1 concurrent session: risk transfer (fas 113) presentation by michael g. wacek casualty loss reserve...
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Concurrent Session:Concurrent Session:Risk Transfer (FAS 113)Risk Transfer (FAS 113)
Presentation by Michael G. Wacek
Casualty Loss Reserve SeminarSeptember 12, 2005
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Risk Transfer Testing of Reinsurance Contracts:Risk Transfer Testing of Reinsurance Contracts:Analysis and RecommendationsAnalysis and Recommendations
CAS Research Working Party on Risk Transfer CAS Research Working Party on Risk Transfer TestingTesting
Michael Wacek, Chairman (Odyssey Re)John Aquino (Benfield)Todd Bault (Sanford Bernstein)Paul Brehm (Guy Carpenter)Beth Hansen (Guy Carpenter)Pierre Laurin (Zurich)Mark Littmann (PricewaterhouseCoopers)Karen Pachyn (GE Insurance Solutions)Debbie Rosenberg (NY State Insurance Department)David Ruhm (Hartford)Mark van Zanden (Catlin)
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ContextContext
CAS Leadership sought to ensure constructive input to AAA, which is engaged in dialogue with NAIC & others on risk transfer issue
Working party formed in June 2005 in anticipation of a call from AAA (COPLFR) for ideas on defining/testing risk transfer in reinsurance contracts
AAA issued call for ideas June 13 with July 15 deadline
Working party produced and submitted draft white paper to COPLFR on July 15, final paper on July 21
Support from Reinsurance Committee and CAS Staff
White paper posted on CAS website on August 1
Possibly a new speed record for a CAS working party!
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DisclaimerDisclaimer
Paper is intended as educational document
Not official position of the CAS
While read by subcommittee of Reinsurance Research Committee before release, not formally peer reviewed by CORP
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COPLFR Call for IdeasCOPLFR Call for Ideas
1. What is an effective test for risk transfer?
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COPLFR Call for IdeasCOPLFR Call for Ideas
1. What is an effective test for risk transfer?
2. What criteria should be used to determine whether a reinsurance contract transfers significant risk to the reinsurer?
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COPLFR Call for IdeasCOPLFR Call for Ideas
1. What is an effective test for risk transfer?
2. What criteria should be used to determine whether a reinsurance contract transfers significant risk to the reinsurer?
3. What safe harbors, if any, should be established so that a full risk transfer analysis does not have to be completed for each and every reinsurance contract (i.e., in what instances is risk transfer “reasonably self-evident” and therefore cash flow testing is not necessary to demonstrate risk transfer)?
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COPLFR Call for IdeasCOPLFR Call for Ideas
1. What is an effective test for risk transfer?
2. What criteria should be used to determine whether a reinsurance contract transfers significant risk to the reinsurer?
3. What safe harbors, if any, should be established so that a full risk transfer analysis does not have to be completed for each and every reinsurance contract (i.e., in what instances is risk transfer “reasonably self-evident” and therefore cash flow testing is not necessary to demonstrate risk transfer)?
4. What are the advantages and disadvantages of the suggested approach versus other approaches commonly used?
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Structure of PaperStructure of Paper
1. Introduction
2. Determining Whether the Contract Transfers “Substantially All” Underlying Insurance Risk
3. “Significant Risk” and the “10-10” Test
4. Toward a Better Test
5. Illustration of the ERD Test
6. Identification of Contracts Subject to “Significant” Risk Requirement that do not Require Individual Testing
7. Possible Evolution of Risk Transfer Measurement
8. Summary
9. Suggested Priorities for Further Research
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Section 1: IntroductionSection 1: Introduction
Context
Disclaimers
Background on FAS 113 / SSAP 62
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Background on FAS 113Background on FAS 113
Implemented 1993
SSAP 62 risk transfer provisions largely same as FAS 113
Effectively, SSAP 62 = FAS 113
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FAS 113 Risk Transfer RequirementFAS 113 Risk Transfer Requirement
One of 2 conditions must be met:
1. Reinsurer has assumed “substantially all” of the underlying reinsurance risk (Paragraph 11), or
2. Reinsurer has assumed “significant” insurance risk and it must be “reasonably possible” that the reinsurer may realize a “significant” loss from the transaction. (Paragraph 9)
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FAS 113 Risk Transfer Testing Flow ChartFAS 113 Risk Transfer Testing Flow Chart
Measure InsuranceRisk Transferred
By Contract
SubstantiallyAll?
Significant?
