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Profit Share Reinsurance document sample
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Reinsurance Structures,
Pro Rata Pricing,
& When Good Pricing Goes Bad
August 8, 2007
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
2
Commission Override Example
Premium L/R Commission Brokerage Composite
Gross 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 Composite
Gross 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%
3
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
4
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
5
Adjustments
Loss Development
Trend – Severity/Frequency
Premium On Level Adjustments
Exposure Adjustments
Adjustments for Limits and Attachment/SIR Changes
Loading for catastrophe
Free cover
Load for ECO/XPL
Summing claims for basket or aggregate cover
Load for Clash
Tort Reform
adjust trend
adjust loss development
Is tort reform retroactive?
6
Loss Development Selection
Incurred
Losses - 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
7
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%
8
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
9
On Leveling Premium
Rate On Level Factors
Parallelogram method or Premium at Present Rates
Premium/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
10
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.
11
Actual Calculation for On Level Factor
Average
Effective Rate Calendar Earned On Level
Date Change "Indexed" Cumulative Year Level Factor
1.000 2001
1/1/2002 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
m
o
s
1.050 1.155 1.299 1.299
1/1/2002 1/1/2003 1/1/2004 1/1/2005
5.00% 10.00% 12.50% 0.00%
-
<--------------------------------------------->
12 mos
Note - On leveling procedure is different for policies attaching
12
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
13
WC On Level Example
(1) (2) (3) (4) (5) (6)
Rate Schedule Rate Change Change
Changes LCM Credit/Debit Changes in LCMin Sched. Cr/Dt
1/1/2002 -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) Factor
1/1/2002 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 piece
2. Aggregate changes
3. Calculate on level factors
14
Change in Average Premium
Does not Equate to change in average rate
Heavy Trucks Light Trucks Total
Premium 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%
15
Losses Occurring with Run-Off
Distortion to On – Level Factors if rates are
decreasing
UEP = 1/3 of Treaty
Premium
1/1/05 12/31/05 12/31/06
16
Risks Attaching with Cut-Off
Distortion to On – Level if rates are increasing
UEP = 1/2 of Treaty
Premium
1/1/02 12/31/02 12/31/03
17
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
18
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
19
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.
20
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 factors
Mature 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?
21
Selecting Loss Costs
Bornhuetter-Ferguson Method - On Level 2007 Trended Ultimate Ultimate
% Rptd Actual Loss Loss
AY EP Reported & LAE Ratio
2001 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%
22
Selecting Ultimate Loss & LAE Costs
Bornhuetter-Ferguson Method - Projected to 2007 Levels
Trended Actual Expected Expected
Reported Ultimate Ultimate
Premium Expected Layer Layer Loss & ALAE
Period On-Level Reported Loss & ALAE Loss & ALAE Cost
LO1-1997 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%
23
Adjusting For Free Cover
Adjusting For Free Cover
Select
layer Exper LC LC
500K limit Gross 65.0% 62.5%
Exposure
250K 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%
24
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 disguise
5. 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.
25
Another “as if”
“as If” I wrote the same distribution
This 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.
26
State Distribution Mix
Texas Only All Other
Trended, Developed Trended ULT Trended ULT Trended ULT Trended ULT
Ultimate Projections Onlevel EP Loss Net LR Onlevel EP Loss Net LR
7/1/2001 - 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%
Total
Trended ULT Trended ULT
Onlevel EP Loss Net LR
40,403,277 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%
27
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
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