Reinsurance Structures,Pro Rata Pricing, & When Good Pricing Goes BadAugust 8, 2007

2

Proportional Reinsurance Structures

Straight Quota share- cede a percentage of losses for an identical percentage of premium. If the commission paid is commensurate with insurers costs, there is an alignment of interests.

1. Used to reduce premium writings relative to surplus

2. Generate commission overrides to offset expense and increase profit

Surplus Quota Share- A form of proportional reinsurance where the reinsurer assumes pro rata responsibility for only that portion of any risk which exceeds the company’s established retentions. May promote writing larger limits compared to historical experience

Promote writing riskier or more volatile business

Variable Quota Share – insured cedes different percentages of business depending on the limit – 0% of 5 M limit, 50% of 10 M limit, etc. Essentially, this can be viewed as a variable quota share contract wherein the reinsurer's pro rata share of insurance on individual risks will increase as the amount of insurance increases, given the same reinsurer's retained line, in order that the primary company can limit its net exposure to one line, regardless of the amount of insurance written

1. May promote the writing of larger or more hazardous risks going forward

2. Encourage reducing limits on more profitable business to improve net results

3

Commission Override Example

Premium L/R Commission Brokerage CompositeGross 50,000,000 65.0% 25.0% 2.0% 92.0%

Cede 40,000,000 65.0% 30.0% 2.0% 97.0%

Net 10,000,000 65.0% 5.0% 2.0% 72.0%

Premium L/R Commission Brokerage CompositeGross 50,000,000 90.0% 25.0% 2.0% 117.0%

Cede 40,000,000 90.0% 30.0% 2.0% 122.0%

Net 10,000,000 90.0% 5.0% 2.0% 97.0%

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Non Proportional Reinsurance

Excess of Loss Flat Rated

Can be appropriate when there is a standard limit and little variability in insured groups If limits vary, a flat rate may promoted more hazardous writing and large limits

Cessions Rated Better when there are a variety of limits or various hazards ceded

Facultative Individual risks – usually priced at higher profit margins than treaty

business. Obligatory – most similar to a treaty

Non-Obligatory Can be used with many types of reinsurance. It means that the insured

can pick what risks it wants to keep and cede the rest.Stop Loss

A form of reinsurance under which the reinsurer pays some or all of a cedant’s aggregate retained losses in excess of a predetermined dollar amount or in excess of a percentage of premium

Often significant adverse selection against reinsurers on these covers as the cedents have a better sense of the ultimate gross loss ratio than the reinsurer

Almost always includes a loss ratio cap May have risk transfer issues

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Basics of Pricing

Components Losses Paid/Reported

Paid Losses– trend issues Reported Losses – Reserve issues Large Losses Cat Losses Claim Counts Triangulations of Losses

Exposure Data Payroll Sales Square Footage Premium Doctors – Base Doctor Equivalents

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Adjustments

Loss DevelopmentTrend – Severity/FrequencyPremium On Level AdjustmentsExposure AdjustmentsAdjustments for Limits and Attachment/SIR ChangesLoading for catastropheFree coverLoad for ECO/XPLSumming claims for basket or aggregate coverLoad for ClashTort Reform

adjust trend adjust loss development Is tort reform retroactive?

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Loss Development Selection

IncurredLosses - PY

3 Months

15 Months

27 Months

39 Months

51 Months

63 Months

75 Months

87 Months

99 Months

1999 42,776 2,543,415 3,706,515 4,070,948 4,589,893 5,635,622 6,232,223 7,104,451 7,910,928

2000 18,265 3,063,379 4,439,324 4,952,021 5,210,846 5,184,224 5,678,068 5,849,854

