Economic Capital Modeling A Key Part of the ERM Process

Economic Capital ModelingA Key Part of the ERM Process

Ronald T. Kuehn, FCAS, MAAA, CERA, CPCU, ARM, FCA

Consulting Actuary, Huggins Actuarial Services, Inc.

Mid-Atlantic Mutual Advantage Convention

August 5, 2014

107th MAMA Convention 2

• Economic Capital is defined as– Sufficient surplus to cover adverse

outcomes or to meet a business objective

– With a given level of risk tolerance

– Over a specified period of time

Definition of Economic Capital

Definition of an Economic Capital Models (ECM)

• One primary tool to assess risk in an insurance organization• Simulates the internal operations of the company

relative to the external environment within which it is operating• Indicates future levels and volatility of

profitability, and • Estimates appropriate amounts of capital to hold


A Brief History of ECM

1980’s•Life Insurance Industry•Cash flow modeling to assess variations from

mortality assumptions used to price life insurance and annuities

1990’s•P & C Insurance Industry – Lacks Correlations•Dynamic Financial Analysis (DFA)•Stochastic approach to estimating hazard

interactions impacting financial condition


A Brief History of ECM

2000’s•Economic Capital Modeling (ECM) •Probability-based scenario generator for future

financial results of an insurance enterprise•Full ECM include Underwriting, Reserve,

Natural Catastrophe, Asset, and Credit Risks

Today•Critical factor – Correlation among Risks•Aggregating these risks into a common model• Producing plausible alternative financial

outcomes


• Model – Company or Product Risk Profiles– Risk Tolerance, Constraints & Strategies– Insurance Pricing & Business strategies– Performance Measurements– Capital Adequacy & Budgeting– Incentive Compensation Investment & Risk-Adjusted Rates of Return– Merger & Acquisition Pricing Details– Capital Allocation Among Business Units

ECM Can ….


Key Risks Being Measured by a Comprehensive Economic Capital Model

ECMKey Risks

CatastropheCat Event

Loss Volatility

ReinsuranceCredit Risk

Program Efficacy

UnderwritingMarket CyclesLoss Volatility

ReservingReserve AdequacyPayment Patterns

OtherInvestment OperationalReputational


ECM– Satisfy rating agency and regulatory

criteria/inquiries– Aid in discussions with rating agencies and regulators– Capital adequacy measured against a company’s risk profile

Benefits of an Economic Capital Model Compliance Related


• A.M. Best’s Supplemental Rating Questionnaire (no longer asks the ECM question as of year-end 2013)– Q 56: ECM – Risk Identification & Monitoring– Q 57: Frequency of Update to ECM and Measurement of

Aggregate Risk– Q 58: Impact of Calendar Year Inflation on Reserves– Strong emphasis on Catastrophe Management (Updated as

of January 14th, 2014)• Preparation of the ORSA summary report• Essential for Solvency II Compliance

Benefits of an Economic Capital Model Compliance Related


More to gain from ECM than compliance• Improves risk awareness at all levels• Enables better risk/reward decisions making• Facilities linking strategy with planning• Empowers firm to improve value for stakeholders• Provides a competitive advantage including reduced

cost of capital (University of Georgia Study 2013)

Benefits of an Economic Capital Model Value Beyond Compliance


A.M. Best 2010 ERM SRQ:• Overall 28% of respondents use ECM to quantify

aggregate risk• Large (55%), • Medium (33%), and • Small (17%)

• 8% use ECM for management compensationNAIC moving with European regulator EIOPA ?

– Solvency II will allow companies capital relief by use of internal ECM rather than standard model

Insurance Companies & ECM


• Savvy Investors, media, and the financial community speak language of risk modeling (VaR, TVaR, PML, etc.) • Demand more disclosure of metrics from ECMs.

