Economic Capital: Validation

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1 Economic Capital: Model Building & Validation Shaun Wang ERM II & Georgia State University June 7,

2 Analysis of Insurance Business Model Internal Value Produce Products (financial contracts which carries risk, promises with unknown cost) Services (may be unrelated to risk taking) External Value Realization Regulation Rating agencies Efficient Cost structure Incentive structure Information technology Target market segments Competitive pressure 2

3 Internal Economy vs. External Market A multi line corporation operates as an internal economy interacting with external economies Essential to use market economy mechanisms Economic capital has emerged as the common currency to facilitate internal economy and external markets Externally, a firm needs sufficient capital to secure financial strength rating Internally, a firm needs to have a mechanism to facilitate efficient operating of internal economy 3

4 Capital Defines the Capacity for doing business 1. Small man lifts light weight 2. Big man lifts heavy weight 3. In reality, insurer economic capital is often determined by rating agencies June 7,

5 Capital defines Maneuver Room: don t hit the wall! June 7,

6 Solvency II, Pillar I. Financial and Capital Requirements Principle based, rather than rule based Economic value based approach 1 year time horizon, however, valuation reflects future multi year time horizon Diversification across risks and risk mitigation Encourage development of internal risk model June 7,

7 Economy Capital: Principles 1. Economic capital should capture all material risk drivers: financial benefits and guarantees associated with the contracts tail risk under extreme conditions (e.g. lapse) 2. Assumptions and methods for a local unit or product line should be consistent with, but not necessarily identical to, those utilized within the company s overall risk assessment process. 7

8 Multiple Multiple Levels Global risk drivers directly flow through valuations of assets and liabilities Capital, interest rate, foreign exchange, commodity, real estate market indices Local Risk drivers specific to a product line Analyzing the whole business processes distribution, pricing, reserving to servicing Product specific details (options, guarantees, lapse) Profit margins and Expenses Competition, Business cycle Regulatory & Accounting environment 8

9 Factor-based approach Uses prescribed valuation assumptions that are the same across all companies, regardless of differences in risk profile Relies on static formulae that may not capture all of the risks of the contract, or does not reflect the relevant risks Example, Basel II operational risk charge 15% of three year average gross income Does this make sense? 9

10 Same Product, Different Regulatory Treatments Consider a credit exposure to an A rated counterparty Banking Regulation EU Credit Insurance EU Life Insurance Treat as commercial loan BIS 1: 8% Capital BIS 2: 2% Capital Treat as credit insurance paying credit insurance premium of 1% pa. Solvency capital = 15% of premiums 0.16% of outstandings Treat as investment t Implicit asset charge = 3% of outstandings 10

11 Two Distinctive Approaches 1. TheSolvency Approach Most relevant when evaluating overall company economic capital Capital allocations to product lines are sensitive to correlation parameters. 2. Market Consistent Approach produces robust indications at the product line level. It needs adjustment for company portfolio effect 11

12 The Solvency Approach 12

13 Market Consistent Valuations Assets Liabilities Excess Capital Capital Ladder SCR: =Solvency Capital Requirement MCR Minimal Capital Requirement Mar rket Value of Assets s Market Value of Available Market Value Margin MVM 13 Best Est Liability Liabili ities

14 Three Tiers of 3.00 Protection 2.50 MVM MCR 2 * MVM SCR 2 * MCR * MVM Mean MVM (75%) MCR (90%) SCR (99.5%) Multiple of Sigma June 7,

15 4 Levels of Diversification Level 1 Withinrisktypes types Level 2 Across risk types Level 3 Across entities, within a given geography Level 4 Across geographies or jurisdictions June 7,

16 Solvency II Parameters Minimal Capital Requirement vs. Solvency Capital Requirement Level 2 Correlation Matrix MCR does not have Default Market Default Life Health NonLife Threshold Multiple Market 100% 25% 25% 25% 25% MCR 90% SCR 99.5% 2.58 Default 25% 100% 25% 25% 50% Life 25% 25% 100% 25% 0% Health 25% 25% 25% 100% 0% NonLife 25% 50% 0% 0% 100% June 7,

17 Level 1 Market Risk Aggregation for SCR Interest Rate Equity Property Spread Concentration Foreign Exchange Interest Rate 100% 0% 50% 25% 0% 25% Equity 0% 100% 75% 25% 0% 25% Property 50% 75% 100% 25% 0% 25% Spread 25% 25% 25% 100% 0% 25% Concentration 0% 0% 0% 0% 100% 0% Foreign Exchange 25% 25% 25% 25% 0% 100% June 7,

