From simulation, what %age of the time will a trend line fitted
to the data have an upward slope, in
spite of the actual downward trend
present in the assumptions?
Can Actuarial Judgment
Overcome Low Credibility?
Problem: Credibility of LDFs drops
rapidly for the most mature DYs.
Culminates in reliance on only one
LDF at the tip of the triangle.
Suggestion: Apply methods that pull
in incremental data prior to the
triangle to raise the credibility of the
LDFs at or near the tip.
Dead on Arrival (DOA) Data
Diagonals
Only Area
(DOA)
Standard
Triangle
Going Out on a BerqSher Limb?
Problem: Adjusted triangle resulting
from a BerqSher method produces
strange progressions of incremental
paids or incurreds.
Suggestion: Take only Y% of each
indicated adjustment. Solve for the
Y% that produces the most
reasonable adjusted triangle. For
example, Y = 60% or 130%.
Bias Inherent in Trimming LDFs
Problem: Often, relying on the Avg X Hi Lo
can result in tossing out most of the large
adverse development while only removing
small favorable developments from the
historical factors.
Suggestion: Try smoothing the historical
data using moving averages over
successive DYs instead. Less bias?
CONCLUSIONS
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Actual variability of future payout
What you think it is.
>>
Actual variability >> low and high
estimates in your range.
Do more homework before making
selections.
Help your audience appreciate how large
the real degree of variability is, while
retaining their confidence in your
professional abilities.