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Reinsurance Structures
and On Level Loss Ratios
Reinsurance Boot Camp
July 2005
Agenda
 Reinsurance Structures
 Calculating an On Level Loss Ratio
•
•
•
•
•
Adjustments to Premium
Adjustments to Losses
Adding in a Catastrophe/Shock load
Dealing with a change in mix of business
Filling in the gaps when data is unavailable
2
Reinsurance Structures
 Standard Structures
• Pro Rata
• Excess of Loss
 NonStandard Structures
• Stop Loss
• Loss Portfolio Transfer
3
What is a Pro Rata Treaty?
 The cedant agrees to share x% of the premium and x% of




the losses of a book of business.
The reinsurer returns some of the premium to the cedant
in the form of a ceding commission.
One Pro Rata Structure, a Quota Share, cedes the same
percentage on all risks.
A Variable Quota Share may cede different percentages
for different limits.
A Surplus Share allows the cedant to retain a given
amount, called a ‘line’, on any one risk and cede the
remaining ‘lines’ to reinsurers.
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Variable Quota Share
Policy Sizes:
10M
5M
1M
% of book
LR
% ceded to VQS
40.00%
50.00%
0.00%
Loss Ratio if this were a QS
Loss Ratio if this were a VQS
50.00%
55.00%
40.00%
54.0%
58.1%
5
10.00%
65.00%
90.00%
Surplus Share
5M
5M
5M
5M
5M
1 line
1 line
1 line
1 line
1 line
<------------------------------ --------------- ------------------------------>
$25M Capacity for any risk
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Uses for Pro Rata Treaties
 Surplus Relief

• Pro Rata Structures reduce net premium which improves
(decreases) the cedant’s net-premium-to surplus ratio
• The ceding commission increases the cedant’s surplus, also
improving (decreasing) the net-premium-to-surplus ratio.
Combined Ratio Improvement, in some cases
• Although straight Pro Rata Structures do not improve loss
ratios, the cedant’s actual overall results can improve if the
ceding commission received exceeds the cedant’s actual
expenses (an “override”).
• Cedant’s overall portfolio results COULD be worse if they
end up ceding out very profitable business instead of
keeping it net.
7
What would I care about if I were
pricing a Pro Rata Treaty?
 Expected Loss Ratio for the covered business
 Volatility of Loss Ratio/Loss Sensitive Features
 Cedant’s actual expenses
 Alignment of Interests
8
Other concerns  Variable QS
• Do I have the appropriate data to estimate a
loss ratio by limit?
 Surplus Share
• Do I have surplus share data that represents
the current line guide?
9
What is an Excess of Loss Treaty?
 For any loss, the cedant retains the first x
dollars and cedes out the next y dollars, in
exchange for premium.
• Per Risk
• Per Occurrence
 Example: 9M x 1M per occurrence
• For a loss sustained on any given
occurrence, the cedant keeps the first 1M
and the reinsurer picks up the next 9M.
10
Uses for Excess of Loss Treaties
 Stabilize loss experience
 Catastrophe Protection
 Increased Risk Capacity
11
What would I care about if I were
pricing an Excess of Loss Treaty?
 Frequency of Layer Losses
 Severity of Layer Losses
 Volatility of Loss Ratio/Loss Sensitive Features
 Alignment of Interests
12
What is a Stop Loss Treaty and
what is it used for?
 The cedant retains the first x of aggregate
losses and cedes out the next y of aggregate
losses to a reinsurer in exchange for premium.
 X can either be a percentage or a fixed dollar
amount
 Stabilizes net results
 Example: 10% excess of a 70% net loss ratio in
exchange for 3% premium.
13
What would I care about if I were
pricing a Stop Loss Treaty?
 Expected Loss Ratio for the covered business
 Volatility around the Loss Ratio
 Special Funding features
 Alignment of Interests
 Accounting considerations
14
What is a Loss Portfolio Transfer
and what is it used for?
 The cedant gives a block of loss reserves to a
reinsurer in exchange for premium.
 Premium considers the discounted value of
those reserves along with a risk charge.
 Enables the cedant to cleanly exit a line of
business and focus on their ‘going concern’
portfolio.
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What would I care about if I were
pricing a Loss Portfolio Transfer?
 Loss Reserve Adequacy
 Latent Liabilities
 Interest Rate Assumptions
 Alignment of Interests
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Calculating an On Level Loss Ratio
 Essential for pricing almost any prospective
reinsurance structure.
 Historical years of premium are adjusted to the
prospective period’s rate and dollar levels.
 Historical years of losses are adjusted to an
ultimate settled basis and trended to the
prospective period’s dollar levels.
 Adjusted losses are ratio-ed to adjusted
premium for an on level loss ratio.