• Developing ECM is costly as it requires:• Acquiring actuarial and financial expertise• Collecting of significant volume data• Analyzing data to develop risk parameters• Licensing or building ECM software platform• Validating the model and organizing the

management process for audit



• RBC (Risk-Based Capital) Ratio– Implemented by the NAIC in the 1990’s– Formulaic estimate of necessary surplus and comparison to

reported surplus– Used to authorize regulatory intervention into financially-

distressed• NAIC ORSA (Own Risk and Solvency Assessment) – Companies with at least $500 M WP – Group with at least $1B WP – Effective circa 2015

Existing Capital Adequacy Measures


• Rating Agency Measures: BCAR and others – Both formulaic and simulation-based– Used as significant input into assignment of financial

strength ratings– Lack full transparency, as not all parameters are made

public



• Economic Capital Models (ECM’s)– Simulation based – Direct calculation of Economic Capital needed– Many other uses in addition to Economic Capital

measure



Balance Sheet Inputs:• Assets

• Cash• Bonds• Common Stock• Other Asset Classes

• Liabilities• Loss and Loss Adjust Reserves by Line / Subline• Payment patterns for Existing Reserves• Unearned Premium Reserve• Other Liabilities

Basic Inputs to an Economic Capital Model


• Direct Written Premium• Claim Payout Pattern for Newly Generated Loss• Underwriting Expenses• Earnings Pattern• Operational Risk – Lognormal Distribution

Basic Inputs to an Economic Capital Model (Line of Business Inputs)


• Frequency and Severity Model – Frequency of Individual Claims with No Correlation– Claim Frequency Distribution - Examples• Poisson – often selected• Negative Binomial• Binomial

Basic Inputs to an Economic Capital Model (Cause of Loss)


• Frequency and Severity Model – Severity of Individual Claims with No Correlation– Claim Severity Distribution - Examples• Lognormal – often selected • Exponential• Gamma• Generalized Pareto• Normal• Uniform• Weibull




• Aggregate Loss Model – Aggregate claims model can incorporate copulas (i.e., correlation between lines of business)• Aggregate Loss Distribution Examples• Lognormal• Generalized Pareto• Normal• Uniform• Weibull



• Selection of Copulas - adds correlation between lines of business• Normal Copula – linear correlation coefficient• Student’s T Copula – varies weight of coefficients in

tail of distribution• HRT Copula – more weight in right tail of

distribution• Partial Perfect Copula – mixes perfect correlation

with uncorrelated


Basic Inputs to an Economic Capital Model (Reinsurance Inputs)

• Reinsurance Contract Terms • Per Risk• Excess • Corridors • Ceded Premium• Ceded Reinsurance Attachment Point• Ceded Reinsurance Limit• Specific Catastrophe Reinsurance Terms

• Reinsurance Catastrophe Modeling Results (i.e. AIR, EQECAT, RMS)


Basic Inputs to an Economic Capital Model (Economic Scenarios)

•Leading edge economic models, providing full market risk and asset class coverage

•Estimates inflationary changes, wage & CPI •Estimates of investment returns and default risk:

• US Treasury bonds• US, United Kingdom, and Euro stock markets• Emerging Markets stocks• Blue Chip Stocks• Corporate and Municipal bonds of varying quality

• Master Limited Partnerships• Real Estate Investment Trusts (REITs)• Mortgage Backed Securities


Basic Outputs from an Economic Capital Model

Outputs include but are not limited to:• Over 180 customizable reports• Cumulative Probability Density Functions• Compare results from differing assumptions• Include effect of catastrophe losses• Calculates Value at Risk (VaR) & Tail Value at

Risk (TVaR)• Pro Forma Financial Statements• Balance Sheet• Income Statement• Number of projected years is flexible


• Value at Risk (VAR) – Maximum loss at no more than one minus the confidence level

• Tail Value at Risk (TVaR) – Expected loss in worst X percentage of distribution; also called CTE

• Risk Adjusted Performance – Measure risk adjusted returns on some established capital amount

• Return on Equity – Simple accounting performance metric

ECM - Key Risk Metrics

Return on Equity = Net Income/Shareholder's Equity


Happy Valley Insurance Company Case Study

Line of Businesses: General Liability Workers’ Compensation Property Miscellaneous

Write Businesses in 13 States on the East Coast


As of 12/31/2014

Liabilities Values

Net L&LAE Reserve $ 22.75 M

Net UEPR $ 23.10 M

Other Liabilities $ 4.72 M

Total Liabilities $ 50.57 M

Capital & Surplus $ 20.87 M

Liabilities & Surplus $ 71.44 M

Happy Valley Insurance CompanyBase Case - Liabilities & Surplus


As of 12/31/2014 Assets Values

Bonds $ 43.40 M Stocks $ 1.25 M Cash $ 5.50 M Other Invested $ 0.30 M Total Invested $ 50.45 M Uncollected Premium $ 17.00 M Other Assets $ 4.00 M Total Assets $ 71.45 M

