Risk-Based Capital Risk-Based Capital DevelopmentsDevelopments

Glenn MeyersGlenn MeyersInsurance Services Office, Inc.Insurance Services Office, Inc.

CAS/SOA Enterprise Risk CAS/SOA Enterprise Risk Management SymposiumManagement Symposium

July 29, 2003July 29, 2003

IntroductionIntroduction

A current initiative of the A current initiative of the International International Association of Insurance Supervisors (IAIS) Association of Insurance Supervisors (IAIS) is to develop a global framework for risk-is to develop a global framework for risk-based capital for insurers.based capital for insurers.

Acting in support of the IAIS, the Acting in support of the IAIS, the International International Actuarial Association (IAA) has formed an Actuarial Association (IAA) has formed an Insurer Solvency Assessment Working Party Insurer Solvency Assessment Working Party (WP(WP) to prepare a paper on the structure for a ) to prepare a paper on the structure for a risk-based solvency assessment system for risk-based solvency assessment system for insurance.insurance.

Terms of Reference of the WPTerms of Reference of the WP

The WP should describe the principles The WP should describe the principles and methods involved in the quantification and methods involved in the quantification of the total funds needed to provide a of the total funds needed to provide a chosen level of confidencechosen level of confidence to to policyholders and shareholders that the policyholders and shareholders that the insurer’s policyholder obligations will insurer’s policyholder obligations will be met.be met.

Terms of Reference of the WPTerms of Reference of the WP

The paper should be specific and practical The paper should be specific and practical enough that its recommended principles enough that its recommended principles and methods could be used as a and methods could be used as a foundation for a foundation for a global risk-based global risk-based solvency capital systemsolvency capital system for for consideration by the IAIS.consideration by the IAIS.

Terms of Reference of the WPTerms of Reference of the WP

The paper should, starting from a The paper should, starting from a coherent coherent risk framework, identify risk measures risk framework, identify risk measures that explicitly or implicitly can be used to that explicitly or implicitly can be used to measure the exposure to loss from risk and measure the exposure to loss from risk and also any also any risk dependenciesrisk dependencies. The paper . The paper should also identify measures that are not should also identify measures that are not effective in this regard.effective in this regard.

Terms of Reference of the WPTerms of Reference of the WP

In balancing its focus between practical versus In balancing its focus between practical versus sophisticated methodologies, the working party sophisticated methodologies, the working party will place will place greater weight on those greater weight on those methodologies with the greatest likelihood of methodologies with the greatest likelihood of practical implementationpractical implementation. However, since . However, since simple methodologies that can be applied to simple methodologies that can be applied to many insurers in a territory or across territories many insurers in a territory or across territories may prove insufficiently reliable or capital may prove insufficiently reliable or capital efficient, efficient, the working party should consider the working party should consider whether risk models developed internally by whether risk models developed internally by insurers can provide a useful and reliable insurers can provide a useful and reliable approach.approach.

Who is on the WP?Who is on the WP?Allan Brender (Canada)Allan Brender (Canada)Peter Boller (Switzerland)Peter Boller (Switzerland)Henk van Broekhoven Henk van Broekhoven (Netherlands) - Vice-(Netherlands) - Vice-ChairpersonChairpersonTony Coleman (Australia)Tony Coleman (Australia)Jan Dhaene (Belgium)Jan Dhaene (Belgium)David Finnis (Australia)David Finnis (Australia)Marc Goovaerts (Belgium)Marc Goovaerts (Belgium)Burt Jay (U.S.)Burt Jay (U.S.)R. Kannan (India)R. Kannan (India)Toshihiro Kawano (Japan)Toshihiro Kawano (Japan)

Sylvain Merlus (France)Sylvain Merlus (France)Glenn Meyers (U.S.)Glenn Meyers (U.S.)Teus Mourik (Netherlands)Teus Mourik (Netherlands)Harry Panjer (Canada)Harry Panjer (Canada)Dave Sandberg (U.S.)Dave Sandberg (U.S.)Nylesh Shah (U.K.)Nylesh Shah (U.K.)Shaun Wang (U.S.)Shaun Wang (U.S.)Stuart Wason (Canada) - Stuart Wason (Canada) - ChairpersonChairpersonHans Waszink (Netherlands)Hans Waszink (Netherlands)Bob Wolf (U.S.)Bob Wolf (U.S.)

Represented are several countries, life, health, P/CRepresented are several countries, life, health, P/Cinsurance company, consultants, regulators and academics.insurance company, consultants, regulators and academics.

Contents of ReportContents of Report

Section 3 – The Purpose of Capital Section 3 – The Purpose of Capital Section 4 – Supplements to Capital Section 4 – Supplements to Capital Section 5 – Working Party’s Approach Section 5 – Working Party’s Approach Section 6 – Risks and Risk Measures Section 6 – Risks and Risk Measures Section 7 – Standardized Approaches Section 7 – Standardized Approaches Section 8 – Company Specific Approaches Section 8 – Company Specific Approaches Section 9 – Reinsurance Section 9 – Reinsurance Section 10 – Total Company RequirementSection 10 – Total Company Requirement