Book Contractas Reinsurance
No
No
Yes
Yes
Book Contractas Deposit
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Not a Critique of FAS 113Not a Critique of FAS 113
Working party agreed to treat FAS 113 as reasonable framework
Subject to fair interpretation of “substantially all”, “reasonably possible” and “significant”
Despite reservations about 1) focus only on reinsurer, and 2) definition of reinsurer loss
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Section 2: Determining Whether the Contract Section 2: Determining Whether the Contract Transfers “Substantially All” Underlying Transfers “Substantially All” Underlying
Insurance RiskInsurance Risk
Relevant risk is “downside risk”
If downside risk assumed by reinsurer is “same” as cedent’s downside risk on unreinsured portfolio, then contract transfers “substantially all” the insurance risk
Trivial case is prorata contract with flat ceding commission = cedent expense ratio and no cap, corridor, slides, PC
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Comparing Cedent and Reinsurer Downside Comparing Cedent and Reinsurer Downside RiskRisk
Two Methods Presented:
Compare cedent and reinsurer U/W margins in U/W loss scenarios
Compare cedent and reinsurer expected U/W deficits
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Comparing Cedent and Reinsurer Downside Comparing Cedent and Reinsurer Downside RiskRisk
Example 2.1Example 2.1
First dollar non-standard auto quota share
Ceding Commission: Minimum – 19.5% @ 73% L/R
1 : 1 slide
30% @ 62.5% L/R
.75 : 1 slide
Maximum – 39% @ 50.5% L/R
Cedent expense ratio = 20%
Cedent U/W breakeven = 80%
Reinsurer FAS 113 breakeven = 80.5%
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Comparing Cedent and Reinsurer Downside Comparing Cedent and Reinsurer Downside Risk-Method 1Risk-Method 1
CHART 1Cedent and Reinsurer Margins
Example 2.1
-40%
-20%
0%
20%
40%
60%
30% 50% 70% 90% 110%
Original Loss Ratio
Pro
fit M
argi
n %
Cedent Margin
Reinsurer Margin
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Comparing Cedent and Reinsurer Downside Comparing Cedent and Reinsurer Downside Risk-Method 2Risk-Method 2
Table 2“Substantially All” Risk Transfer Analysis – Method 2
Reinsurer vs. Cedent margins in Downside Scenarios Example 2.1
Breakeven Loss Ratio Freq(UL) Sev(UL) EUD
Cedent 80.0% 11.3% 8.3%
0.940%
Reinsurer 80.5% 10.5% 8.5% 0.886%
Difference -0.5% 0.8% -0.2% 0.054%
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Comparing Cedent and Reinsurer Downside Comparing Cedent and Reinsurer Downside RiskRisk
Example 2.1Example 2.1
“Substantially All” < “All”
Reinsurer downside risk only slightly less than cedent’s
“Substantially All” condition met (both methods)
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Comparing Cedent and Reinsurer Downside Comparing Cedent and Reinsurer Downside RiskRisk
Straightforward for prorata
Potentially applicable to excess, too
Other scenarios
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Section 3: “Significant” Risk Transfer and Section 3: “Significant” Risk Transfer and the “10-10” Testthe “10-10” Test
“10% chance of 10% loss” (“10-10” test) common benchmark for significance testing
Present value U/W result at 90th percentile is a loss ≥ 10% of p.v. premiums
VaR90% ≥ 10%
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Problems with “10-10”Problems with “10-10”
Not sufficiently discriminating
Some say “10-10” not stringent enough
Some traditional reinsurance contracts do not “pass”:o Low freq/high severity (typically XL)o High freq/low severity (typically QS)
Unintended consequences for reinsurance pricing
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““10-10” Cat Example 3.110-10” Cat Example 3.1
U/W result at 90th percentile is 10% profit
Contract “fails”
In practice, since everyone sees cat xl as risky, test failure typically ignored
Ad hoc exception for “cat” problematical – how much “cat” is enough to qualify?