Happy Valley Insurance CompanyBase Case - Assets by Class


As of 12/31/2014

Lines of Business Gross EP Ceded EP Net EP General Liability $ 6.40 M $ 0.60 M $ 5.80 M Workers’ Compensation $ 3.70 M $ 1.00 M $ 2.70 M Property $ 35.90 M $ 11.00 M $ 24.90 M Total All Lines $ 46.00 M $ 12.60 M $ 33.40 M

Happy Valley Insurance CompanyBase Case - Earned Premium 2015


Reinsurance For All Years 2015 - 2019Line of

BusinessBase CaseRetention

General Liability $1.10 M Workers' Comp $0.50 M Property Per Risk $0.50 M

Line of Business

Catastrophe Layers

Property Cat $ 4.00 M X/S $ 6.00 M $10.00 M X/S $10.00 M $20.00 M X/S $20.00 M $40.00 M X/S $40.00 M

Happy Valley Insurance CompanyBase Case - Reinsurance Program

107h MAMA Convention 30

Surplus at Various Confidence IntervalsProbability 2015 VaR 2019 VaR

0.010% $ (7.49) M $ (27.03) M 0.079% $ 0 M $ (14.46) M 0.491% $ 7.16 M $ 0 M 0.500% $ 7.21 M $ 0.09 M

50.000% $ 23.53 M $ 32.29 M 75.000% $ 24.57 M $ 36.60 M 99.000% $ 26.39 M $ 43.68 M 99.500% $ 26.62 M $ 44.49 M

Mean $ 22.58 M $ 30.81 M Year - End 2014 Surplus $ 20.87 M

*Results of 100,000 Monte Carlo Simulations

Solvency II Standard

Happy Valley Insurance CompanyBase Case ECM Results


•In the Base Case scenario, Happy Valley invests in:•Government bonds, •Blue chip stocks •Cash•Miscellaneous other assets

•In the Alternative Investment Scenario, Happy Valley increases its investment in:

•Blue chip stocks and •Adds a substantial investment in master limited

partnerships (MLP’s)

Happy Valley Insurance CompanyAlternative Investment Scenario


Investment PercentageAssets Yield Base Case Alternative

Bonds 2.50% 60.70% 45.00% Stocks 0.00% 1.70% 3.50% MLP's 6.00% 0.00% 14.00% Cash 0.10% 7.70% 7.70% Other 0.00% 29.90% 29.80% Total 100.00% 100.00%

Happy Valley Insurance CompanyComparison of Investment Distribution



0.010% $ (6.91) M $ (27.15) M 0.080% $ 0 M $ (13.01) M 0.340% $ 6.27 M $ 0 M 0.500% $ 7.45 M $ 2.41 M

50.000% $ 23.75 M $ 34.78 M 75.000% $ 25.10 M $ 39.69 M 99.000% $ 28.08 M $ 49.75 M 99.500% $ 28.56 M $ 51.15 M




Happy Valley Insurance CompanyAlternative Investment Scenario ECM Results

Happy Valley Insurance CompanyAlternative Investments


•In the Base Case scenario, Happy Valley invests in:•Government bonds•Blue chip stocks •Cash•Miscellaneous other assets

•In the second alternative, Happy Valley uses excess surplus, to buy small, profitable personal auto insurer

•Costs $2.3 million over book value•Assumes $5.0 million in net loss & loss adjustment

reserves •Assumes $3.5 million in unearned premium reserves

Happy Valley Insurance Company Case Study - Buys Small Auto Insurer


As of 12/31/2014

Liabilities Values Net L&LAE Reserve $ 27.75 M

Net UEPR $ 26.60 M


Total Liabilities $ 59.07 M Capital & Surplus $ 18.53 M Liabilities & Surplus $ 77.61 M

