July 8, 2010

A Reinsurer’s Perspective on Capital and Property Cat PricingRon Wilkins, FCAS, MAAAVice President and Corporate Actuarial ManagerMarch 20, 2012

The following presentation is for general information, education and discussion purposes only, in connection with the Casualty Actuarial SocietyRPM Seminar. Any views or opinions expressed, whether oral or in writing are those of the speaker alone. They do not constitute legal orprofessional advice; and do not necessarily reflect, in whole or in part, any corporate position, opinion or view of Partner Re ,or its affiliates, or a corporate endorsement, position or preference with respect to any issue or area covered in thepresentation.

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Outline

Risk Management Culture Attributed Capital and Pricing Managing Catastrophe Risk Property Portfolio Model

PartnerRe's Risk Management Culture

Transparent risk management communication both internally and externally

Risk assumption and risk management at core of the company’s value proposition

Embedded in strategy and stated goals of the company: To satisfy client needs and provide unquestioned ability to pay claims, while providing attractive risk adjusted returns to shareholders

Appreciation of risk, capital, returns, correlations, processes, limits and controls embedded throughout organization

4

5

Risk Appetite

Potential creation of value over time for assuming risks

UNACCEPTABLE

Inadequate compensation

for risk ta

ken

UNACCEPTABLE AT ANY PRICE

Beyond our appetite or capacity to absorb downside of risk

Capital/Value @ Risk

Potential loss of value

GENERALLY ACCEPTABLE RISK / RETURN

Return

Expected value creation per unit o

f risk over ti

meBEWARE

Appears very well

compensated but too good

to be true.

Attributed Capital and Pricing

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7

Framework for Capital Attribution

Board and CEO risk appetite: expressed as tolerance for loss from specific large risks to “unlikely” and “remote” events as a percent of economic capital

Limits and solvency thresholds Models – tail risk metrics, catastrophe and non-Cat Uncertainty – additional loads Capital – attributed to the product line, diversification is

considered Pricing – capital based on a mixture of the treaty’s

product line and its individual features

Required Capital

Modeled Loss Curve

1-in-100 1-in-250

Return Period

Capital Coverage = board appetite

Eco

no

mic

Cap

ital

Estimate of known un-modeled loss

MinimumRequiredEconomicCapital

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Attributed Capital: Serves Multiple Purposes

Common view of risk across the organization achieved through attributing capital to every treaty and investment class

Attributed capital forms the basis for Determining deployed capital Profitability measurement for pricing purposes Hindsight performance measurement and annual incentive

Principle and process of attributing capital Each business unit has control over tactical capital deployment

so diversification between classes within unit considered with the exception of catastrophe risk

Iterative process during plan and dynamic process during pricing

A

C

Soft Market

Hard Market

A = Hard Market Risk and Returns

B = Transitional Market Returns; but high risk

C = Soft Market; reduced Risk in period of narrow spreads

RISK

Tactical Capital Deployment

EXPECTEDRETURN

LOWERRETURN TO BUYDOWN RISK

RISK REDUCTION

TransitionalMarket

B

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Attributed Capital: Profitability Measurement

Attritional loss distributions and Cat event loss tables are inputs into the Group Capital Model

Capital charges are calibrated from model output Additional loads reflect risk appetite and unknowns Leverage ratios calibrated to product line level Underwriting risk – capital to premium ratio Reserving risk – capital to reserve ratio Selected capital will depart from product line leverage based on

features of each individual treaty.

Hypothetical Example – Relatively volatile transaction capital to premium (product line) = 75% capital to premium (transaction) = 95% capital to premium (selected) = 85%

Managing Catastrophe Risk

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Managing Catastrophe Risk - Introduction

Manage the maximum foreseeable loss from any one catastrophe event

Manage the annual aggregate for multiple events Monitor and control limits for each exposure zone The company’s approach combines

Vendor models Proprietary modeling Qualitative underwriting Maintaining a geographically diversified book of business

Managing Catastrophe Risk - Pricing Approach

Proprietary and vendor models’ output

Actuarial techniques Loss history – can be used to

calibrate vendor models Statistical models for poorly

modeled or non-modeled perils

Cat risk is encapsulated in an event loss table

Balancing quantitative and qualitative analyses

Pricing is based on a balance of information from:

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Managing Catastrophe Risk - Event Loss Tables