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Data Needs - Premium
 Historical Premium
•
•
•
•
Earned Premium if Losses Occurring treaty
Written Premium if Risks Attaching treaty
Historical Rate Changes
Premium/Exposure Trend if Exposure Base
is Inflation Sensitive
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Data Needs - Losses
 Historical Paid a/o Incurred Losses and ALAE
•
•
•
•
•
Accident Year if Losses Occurring treaty
Policy Year if Risks Attaching treaty
Loss Development Triangle
Loss Trend
Catastrophe/Shock losses separately
19
Adjustments to Premium
 Rate On Level Factors
• Parallelogram method
• Premium at Present Rates
 Premium/Exposure Trend
• Yes if exposure base is insured value, sales,
revenues, etc.
• No if exposure base is square feet, per
vehicle, per employee, per doctor, etc.
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Rate On Level Factors
 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.
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Rate On Level Factors
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
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1.000
1.050
1.155
1.299
m
o
s
1.050
1/1/2002
5.00%
1.155
1.299
1/1/2003
10.00%
1/1/2004
12.50%
<---------------------------------------------->
12 mos
22
1.299
1/1/2005
0.00%
Premium/Exposure Trend
 Trend from:
• Average Earned Date of experience period
for Losses Occurring
• Average Written Date of experience period
for Risks Attaching
 Trend to:
• Average Earned Date of prospective period
for Losses Occurring
• Average Written Date of prospective period
for Risks Attaching
23
Adjustments to Losses
 Catastrophe/Shock losses should be separated out.
 “NonCat” Incurred Losses need to be adjusted to
ultimate, settled basis.
• Use cedant’s own loss development triangle
• Supplement with industry/peer data if necessary
 Ultimate, settled “noncat” losses need to be trended to
prospective period.
• Trend from average date of loss of experience period
• Trend to average date of loss of prospective period
24
Incurred Loss Development
Triangle (in thousands)
Accident
Year
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
3
1,149
1,245
1,181
973
986
773
611
606
1,011
754
707
789
797
15
8,460
5,672
5,432
5,289
5,881
5,202
4,487
4,332
5,352
3,878
3,513
4,690
-
27
9,433
6,133
6,913
6,124
7,187
6,080
6,609
5,651
6,274
4,914
4,677
-
39
10,176
6,816
6,955
7,714
8,281
7,184
7,165
6,369
7,713
5,999
-
51
10,782
6,951
7,453
7,762
8,737
7,663
7,646
6,758
8,684
-
63
11,050
7,071
7,881
8,172
8,896
8,006
7,723
7,554
-
25
75
11,152
6,977
7,894
8,222
8,920
8,196
7,782
-
87
11,143
7,009
7,905
8,305
8,950
8,310
-
99
11,129
7,039
7,907
8,314
8,967
-
111
11,134
7,040
7,908
8,318
-
123
11,134
7,042
7,908
-
135
11,134
7,098
-
147
11,134
-
Loss Development (cont’d)
Age to Age Factors or Link Ratios
Accident Year
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
3-15
7.3650
4.5540
4.6000
5.4360
5.9650
6.7280
7.3470
7.1500
5.2950
5.1430
4.9670
5.9470
15-27
1.1150
1.0810
1.2730
1.1580
1.2220
1.1690
1.4730
1.3040
1.1720
1.2670
1.3320
27-39
1.0790
1.1110
1.0060
1.2600
1.1520
1.1820
1.0840
1.1270
1.2290
1.2210
39-51
1.0600
1.0200
1.0720
1.0060
1.0550
1.0670
1.0670
1.0610
1.1260
51-63
1.0250
1.0170
1.0570
1.0530
1.0180
1.0450
1.0100
1.1180
63-75
1.0090
0.9870
1.0020
1.0060
1.0030
1.0240
1.0080
75-87
0.9990
1.0050
1.0010
1.0100
1.0030
1.0140
87-99
0.9990
1.0040
1.0000
1.0010
1.0020
99-111 111-123 123-135 135-147
1.0000 1.0000 1.0000 1.0000
1.0000 1.0000 1.0080
1.0000 1.0000
1.0000
147-Ult
A-A Averages
3 Yr Weighted
5 Yr Weighted
All Yr Weighted
Industry A-A
3-15
5.3692
5.6288
5.7665
15-27
1.2450
1.3044
1.2174
1.5055
27-39
1.1925
1.1660
1.1386
1.2383
39-51
1.0867
1.0757
1.0595
1.1096
51-63
1.0551
1.0463
1.0408
1.0490
63-75
1.0111
1.0083
1.0059
1.0234
75-87
1.0090
1.0067
1.0051
1.0121
87-99
1.0011
1.0010
1.0010
1.0070
99-111 111-123 123-135 135-147
1.0003 1.0001
