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Dave Ingram, MAAA, FSA, CERA, FRM, PRM Chair of IAA Enterprise & Financial Risk Committee Executive Vice President, Willis Re September, 2012

Using Economic Capital, Stress Tests and ERM to enhance Insurance Supervision

Part 1: Quantifying and Aggregating Risks, Using Internal Models

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DISCLAIMER

•  This presentation represents the opinions of the presenter, David Ingram. These are not necessarily the views of the International Actuarial Association or his employer, Willis Re.

•  In the area of Risk Management it is always dangerous to rely on the opinions and analysis of a third party without verifying with your own research, thought, and analysis.

•  This presentation is no exception to that rule.

A Word From Our Lawyers

•  Willis Re Inc. is a reinsurance broker. Willis Re Inc. is not a law firm, investment advisor or tax advisor. We do not give legal, investment or tax advice and nothing herein constitutes nor should be construed as such. Such ideas are offered for discussion purposes only and do not constitute advice of any kind. It is believed that the information used in creating this presentation is correct, but no representations are made as to its completeness or accuracy, nor are any warranties made as to its fitness for any purpose. You and your advisors must make an independent assessment regarding all such matters.

•  Any comments or observations made herein are for academic purposes only and are not for the purposes of reliance. Any such comments do not reflect the views of Willis Re Inc. or its clients.

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Plan for Discussion

Using Economic Capital, Stress Tests and ERM to enhance Insurance Supervision

–  Part 1: Quantifying and Aggregating Risks Using Internal Models

–  Part 2: Developing Stress and Scenario Testing in a Risk-based Solvency Regime

–  Part 3: ERM and ORSA – Assuring a Necessary Level of Risk Control

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Why Do We Need This? Two assumptions have been embedded in our approach to supervision of insurance: 1.  Risks are similar from company to company and year to

year and we know how to assess the size of risk 2.  All companies manage risks about the same and

usually with an acceptable level of effectiveness

Both may have been correct at some point in time in the past, but neither are true now.

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No Longer Correct?

1.  Risks that are labeled the same may be very different from company to company and from year to year.

–  A rule of thumb such as premium to surplus ratio standards have little explanatory power

2.  Actual risk management practice varies significantly from company to company

–  Capital is no substitute for the lack of risk management –  A company with poor risk management will eventually lose all of

their capital, regardless of the amount

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Insurers

•  Most insurers historically operated under these embedded assumptions as well

•  Some have recognized that they are no longer correct and have already adopted: –  Economic Capital / Internal Models –  Stress Tests –  Enterprise Risk Management

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Often after experiencing large losses that were to some extent caused by too much reliance on these assumptions

What Do Insurers Get From This?

•  Economic Capital / Internal Model – Provides a consistent view of all risks and a view of the total risk

•  Stress Tests – Provide a check on ECM and a method for assessing Emerging Risks

•  Enterprise Risk Management – Extension of the ideas of risk management to all risks and to the aggregate risk amount

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What Can Supervisors Get from This?

•  Economic Capital / Internal Model – Provides a consistent view of all risks and a view of the total risk

•  Stress Tests – Provide a check on ECM and a method for assessing Emerging Risks

•  Enterprise Risk Management – Extension of the ideas of risk management to all risks and to the aggregate risk amount

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Traditional Risk Management

•  Applies risk management ideas separately to the largest risks of the insurer

•  Risk measures are usually different and totally inconsistent with each other –  No easy way to know which risk is largest, second, etc. –  No easy way to know if company is being very conservative on

one risk and aggressive on another –  No easy way to know if the total amount of risk of an insurer is

growing relative to the amount of capital or not

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Your Speaker - David Ingram

Was Senior Director ERM in the Insurance Ratings Group of Standard & Poors (2005 – 2008)

–  Primary author of initial S&P Criteria for evaluating ERM (2005) –  Trained S&P Analysts in US, Europe, Asia, Australia and South

America for ERM reviews (2006 - 2007) –  Performed over 150 ERM reviews of Insurers (2005 – 2008) –  Developed and implemented Level II in depth ERM reviews of larger

insurers (2006 - 2008) –  Developed initial proposals for S&P review of Internal Models (2008)

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CONFIDENTIAL AND PROPRIETARY. Permission to reprint or distribute any content from this presentation requires the written approval of Standard & Poor’s. August 2005

What Is the Difference Between Risk Management and ERM?