-

20,000,000

40,000,000

60,000,000

80,000,000

100,000,000

0 200 400 600 800 1000

Use table to compute remote return period losses Some major United States peril zones:

• South East Hurricane• North East Hurricane• Southern California Earthquake• Northern California Earthquake

Event Number Mean Loss Frequency Description

102001 39,233,238.24 0.001628% Class 2 Hurr FL

102002 56,159,115.56 0.003015% Class 4 Hurr NY

102003 34,896,366.84 0.002702% Class 3 Hurr MA

102004 45,305,203.88 0.002741% Class 5 Hurr FL

102006 44,888,362.68 0.002330% …

102007 42,268,580.35 0.003178%102008 46,426,644.46 0.002980%102009 41,640,576.96 0.002169%102010 37,393,727.13 0.002324%102012 37,398,656.75 0.001895%102013 38,435,115.50 0.001794%102014 21,711,491.12 0.002704%102015 23,800,957.37 0.002177%102016 24,824,763.83 0.002150%102017 25,429,748.48 0.002923%102018 19,905,788.97 0.003125%102019 19,838,504.55 0.001785%102022 19,776,686.34 0.001693%102023 19,702,744.07 0.002338%102024 20,038,266.45 0.003079%102025 20,008,866.45 0.001952%102026 18,486,003.06 0.002508%102027 8,668,954.98 0.002520%

… … …

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Managing Catastrophe Risk - Secondary Perils

Earthquakes, hurricanes, and terrorist attacks are catastrophic perils for which vendor-licensed and in-house Cat models play a crucial role.

Secondary perils are defined as all non Earthquake, non Hurricane, and non Terrorism perils: Tornado, Hail, Convective storms Flood Freeze, Winter Storms

Experienced based approach: Burning costs Actuarial methods using loss distributions Monte-Carlo simulation of loss data Market share / market loss analyses

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Combining Attritional and Cat losses

Attritional portfolio simulation model output: Rectangle of simulated loss outcomes One row for each simulated year One column for each product line

Cat risk, event loss table: One row for each event in the model’s event set. One column for each cat-exposure product line.

Combine attritional and Cat assuming independence Modeled output is used to create metrics and exhibits:

Risk versus return profile of lines, business units, and the Group Diversification ratios

Combining Attritional and Cat lossesAttritional: Fire and other non-Cat perils

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Natural Catastrophes:

Property Portfolio Model

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Property Portfolio Model - Framework

Begin with individual reinsurance treaties Combine to the product line level (using a copula) Combine multiple lines into a portfolio (using a copula)

Property is combined with other lines when calculating the Group’s economic capital.

This results in a model of the attritional portfolio

Catastrophe risk is modeled in event loss tables Combine attritional and catastrophe distributions by

assuming independence This results in a model of the overall portfolio, attritional

plus catastrophe. Property is a component of this model (represented as a separate column or set of columns).

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Property Portfolio Model - Attritional

For attritional risk, we use a copula model. Not for Cat. Construct a product line loss distribution by combining

the attritional distributions of individual treaties Select correlations between product lines Simulate nominal losses from the distributions,

considering correlations among the product lines. Convert nominal losses into financial losses:

Premium and expenses are treated as fixed Discount factors are based on the risk-free yield curve and the

duration of the product line Financial Loss = PV(Loss) + PV(Expenses) – PV(Premium)

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Property Portfolio Model - Attritional Loss Distribution

Discrete model of how annual non-Cat losses are spread over the range of possible outcomes.

Selecting the loss distribution for a single treaty: Estimate the probability that the layer will be loss free and the

probability of a full limit loss. Benchmark curves are based on product line and layer. If the

experience is extensive consider historical experience as a basis for an estimate of annual variability.

Larger subject base implies smaller relative volatility Consider features that significantly modify ultimate cash flows:

Annual Aggregate Deductible Reinstatements Loss Ratio Cap Sliding scale commission

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Copula Model Background

A copula is defined as the joint cumulative distribution function of k uniform random variables.

Key idea: The correlation relationship is generated separately from the marginal densities.

Gaussian copula80% correlation

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Copula Model Background – The Gaussian Copula

Correlation Matrix k is the number of units in the model. The matrix is k by k. Correlation coefficients represent the closeness of outcomes

across units in the model. Positive semi-definite - This means that the correlations are

consistent with each other. The units could be treaties, product lines, or business units

which combine multiple product lines.