TABLE 3Catastrophe Loss Distribution for Example 3.1
Cat Loss as
% of Limit
Cat Loss as % of
Premiums
Probability of Given
Loss
0% 0% 67%
5% 50% 20%
10% 100% 10%
100% 1000% 3%
5% 50% 100%
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““10-10” Quota Share Example 3.210-10” Quota Share Example 3.2
TABLE 4
On-Level Loss Ratio Experience
For Quota Share in Example 3.2
(1) (2) (3) (4) (5) (6) (7) (8)
Accident Year
Reported L/ R
Age to Ult Factors
Est Ult L/ R
Prem On-Level Factors
Loss On-Level Factors
On-Level L/ R
ix ln ix
1
92.8%
1.039
96.4%
1.963
1.364 67.0% -0.401
2 75.6% 1.048 79.3% 1.737 1.307 59.7% -0.516
3 77.0% 1.095 84.3% 1.376 1.246 76.4% -0.269
4 61.2% 1.141 69.9% 1.139 1.181 72.5% -0.321
5 52.5% 1.415 74.3% 1.061 1.111 77.8% -0.251
Mean x 70.7% -0.352
Var* 2s 0.554% 1.18%
*Unbiased St. Dev.* s 7.45% 10.88%
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““10-10” Quota Share Example 3.210-10” Quota Share Example 3.2
Pitfalls of fitting a distribution to on-level loss ratios
Adjustments to historical loss ratios often have smoothing effect
Importance of parameter uncertainty
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““10-10” Quota Share Example 3.210-10” Quota Share Example 3.2Sources of Parameter Uncertainty in On-Level Loss Sources of Parameter Uncertainty in On-Level Loss
Ratio EstimatesRatio Estimates
The ultimate loss estimates might be wrong;
The rate level history might be inaccurate;
The prospective rate changes assumptions might be wrong;
The historical claim trend estimates might be inaccurate;
The prospective claim trend assumptions might be wrong;
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““10-10” Quota Share Example 3.210-10” Quota Share Example 3.2More More Sources of Parameter Uncertainty in On-Level Sources of Parameter Uncertainty in On-Level
Loss Ratio EstimatesLoss Ratio Estimates
The prospective loss ratios might not be distributed according to chosen model (e.g. lognormal)
The distribution assumption (e.g. lognormal) is right, but the “best fit” parameters might not be the true parameters
Cash flow timing assumptions, particularly regarding claims, might be wrong
The prospective exposure mix might be different from expected
For multi-year reinsurance contracts, the level of parameter uncertainty from all sources increases as the length of the coverage period increases
Other
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““10-10” Quota Share Example 3.210-10” Quota Share Example 3.2
Fitted distribution (ignoring parameter uncertainty) yields VaR90% = 2% => contract “fails”
Adjusted distribution (for parameter uncertainty – judgmental) yields VaR90% = 6% => contract still “fails”
Does not seem like right result
Problem is with “10-10”
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““10-10” Quota Share Example 3.310-10” Quota Share Example 3.3 A quota share of a portfolio with expected volatility of S&P
500 (given by σ = VIX) would frequently “fail” the “10-10” test
Quota share with expected L/R = 70%, commission = 25%, one year claim lag, requires σ ≥ 21% to yield VaR90 ≥ 10%
Chart of historical expected S&P 500 volatility (VIX)
CHART 3
Source: Yahoo! Finance
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““10-10” Quota Share Example 3.310-10” Quota Share Example 3.3
Unless intention is to set the bar for significant risk at a level higher than the typical volatility of the S&P 500, the “10-10” test defines too high a threshold
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““10-10” Unintended Consequences for 10-10” Unintended Consequences for Reinsurance PricingReinsurance Pricing
Implies unrealistic price controls on reinsurers, especially for low volatility business
Excerpt from Table 6 shows minimum permissible loss ratios for contracts without commissions, interest @ 5%
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““10-10” Unintended Consequence for 10-10” Unintended Consequence for Reinsurance PricingReinsurance Pricing
TABLE 6
Minimum Permissible Loss RatioImplied by “10-10”
Contracts with No Ceding CommissionInterest at 5% per annum
By σ and Claim Lag
σ No Lag 1 Yr Lag 2 Yr Lag 3 Yr Lag
10.0% 97.3% 102.1% 107.2% 112.6%
12.0% 95.0% 99.8% 104.7% 110.0%
15.0% 91.8% 96.4% 101.2% 106.3%
20.0% 86.8% 91.2% 95.8% 100.5%
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Section 4: Toward a Better TestSection 4: Toward a Better Test
Two Major Shortcomings of “10-10”
Its focus on loss only at 90th percentile ignores information in the tail
o It would be better to take account of loss potential in right tail, which can be extreme (e.g. cat XL)
Its requirement that both probability and loss exceed 10% is arbitrary
o Why 10%?
o Why not “5-20”, “20-5”, etc.?