2001 112,366 8,322,590 15,339,602 15,691,784 15,903,253 15,888,604 16,115,445

2002 114,280 8,189,697 16,424,303 18,293,479 20,109,521 20,102,536

2003 206,477 8,773,920 24,078,043 28,048,880 23,673,715

2004 214,908 8,748,828 16,251,552 16,401,519

2005 555,959 7,353,855 10,415,023

2006 531,988 10,820,728

2007 741,381

1999 59.46 1.46 1.10 1.13 1.23 1.11 1.14 1.11

2000 167.72 1.45 1.12 1.05 0.99 1.10 1.03

2001 74.07 1.84 1.02 1.01 1.00 1.01

2002 71.66 2.01 1.11 1.10 1.00

2003 42.49 2.74 1.16 0.84

2004 40.71 1.86 1.01

2005 13.23 1.42

2006 20.34

Strt Average 61.21 1.82 1.09 1.03 1.06 1.07 1.09 1.11 Tail Factor

Wtd Average 32.17 1.93 1.09 0.98 1.02 1.05 1.09 1.11

NCCI AY 1.395 1.075 1.03 1.019 1.014 1.011 1.009 1.086

Selected 32.17 1.93 1.09 1.00 1.02 1.03 1.03 1.03 1.09

Ultimate 82.68 2.57 1.33 1.22 1.22 1.19 1.16 1.12 1.09

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Umbrella Quota Shares use Excess Trend

Ground up Ground up 500,000 500,000

Losses Trend x/s x/s

@12/31/2006 1.05 500,000 500,000

Loss

1 100,000 105,000 - -

2 300,000 315,000 - -

3 500,000 525,000 - 25,000

4 900,000 945,000 400,000 445,000

Total 1,800,000 1,890,000 400,000 470,000

Overall trend 5% Excess trend 18%

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Excess Losses Deductibles and Layering

Excess Trending and Layering Example Trended Trended

Trended Loss Loss +

AY SIR Limit Loss LAE LAE/ Trend Loss + Loss + XS SIR LAE

(Loss+SIR) 5% SIR SIR XS 500 XS 500

2002 100,000 1,000,000 500,000 150,000 25.0% 1.276 600,000 765,769 165,769 207,211

2002 100,000 1,000,000 650,000 300,000 40.0% 1.276 750,000 957,211 357,211 500,096

2002 100,000 2,000,000 800,000 200,000 22.2% 1.276 900,000 1,148,653 500,000 611,111

2002 100,000 2,000,000 950,000 400,000 38.1% 1.276 1,050,000 1,340,096 500,000 690,476

2002 100,000 1,000,000 250,000 200,000 57.1% 1.276 350,000 446,699 - -

2002 100,000 1,000,000 400,000 300,000 60.0% 1.276 500,000 638,141 38,141 61,025

Total 600,000 8,000,000 3,550,000 1,550,000 4,150,000 5,296,568 1,561,121 2,069,919

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On Leveling Premium

Rate On Level Factors Parallelogram method or Premium at Present RatesPremium/Exposure Trend Yes if exposure base is inflationary

insured value Sales revenues

No if exposure base is square feet # vehicles # employees # doctors – should consider translating into base doctor

equivalents Trend from: Average accident date of experience period to average accident

date of prospective period

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On Leveling Premium

Rate Changes should consider changes to base rates, schedule credits and debits, tier rating, LCMs. They should also be adjusted for changes in limits and attachment points on the underlying policies.

Parallelogram method uses geometry to calculate on level factors.

Premium at Present Rates re-rates all historical policies using prospective rates.

Minimum Premiums can have a significant impact on rates. The impact is negative when rates are rising and positive when rates are falling. In a rate environment where rate increases have been significant the last few years the actual on level will be overstated.

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Actual Calculation for On Level Factor

Effective Date

Rate Change "Indexed" Cumulative

Calendar Year

Average Earned Level

On Level Factor

1.000 20011/1/2002 5.00% 105.00% 1.050 2002 1.025 1.268 1/1/2003 10.00% 110.00% 1.155 2003 1.103 1.179 1/1/2004 12.50% 112.50% 1.299 2004 1.227 1.059 1/1/2005 0.00% 100.00% 1.299 2005 1.299 1.000

Assume: Losses Occurring Treaty incepting 1/1/2005

12 1.000 1.050 1.155 1.299

mos

1.050 1.155 1.299 1.299

1/1/2002 1/1/2003 1/1/2004 1/1/20055.00% 10.00% 12.50% 0.00%

<---------------------------------------------->12 mos

Note - On leveling procedure is different for policies attaching

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Shifting Distributions and On Level Factors

