Adding a Cat Load to Property Reinsurance

Pricing

One Reinsurer’s ApproachJune 1, 2005 - CAGNY

2

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

3

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!

4

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.

5

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?

6

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

7

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)

8

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.

9

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?

10

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?

11

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.

12

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

13

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 Loss Ratio Flat Commis

Cost of Comm Adj & Profit Comm Brokerage

Combined Ratio

10.0% 49.06% 27.50% 1.03% 1.00% 78.59%20.0% 51.99% 27.50% 0.15% 1.00% 80.64%30.0% 54.50% 27.50% 0.00% 1.00% 83.00%40.0% 56.82% 27.50% 0.00% 1.00% 85.32%50.0% 59.08% 27.50% 0.00% 1.00% 87.58%60.0% 61.31% 27.50% 0.00% 1.00% 89.81%70.0% 63.74% 27.50% 0.00% 1.00% 92.24%80.0% 67.02% 27.50% 0.00% 1.00% 95.52%90.0% 72.02% 27.50% 0.00% 1.00% 100.52%95.0% 76.11% 27.50% 0.00% 1.00% 104.61%98.0% 80.85% 27.50% 0.00% 1.00% 109.35%99.0% 83.48% 27.50% 0.00% 1.00% 111.98%99.9% 91.22% 27.50% 0.00% 1.00% 119.72%

Average: 60.00% 27.50% 0.26% 1.00% 88.76%

14

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 CDF Cat Loss $$$'sCat Loss

Ratios

1 50.0% 0 0.00%2 60.0% 5,600,000 11.20%3 70.0% 17,200,000 34.40%4 80.0% 27,000,000 54.00%5 85.0% 35,000,000 70.00%6 90.0% 42,000,000 84.00%7 95.0% 53,000,000 106.00%8 97.5% 71,000,000 142.00%9 99.0% 101,000,000 202.00%

10 99.9% 135,000,000 270.00%

15

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 Probability Loss Ratio

Flat Commis

Cost of Comm Adj & Profit

Comm BrokerageCombined

Ratio10.0% 27.51% 27.50% 7.50% 1.00% 63.51%20.0% 29.16% 27.50% 7.00% 1.00% 64.66%30.0% 30.68% 27.50% 6.55% 1.00% 65.73%40.0% 32.66% 27.50% 5.95% 1.00% 67.11%50.0% 37.79% 27.50% 4.41% 1.00% 70.70%60.0% 59.50% 27.50% 0.00% 1.00% 88.00%70.0% 77.98% 27.50% 0.00% 1.00% 106.48%80.0% 94.13% 27.50% 0.00% 1.00% 122.63%90.0% 131.31% 27.50% 0.00% 1.00% 159.81%95.0% 169.04% 27.50% 0.00% 1.00% 197.54%98.0% 231.51% 27.50% 0.00% 1.00% 260.01%99.0% 236.67% 27.50% 0.00% 1.00% 265.17%99.9% 303.57% 27.50% 0.00% 1.00% 332.07%

Average: 60.00% 27.50% 3.67% 1.00% 92.17%

16

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.

17

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?

18

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.

19