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

Reinsurance Products Requiring Adjustments to Capital Model: 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? NWP capital factors Net loss & LAE reserve capital factors Surplus Credit risk Potential Shock Loss (PMLs) Stress Tests

Origin of NWP Risk Capital Factors

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

Impact of Traditional Quota Share on NWP Risk Capital Factors

Impact of Capped Quota Share on NWP Risk Capital Factors

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

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

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

Impact of Adverse Development Cover on Reserve Risk Required Capital

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

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

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

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

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

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: 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.

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 1 0.35 0.35 Exhaustion prob. 1 0.25 0.25 Peril 3 0.10 0.30 Peril modeler 3 0.10 0.30 Data quality 3 0.10 0.30 Certainty of bus. 2 0.10 0.20 Total 1.70 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%.

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%

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

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

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

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.

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%

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.

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

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