•  Across ALL of the significant risks of the Enterprise

•  Consistently across the risks

•  Consistently with the fundamental objectives of the enterprise

An ERM Program comprehensively applies Risk Management…

S&P Decided that . . .

•  S&P had to give an opinion on the financial strength of the entire enterprise –  Piecemeal Risk Management did not take

responsibility for the entire enterprise •  ERM means that the management was looking

at risk for the entire enterprise –  ERM implies that the actions of management were

aligned with the concerns of the rating agency

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CONFIDENTIAL AND PROPRIETARY. Permission to reprint or distribute any content from this presentation requires the written approval of Standard & Poor’s. August 2005

ERM Evaluation Components

Risk Management Culture

Risk Control

Processes

Emerging Risks Mgmt

Risk & Economic Capital Models

Strategic Risk Management

S&P Findings

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S&P Findings (2012)

•  For 40+ of the largest US insurers

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Overall Culture Risk Controls Emerging Risks Models SRMExcellent 12% 17% 12% 12% 0% 12%Strong 36% 74% 67% 36% 57% 43%Adequate 52% 10% 21% 52% 43% 45%Weak 0% 0% 0% 0% 0% 0%

Market Credit Insurance Operating Risk Controls Excellent 5% 2% 12% 7% 12%Strong 60% 55% 67% 50% 67%Adequate 36% 43% 19% 43% 21%Weak 0% 0% 2% 0% 0%

Why the Low Take Up ERM by S&P rated universe?

•  85% of all insurers and 52% of the largest insurers have only Adequate or Weak ERM

•  Seven years after S&P added ERM to the insurance ratings process!

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Insurers have different objectives for their ERM

•  Satisfying Regulator or Rating Agency Compliance

•  Holding the Right Amount Capital Management

•  No single risk can do serious harm Diversification

•  Limit Risk to Limit Losses Loss Controlling

•  Get Paid for Taking Risks Risk Pricing

•  Make Risk Reward Trade-offs Risk Steering

Emphasis varies with Objective – Emphasis on ERM practices – Emphasis on Internal Model

Some ERM/Capital regimes (S&P, Solvency II) assume uniform ERM Objectives

–  Usually Capital Management and Risk Steering

Many insurers do not agree with those objectives!

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QUANTIFYING AND AGGREGATING RISKS USING INTERNAL MODELS •  Modelling dependencies and diversification effects •  Integrating threat scenarios and statistical risk models •  Modelling group risks

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Uses of Internal Models

a. System of governance b. Risk-management system c. Decision-making process d. Economic capital assessment e. Economic capital allocation f. Solvency capital assessment g. Solvency capital allocation

21 Source: CIEOPS L2 Advice Internal Model Approval

Uses of Internal Models

•  Capital Management •  Risk Management •  Performance Management •  Product Management

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Internal Model usage

Capital Management •  Maintaining retained risk at a level that is supported by capital •  Assist with decisions on use of capital via capital allocation,

capital budgeting & return on risk •  Making strategic choices regarding business mix that produce

superior risk adjusted returns •  Strategic Asset Allocation

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Internal Model Usage

Risk Management •  Identification of risk concentrations to improve ability to

avoid large losses •  Control processes over total risk for business units or

product lines or territories •  Understanding, communicating and tracking of risk

profile •  Demonstrating ERM program to Rating Agencies

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Internal Model Usage

Performance Management •  Measurement of risk adjusted returns •  Designing strategies for business units to produce

superior risk adjusted business returns •  Goal Setting, management and monitoring of risk

adjusted performance •  Risk adjusted incentive compensation

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Internal Model Usage

Product Management •  Apply uniform standards across a large organization for

product risk and returns •  Product Pricing that is a fair price for the risk taken •  Large case pricing