Inputs Rate Changes Premium Premium %

(1) (2) (3) (4) (5) (6) (7)

Texas Florida Texas Florida Total Texas Florida

1/1/2002 -30% 0% 500 4,000 4,500 11% 89%

1/1/2003 -20% 0% 500 3,000 3,500 14% 86%

1/1/2004 10% 0% 1,000 1,000 2,000 50% 50%

1/1/2005 20% 30% 1,500 1,000 2,500 60% 40%

1/1/2006 15% 10% 2,000 1,000 3,000 67% 33%

1/1/2007 -10% 0% 2,000 750 2,750 73% 27%

Incorrect (8) (9) (10) (11)

Prem-Wtd 1 + (8) Rolling On-Level

Rate Change Product of (9) Factor

1/1/2002 -3% 0.967 0.967 1.329

1/1/2003 -3% 0.971 0.939 1.368

1/1/2004 5% 1.050 0.986 1.303

1/1/2005 24% 1.240 1.223 1.051

1/1/2006 13% 1.133 1.386 0.927

1/1/2007 -7% 0.927 1.285 1.000

Correct Texas Florida Total

(12) (13) (14) (15) (16) (17) (18)

1 + (1) Rolling On-Level 1 + (2) Rolling On Level Prem-Wtd

Product of (12) Factor Product of (15) Factor On-Level Facotr

1/1/2002 0.700 0.700 1.093 1.000 1.000 1.430 1.393

1/1/2003 0.800 0.560 1.366 1.000 1.000 1.430 1.421

1/1/2004 1.100 0.616 1.242 1.000 1.000 1.430 1.336

1/1/2005 1.200 0.739 1.035 1.300 1.300 1.100 1.061

1/1/2006 1.150 0.850 0.900 1.100 1.430 1.000 0.933

1/1/2007 0.900 0.765 1.000 1.000 1.430 1.000 1.000

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WC On Level Example

(1) (2) (3) (4) (5) (6)Rate Schedule Rate Change Change

Changes LCM Credit/Debit Changes in LCMin Sched. Cr/Dt1/1/2002 -30% 1.50 0% -30.0% 0.0% 0.0%1/1/2003 -20% 1.50 0% -20.0% 0.0% 0.0%1/1/2004 10% 1.50 5% 10.0% 0.0% 5.0%1/1/2005 20% 1.70 0% 20.0% 13.3% -4.8%1/1/2006 15% 1.70 -5% 15.0% 0.0% -5.0%1/1/2007 -10% 1.75 -10% -10.0% 2.9% -5.3%

(7) (8) (9) (10) (11) (12)1 + (4) 1 + (5) 1 + (6) (7)*(8)*(9) Rolling On-Level

Product of (10) Factor1/1/2002 70.0% 100.0% 100.0% 0.70 0.70 1.15 1/1/2003 80.0% 100.0% 100.0% 0.80 0.56 1.43 1/1/2004 110.0% 100.0% 105.0% 1.16 0.65 1.24 1/1/2005 120.0% 113.3% 95.2% 1.30 0.84 0.96 1/1/2006 115.0% 100.0% 95.0% 1.09 0.92 0.88 1/1/2007 90.0% 102.9% 94.7% 0.88 0.80 1.00

1. Calculate change for each piece2. Aggregate changes3. Calculate on level factors

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Change in Average Premium

Does not Equate to change in average rate

Heavy Trucks Light Trucks TotalPremium Trucks Average Premium Trucks Average Average

2005 2,000,000 400 5,000 1,000,000 400 2,500 3,750

2006 4,000,000 1,000 4,000 500,000 200 2,500 3,750

Total -20% 0% 0%

Actual Rate Change -17.8%

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Losses Occurring with Run-Off

Distortion to On – Level Factors if rates are decreasing

1/1/05 12/31/05 12/31/06

UEP = 1/3 of Treaty Premium

17

Risks Attaching with Cut-Off

Distortion to On – Level if rates are increasing

1/1/02 12/31/02 12/31/03

UEP = 1/2 of Treaty Premium

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Premium On Level Adjustments

