Reinsurance and
Rating Agency Models
Thomas M. Mount, ACAS, MAAA
A.M. Best Company
Reinsurance Products Requiring
Adjustments to Capital Model:
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Capped Quota Share
Aggregate Stop Loss
Loss Portfolio Transfers
Adverse Development Covers
Catastrophe Bonds
Sidecars
Where do Frequent Adjustments to
BCAR Occur due to Reinsurance?
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NWP capital factors
Net loss & LAE reserve capital factors
Surplus
Credit risk
Potential Shock Loss (PMLs)
Stress Tests
Origin of NWP Risk
Capital Factors
Lognorm(1.9607, 0.11756) Shift=-2.0183
6
5
1% in tail
4
3
2
1
0
-0.5
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
(Profit)/Loss % (All years)
industry
mean
break
even
Capital factor
99%
0.4
Origin of Reserve Risk
Capital Factors
Industry Reserve Capital Factor Calc.
2.5
2
1% in tail
1.5
1
0.5
0
-30%
-20%
-10%
0%
10%
20%
30%
(Favorable)/Adverse Reserve Development % of Original Reserves
zero
defic.
capital factor
99%
40%
Impact of Traditional Quota Share on
NWP Risk Capital Factors
Treatment of Traditional Quota Share
Capital Charge = 31% of NWP
100% of
NWP Risk to
Primary Company
31% of
Reinsurer's NWP
20% of
NWP Risk to
Primary Co.
80% of
NWP Risk to
Reinsurer
31% of
Primary Co's NWP
ELR = 78%
100% of
NWP
Primary Company
80% of
NWP
Reinsurer
BEFORE Quota Share
Assumptions:
Primary Co. NWP = $100M
Capital Charge = 31%
BCAR Treatment: Primary Co. NWP = $100M
(pg 6)
Primary Co. NWP Required Capital = $31M
20% of
NWP
Primary Co.
AFTER Quota Share
Assumptions:
Primary Co. cedes 80%
Primary Co. NWP after QS = $20M
Capital Charge = 31%
BCAR Treatment: Primary Co. NWP = $20M
(pg 6)
Primary Co. NWP Required Capital = $6.2M
Impact of Capped Quota Share on
NWP Risk Capital Factors
109%
16% of Reinsurer's NWP
31% of
Reinsurer's NWP
Risk to Primary Company
93%
15% of Reinsurer's NWP
Risk to
Primary
Co.
31% of
Primary Co's NWP
Risk To Reinsurer
78%
80% Share to
Reinsurer
20% Share to
Primary Co.
AFTER Quota Share and Loss Ratio Cap
Assumptions:
BCAR Treatment:
(pg 6)
Primary Co. cedes 80%
Primary Co. NWP after QS = $20M
Capital Charge = 31% (prior to QS transactions)
Reinsurer Maximum Loss Ratio = 93%
Primary Company's Ultimate Loss Ratio = 78% (prior to QS transactions)
Primary Co. NWP = $20M
Primary Co. NWP Required Capital = $6.2M + $12.8M = $19.0M
= .31 * $20M + .16 * 80M
Primary Co. Capital Factor = .95 (after QS transactions)
= $19M of Req Capital / $20M of NWP
Capped Quota Share
Summary of Impact on BCAR
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NWP capital factors increased to reflect retained
risk in excess of retained premium
Additional premium charges, sliding scale
contingent commissions, etc can also increase
retained risk
Smaller impact on reserve capital factors
Reinsurance dependence factor may increase
Credit risk required capital increases
Overall BCAR is Improved - due to transfer of risk
to reinsurer but at a rate lower than cession
percentage
Impact of Aggregate Stop Loss on
APHS and Reserve Risk Required Capital
Company With ASL
Company Without ASL
Required Capital
$26 M
Required Capital
$26 M
75% LR
ceded to ASL
$100 M Undisct'd
Initial Assumptions:
Reported Surplus
Pre ASL Reserve
Reserves ceded to ASL
Net Reserve after ASL
Deficiency
Needed Reserve for Required Capital calc
Discount Factor
Discnt'd Needed Reserve for Required Capital Calc
Capital Factor
Required Capital
Reserve Equity
Surplus Gain from ASL
APHS
215
100
100
0
0
100
85
85
0.300
26
15
15
215
75% LR
Reported Reserve
$100 M Undisct'd
M
M
M
M
M
M
%
M
M
M
M
M
Initial Assumptions:
Reported Surplus
Pre ASL Reserve
Reserves ceded to ASL
Net Reserve after ASL
Deficiency
Needed Reserve for Required Capital calc
Discount Factor
Discnt'd Needed Reserve for Required Capital Calc
Capital Factor
Required Capital
Reserve Equity
Surplus Gain from ASL
APHS
200
100
0
100
0
100
85
85
0.300
26
15
0
215
M
M
M
M
M
M
%
M
M
M
M
M
Aggregate Stop Loss
Summary of Impact on BCAR
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ASL can impact premium and reserve risks