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Risk Capital Determination Methods

1.  Standard factors 2.  USP Models 3.  Stress tests 4.  Simplified stochastic 5.  Partial internal models 6.  Full internal models 7.  Multi-year models with Management

Actions

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Standard Factors

Pro: Consistency

Con: Potentially Inaccurate

Assms: Risks are all the same

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USP Models

Pro: Capture insurer differences

Con: Less Consistent

Assms: Risk factors are not changed often

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Stress Tests

Pro: Consistency and Accuracy improves over factors

Con: More expensive than factors

Assms: Scenarios for different risks can be consistent

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Simplified Stochastic

Pro: Develops entire gain and loss distribution

Con: Potentially Inaccurate due to limited number of sub models

Assms: Broad risk classes have static gain and loss distribution

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Partial Internal Model

Pro: Most important risks are analyzed with best practice techniques

Con: Consistency between risks, anti-selection by insurers

Assms: Only some risks are complex enough to require full modeling

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Full Internal Model

Pro: Creates full gain and loss distribution for all risks

Con: Expensive and time consuming

Assms: Parameter & Model risks usually assumed to be minimal

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Multi-Year Model with Management Actions

Pro: Actually captures expected reality i.e. company expects to continue operating

Con: Management actions are difficult to model realistically

Assms: Mgt correctly reacts to future problems

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FULL INTERNAL MODELS

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Full Internal Model Approaches to Risk Quantification

•  Life Insurance Risks – Process Models –  Data on initial policyholder status –  Random scenario generators of key economic

variables •  Interest Rates, Equity Returns, Inflation •  Claims rates – blend of own experience and industry tables

–  Rules about Insurance Contract values –  Assumptions about policyholder option exercise –  Generate cashflows and Income statement / Balance

sheet impact

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Full Internal Model Approaches to Risk Quantification

•  Non-Life Insurance Risks – Outcomes models –  Data on initial policyholder status –  History of claims volatility

•  Frequency and severity – own experience and industry •  Usually separate between Large and Attritional claims

–  Rules about reinsurance coverage –  Assumptions about future frequency and severity of

Large and Attritional claims –  Monte Carlo modeling to combine Large and

Attritional claims –  Combine with premium information to generate gain/

loss distribution from insurance 37

Full Internal Model Approaches to Risk Quantification

•  Reserve Development (Technical Provision inadequacy) – Based upon parameter uncertainty – Based upon potential for true inadequacy

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Full Internal Model Approaches to Risk Quantification

•  Investment Credit Risk – Outcomes models – Frequency /Severity (Actuarial Method) – Equity Market Implied (Merton Method) – CDS Market Implied (Credit Spreads)

– With or without reflection of fluctuations in market values due to spread volatility

– Same approach for counterparty credit (reinsurers)

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Full Internal Model Approaches to Risk Quantification

•  Investment Equity Risk – Outcomes models – Historical Volatility Models – Market Consistent Volatility Models – Opinion based Models – Regime Switching vs. Log Normal models – For direct equity holdings – Risk in Life products use Life Models

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Full Internal Models Approaches to Risk Quantification

•  Interest Rate Risk – ALM Models – Use Life Models for risk embedded in products – For Non-Life and direct holdings for surplus

account •  Earnings Fluctuations and MV fluctuations •  Most interest rate models have troubling inadequacies

–  Because interest rates are often managed by central banks – No Random Walk

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Full Internal Models Approaches to Risk Quantification

•  Operational Risk – Frequency Severity Models – Significant operational risk events are rare

and usually company specific – Therefore data is an important issue

•  i.e. there is never enough to create a reliable model

•  Few firms that model Op Risk rely on the values from their models for company decision making

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Full Internal Models Output

•  Distribution of Gains and Losses for each modeled “cell” – Cell may be a product or investment type – Aggregated to major risk Class