Written Premium

Renewal Expiring Rate Actual Submission

Policy Policy Increase On Level On Level

2001 1,527,828 935,044 63% 2.86 5.00

2002 3,748,682 2,066,040 81% 1.58 3.02

2003 3,740,033 3,191,744 17% 1.35 1.65

2004 3,455,287 3,205,047 8% 1.25 1.39

2005 2,021,483 1,807,096 12% 1.12 1.28

2006 1,750,713 1,567,789 12% 1.00 1.13

2007 0% 1.00 1.00

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Limits/Attachments Adjustments

When a company’s limits and attachments have shifted, adjustments must be made to the analysis! Trend past historical limits – this will underestimate your

costs if the losses were truncated. Only works if the policy limits have adjusted due to inflation.

Price lower “fully exposed” layer and use exposure rating relativities to adjust to current layer. This approach is easiest if everything is fully exposed. If there are few losses in the layer, you need to convince yourself that the experience is not credible.

Adjust using exposure rating differential based on limits distribution profile in each year

Calculate a loss distribution based on current experience and run against new limits

Attachments shifting downwards are the easiest to adjust for by subtracting old attachment out after trending and adding new attachment

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Pricing for Contract Provisions

Multi-Year Policies- Need to consider the impact on trend and development for multi-year

policies Impact on the risk of a deal where your exposure now extends several

years. Funding Requirements – this is generally ignored in pricing but shouldn’t be

Requirement when rating or surplus drops or reinsurer stops writing new business. Companies that agreed to these provisions found themselves quickly out of business when there rating dropped.

Some Surety deals require funding at every 12/31 This usually require and LOC and this cost should be priced into the

business Errors & Omissions clauses covering business excluded by the treaty if

bound accidentally. Ex Gratia payments – anyone dealing with a large insured may find

themselves paying claims just to keep them happy. If the deal is marginal to begin with, this would eliminate some of the expected profit.

Some swing rated treaties allow for losses to be deemed $0 and pay only the minimum. It is important to look at the NPV of the deal in all situations and realize that the client will act to maximize that. The end result is that the likely outcomes will be minimum premiums until you are in a loss position.

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Select Projected Loss Cost

Select for Stability?Have there been changes in the writings. Tort Reform

Select for Responsiveness?Recent years effected by large development

factorsMature years may be over trended or rate

changes may be overstated.What if a company renews 60% of the book

each year?

Somewhere in the middle?

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Selecting Loss Costs

Bornhuetter-Ferguson Method - On Level 2007 Trended Ultimate Ultimate% Rptd Actual Loss Loss

AY EP Reported & LAE Ratio2001 97,136,535 58.4% 26,378,729 61,658,495 63%2002 245,497,267 45.5% 155,776,556 263,318,382 107%2003 311,053,329 38.8% 118,292,341 265,564,950 85%2004 313,876,233 29.5% 43,528,674 211,379,641 67%2005 324,899,561 31.7% 7,781,840 168,900,017 52%2006 295,755,900 14.6% 15,187,567 196,417,940 66%

2001-2005 1,292,462,924 351,758,141 970,821,485 75%All Years 1,588,218,824 366,945,707 1,167,239,425 73%

2001-2004 967,563,364 343,976,301 801,921,468 83%

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Selecting Ultimate Loss & LAE CostsBornhuetter-Ferguson Method - Projected to 2007 Levels

Trended Actual Expected ExpectedReported Ultimate Ultimate

Premium Expected Layer Layer Loss & ALAEPeriod On-Level Reported Loss & ALAE Loss & ALAE CostLO1-1997 30,273,314 98.2% 27,855,627 28,256,620 93.3%LO1-1998 30,698,075 95.6% 28,858,660 29,858,013 97.3%LO1-1999 33,463,360 93.6% 25,633,338 27,197,238 81.3%LO1-2000 37,888,220 92.7% 40,807,420 42,827,689 113.0%LO1-2001 59,286,210 92.1% 45,427,366 48,838,636 82.4%LO1-2002 81,502,437 91.2% 57,230,366 62,494,969 76.7%LO1-2003 102,264,131 88.7% 71,151,490 79,649,037 77.9%LO1-2004 77,529,317 82.4% 39,243,923 49,211,350 63.5%LO1-2005 67,579,183 74.0% 33,437,255 46,325,335 68.5%LO1-2006 66,791,355 49.5% 21,937,234 46,633,361 69.8%Total 587,275,602 391,582,677 461,292,249 78.5%2001-2006 454,952,632 268,427,633 333,152,689 73.2%