Happy Valley Insurance CompanyBuy Auto Insurer - Liabilities & Surplus


As of 12/31/2014Assets Values

Bonds $49.60 MStocks $1.25 MCash $5.50 MOther Invested $0.30 M

Total Invested $56.65 M

Uncollected Premium $17.00 MOther Assets $4.00 M

Total Assets $77.65 M

As of 12/31/2014 Assets Values


Happy Valley Insurance Company Buy Auto Insurer - Assets by Class


As of 12/31/2014 Lines of Business Gross EP Ceded EP Net EP

Personal Auto $ 7.20 M $ 2.00 M $ 5.20 M General Liability $ 6.40 M $ 0.60 M $ 5.80 M Workers’ Compensation $ 3.70 M $ 1.00 M $ 2.70 M Property $ 35.90 M $ 11.00 M $ 24.90 M Total All Lines $ 53.20 M $ 14.60 M $ 38.60 M

Happy Valley Insurance CompanyBuy Auto Insurer - Earned Premium 2015



0.010% $ (9.48) M $ (27.17) M 0.100% $ 0 M $ (10.75) M 0.480% $ 5.13 M $ 0 M 0.500% $ 5.22 M $ 0.15 M

50.000% $ 21.53 M $ 31.90 M 75.000% $ 22.60 M $ 36.22 M 99.000% $ 24.47 M $ 43.42 M 99.500% $ 24.71 M $ 44.19 M




Happy Valley Insurance CompanyBuy Auto Insurer - ECM Results


•In the third alternative scenario, Happy Valley reduces its reliance on reinsurance by:

•Doubling retention on General Liability•Doubling retention on Property Per Risk •Eliminating first Catastrophe layer

Happy Valley Insurance Company Case Study – Alternative Reinsurance

107th MAMA Convention 40Graphic: RadientSkies/123RF.com

As of 12/31/2014 - Same as Base Case

Liabilities Values


Net UEPR $ 23.10 M





Happy Valley Insurance CompanyAlternative Reinsurance – Liabilities & Surplus


As of 12/31/2014 – Same as Base CaseAssets Values


Happy Valley Insurance CompanyAlternative Reinsurance - Assets by Class




AlternativeRetention

General Liability $1.10 M $2.20 M Workers' Comp $0.50 M $0.50 M

Property Per Risk $0.50 M $1.00 MLine of

BusinessCatastrophe

Original LayersCatastrophe

Alternative Layers Property Cat $ 4.00 M X/S $ 6.00 M $10.00 M Retention

$10.00 M X/S $10.00 M $10.00 M X/S $10.00 M $20.00 M X/S $20.00 M $20.00 M X/S $20.00 M $40.00 M X/S $40.00 M $40.00 M X/S $40.00 M

Happy Valley Insurance CompanyComparison of Reinsurance Program

107h MAMA Convention 43Graphic: RadientSkies/123RF.com


0.010% $ (11.81) M $ (31.88) M 0.166% $ 0 M $ (9.60) M 0.500% $ 4.65 M $ (1.04) M

0.588% $ 5.31 M $ 0 M 50.000% $ 24.48 M $ 37.19 M 75.000% $ 25.53 M $ 42.23 M 99.000% $ 27.35 M $ 50.48 M 99.500% $ 27.58 M $ 51.41 M




Happy Valley Insurance CompanyAlternative Reinsurance - ECM Results


•In the Base Case scenario, Happy Valley invests in:•Government bonds•Blue chip stocks •Cash•Miscellaneous other assets

•In the fourth alternative scenario, Happy Valley begins to pay its shareholders $1.8 million of dividends per year beginning in 2015 to reduce under-utilized surplus.

Happy Valley Insurance Company Case Study – $1.8 M Dividend Per Year

107th MAMA Convention 45Graphic: CSA Images / B&W Engrave Ink Collection / Getty Images

As of 12/31/2014 - Same as Base Case

Liabilities Values


Net UEPR $ 23.10 M





Happy Valley Insurance Company $1.8 M Dividend Per Year – Liabilities & Surplus


As of 12/31/2014 – Same as Base CaseAssets Values


Happy Valley Insurance Company $1.8 M Dividend Per Year - Assets by Class




General Liability $1.10 M Workers' Comp $0.50 M

Property Per Risk $0.50 MLine of

BusinessCatastrophe

Original Layers Property Cat $ 4.00 M X/S $ 6.00 M

$10.00 M X/S $10.00 M $20.00 M X/S $20.00 M $40.00 M X/S $40.00 M

Happy Valley Insurance Company $1.8 M Dividend Per Year - Same as Base Case

Reinsurance Program

107h MAMA Convention 48Graphic: CSA Images / B&W Engrave Ink Collection / Getty Images