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Underwriting Risk

Underwriting Income Equity Market Risk

Percentile Gross Net99.8% 83.4 76.3 99.6% 81.4 73.9 99.0% 75.5 68.1 95.0% 63.6 56.0 90.0% 56.7 48.9 75.0% 44.2 36.1 50.0% 27.7 20.1 25.0% 9.3 5.1 10.0% (9.9) (8.9)

5.0% (22.5) (17.2)1.0% (49.6) (35.9)0.4% (64.8) (46.4)0.2% (74.8) (53.6)

Underwriting Income

-

20

40

60

80

100

120

140

160

180

200

Gross Net-100

-80

-60

-40

-20

0

20

40

60

80

1001 in 400 good

1 in 250 good

1 in 200 good

1 in 100 good

1 in 20 good

1 in 4 good

1 in 4 bad

1 in 20 bad

1 in 100 bad

1 in 200 bad

1 in 250 bad

1 in 400 bad

Average

–  Current reinsurance program reduces underwriting risk – but is it the most effective strategy?

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Reserve Risk

Reserve Risk

PercentileReserve

Development99.8% (23.8)99.6% (21.5)99.0% (18.9)95.0% (13.3)90.0% (10.4)75.0% (5.5)50.0% (0.1)25.0% 5.5 10.0% 10.3

5.0% 13.4 1.0% 19.1 0.4% 21.7 0.2% 22.9

Distribution of Reserve Development

unde

r -25

-25

to -2

0

-20

to -1

5

-15

to -1

0

-10

to -5

-5 to

0

0 to

5

5 to

10

10 to

15

15 to

20

20 to

25

25 to

30

30 a

nd a

bove

favorable unfavorable

favo

rabl

e un

favo

rabl

e

–  Significant reserve volatility – but potential for favorable as well as unfavorable loss development

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Equity Market Risk

Equity Market Risk Reserve Risk

PercentileStock

ReturnStock Price

Change99.8% 86.4% 57.1 99.6% 71.0% 46.9 99.0% 54.2% 35.8 95.0% 40.3% 26.6 90.0% 33.6% 22.2 75.0% 22.9% 15.1 50.0% 10.2% 6.7 25.0% -2.3% (1.5)10.0% -12.3% (8.2)

5.0% -20.1% (13.3)1.0% -37.0% (24.4)0.4% -41.3% (27.3)0.2% -52.8% (34.9)

Distribution of Equity Value Change

unde

r -25

-25

to -2

0

-20

to -1

5

-15

to -1

0

-10

to -5

-5 to

0

0 to

5

5 to

10

10 to

15

15 to

20

20 to

25

25 to

30

30 to

35

35 to

40

40 a

nd a

bove

favorable unfavorable

–  Volatility of stock portfolio is skewed favorable but potential magnitude of downside exceeds that of reserve volatility

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Credit Risk

Credit Risk

PercentileCredit

Losses99.8% 0.0 99.6% 0.0 99.0% 0.0 95.0% 0.0 90.0% 0.0 75.0% 0.0 50.0% 0.0 25.0% 0.0 10.0% 0.0

5.0% 0.0 1.0% 3.0 0.4% 3.0 0.2% 9.5

Credit Defaults(Bonds + Reinsurance Recoverables)

95%

96%

97%

98%

99%

100%

0 5 10 15 20 25 30

Default ($M)

Non-

Exce

edan

ce

Prob

abili

ty

–  Likelihood of default event is very small –  Magnitude of exposure is also significantly smaller than other risks

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Interest Rate Risk

Interest Rate Risk

PercentileNet Inv. Income

99.8% 40.1 99.6% 39.6 99.0% 38.8 95.0% 37.1 90.0% 36.2 75.0% 34.7 50.0% 33.0 25.0% 31.3 10.0% 29.8

5.0% 28.9 1.0% 27.2 0.4% 26.4 0.2% 25.9

Distribution of Bond Interest Income ($M)

unde

r 25

25 to

26

26 to

27

27 to

28

28 to

29

29 to

30

30 to

31

31 to

32

32 to

33

33 to

34

34 to

35

35 to

36

36 to

37

37 to

38

38 to

39

39 to

40

40 a

nd a

bove

–  This risk does not create downside in and of itself, but increases vulnerability to other risks

