CONFIDENTIAL MATERIALS

CATASTROPHE MODELING, PORTFOLIO BUILDING AND

OPTIMIZATION

2

Why Use Multiple Models ?

Natural Bias Any model encompasses inherent biases

Input data and methodology Technical biases of the developer Simple errors and inconsistencies

Single model users nearly always “optimise into the model”

Single model users are very susceptible to model change

Assessing/Normalising Model Bias Independent hazard/vulnerability tests

No-one knows the “right” answer – some reasonability should apply Complexities of wind speed vs loss makes comparison difficult

Internal consistency Many simple tests for this e.g. compare expected loss costs by Country and sub region Information easily obtainable within the model

3

European WindstormNumber of Countries with losses in Recent Events

Taking major events of last 30 years how many countries had meaningful losses in each event (>$50m)?

Vendors Reinsurer A Reinsurer BCapella 5 4 487J 5 4 3Daria 6 7 6Herta 5 5 3Vivian 5 8 5Wiebke 5 7 3Anatol 4 3 4Lothar 4 3 3Martin 4 2 2Jeanette 4 4 4Erwin 4 4 4

Avg 4.64 4.64 3.73

4

European WindstormModel Diversity

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

Ratio of the event

set

1 2 3 4 5 6 7 8 9 10 11 12

Number of countries hit

Pan European Events

Model A (2.754)

Model B (5.922)

Model C (6.335)

5

European wind% Events hitting each country

MODEL A raw MODEL B raw MODEL C raw

Europe Frequency 2.7554 5.92286 6.335775

Europe 100.0% 100.0% 100.0%

Belgium 33.5% 9.0% 40.6%

Denmark 39.4% 15.9% 37.4%

France 69.4% 21.7% 48.4%

Germany 51.3% 14.9% 55.0%

Netherlands 40.4% 45.7% 49.8%

Switzerland 52.8% - -

UK 86.6% 87.0% 72.4%

Austria 44.1% - 0.0%

Sweden 63.6% 22.4% 37.8%

Ireland 76.7% 22.8% 59.0%

6

European windstormInternal Consistency

Looking at expected loss cost and at the 99th percentile - the spread is large

Check Denmark for internal consistency comparing Res/Com for models A and C – Which relationship makes most sense ?

Model Zone Mean 99 Mean 99

A Belgium 0.0023% 0.0355% 0.0097% 0.1394%B Belgium 0.0116% 0.1189% 0.0094% 0.0948%C Belgium 0.0050% 0.1065% 0.0054% 0.1166%

A Denmark 0.0055% 0.1027% 0.0179% 0.2857%B Denmark 0.0219% 0.2976% 0.0123% 0.1865%C Denmark 0.0128% 0.2137% 0.0072% 0.1386%

A Netherlands 0.0059% 0.1173% 0.0160% 0.2417%B Netherlands 0.0141% 0.0974% 0.0122% 0.0913%C Netherlands 0.0041% 0.0755% 0.0081% 0.1429%

*Loss cost is calculated by Industry loss/Industry exposure

Commercial Residential

7

Are commercially available Property Cat models a comprehensive view of risk?

REMS vs. AIR - US Perils1.00 = REMS Max. Loss

-

0.20

0.40

0.60

0.80

1.00

95.00% 96.00% 97.00% 98.00% 99.00% 100.00%

REMS AIR - I AIR - II

Additional perils captured in REMS© increase loss estimates relative to vendor models (e.g. winter freeze, eastern European flood, Australian Hail and others)

Secondary factors like post-event inflation (demand surge) and fire following earthquake need to examined specifically to determine if they are adequately increasing loss estimates

Secondary factors are important differentiators of risk.

REMS vs. RMS - US Perils1.00 = REMS Max. Loss

-

0.20

0.40

0.60

0.80

1.00

95.00% 96.00% 97.00% 98.00% 99.00% 100.00%

REMS RMS-I RMS-II

1/250 PML for US PerilsAIR vs. I vs. II RMS vs. I vs. II

Basic vendor model 0.47 0.56 REMS w/o add'l perils 0.57 22.2% 0.57 1.8%REMS 0.69 47.9% 21.0% 0.69 23.3% 21.2%

Vendor I = Basic vendor model for major perils with no add'l loss costs for post-event inflation or fire following EQ

Vendor II = REMS model including secondary factors but excluding perils not in vendor model

REMS = REMS model including secondary factors and capturing all perils

8

Modeling Malpractice

Poor model or incomplete model

Pilot error – model is used incorrectly or with incorrect ‘dial settings’

Good model used for the wrong purpose

Too much or too little trust in the models; results = estimates not “facts”

Unstable model where small changes in assumptions drive large changes in results

Black box model where users are unable to link which assumptions are driving results

Too much output – leaves users lost in piles of data

Cumbersome model – takes too much time to run or does not provide the info needed to make decisions in a timely way

Separation of modeling from underwriting – All our modellers are underwriters and all our underwriters are modellers.

9

All lines of business should be incorporated into the same risk management framework to effectively manage entity risk

Cat Model needs to integrate with other Risk Models: Flexible framework to add other lines A tool for underwriters to make risk decisions An exposure management system to track and control risk aggregations.

Do not rely on commercially available models; each book of business must be captured stochastically

Not every line of business can be modeled with the same level of sophistication and refinement as Property Cat At Renaissance, we built proprietary models for terrorism and workers comp cat that are

built off of the analytics and ‘engineering’ of the REMS© Property Cat models; capture correlation with Cat

Other lines of business modeled using stand-alone stochastic distributions; more judgment involved but approach needs to be compatible

Facilitates a complete aggregation of risk no gaps in the model or risk analysis

10

ExpectedProfit

ExpectedProfit

ExpectedProfit

RequiredCapital

CapitalRules:

New DealBeginningPortfolio

ProbabilityDistribution

RequiredCapital

Portfolio &Contract “A”ProbabilityDistribution

RequiredCapital

Calculation of marginal ROE by contract

11

Portfolio Construction Matters

Opt Universe Opt Port x OLW Opt Port

Exp Profit 35% 59% 45%

99.60% -355% -233% -82%

Zero Profit Prob 20% 11% 9%

Return Period 5.0 8.7 11.4

Default Prob 7.77% 3.21% 0.24%

Return Period 13 31 417

Portfolios: Opt Universe: Reinsurance CAT Market - equal share Opt Port x OLW: Optimal Portfolio no retro Opt Port: Optimal Portfolio with retro

Optimization: Maximize Expected Profit for a given level of capital No more than 50% of any placement Deals taken from Reinsurance CAT Market

Results:

12

Portfolio Construction Matters

-800%

-700%

-600%

-500%

-400%

-300%

-200%

-100%

0%

100%

200%

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

Exceedence Probability

Pro

fit

(Lo

ss

) a

s P

erc

en

t o

f P

rem

ium

Opt UnivOpt PortOpt x OLW

13

Be Very Afraid:

Allison

Sydney Hail

Tiawan Earthquake

World Trade Center

Four Storms in Florida

Anatol

Tsunami

Turkey Earthquake

Bushfires (California & Australia)

Canadian Freeze

1999 Storms

The List goes on…..