Adding a Cat Load to
Property Reinsurance
Pricing
One Reinsurer’s Approach
June 1, 2005 - CAGNY
Agenda
 Early Disclaimers
 Property Reinsurance Pricing: Laying the
Groundwork before adding a Cat Load
 What do you do with Cat Modeling Input and
Output?
 How do you incorporate a Cat Load into Cash
Flow Modeling?
 Can you judge a company by its Cat Modeling?
 Questions/Comments
2
Early Disclaimers
 Scope of discussion




• Not HOW to run cat models
• Rather, analyzing inputs and outputs
Focus on RMS
Types of treaties
• Per Risk
• Quota Shares
• Endurance in N.A. doesn’t price pure cat treaties
More ways to “skin the cat” than presented here
Comments and suggestions welcome!
3
Property Reinsurance Pricing:
Getting the ball rolling…
 Analyze cat vs. non-cat separately
 Exposure rate
• PSOLD, Loss to Value Curves, etc.
• Use gross non-cat loss ratios
 Experience rate
• Both non-cat and cat only basis
• Consider including some cats in non-cat
analysis
• Hurricanes w/significant flood (Floyd, Allison)
• Tornado and hail events
 Once non-cat burn is selected, add cat load
 Monte Carlo Simulation models are used to value
any loss sensitive features.
4
Examining your EDM: Avoiding
“Garbage in, Garbage out”
 EDM Content
• Perils
• Regions
 Examine “Post Import Summary”
• % of locations with
• street address
• construction code
• occupancy code
• Compare to prior years’ Summary
• Compare TIVs with limits profile
 How old is the EDM?
5
Trending the EDM prior to modeling
 “Average exposure date”: 6 months prior to EDM date
stamp
• Example: Date Stamp = 12/31/2004
• EDM has policies in force at 12/31/2004
• These policies incept 1/1/2004 - 12/31/2004
• 7/1/2004 is average exposure date
 Trend TIVs to prospective treaty period
• Average prospective date of loss = ‘trend to’ date
• Damage curve based on property values at time of
loss
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Dealing with your Output: What do
you do with your results?
 Treaty cat loss ratio
•
•
(Modeled treaty cat loss) / (Inforce on-leveled premium)
Onlevel consistent with EDM date stamp
 Note: not PROSPECTIVE Subject Premium!
•
Ratio would be too low if real growth in portfolio.
• Example: 2004 EDM produces losses of 2M
• 2004 WP = 20M
• 2005 WP = 35M due to expansive growth
• Cat loss ratio = 2M / 20M
 On-level for rate changes.
•
Otherwise, ratio too low if there were rate decreases
• Example: 2004 EDM produces losses of 3M
• 2004 WP = 30M
• Onlevel 2004 premium at 2005 rates = 25M
• Cat loss ratio = 3M / 25M
 Adjust for any part of Subject Premium not covered by cat
model (e.g. International)
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What happens if you only get aggregate
cat modeling data for a per risk treaty?
 Suppose client unable to provide EDM
• If Unicede file (aggregate data) available, run
Catrader to get gross losses
 Use gross cat loss ratio in exposure rating model
• Allow property curves to layer gross cat losses
• We reselect curves that give more weight to wind
 There may be other methods to consider, but since we
are more of an RMS company, this is what we do.
8
Examining your Cat Experience
 Take a longer time horizon
• Example: may choose 5 year average for
non-cat, but all year average for cat
 Has the book shifted?
• More coastal exposure?
• Change in management?
• Other?
9
How do you choose between Cat
Experience and Cat Modeling Results?
 Shifts in the book