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Adjusting For Free Cover

Adjusting For Free CoverSelect

layer Exper LC LC

500K limit Gross 65.0% 62.5%

Exposure250K xs 250K 6.2% 6.5% 6.5%700K xs 300K 8.4% 6.5% 7.5%500K xs 500K 4.0% 2.7% 3.6%1M xs 1M 2.4% 2.2%3M xs 2M 1.6% 1.5%5M xs 5M 0.8% 0.7%Stat xs10 0.9% 0.8%

Stat XS 500 9.8% 8.8%Unlimited Gross 71.3%

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Other Considerations

“As If” A term used to restate the treaty statistics for prior years to accord

with the current (or proposed) limits, terms and conditions Sometimes also used to show results as if exceptional losses had not occurred.

1. “As If” – short for “As If I only wrote profitable business”1. Exclude line of business no longer written

Does it exclude both losses and premium? Did it also impact the rate changes as well?

2. Exclude these losses since they are excluded from the treaty. There are always exposures not included and there will always be exposures included now but not included in the future.

3. Excludes Underwriter “F” 4. Current insureds only – BEWARE – this is an “as if” in disguise5. Do you get to exclude future losses from business they will

decide to get out of next year? If not, beware of “as if” results.

2.

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Another “as if”

“as If” I wrote the same distributionThis is harder to dispute since the basis is well

grounded in actuarial science. Take the historical losses and premium and adjust it to the current exposures written. If the book was predominantly GL and now it

is predominantly products we should adjust the mix to the current business mix.

If the book is predominantly Texas historically and is currently Missouri we should adjust the historical state experience to match the current mix.

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State Distribution Mix

Texas Only All OtherTrended, Developed Trended ULT Trended ULT Trended ULT Trended ULTUltimate Projections Onlevel EP Loss Net LR Onlevel EP Loss Net LR7/1/2001 - 6/30/2002 20,414,358 5,988,236 29.3% 19,988,919 1,767,808 8.8%7/1/2002 - 6/30/2003 12,110,112 9,175,143 75.8% 13,943,125 1,553,672 11.1%7/1/2003 - 6/30/2004 4,907,744 2,098,588 42.8% 3,893,848 675,617 17.4%7/1/2004 - 6/30/2005 1,707,479 1,773,972 103.9% 3,513,549 966,226 27.5%7/1/2005 - 6/30/2006 651,002 267,741 41.1% 3,345,209 2,531,425 75.7%7/1/2006 - 3/31/2007 56,079 30,079 53.6% 1,414,658 758,768 53.6%Total 01-06 39,790,695 19,303,679 48.5% 44,684,650 7,494,749 16.8%

TotalTrended ULT Trended ULT

Onlevel EP Loss Net LR40,403,277 7,756,044 19.2%26,053,237 10,728,815 41.2%8,801,593 2,774,205 31.5%5,221,027 2,740,198 52.5%3,996,211 2,799,166 70.0%1,470,737 788,847 53.6%

84,475,345 26,798,427 31.7%

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Pricing New Business – Start Ups

The class of “2001” created several insurance and reinsurance start ups. Many of these companies wanted reinsurance and had no experience. For them the “clean slate” was a plus. What information is available to price start up.

Similar treaty business – Can this treaty perform significantly better than established books of similar business?

New business is bought with cheaper prices Benchmarking Rate comparisons

Overall industry experience Stat Bulletins – NCCI, ISO One Source – Annual Statement Data Broker or Trade Group Studies External or Internal actuarial rate studies

Pricing hurdles for start ups. Return requirements – should they be higher? Execution risk Different structure for a start ups – lower cede, loss ratio cap, loss

corridors or sliding scale commission What happens when the only business you write in a line are start

ups? Time to question the pricing assumptions