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.
2.
Used to reduce premium writings relative to surplus
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.
2.
May promote the writing of larger or more hazardous risks going forward
Encourage reducing limits on more profitable business to improve net results
2
Commission Override Example
Gross
Premium
50,000,000
L/R
65.0%
Commission
25.0%
Brokerage
2.0%
Composite
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%
Gross
Premium
50,000,000
L/R
90.0%
Commission
25.0%
Brokerage
2.0%
Composite
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
7,910,928
1999
42,776
2,543,415
3,706,515
4,070,948
4,589,893
5,635,622
6,232,223
7,104,451
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
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
Wtd Average
32.17
NCCI AY
1.82
1.09
1.03
1.06
1.02
1.93
1.09
0.98
1.395
1.075
1.03
1.00
1.22
Selected
32.17
1.93
1.09
Ultimate
82.68
2.57
1.33
7
1.07
1.09
1.11
1.11
Tail Factor
1.05
1.09
1.11
1.014
1.011
1.009
1.086
1.02
1.03
1.03
1.03
1.09
1.22
1.19
1.16
1.12
1.09
1.019
Umbrella Quota Shares use Excess Trend
Ground up
Ground up
Losses
Trend
@12/31/2006
1.05
500,000
x/s
500,000
x/s
500,000
500,000
Loss
1
100,000
105,000
-
-
2
300,000
315,000
-
-
3
500,000
525,000
-
4
900,000
945,000
400,000
445,000
Total
1,800,000
1,890,000
400,000
470,000
Overall trend
5%
8
Excess trend
25,000
18%
Excess Losses Deductibles and
Layering
Excess Trending and Layering Example
Trended
AY
Total
SIR
Limit
Loss
LAE
Trended
Trended
Loss
Loss +
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
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
Effective
Date
Rate
Change
1/1/2002
1/1/2003
1/1/2004
1/1/2005
5.00%
10.00%
12.50%
0.00%
"Indexed"
Calendar
Year
2001
2002
2003
2004
2005
Cumulative
1.000
1.050
1.155
1.299
1.299
105.00%
110.00%
112.50%
100.00%
Average
Earned
Level
On Level
Factor
1.025
1.103
1.227
1.299
1.268
1.179
1.059
1.000
Assume: Losses Occurring Treaty incepting 1/1/2005
12
1.000
1.050
1.155
1.299
m
o
s
1.050
1/1/2002
5.00%
1.155
1/1/2003
10.00%
<---------------------------------------------->
12 mos
Note - On leveling procedure is different for policies attaching
12
1.299
1/1/2004
12.50%
1.299
1/1/2005
0.00%
Shifting Distributions and On Level Factors
Inputs
Rate Changes
Premium
(1)
(2)
Texas
Florida
Premium %
(3)
Texas
(4)
(5)
(6)
(7)
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)
Prem-Wtd
1 + (8)
Rate Change
(10)
(11)
Rolling
On-Level
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
1/1/2002
1/1/2003
1/1/2004
1/1/2005
1/1/2006
1/1/2007
(1)
Rate
Changes
-30%
-20%
10%
20%
15%
-10%
(7)
1 + (4)
1/1/2002
1/1/2003
1/1/2004
1/1/2005
1/1/2006
1/1/2007
70.0%
80.0%
110.0%
120.0%
115.0%
90.0%
(2)
(3)
Schedule
LCM Credit/Debit
1.50
0%
1.50
0%
1.50
5%
1.70
0%
1.70
-5%
1.75
-10%
(8)
1 + (5)
(9)
1 + (6)
100.0%
100.0%
100.0%
113.3%
100.0%
102.9%
100.0%
100.0%
105.0%
95.2%
95.0%
94.7%
1. Calculate change for each piece
2. Aggregate changes
3. Calculate on level factors
14
(4)
Rate
Changes
-30.0%
-20.0%
10.0%
20.0%
15.0%
-10.0%
(5)
(6)
Change Change
in LCMin Sched. Cr/Dt
0.0%
0.0%
0.0%
0.0%
0.0%
5.0%
13.3%
-4.8%
0.0%
-5.0%
2.9%
-5.3%
(10)
(11)
(12)
(7)*(8)*(9) Rolling On-Level
Product of (10) Factor
0.70
0.70
1.15
0.80
0.56
1.43
1.16
0.65
1.24
1.30
0.84
0.96
1.09
0.92