0.010% $ (9.29) M $ (38.10) M 0.100% $ 0 M $ (22.44) M 0.500% $ 5.41 M $ (10.74) M

2.480% $ 11.08 M $ 0 M 50.000% $ 21.73 M $ 23.06 M 75.000% $ 22.77 M $ 27.39 M 99.000% $ 24.59 M $ 34.45 M 99.500% $ 24.82 M $ 35.25 M




Happy Valley Insurance Company $1.8 M Dividend Per Year - ECM Results


Scenarios 1 2 3 4 5

Key MetricsBase Case

Alternative Investment

Buy Auto Insurer

Alternative Reinsurance

Pay $1.8 M Dividends

2015 BCAR 257.13% 262.53% 211.44% 255.82% 234.02%

2019 BCAR 271.77% 287.90% 241.83% 283.02% 199.51%

1 Yr Prob. of Ruin 0.08% 0.08% 0.10% 0.17% 0.10%

5 Yr Prob. of Ruin 0.49% 0.34% 0.48% 0.59% 2.48%

12/31/2014 Surplus (M) $20.87 $20.87 $18.53 $20.87 $20.87

12/31/2019 Surplus (M) $30.81 $33.64 $30.47 $35.43 $21.44

5 Yr Annual Adj. ROE 8.10% 10.02% 10.45% 11.16% 7.84%

Happy Valley Insurance CompanyComparison of Key Metrics for Scenarios


Initial Allocation of Year-End 2014 Surplus at 99% VaR

LOB 99% VaRPercent of

TotalCapital

Allocation Casualty $ 4.221 M 13.69% $ 2.857 M

Workers' Compensation $ 1.900 M 6.16% $ 1.286 M

All Other $ 2.551 M 8.27% $ 1.727 M

Property $ 22.165 M 71.88% $ 15.003 M

Total $ 30.837 M 100.00% $ 20.873 M

Happy Valley Insurance CompanyInitial Capital Allocation Using Net 99% VaR


Initial Allocation of Year-End 2014 Surplus at 50% VaR

LOB 50% VaRPercent of

TotalCapital

Allocation Casualty $ 2.335 M 12.83% $ 2.679 M

Workers' Compensation $ 1.504 M 8.27% $ 1.726 M

All Other $ 0.905 M 4.97% $ 1.038 M

Property $ 13.452 M 73.93% $ 15.431 M

Total $ 18.197 M 100.00% $ 20.873 M

Happy Valley Insurance CompanyInitial Capital Allocation Using Net 50% VaR



Mr. Kuehn is professionally active; he served as the chairman of the Casualty Loss Reserve Seminar (CLRS). He has also served on the on the Casualty Practice Council of the American Academy of Actuaries, the CAS Examination Committee and Committee for Consultants’ Interests, and as past President, Education Chairman and Board Member of the Casualty Actuaries of the Mid-Atlantic Region (CAMAR). He currently serves on the Board of the Insurance Society of Philadelphia (ISOP), and he is a member of the ORSA subgroup of the ERM Committee of the Risk Management and Financial Reporting Council of the American Academy of Actuaries. His over forty three years in business have given him a thorough knowledge of the property-casualty business both from a company and consulting viewpoint.

Ronald T. (Rusty) Kuehn , FCAS, MAAA, CERA, CPCU, ARM, FCA Mr. Kuehn is a consulting actuary with Huggins Actuarial Services, Inc. In his consulting practice he specializes in medical malpractice, private passenger automobile, workers’ compensation and commercial lines coverage working for insurance carriers, self-insured healthcare systems, self-insured corporations, brokers, municipal bond and mortgage insurance experience, and other types of clients.

Contact Information:E-mail: [email protected] Phone: 610-892-1823www.hugginsactuarial.com


Economic Capital ModelingA Key Part of the ERM Process

Ronald T. Kuehn, FCAS, MAAA, CERA, CPCU, ARM, FCA

Consulting Actuary, Huggins Actuarial Services, Inc.

Mid-Atlantic Mutual Advantage Convention

August 5, 2014

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Economic Capital Modeling A Key Part of the ERM Process