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Toward a Better TestToward a Better TestAddressing the First ShortcomingAddressing the First Shortcoming
Replace VaR90% with TVaR90%
TVaR90% = mean severity losses at and beyond 90th percentile
Idea suggested in VFIC’s 2000 paper
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Toward a Better TestToward a Better TestAddressing the Second ShortcomingAddressing the Second Shortcoming
Relax requirement that BOTH probability and severity of loss > 10%
Note that expected reinsurer deficit (ERD) = Freq(loss) x Sev(loss)
o Freq(loss) = Prob (p.v. loss > 0)o Sev(loss) = E(p.v. loss | p.v. loss > 0) = TVaR at breakeven
ERD reflects frequency and severity in a single measure
Define “significant” risk as ERD = Freq(loss) x Sev(loss) > A
We illustrate A = 1%
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Toward a Better TestToward a Better Test
ERD ≥ A is a variable TVaR standard:
Sev (loss) = TVaR1-Freq ≥ A Freq (loss)
ERD > A defines a “risk transfer frontier” that encompasses a wide variety of frequency – severity combinations
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Toward a Better TestToward a Better Test
CHART 6 Risk Transfer Frontier: ERD > 1% vs. Various TVaR
0%
20%
40%
60%
80%
100%
0% 20% 40% 60% 80% 100%
Frequency
Sev
erit
y
ERD
TVaR 10-10
TvaR 5-20
TVaR 20-5
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Toward a Better TestToward a Better Test
To address the issue of contracts that have been engineered
to remove most or all of the potential for loss in the right tail,
the paper suggests consideration of a supplemental
requirement that there be the potential for a reinsurer loss of
some minimum threshold, say, 15% or 20% of premiums.
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FAS 113 Risk Transfer Testing Flow Chart FAS 113 Risk Transfer Testing Flow Chart (Expanded)(Expanded)Measure InsuranceRisk Transferred
By Contract
SubstantiallyAll?
ERD > 1%?
Book Contractas Reinsurance
No
Yes
Yes
Book Contractas Deposit
MeasureSignificance
Downside> x?
No
Yes
No
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Section 5: Illustration of the Section 5: Illustration of the ERDERD Test Test(A = 1%)(A = 1%)
Cat XL example 3.1 now passes
Any Cat XL with rate on line < 50% passes
Primary QS example 3.2 now passes
Primary QS example 3.3 (S&P 500 volatility) passes more often
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Illustration of the Illustration of the ERDERD Test Test >> 1% Test 1% TestExpected Loss Ratio = 70% (Lognormal) with Expected Loss Ratio = 70% (Lognormal) with
Loss CorridorLoss Corridor
TABLE 9ERD Risk Transfer Analysis for
ContractWith 25% Ceding Commission and
Loss Ratio Corridor from 75% to 80%
σ Freq Sev ERD
10% 3.1% 3.2% 0.10%
15% 9.1% 6.0% 0.59%
20% 15.6% 9.2% 1.43%
25% 19.7% 12.6% 2.47%
30% 22.4% 16.2% 3.63%
40% 25.6% 23.9% 6.13%
50% 26.9% 32.4% 8.74%
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Illustration of the Illustration of the ERDERD Test Test >> 1% Test 1% TestExpected Loss Ratio = 70% (Lognormal) with Expected Loss Ratio = 70% (Lognormal) with
Loss CapLoss Cap
TABLE 10ERD Risk Transfer Analysis for
ContractWith 25% Ceding Commission and
Loss Ratio Cap of 95%
σ Freq Sev ERD
10% 11.0% 3.8% 0.41%
15% 19.5% 6.5% 1.27%
20% 24.5% 8.9% 2.18%
25% 27.6% 10.7% 2.94%
30% 29.4% 12.0% 3.53%
40% 31.1% 13.8% 4.29%
50% 31.4% 14.9% 4.69%
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Illustration of the Illustration of the ERDERD Test Test >> 1% Test 1% TestExcess Swing Plan ExampleExcess Swing Plan Example
CHART 7Excess Swing Plan Example
Claim Distribution
0%2%4%6%8%
10%12%
0 2 4 6 8 10 12 14 16 18 20 22
Claim Count
Pro
b
CHART 8 Excess Swing Plan Example
Premium Rate by Claim Count
0%
5%
10%
15%
20%
0 2 4 6 8 10 12 14 16 18 20 22
Claim Count
Pre
m R
ate
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Illustration of the Illustration of the ERDERD Test Test >> 1% Test 1% TestExcess Swing Plan ExampleExcess Swing Plan Example
TABLE 11ERD Risk Transfer Analysis
Swing-Rated vs. Flat-Rated Excess
Plan Rate Freq Sev ERD
Swing 9.71% 3.2% 30.4% 0.97%
Flat 11.43% 18.0% 26.2% 4.70%
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Illustration of the Illustration of the ERDERD Test Test >> 1% Test 1% TestIndividual Risks (Total Loss Analysis)Individual Risks (Total Loss Analysis)
TABLE 12
ERD / Max Downside For Individual Risk Contracts
By Rate on Line
Rate on Line
Limit Loss Prob
ERD
Reinsurer Max
Downside
