1. Reinsurance and Rating Agency Models
Thomas M. Mount, ACAS, MAAA
A.M. Best Company

2. Reinsurance Products Requiring Adjustments to Capital Model:
Capped Quota Share
Aggregate Stop Loss
Loss Portfolio Transfers
Adverse Development Covers
Catastrophe Bonds
Sidecars

3. Where do Frequent Adjustments to BCAR Occur due to Reinsurance?
NWP capital factors
Net loss & LAE reserve capital factors
Surplus
Credit risk
Potential Shock Loss (PMLs)
Stress Tests

4. Origin of NWP Risk Capital Factors

5. Origin of Reserve Risk Capital Factors
Industry Reserve Capital Factor Calc.
0.5 1
1.5 2
2.5
-30%
-20%
-10% 0%
10%
20%
30%
40%
(Favorable)/Adverse Reserve Development % of Original Reserves
1% in tail
zero
defic.
99%
capital factor

6. Impact of Traditional Quota Share on NWP Risk Capital Factors

7. Impact of Capped Quota Share on NWP Risk Capital Factors

8. Capped Quota Share Summary of Impact on BCAR
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

9. Impact of Aggregate Stop Loss on APHS and Reserve Risk Required Capital

10. Aggregate Stop Loss Summary of Impact on BCAR
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

11. Impact of Adverse Development Cover on Reserve Risk Required Capital

12. Adverse Development Cover Summary of Impact on BCAR
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

13. 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
Direct impact on balance sheet strength & FSR

14. Effect of Reinsurance on Stress Test
What does BCAR score look like after first event happens?
Potentially Main driver of our view of balance sheet strength
Look at Impact of 1st event on insurer’s balance sheet:
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
Add to reserve page if exposed to potential development on the booked loss
Use 80% of net loss

15. Effect of Reinsurance on Stress Test
After all those adjustments:
STILL EXPOSED TO A SECOND EVENT !!!
Reduce surplus by second event
Larger of 1/100 Wind, 1/100 EQ, or Recent actual event
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
Better than aggregate season
Validated in 2004, 2005

16. Effect of Reinsurance on Stress Test
Stressed BCAR can fall up to 30 points from current required capital as determined by committee
15 points for most cos (i.e. 1 FSR level)
30 points for cos with
Good Catastrophe management
Financial Flexibility
Potentially Greater Flexibility for Dedicated Subs of Strong Parent Companies
Issue is willingness to recapitalize

17. 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.

18. Measuring Basis Risk: Mechanical Steps
AMBest’s method of estimating basis risk:
Calculate a score based on a scoring table and correlate the score to a reinsurance credit table*.
Calculate a ratio based on PML impact that directly ties to reinsurance credit*.
Take the lesser of the results from steps 1 and 2.
Other considerations.
* Information used in this calculation is provided by the peril modeler or sponsor.

19. Complete Step 1: Basis Risk Score
Index Re Basis Risk Scoring Table
Sum up weighted score (ie, 1.70)
Determine Basis Risk Score based on the following AMB table:
Score
Weight
Wt x Score
Shortfall
Exhaustion prob
Peril
Peril modeler
Data quality
Certainty of bus
Total
Scoring-based reins credit 81%
AMB Scoring-Based
Reinsurance Credit Scale
Summed
Basis Risk
Score
Credit
90% 1
75% 2
50% 3
30% 4
10% 5
81%
1.70
Scoring-based reinsurance credit is 81%.

20. Step 2 - Capital Effectiveness Ratio
PML Before Adding the Effect of the Bond – PML After Adding the Effect of the Bond
Capital
Effectiveness =
Ratio
90% x
Bond Principal Balance
$800,000,000 – $700,000,000
= 90% x
$125,000,000
= 90% x 80.0%
= 72%

21. Step 3: Absolute Reinsurance Credit
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

22. Cat Bond Summary
Indemnity based – 100% credit for modeled impact in PML layer
Parametric/Indexed/Modeled – reduced credit due to basis risk
Amount of reins credit given to Cat Bond IMPACTS balance sheet strength & FSR of issuer

23. Sidecars – Role of Structured Finance Group
Rate the debt of sidecars and, where appropriate, issue ICRs.
Calculate the “tail risk” to insure the appropriate reinsurance credit is given to the sponsor of the sidecar

24. Determining Tail Risk?
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.

25. AMBest’s Assumed One -Yr Average Impairment Rates
FSR Rating
Annual Default Probability
Return Period
Confidence Interval
0.03%
3,333
99.97%
0.06%
1,667
99.94%
0.21%
476
99.79%
0.27%
370
99.73%

26. Sidecar’s Aggregate Exceedence Curve
Confidence Interval
Return Period
Stressed* Losses
(Stress factor: 110%)
Losses
90.00%
96.00%
98.00%
99.00%
99.60%
99.73%
99.80% 10 25 50
100
250
370
500
100,000
150,000
200,000
250,000
300,000
330,000
350,000
110,000
165,000
220,000
275,000
330,000
363,000
385,000
*Use stressed losses if not confident with modeled loss.

27. Calculating Tail Risk: Illustration
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 A-
0.27%
99.73%
$363,000
$110,000
$53,000
$163,000
$200,000 v u u u v w w 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

28. Sidecar Summary Modeling of AEP curves extremely important
Direct impact on the balance sheet strength & FSR of the sponsor