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Enterprise Risk Model

Contribution to Net Pretax Income

PercentileUnderwriting

IncomeReserve

Development Equity RiskDefault Losses

Interest Income

99.8% 76.3 23.8 57.1 0.0 40.1 99.6% 73.9 21.5 46.9 0.0 39.6 99.0% 68.1 18.9 35.8 0.0 38.8 95.0% 56.0 13.3 26.6 0.0 37.1 90.0% 48.9 10.4 22.2 0.0 36.2 75.0% 36.1 5.5 15.1 0.0 34.7 50.0% 20.1 0.1 6.7 0.0 33.0 25.0% 5.1 (5.5) (1.5) 0.0 31.3 10.0% (8.9) (10.3) (8.2) 0.0 29.8

5.0% (17.2) (13.4) (13.3) 0.0 28.9 1.0% (35.9) (19.1) (24.4) (3.0) 27.2 0.4% (46.4) (21.7) (27.3) (3.0) 26.4 0.2% (53.6) (22.9) (34.9) (9.5) 25.9

–  Underwriting has largest downside potential, followed by equity risk –  However, reserve risk also significant, with greater magnitude than

equity risk in the “moderately bad” scenarios 49

Aggregation of risk Aggregation of Risks

Interpolation Contribution to Net Pretax Income

PercentileAgg Risk:

Independent 25% 50% 75%Agg Risk:

Dependent99.8% 135.1 150.6 166.2 181.8 197.4 99.6% 128.3 141.7 155.1 168.5 181.9 99.0% 120.3 130.6 141.0 151.3 161.6 95.0% 103.2 110.7 118.1 125.6 133.0 90.0% 93.8 99.8 105.7 111.7 117.7 75.0% 78.2 81.5 84.8 88.1 91.4 50.0% 60.0 60.0 60.0 59.9 59.9 25.0% 41.9 38.8 35.7 32.6 29.5 10.0% 25.4 19.7 13.9 8.2 2.5

5.0% 15.2 7.7 0.1 (7.4) (14.9)1.0% (7.1) (19.1) (31.2) (43.2) (55.2)0.4% (16.9) (30.6) (44.4) (58.2) (72.0)0.2% (24.5) (42.1) (59.8) (77.4) (95.0)

–  Most conservative aggregation: view risks as fully dependent •  Historical evidence suggests strong “tail correlation” – i.e. risks that ordinarily do not move in

sync with one another are correlated in extreme downside •  Therefore, viewing risks as independent is not prudent risk management

–  Intermediate weightings illustrate sensitivity to dependency assumption 50

Combining Risks

Four common methods for combining risks – All or Nothing Approach (NAIC – US) – Correlation Matrix (Solvency II, S&P) – Copulas (Internal Models) – Common Drivers – Scenario Embedded

(Internal Models)

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All or Nothing

• NAIC RBC approach is to consider that risks are either 100% or 0% correlated

• Total Risk = Square Root (a2 + b2 + c2) + d + e + f – Where a, b, c are 0% correlated and d,e,f are

100% correlated

Correlation Matrix

•  The most commonly used method for combining risks

•  Relatively simple math – Based upon Correlation Coefficient

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IAAus – Tillinghast study

“Research and Data Analysis Relevant to the Development of Standards and Guidelines on Liability Valuation for General Insurance,” Robyn Bateup and Ian Reed

Assumed Total Variance Correlation Matrix between Lines of Business GL CTP

(Auto) WC Prof

Liab Assumed

Re Fire / Prop

Motor HO Other

GL 1.00

CTP (Auto) 0.25 1.00

WC 0.25 0.35 1.00

Prof Liab 0.25 0.25 0.25 1.00

Assumed Re 0.25 0.25 0.25 0.25 1.00

Fire / Prop 0.00 0.00 0.00 0.00 0.05 1.00

Motor 0.00 0.25 0.00 0.00 0.05 0.10 1.00

HO 0.00 0.00 0.00 0.00 0.05 0.10 0.20 1.00

Other 0.00 0.00 0.00 0.00 0.05 0.05 0.10 0.10 1.00

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Solvency II – QIS5

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Solvency II _QIS5

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Solvency II – QIS5

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Standard & Poor’s Correlation Matrix