More flexible than closed form multivariate models: Correlation assumptions are kept separate from the individual

loss distributions Some multivariate models only allow the user to adjust one

parameter for correlation.

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Copula Model Background – Hypothetical Inputs

Correlation Matrix example – between product lines:

Loss distribution example Discrete form More points in the tail Represents a product line,

such as Property National

  Prop - Natl Prop - Regl Auto Crop

Prop - Natl 100%      

Prop - Regl 75% 100%    

Auto 20% 20% 100%  

Crop 25% 25% 5% 100%

cumulativeprobability

lossratio

10% 28%20% 32%30% 35%40% 46%50% 58%60% 63%70% 70%80% 88%90% 115%95% 210%96% 280%97% 360%98% 450%99% 720%

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Copula Model Parameters - Correlation Matrix - Key Input / Assumption

Consider correlations between loss ratios (not losses) Rate adequacy in different lines is subject to a market cycle

When selecting correlations across lines consider: Geography: Regional versus national Perils: for example, drought is a crucial driver of crop insurance

results but probably irrelevant for casualty Macroeconomic forces: Impact premium and losses in several

lines at once Inflationary trends Tort environment trends Unemployment rate and GDP growth

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Copula Model Parameters - Correlation Matrix - Key Input / Assumption

When selecting correlations across treaties consider: If an insurer buys a tower of several excess of loss layers, then

those layers would probably be highly correlated If two reinsurance treaties cover national property E&S insurers

who participate in towers on the same large buildings, that would suggest higher correlation

Density of risks: can a single fire destroy multiple buildings? Some risks that are lumped into the attritional distribution are

truly more catastrophic in nature, such as winter storm damage.

Techniques for selecting correlation coefficients: Estimate using historical company or industry data. Expert opinion Stress testing – important in practice

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Series1

1,000,000

4,000,000

5,000,000

10,000,000

20,000,000

Layering

The primary insurer has decided to retain the first million of each occurrence and cede the rest.

Above one million, the risk is ceded to reinsurers, split into four excess of loss layers.

It is common in practice for a single layer to be shared by several reinsurers.

Can also represent coverage for a large building, layered among Excess & Surplus insurers.

$4M xs $1M: First excess layer ceded to reinsurers.

First million of each occurrence is retained by primary insurer.

$5M xs $5M: Second excess layer ceded to reinsurers.

$10M xs $10M: Third excess layer ceded to reinsurers.

$20M xs $20M: Fourth excess layer . This is shared, 50% each, by two competing reinsurers,

Overall, the primary insurercedes $39M xs $1M.

20,000,000

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Copula Model Parameters - Additional Thoughts

Gaussian is a common starting point, but modelers should consider whether it provides a heavy enough tail

t-copula has stronger tail correlation Degrees of freedom parameter – influences the degree of tail

correlation Like the Gaussian in that the modeler specifies the entire matrix

Copula selection could be thought of holistically, in the context of related assumptions: Correlation coefficient selection Loss distributions Handling of treaty features such as loss ratio caps

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Goals of the Portfolio Risk-Return Model

Monitor Reinsurance Portfolio Exhibits discussed at Quarterly senior management meeting Analysis covers the risk-versus-return position, how it has

recently changed, and where it is moving.

Evaluate Strategic Decisions Typical question: “How would the risk and return change if we

significantly added volume to a particular product line?” Acquisitions, product line growth, and market segmentation

present strategic questions. Parameter assumptions are sensitivity tested.

Stand Alone(700)

Diversified BU(450)

Diversified US(300)

300200 150

300

200

100

100

50

30

250400

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Diversification Analysis: 1-in-100 Year TVaR Financial Losses ($ MM) – Hypothetical Example

Diversification Ratios

In-force 2010 In-force 2009

Stand Alone: Each product line is treated as its own business. Add TVaR across lines.

Div BU: Diversification credit is given between lines within a BU, but not between BUs.

Div US: Full diversification credit is given.

In this hypothetical example, diversification decreased from 2009 to 2010, due to a reduction in diversification in BU1.