Benefit to premium and reserves depends on layer
ceded
Always need to add back ceded premium
Need to increase reserve required capital by amount
of required capital on ceded reserve
Schedule P may be distorted, Deficiency distorted
Reinsurance recoverables increased
Reinsurance dependence factor increased
Credit risk required capital increased
Overall BCAR improves depending on the layer ceded
Impact of Adverse Development Cover on
Reserve Risk Required Capital
206,590
306,590
0
150,000
250,000
0
Capital Charge
Dollars
Ceded Layer
Deficiency
Booked Reserves
1,000,000
1,000,000
Before ADC
After ADC
as of 12/31/01
Adverse Development Cover
Summary of Impact on BCAR
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Surplus increased for prepaid deficiency
Surplus reduced for cost of ADC
Reserve required capital reduced
Reinsurance recoverables increased
Reinsurance dependence factor increased
Credit risk required capital increased
Overall BCAR is Improved - due to transfer of
reserve risk to reinsurer
Effect of Reinsurance on
Modeled PML

Published capital score (BCAR)

Surplus reduced by first event
Greater of 1/100 Wind,1/250 EQ, Recent actual loss
 Per Occurrence curve
 Net of reinsurance
 Gross of reinstatement prem
 Net of 35% FIT
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Direct impact on balance sheet strength & FSR
Effect of Reinsurance on Stress Test
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What does BCAR score look like after first event
happens?
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Potentially Main driver of our view of balance sheet
strength
Look at Impact of 1st event on insurer’s balance
sheet:
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Surplus reduced by 1st event
Recoverables go up by ceded portion of 1st event loss (we
use 80% of recoverable)
Downgrade reinsurers one FSR level (incr credit risk)
Net reserves increase by pre-tax net loss
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Add to reserve page if exposed to potential development on the
booked loss
Use 80% of net loss
Effect of Reinsurance on Stress Test
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After all those adjustments:
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STILL EXPOSED TO A SECOND EVENT !!!
Reduce surplus by second event
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Larger of 1/100 Wind, 1/100 EQ, or Recent actual event
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Net of reins, gross of reinstate, net of 35% FIT, per occur
Direct Impact on balance sheet strength and FSR
Wanted 2 separate large per occurrence events
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Better than aggregate season
Validated in 2004, 2005
Effect of Reinsurance on Stress Test
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Stressed BCAR can fall up to 30 points from
current required capital as determined by
committee
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15 points for most cos (i.e. 1 FSR level)
30 points for cos with
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Good Catastrophe management
Financial Flexibility
Potentially Greater Flexibility for Dedicated Subs of Strong
Parent Companies
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Issue is willingness to recapitalize
CAT Bonds:
Why Does AMBest Measure Basis Risk?
AMBest’s
objective in measuring basis risk
is to determine how much reinsurance
credit should be given to certain types of
parametric* Cat Bonds in the BCAR
analysis.
*For the purpose of this document and discussion, AMB considers non-indemnity
catastrophe bonds as parametric catastrophe bonds.
Measuring Basis Risk: Mechanical Steps
AMBest’s method of estimating basis risk:
1.
Calculate a score based on a scoring table and
correlate the score to a reinsurance credit table*.
2.
Calculate a ratio based on PML impact that directly
ties to reinsurance credit*.
3.
Take the lesser of the results from steps 1 and 2.
4.
Other considerations.
* Information used in this calculation is provided by the peril modeler or
sponsor.