• Has management changed the book’s direction?
• Limits shifting up or down
• More or less cat exposed
• Changes in terms and conditions
Loss data quality
EDM data quality
Validity of Cat Model for these exposures & policies
Agreement of modeled results with recent experience
How much weight would you EVER give to cat
experience anyway?
10
Loss Sensitive Features: Why
including a Cat Distribution matters
 If you model all your property exposure using
just one distribution, you are likely missing the
inherent volatility in the cat; you are
subsequently understating the value that the
loss sensitive feature could have. This could
lead you to make a decision that you may one
day regret.
 And that day usually happens between August
and November, in places like Florida.
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Example:
 Assumptions:
•
•
•
•
•
•
•
•
Subject Premium = 50M
Total Loss Ratio = 60%
Non-cat Loss Ratio = 30%
Cat Loss Ratio = 30%
Ceding Commission = 27.5%
Brokerage = 1%
Profit Commission = 30% after 20%
One year deal; no deficit/credit carryforwards
considered
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What your results look like if you use a
lognormal to model all losses together
 Assume a mean of 60%
with a CV of 15%
Aggregate Distribution of Profitability Statistics
Cumulative
Probability
10.0%
20.0%
30.0%
40.0%
50.0%
60.0%
70.0%
80.0%
90.0%
95.0%
98.0%
99.0%
99.9%
Average:
Loss Ratio
Flat Commis
49.06%
27.50%
51.99%
27.50%
54.50%
27.50%
56.82%
27.50%
59.08%
27.50%
61.31%
27.50%
63.74%
27.50%
67.02%
27.50%
72.02%
27.50%
76.11%
27.50%
80.85%
27.50%
83.48%
27.50%
91.22%
27.50%
60.00%
27.50%
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Cost of
Comm Adj &
Profit Comm
1.03%
0.15%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.26%
Brokerage
1.00%
1.00%
1.00%
1.00%
1.00%
1.00%
1.00%
1.00%
1.00%
1.00%
1.00%
1.00%
1.00%
1.00%
Combined
Ratio
78.59%
80.64%
83.00%
85.32%
87.58%
89.81%
92.24%
95.52%
100.52%
104.61%
109.35%
111.98%
119.72%
88.76%
Modeling the Cat and Non-Cat
separately - Assumptions
 Assume a non-cat mean of 30% with a CV of 10%, a
cat mean of 30% and a cat distribution from RMS’s
AEP curve.
SP
50,000,000
Scenario
1
2
3
4
5
6
7
8
9
10
CDF
50.0%
60.0%
70.0%
80.0%
85.0%
90.0%
95.0%
97.5%
99.0%
99.9%
Cat Loss $$$'s
0
5,600,000
17,200,000
27,000,000
35,000,000
42,000,000
53,000,000
71,000,000
101,000,000
135,000,000
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Cat Loss
Ratios
0.00%
11.20%
34.40%
54.00%
70.00%
84.00%
106.00%
142.00%
202.00%
270.00%
What your results look like if you model
the Cat and Non-Cat separately
 Using the assumptions on
the previous page:
Aggregate Distribution of Profitability Statistics
Cumulative
Flat
Probability
Loss Ratio Commis
10.0%
27.51%
27.50%
20.0%
29.16%
27.50%
30.0%
30.68%
27.50%
40.0%
32.66%
27.50%
50.0%
37.79%
27.50%
60.0%
59.50%
27.50%
70.0%
77.98%
27.50%
80.0%
94.13%
27.50%
90.0% 131.31%
27.50%
95.0% 169.04%
27.50%
98.0% 231.51%
27.50%
99.0% 236.67%
27.50%
99.9% 303.57%
27.50%
Average:
60.00%
27.50%
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Cost of Comm
Adj & Profit
Comm
Brokerage
7.50%
1.00%
7.00%
1.00%
6.55%
1.00%
5.95%
1.00%
4.41%
1.00%
0.00%
1.00%
0.00%
1.00%
0.00%
1.00%
0.00%
1.00%
0.00%
1.00%
0.00%
1.00%
0.00%
1.00%
0.00%
1.00%
3.67%
1.00%
Combined
Ratio
63.51%
64.66%
65.73%
67.11%
70.70%
88.00%
106.48%
122.63%
159.81%
197.54%
260.01%
265.17%
332.07%
92.17%
Can you judge a company by its
Cat Modeling?
 Meeting the company’s cat modeler can clarify
• Company’s pricing of property business
• How company assesses cat risk
• How much company values data quality
• How well company can monitor and control its book
 Understanding what the client deems important can give
you great insight over whether they are someone you
even want to reinsure.
 Any reinsurer has finite cat capacity: so must rank
clients to reflect differing levels of quality in making
underwriting decisions.
16
The Spanish Inquisition: Cat Style
 Do you run Riskbrowser “pre-binding” or “post








binding”?
Do you run all regions for all perils?
How diligent are you about capturing street address?
Construction code? Occupancy code?
Do you “turn on” demand surge? Storm surge?
What about secondary uncertainty?
How do you think about capital allocation?
How often do you “roll up” your portfolio?
How often do you inspect insured locations?
Do you use an external source to help keep up with
proper valuations?
Do you really know the values of those 25,000
locations on that large schedule of properties?
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Some definitions
 Primary uncertainty
• Whether or not an event will occur, and if an event
does occur, which event it will be.
 Secondary uncertainty
• Uncertainty in the size of loss, given that a specific event
has occurred.
 Demand Surge
• Increases in claims costs following a major event, due
to economic, social, and operational factors in the
post-event environment.
 Storm surge
• Rising ocean water levels along hurricane coastlines
that can cause widespread flooding.
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