0.5% 0.05% 9.95% 19900% 1.0% 0.10% 9.90% 9900% 2.5% 0.25% 9.75% 3900% 5.0% 0.50% 9.50% 1900% 10.0% 1.00% 9.00% 900% 25.0% 2.50% 7.50% 300% 50.0% 5.00% 5.00% 100% 75.0% 7.50% 2.50% 33% 83.3% 8.33% 1.67% 20% Assumptions. - Investment income effects ignored - Bernoulli probability of limit loss - Total limit loss ratio 10%
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Section 6: Identification of Contracts Subject Section 6: Identification of Contracts Subject to Significant Risk Requirement that Do Not to Significant Risk Requirement that Do Not
Require Individual TestingRequire Individual Testing
Individual testing of every contract would be burdensome (and unnecessary)
Paper shows that several groups of contracts will pass ERD ≥ 1% under very general conditions
o Individual risks
o Most cat XL contracts
o Most other XL contracts
o Contracts with expected L/R > minimum permissible loss ratio
o Contracts with immaterial premiums
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Section 7: Possible Evolution of Risk Transfer Section 7: Possible Evolution of Risk Transfer MeasurementMeasurement
Right Tail Deviation (RTD) framework (Wang)
Same framework for risk transfer testing and risk loading
Like ERD framework, Cat XL passes significance test
Method can address some highly structured contract scenarios
Most complex, less understandable to non-actuaries
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Section 8: SummarySection 8: SummaryResponse to COPLFR Question 1Response to COPLFR Question 1
1. What is an effective test for risk transfer?
Transfer of “Substantially All” Risk
o Comparison of cedent/reinsurer underwriting downside scenarios
o Comparison of cedent/reinsurer EUDs
Transfer of “Significant” Risk
o ERD Test
o RTD Test
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Section 8: SummarySection 8: SummaryResponse to COPLFR Question 2Response to COPLFR Question 2
2. What criteria should be used to determine whether a reinsurance contract transfers significant risk to the reinsurer?
ERD ≥ A (illustrated with A = 1%)
Possible supplemental requirement for minimum downside potential (perhaps 15% - 20%)
Alternatively, RTD framework Qualified Premium / Premium ≥ 100%
Other reasonable approaches
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Section 8: SummarySection 8: SummaryResponse to COPLFR Question 3Response to COPLFR Question 3
3. What safe harbors, if any, should be established so that a full risk transfer analysis does not have to be completed for each and every reinsurance contract (i.e., in what instances is risk transfer “reasonably self-evident” and therefore cash flow testing is not necessary to demonstrate risk transfer)?
Contracts meeting “substantially all” risk conditions don’t need to be tested for “significant” risk
Groups of contracts can be “pre-qualified” as containing significant risk on the basis of ERD ≥ 1 (examples):
o Individual risk contractso Short tail XL treaties in standard cat formato Other XL treaties with aggregate limits ≥ 1 occ/risk limit or
200% of premiums (whichever is greater)*o Treaties having expected loss ratio ≥ minimum permissible
loss ratio implied by ERD ≥ 1%o Contracts involving immaterial premiums
* No commission, ROL ≤ 500%
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Section 8: SummarySection 8: SummaryResponse to COPLFR Question 4Response to COPLFR Question 4
4. What are the advantages and disadvantages of the suggested approach versus other approaches commonly used?
At practical level, “10-10” is inadequate because it fails individual risk contracts, cat XL treaties, some primary QS treaties
At more conceptual level, “10-10” fails to account for risk in the tail, is arbitrary in requiring both 10% chance and 10% loss, frequently classifies S&P 500 as not significantly risky
At same time “10-10” reviewed by some as not stringent enough
ERD ≥ 1% with supplemental minimum downside potential requirement addresses all “10-10” shortcomings
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Section 9: Suggested Priorities for Further Section 9: Suggested Priorities for Further ResearchResearch
Consensus on Thresholds
° Difference between “all” and “substantially all”
° ERD ≥ A: What value of A is appropriate? Is 1% OK?
° Determination of contract categories that do not require individual testing because significance of risk can be demonstrated in advance.
Other
° Other methods for testing “substantially all” risk transfer
° Continued research on methods other than ERD (e.g., Wang’s RTD)
° Continued research on methods for dealing with parameter uncertainty