Business Unit (1) Within BU % (2) Across BU % (3) Total %

BU1 60 20 80BU2 33 33 67BU3 33 17 50

Overall 44 18 61

Business Unit (1) Within BU % (2) Across BU % (3) Total %

BU1 50 20 70BU2 33 33 67BU3 33 17 50

Overall 36 21 57

Stand Alone(800)

Diversified BU(450)

Diversified US(310)

300200 150

300

200100

200

80

40

350

490

Diversification Benefit BU1 BU2 BU3

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BU1 200 17 250 180 500

BU2 300 8 250 12 500

BU3 500 4 250 12 500

Overall 1000 4 250 8 500

Return Period For Fixed Dollar Losses – Hypothetical Example

In-force 2009

(By Business Unit and Overall, Financial Losses)

Perspective: Look at a fixed meaningful amount of loss to the firm (such as $50 MM) and ask how often such a full-year loss is expected.

The U.S. return period for $50 MM increased from eight to ten years.

Lengthening return periods of adverse outcomes correspond to decreasing firm risk.

In-force 2010

    25 MM 50 MM

Business UnitPremiumin-force

Return periodin years Market loss

Return periodin years Market loss

BU1 200 20 250 200 500

BU2 300 10 250 15 500

BU3 500 5 250 15 500

Overall 1000 5 250 10 500

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Event Set Analysis – Integrates Cat and Non-Cat RiskHypothetical example centered around 100-year return period

In-force 2010 – millions USD

Quantile Agriculture Casualty Property All Others Total  PV Profits PV Tech Ratio PV Profits PV Tech Ratio PV Profits PV Tech Ratio PV Profits PV Tech Ratio PV Profits PV Tech Ratio

98.95 5 90 (200) 140 1 90 (76) 90 (270) 120 98.96 (10) 100 (130) 135 (40) 110 (91) 100 (271) 121 98.97 (5) 100 (70) 110 (130) 140 (66) 90 (271) 121 98.98 20 80 (200) 140 (20) 100 (72) 90 (272) 122 98.99 (20) 120 (130) 135 (30) 100 (92) 120 (272) 122 99.00 (10) 110 (25) 100 (160) 150 (78) 90 (273) 123 99.01 (20) 120 (200) 130 30 80 (83) 95 (273) 123 99.02 (10) 110 0 90 (250) 160 (14) 85 (274) 124 99.03 (10) 110 (150) 130 (50) 110 (64) 87 (274) 124 99.04 10 80 (200) 137 (10) 100 (75) 90 (275) 125 99.05 0 100 0 100 (200) 160 (75) 90 (275) 125

In-force 2009 – millions USD98.95 (40) 110 0 90 (200) 160 (60) 90 (300) 125 98.96 10 90 50 80 (300) 190 (61) 90 (301) 126 98.97 (20) 100 70 80 (300) 190 (51) 85 (301) 126 98.98 (10) 100 0 90 (200) 160 (92) 100 (302) 127 98.99 30 80 (100) 120 (200) 160 (32) 75 (302) 127 99.00 (10) 100 (100) 120 (150) 140 (43) 75 (303) 128 99.01 5 90 (70) 110 (150) 140 (88) 100 (303) 128 99.02 (80) 125 (50) 100 (100) 120 (74) 95 (304) 129 99.03 10 90 (130) 125 (100) 120 (84) 100 (304) 129 99.04 (90) 135 (20) 100 (120) 125 (75) 95 (305) 130 99.05 0 90 (180) 150 (80) 110 (45) 75 (305) 130

Event set perspective: examine specific tail events to identify what drove them.

In 2010 the 1-in-100 year event was property driven, but in 2009 it was a combined property and casualty event.

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Return versus Risk: Hypothetical Example

In-force 2010 vs. In-force 2009

Finance perspective: plot return on the vertical axis and risk on the horizontal axis.

Movements to the Northwest are unambiguously good: lower risk and higher return

BU1 reduced risk and improved returns, which drove a portfolio-wide improvement.

The other two business units were stable.

20 25 30 35 40 45 50 55 60 65 700

5

10

15

20

25

BU3

BU1 - 2009

Overall - 2009

Overall - 2010BU2

BU1 - 2010

TVaR of Financial Losses At 99% Level Divided By PV Losses

RO

P E

xcl

OH

(%

)

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Conclusion

A simulation model of economic capital can be a key component of a reinsurer’s capital attribution approach

Property Cat risk needs to be integrated into the portfolio model for purposes of: Tracking key risk, return, and diversification metrics Capital attribution

Capital deployment can be an iterative process: Transaction-level analysis is incorporated into the selected Cat

event tables and attritional loss distributions Transactions and lines are combined to the unit and Group

levels in the portfolio model Management risk appetite is built into pricing leverage ratios Leverage ratios are key inputs to transaction pricing