0.88
0.88
0.80
1.00
Change in Average Premium
Does not Equate to change in average rate
Heavy Trucks
Premium
Light Trucks
Total
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%
Actual Rate Change
-17.8%
15
0%
0%
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
16
12/31/06
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
17
12/31/03
Premium On Level Adjustments
Written Premium
Renewal
Expiring
Policy
Policy
Rate
Increase
Actual
Submission
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
0%
1.00
1.00
2007
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
% Rptd
AY
EP
2001
97,136,535
58.4%
2002
245,497,267
45.5%
2003
311,053,329
38.8%
2004
313,876,233
29.5%
2005
324,899,561
31.7%
2006
295,755,900
14.6%
2001-2005
All Years
2001-2004
1,292,462,924
1,588,218,824
967,563,364
22
Trended
Actual
Reported
26,378,729
155,776,556
118,292,341
43,528,674
7,781,840
15,187,567
Ultimate
Loss
61,658,495
263,318,382
265,564,950
211,379,641
168,900,017
196,417,940
351,758,141
366,945,707
343,976,301
970,821,485
1,167,239,425
801,921,468
Ultimate
Loss
& LAE Ratio
63%
107%
85%
67%
52%
66%
75%
73%
83%
Selecting Ultimate Loss & LAE Costs
Bornhuetter-Ferguson Method - Projected to 2007 Levels
Trended Actual
Reported
Premium
Expected
Layer
Period
On-Level
Reported
Loss & ALAE
LO1-1997
30,273,314
98.2%
27,855,627
LO1-1998
30,698,075
95.6%
28,858,660
LO1-1999
33,463,360
93.6%
25,633,338
LO1-2000
37,888,220
92.7%
40,807,420
LO1-2001
59,286,210
92.1%
45,427,366
LO1-2002
81,502,437
91.2%
57,230,366
LO1-2003
102,264,131
88.7%
71,151,490
LO1-2004
77,529,317
82.4%
39,243,923
LO1-2005
67,579,183
74.0%
33,437,255
LO1-2006
66,791,355
49.5%
21,937,234
Total
587,275,602
391,582,677
2001-2006
454,952,632
268,427,633
23
Expected
Ultimate
Layer
Loss & ALAE
28,256,620
29,858,013
27,197,238
42,827,689
48,838,636
62,494,969
79,649,037
49,211,350
46,325,335
46,633,361
461,292,249
333,152,689
Expected
Ultimate
Loss & ALAE
Cost
93.3%
97.3%
81.3%
113.0%
82.4%
76.7%
77.9%
63.5%
68.5%
69.8%
78.5%
73.2%
Adjusting For Free Cover
Adjusting For Free Cover
layer
Exper LC
500K limit Gross
250K xs 250K
700K xs 300K
500K xs 500K
1M xs 1M
3M xs 2M
5M xs 5M
Stat xs10
Stat XS 500
Unlimited Gross
Exposure
6.2%
8.4%
4.0%
2.4%
1.6%
0.8%
0.9%
Select
LC
65.0%
62.5%
6.5%
6.5%
2.7%
6.5%
7.5%
3.6%
2.2%
1.5%
0.7%
0.8%
9.8%
8.8%
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
Trended, Developed
Ultimate Projections
7/1/2001 - 6/30/2002
7/1/2002 - 6/30/2003
7/1/2003 - 6/30/2004
7/1/2004 - 6/30/2005
7/1/2005 - 6/30/2006
7/1/2006 - 3/31/2007
Total 01-06
Onlevel EP
20,414,358
12,110,112
4,907,744
1,707,479
651,002
56,079
39,790,695
All Other
Trended ULT
Trended ULT
Loss
Net LR
5,988,236
29.3%
9,175,143
75.8%
2,098,588
42.8%
1,773,972
103.9%
267,741
41.1%
30,079
53.6%
19,303,679
48.5%
Onlevel EP
19,988,919
13,943,125
3,893,848
3,513,549
3,345,209
1,414,658
44,684,650
Total
Onlevel EP
40,403,277
26,053,237
8,801,593
5,221,027
3,996,211
1,470,737
84,475,345
27
Trended ULT Trended ULT
Loss
Net LR
7,756,044
19.2%
10,728,815
41.2%
2,774,205
31.5%
2,740,198
52.5%
2,799,166
70.0%
788,847
53.6%
26,798,427
31.7%
Trended ULT Trended ULT
Loss
Net LR
1,767,808
8.8%
1,553,672
11.1%
675,617
17.4%
966,226
27.5%
2,531,425
75.7%
758,768
53.6%
7,494,749
16.8%
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
28