18 Level 1 Life Insurance Risk Correlation (for SCR) Life.Corr Mortality Longevity Disability Lapse Expenses Revision CAT Mortality 100% 0% 50% 0% 25% 0% 0% Longevity 0% 100% 0% 25% 25% 25% 0% Disability 50% 0% 100% 0% 50% 0% 0% Lapse 0% 25% 0% 100% 50% 0% 0% Expenses 25% 25% 50% 50% 100% 25% 0% Revision 0% 25% 0% 0% 25% 100% 0% CAT 0% 0% 0% 0% 0% 0% 100% June 7,

19 Level 1 Non Life Correlation Matrix (for SCR) Fire and Accident Motor, Marine, Credit Worker Motor, other Thirdparty expense Assistanc eous non- Legal Miscellan Complem and third aviation and NP reins NP reins NP reins compensa other damage entary health/def party and suretyshi property casualty MAT tion classes to liability s e life health ault liability transport p property insurance SCR.NonLife.Corr Worker compensation 100% 50% 50% 25% 25% 25% 25% 50% 25% 50% 25% 50% 25% 25% 25% Complementary health 50% 100% 50% 25% 25% 25% 25% 25% 25% 25% 25% 50% 25% 25% 25% Accident and health/default 50% 50% 100% 25% 25% 25% 25% 25% 25% 50% 25% 50% 25% 25% 25% Motor, third party liability 25% 25% 25% 100% 50% 50% 25% 50% 25% 50% 25% 50% 25% 25% 25% Motor, other classes 25% 25% 25% 50% 100% 25% 25% 25% 25% 50% 50% 50% 25% 25% 25% Marine, aviation and transportt 25% 25% 25% 50% 25% 100% 25% 25% 25% 25% 50% 50% 25% 25% 50% Fire and other damage to property 25% 25% 25% 25% 25% 25% 100% 25% 25% 25% 50% 50% 50% 25% 50% Third-party liability 50% 25% 25% 50% 25% 25% 25% 100% 50% 50% 25% 50% 25% 50% 25% Credit and suretyship 25% 25% 25% 25% 25% 25% 25% 50% 100% 50% 25% 50% 25% 50% 25% Legal expenses 50% 25% 50% 50% 50% 25% 25% 50% 50% 100% 25% 50% 25% 50% 25% Assistance 25% 25% 25% 25% 50% 50% 50% 25% 25% 25% 100% 50% 50% 25% 25% Miscellaneous nonlife insurance 50% 50% 50% 50% 50% 50% 50% 50% 50% 50% 50% 100% 25% 25% 50% NP reins property 25% 25% 25% 25% 25% 25% 50% 25% 25% 25% 50% 25% 100% 25% 25% NP reins casualty 25% 25% 25% 25% 25% 25% 25% 50% 50% 50% 25% 25% 25% 100% 25% NP reins MAT 25% 25% 25% 25% 25% 50% 50% 25% 25% 25% 25% 50% 25% 25% 100% June 7,

20 Diversification Theory Tested Some 20 years ago, a scholar made the following bold prediction: In years time, there would be very few small companies. This is equivalent to saying In the jungle only tigers and lions can survive in the long run because they are big and strong Such prediction turned out to be wrong! June 7,

21 Personal Auto Liability Wide Company to company variations Mean_LR_Direct Stdev_LR 0.8 mean+2*stdev June 7,

General Liability Wide Company to company variations 2 1.8 1.6 14 1.

2 0 1 10 19 28 37 46 55 64 73 82 91 100 109 118 127 136 145 154 163 172

22 General Liability Wide Company to company variations Mean_LR_Direct Stdev_LR 0.8 mean+2*stdev June 7,

23 Major Challenges 1. Different contracts have different time horizons: how to reflect time diversification? 2. Pitfalls: capital allocations based on solvency models can be out of touch of local real risks 3. Inconsistent with ihmarket pricing ii June 7,

24 Market Consistent Approach 24

25 What is the Fair Price? Based on CAPM type of approach, we can derive a market price risk for risk X as: λ 0 X = λ 0 M ρ * X Note: Risk-adjusted correlation parameter affects the valuation of fair price for insurance risks 25