147-Ult
1.0000
1.0034
1.0209
15-27
1.3044
15-Ult
1.7817
27-39
1.1660
27-Ult
1.3659
39-51
1.0757
39-Ult
1.1714
51-63
1.0463
51-Ult
1.0890
63-75
1.0083
63-Ult
1.0409
75-87
1.0067
75-Ult
1.0323
87-99
1.0010
87-Ult
1.0254
99-111 111-123 123-135 135-147
1.0003 1.0001 1.0031 1.0000
99-Ult
111-Ult 123-Ult 135-Ult
1.0244 1.0240 1.0240 1.0209
147-Ult
1.0209
147-Ult
1.0209
Selected A-A
Cumulative
3-15
5.6288
3-Ult
10.0285
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1.0003
1.0042
1.0001
1.0043
1.0031
1.0034
Developing Incurred Losses
Accident
Year
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
Incurred to
Date
11,133,572
7,097,812
7,908,201
8,318,037
8,967,305
8,310,435
7,782,007
7,554,340
8,683,535
5,998,513
4,677,324
4,690,465
797,387
As of
147
135
123
111
99
87
75
63
51
39
27
15
3
27
A-U LDF
1.0209
1.0209
1.0240
1.0240
1.0244
1.0254
1.0323
1.0409
1.0890
1.1714
1.3659
1.7817
10.0285
Ultimate
Incurred
11,366,031
7,245,896
8,097,903
8,518,076
9,186,060
8,521,576
8,033,571
7,863,045
9,456,709
7,026,830
6,388,595
8,356,805
7,996,613
Loss Trend
Accident
Year
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
Loss Trend
5.00%
5.00%
5.00%
5.00%
5.00%
5.00%
5.00%
5.00%
5.00%
5.00%
5.00%
5.00%
5.00%
Trend
Ultimate
Losses
Adjusted
Losses
1.7959
1.7103
1.6289
1.5513
1.4775
1.4071
1.3401
1.2763
1.2155
1.1576
1.1025
1.0500
7,245,896
8,097,903
8,518,076
9,186,060
8,521,576
8,033,571
7,863,045
9,456,709
7,026,830
6,388,595
8,356,805
7,996,613
13,012,589
13,850,162
13,875,048
14,250,593
12,590,249
11,304,041
10,537,233
12,069,424
8,541,155
7,395,598
9,213,377
8,396,443
Trending from Average Date of Loss of Experience Period
To Average Date of Loss of Prospective Period
Assume Losses Occurring Treaty incepting 1/1/2005
To Average Date of Loss of Prospective Period is 7/1/2005
28
On Level Loss Ratios: Making a Selection
 Select for Stability?
 Select for Responsiveness?
 Somewhere in the middle?
29
Stability versus Responsiveness
Accident
Year
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
All Yrs
Last 5 Yrs
Adjusted
Premium
Adjusted Losses
On Level Loss
Ratio
14,489,888
13,221,211
14,472,544
16,611,175
16,999,150
15,608,719
15,017,621
14,808,196
14,007,255
13,864,945
15,192,489
16,798,050
13,012,589
13,850,162
13,875,048
14,250,593
12,590,249
11,304,041
10,537,233
12,069,424
8,541,155
7,395,598
9,213,377
8,396,443
89.80%
104.76%
95.87%
85.79%
74.06%
72.42%
70.17%
81.51%
60.98%
53.34%
60.64%
49.98%
181,091,243
74,670,934
135,035,911
45,615,997
74.57%
61.09%
Selection
67.83%
30
Adding a Catastrophe Load
 Catastrophe Load
• By definition, catastrophes are low
frequency, high severity.
• Your experience period may not even
have had such a loss…yet…
• There are plenty of catastrophe exposure
models available for property however.
• Catastrophe experience should be
reviewed, but given little weight due to its
inherently volatile nature.
31
Adding a Shock Load
 Loss Experience versus Loss Exposure
 Calculate a limited loss ratio at low stable level.
 Add a load for larger losses that you are
exposed to, but haven’t experienced yet.
• Use exposure curves to add an excess
charge above that limited level
• Amortize in some large but possible loss
32
Dealing with a Shift in Business Mix
 A loss ratio analysis done on an “all lines
combined” basis will miss shifts in the business
mix.
 Should analyze each line of business
separately and then weight results on
prospective premium by line.
33
Dealing with Start-Ups and No Data
 New line of business for a company
 New company altogether
34
What to think about in “no data” situations
 Competitor experience or rate comparisons, but
consider:
• Growing pains/distractions in new line
• Competitive advantage?
• Position in the market cycle?
• “Burning your way in”
• Track record at prior carriers
• Rating of current carrier/current paper
• Company infrastructure established?
• Smaller but growing book and volatility
35