Complete Step 1: Basis Risk Score
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Sum up weighted score (ie, 1.70)
Determine Basis Risk Score based on
the following AMB table:
AMB Scoring-Based
Reinsurance Credit Scale
Credit
Summed
Basis Risk
Score
90%
1
75%
2
50%
3
30%
4
10%
5
81%

1.70
Scoring-based reinsurance credit is 81%.
Index Re Basis Risk Scoring Table
Score Weight Wt x Score
Shortfall
1 0.35
Exhaustion prob. 1 0.25
Peril
3 0.10
Peril modeler
3 0.10
Data quality
3 0.10
Certainty of bus. 2 0.10
Total
Scoring-based reins credit
0.35
0.25
0.30
0.30
0.30
0.20
1.70
81%
Step 2 - Capital Effectiveness Ratio
Capital
Effectiveness =
Ratio
90% x
PML Before Adding the Effect
of the Bond – PML After
Adding the Effect of the Bond
Bond Principal Balance
= 90% x
$800,000,000 – $700,000,000
= 90% x 80.0%
= 72%
$125,000,000
Step 3: Absolute Reinsurance Credit
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Absolute reinsurance credit is the lower of:
 Scoring-based reinsurance credit (step 1)
 Capital effectiveness ratio (step 2)
The reinsurance credit is 72% of Cat Bond
issue, calculated as follows:
72% x $125 mil = $90.0 mil
81%
72%
The adjusted per Occurrence PML is:
= per Occurrence PML - Reinsurance Credit Amount
= $750 mil - $90 mil
= $660 mil
Compare to:
 Taking full limit credit = $625 = $750 - $125
 Taking modeled credit = $650 = $750 - $100
Cat Bond Summary
based – 100% credit for
modeled impact in PML layer
Indemnity
– reduced
credit due to basis risk
Parametric/Indexed/Modeled
Amount
of reins credit given to Cat Bond
IMPACTS balance sheet strength & FSR of
issuer
Sidecars –
Role of Structured Finance Group
1.
Rate the debt of sidecars and, where
appropriate, issue ICRs.
2.
Calculate the “tail risk” to insure the appropriate
reinsurance credit is given to the sponsor of the
sidecar
Determining Tail Risk?
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Tail Risk is the risk that must be borne by the
sponsor if the sidecar is not sufficiently
capitalized to support the reinsurance
transaction.
In order to determine Tail Risk, the following
question must be asked: “What capital level
is required in order to maintain a sidecar’s
assumed FSR?”
The “shadow rating” for the sidecar is the
same as that of the sponsoring company.
AMBest’s Assumed One -Yr Average
Impairment Rates
A+
A
A-
Annual Default Probability 0.03%
0.06%
0.21%
0.27%
Return Period
3,333
1,667
476
370
Confidence Interval
99.97%
99.94%
99.79%
99.73%
FSR Rating
A++
Sidecar’s Aggregate Exceedence Curve
Confidence
Interval
Return
Period
Losses
Stressed*
Losses
(Stress factor: 110%)
90.00%
10
100,000
110,000
96.00%
25
150,000
165,000
98.00%
50
200,000
220,000
99.00%
100
250,000
275,000
99.60%
250
300,000
330,000
99.73%
370
330,000
363,000
99.80%
500
350,000
385,000
*Use stressed losses if not confident with modeled loss.
Calculating Tail Risk: Illustration
1.
2.
3.
4.
5.
6.
7.
8.
9.
Aggregate Exceedence Curve
Shadow Rating of the sidecar
Annual Default Probability assoc with FSR
Confidence Interval
Obtain the Required Collateral
Initial Sidecar Collateral
Retained Cash
Total Sidecar Collateral (step 6 + step 7)
Tail Risk:
= Max
0, Required Collateral (step 5) – Total Collateral (step 8)
Previous page
A0.27%
99.73%
$363,000
$110,000
$53,000
$163,000
$200,000
u Source: AMBest’s Assumed 1-Year Average Impairment Rates table
v Source: Sidecar Aggregate Exceedence Curve table
w Source: Sidecar’s pro-forma Financial Statements
v
u
u
u
v
w
w
Sidecar Summary
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Modeling of AEP curves extremely
important
Direct impact on the balance sheet
strength & FSR of the sponsor