26 Fair Profit Margin & Implied Economic Capital The fair profit margin for risk X implies an amount of economic capital for risk ik 0 λ σ ( k) ) X EC X ( k) = TEROE is a target excess rate of return (over the risk free rate). For instance, TEROR = 10%. λ 0 is the long term target market price of risk for the risk, which has already reflected the riskadjusted correlation with reference portfolios. TEROE 26

27 Focus on the overall underwriting results, look beyond the losses Many factors New regulation Rate levell Unexpected inflation Loss frequency Level Loss Variation vs.. Loss Ratio Variation Loss Variation vs. Loss Ratio Variation Loss severity Loss Loss Ratio Year 27

28 ensity P rob ab ility D Method for Calculating Capital Charges for Underwriting Operations Bi-Model Distribution Density Apply Wang transform to stylized loss ratio distribution for a line of business to get downside sigma Use benchmark price to back out required capital charge 0 0% 100% 200% 300% 400% 500% Loss Ratio 28

29 Apply Wang transform to derive Capital Charge Factors for ground up risks ik Sharpe Ratio Excess Rate of Return % UW Year Payout Annualized Annual Capital Line of Business Volatility Duration Volatility Charge Factor PPA Liab 4.0% % 0.08 Prem/Ops Small 11.3% 3 6.5% 0.20 Prem/Ops Large 26.4% % 0.32 Comml Auto NonFleet 6.9% % 0.11 Comml Auto Fleet 18.0% % 0.28 Worker Comp Small 12.6% % 0.12 Worker Comp Large 28% %

30 Risk Relativity based on severity only (excess biz vs. ground up) up) 150 xs xs xs500 1M xs 1M 3M xs 2M 5M xs 5M Pers Auto Liab 1.67 Comm Auto Liab NonFleet Comm Auto Liab Fleet Prems/Op Small

31 Lambda and Time Horizon Under Geometric Brownian motion λ( T ) = T λ(1) Empirical relationship 0.6 λ ( T ) T λ (1) This adjustment essential to avoid double counting In application to a product line, T T can be average duration of contract 31

32 Improper Reflection of Duration Can Yield Wildly Unstable Capital lallocation Results λ(t) = T * λ(1) λ(t) = λ(1) In 2001, the CAS Philbrick & Bohra & Painter * Weist ** called for papers pp to analyze a % of % of Surplus Surplus hypothetical Allocated Allocated Ratio insurer, recommend a Workers Comp 41% 11% reinsurance Auto Liab 26% 29% 0.90 HO/CMP Prop 11% 51% 0.22 program, allocate Auto Phys Dmg 1% 1% 1.00 capital, etc Ref: Gary Venter, Feb 2002 Actuarial Review Relative GL/CMP Liab 21% 8% 2.63 Total 100% 100% * From Swiss Re ** From Munich-American Re 32

33 Regulation should recognize diversification & risk transfer Encourage growth of financial conglomerates Revenue diversification in many market segments, Scaleof Economy brand recognition Growth thin emerging markets kt (participate i t in the wealth creation process) Recognize e economic driven en risk transfer Free up locked capital while maintaining sound solvency June 7,

34 Harmonization: level playing field Internal Market via Group Diversification Risk pooling agreements between subsidiaries Group guarantee serves as a stop loss contract External Market via Risk Transfer Allow for Company Internal Model approach that explicitly quantifies the effect of risk iktransfer Set MCR as the floor June 7,

35 Interactions betweeninsurance & investment ROC = Premium UWMargin + Capital Asset InvReturn Capital Return on Capital has double leverage Higher UW risk, requires higher UW Margin Long tailed lines Riskier investment Higher g Expected Profit, but also higher economic capital 35

36 Life Insurance Products Dynamic Cash flowtesting Mortality rates Interest rates Equity linked products Lapse rates and surrender charges Realistic vs. Risk neutral scenarios Margin based business model: funding cost Product innovations require more interactions with capital market (dynamic hedging) 36

37 The Evolving Business Model of Insurance Holding the bag versus Risk trader Hedging cost volatility The impact of regulation June 7,

Economic Capital and Diversification at Group Level

Economic Capital and Diversification at Group Level Shaun Wang Georgia State University ERM-II Scientific Director Outline. Identify the Issue Group Diversification Solvency II, CRO Forum, IASB 2. Mathematical