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S&P Commentary •  Standard & Poor's gives explicit credit for diversification within the capital

model, albeit at levels likely to be more conservative than those used by many insurers in their internal models. The approach reflects our conservative view on correlations in the tail, through the application of correlation matrices specifically designed for this model. It also partly reflects the limitations on the fungibility of diversification credits across a consolidated group.

•  There is limited data to credibly model and project tail correlations. Study of company- and industry-level correlation matrices has highlighted numerous methodologies and factors being employed, and these have led to significant variation in the amount of diversification credit being assumed by companies in their models.

•  Given the uncertainties around tail correlations, a 50% haircut is applied to the resulting diversification credit.

Correlation Matrix

•  The most commonly used method for combining risks

•  Relatively simple math

•  Problem: – assumes that all distributions are normal – and correlation is constant over time and over

the distribution

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Tail Dependency

•  Technical term that indicates that correlations are higher for remote losses

•  “in a crisis all correlations go to 1”

•  Models that ignore tail correlation will overstate the diversification benefit for large losses

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Copulas •  Linear correlation ρ(X,Y) = Cov(X,Y) / σXσY

–  Commonly used, easy to calculate, but ignores tail dependency

•  Copulas define a complete dependence structure –  Normal

•  Easy to work with, but no tail dependency –  Gumbel

•  More weight in right tail •  Difficult to parameterize if more than 2 variables

–  Student t •  Equal dependence in both tails •  Tractable for more than 2 variables •  Can be used to approximate Normal copula if desired

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Copulas

•  http://www.casact.org/education/reinsure/2010/handouts/CS24-zurbuchen.pdf •  Additional sources

–  “Modelling Dependence with Copulas and Applications to Risk Management”, Embrechts, et. al.

–  “Correlation”, Thomas Struppeck –  “Understanding Relationships Using Copulas”, Frees and Valdez

Copulas

•  Allow modeler to build in tail dependencies

•  Problems: – Requires more data – Very difficult to explain (Black Box effect)

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Common Drivers (Embedded in Scenarios)

•  Seek to identify and model the common drivers of the risks – Embed in Economic Scenario Generator (ESG)

•  Financial Market risks and inflation risk (Life) –  Embed relations between stock, bond and other investment

markets

•  Missestimation of Loss Trend (Non-Life) –  Link different non-life lines to inflation and each other –  Link reserve risk to investment risk

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Common Drivers

•  Will then have all models using the exact same scenarios

•  Simply add up results across all models •  Diversification impact is totally “behind the

scenes” •  Problems:

–  Technically very difficult (often rely on third party vendors)

–  Black Box (few understand) 66

Diversification Issue

Parameter Risk is Enormous

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Integrating Threat Scenarios into Internal Models

•  Need to turn the threat scenario into another risk type – Usually an Excess Loss from some major

outlier event – Create a Pareto Loss distribution

•  Heavy weight to extreme loss •  Low loss below extreme

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Swiss Re Example

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Modeling Group Risks •  Internal Model for a group may be:

•  A combination of internal models for the group members •  A massive group model that may or may not recognize

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Swiss Re Example

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Internal Models Conclusions

•  Internal Models are important for accurate estimation of risk –  When insurer has unusual risks and/or unusual mix of risks –  When risks are unstable

•  Internal Models provide comparable values for all risks –  Allows development of total risk of Insurer

•  Internal Models are complex and highly assumption dependent –  Handle with Care!

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Contact Information

Dave Ingram EVP Willis Re +1 212 915 8039 Dave.ingram@willis.com

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Sources

1.  IAA Note on the Use of Internal Models for Risk and Capital Management Purposes by Insurers (2010)