Contents of ReportContents of Report

Appendix A – Life Insurance Case Study Appendix A – Life Insurance Case Study Appendix B – Non-Life Insurance Case Study Appendix B – Non-Life Insurance Case Study Appendix C – Health Insurance Case Study Appendix C – Health Insurance Case Study Appendix D – Market Risk Appendix D – Market Risk Appendix E – Credit Risk Appendix E – Credit Risk Appendix F – Lessons from Insurer Failures Appendix F – Lessons from Insurer Failures Appendix G – Introduction to Insurance Risk Appendix G – Introduction to Insurance Risk Appendix H – Analytic Methods Appendix H – Analytic Methods Appendix I – CopulasAppendix I – Copulas

General Insurance Case StudyGeneral Insurance Case Study

Proposal for “Standardized Approach”Proposal for “Standardized Approach”

Illustrative “Internal Model”Illustrative “Internal Model”

Desirable Properties of a Desirable Properties of a Standard FormulaStandard Formula

SimplicitySimplicity – The formula can be put on a – The formula can be put on a spreadsheet. This may allow for some complexity spreadsheet. This may allow for some complexity in the formulas, as long as the objective of the in the formulas, as long as the objective of the formulas is clear.formulas is clear.Input AvailabilityInput Availability – The inputs needed for the – The inputs needed for the formula are either readily available, or can be formula are either readily available, or can be reasonably estimated with the help of the appointed reasonably estimated with the help of the appointed actuary. actuary. ConservativeConservative – When there is uncertainty in the – When there is uncertainty in the values of the parameters, the parameters should be values of the parameters, the parameters should be chosen to yield a conservative estimate of the chosen to yield a conservative estimate of the required capital required capital

A Proposal for a Standard FormulaA Proposal for a Standard Formula

The formula is sensitive to:The formula is sensitive to:

The volume of business in each line of The volume of business in each line of business;business;

The overall volatility of each line of The overall volatility of each line of insurance;insurance;

The reinsurance provisions; and The reinsurance provisions; and

The correlation, or dependency structure, The correlation, or dependency structure, between each line of business.between each line of business.

Features of the FormulaFeatures of the FormulaInput for insurance lossesInput for insurance losses– Expected losses for current businessExpected losses for current business– Loss Reserves (at expected values of payout)Loss Reserves (at expected values of payout)

Parameters - Specified by regulator (??)Parameters - Specified by regulator (??)– Claim severity distribution by line of businessClaim severity distribution by line of business– Claim count distributionClaim count distribution– Dependency model parameters (see next slide)Dependency model parameters (see next slide)

Calculates first two moments of aggregate loss Calculates first two moments of aggregate loss distribution. Using lognormal approximation:distribution. Using lognormal approximation:

Capital = TVaRCapital = TVaR99%99% – Expected Loss – Expected Loss

Dependency Model ParametersDependency Model Parameters

Common shock modelCommon shock model– Uncertainty in trend affects all lines simultaneouslyUncertainty in trend affects all lines simultaneously– Magnitude of shock varies by line of businessMagnitude of shock varies by line of business

Catastrophes treated separatelyCatastrophes treated separately

Capital = TVaRCapital = TVaR99%99% – Expected Loss + Cat PML – Expected Loss + Cat PML

Calculate Cat PML with a catastrophe modelCalculate Cat PML with a catastrophe model

Example on SpreadsheetExample on Spreadsheet

Big Insurer – ABC Insurance CompanyBig Insurer – ABC Insurance Company

Small Insurer – XYZ Insurance CompanySmall Insurer – XYZ Insurance Company

ABC Volume = 10 times XYZ VolumeABC Volume = 10 times XYZ Volume– Otherwise they are identicalOtherwise they are identical

Moving Toward an Internal ModelMoving Toward an Internal Model

Recall WP recommendationsRecall WP recommendations– That the “Standard Model” be deliberately That the “Standard Model” be deliberately

conservative.conservative.

Several modifications to the “Standard Several modifications to the “Standard Model” are possible.Model” are possible.

Insurer internal model are to be subject to Insurer internal model are to be subject to standards for risk-based capital formulas.standards for risk-based capital formulas.

Requirements for Internal ModelsRequirements for Internal Models

The insurer should have an The insurer should have an independent independent internal risk management unitinternal risk management unit, responsible for , responsible for the design and implementation of the risk-based the design and implementation of the risk-based capital model.capital model.

The insurer’s Board and senior management The insurer’s Board and senior management should be actively involved in the should be actively involved in the risk control risk control processprocess, which should be demonstrated as a , which should be demonstrated as a key aspect of business management.key aspect of business management.

Requirements for Internal ModelsRequirements for Internal Models

The model should be The model should be closely integrated with closely integrated with the day-to-day management processesthe day-to-day management processes of the of the insurer.insurer.

An An independent reviewindependent review of the model should be of the model should be carried out on a regular basis. (Amongst other carried out on a regular basis. (Amongst other considerations, it should be recognised that considerations, it should be recognised that evolution of the modelling capabilities is to be evolution of the modelling capabilities is to be encouraged) encouraged)

Operational risks should be fully consideredOperational risks should be fully considered

Example of Internal ModelExample of Internal Model

More realistic claim severity distributionsMore realistic claim severity distributions

Richer dependency structureRicher dependency structure– Parameter uncertainty in claim frequency as Parameter uncertainty in claim frequency as

well as claim severitywell as claim severity– Parameter uncertainty in claim frequency Parameter uncertainty in claim frequency

applied across groups of lines.applied across groups of lines.

Example of Internal ModelExample of Internal Model

Calculates aggregate loss distribution Calculates aggregate loss distribution directly rather than by momentsdirectly rather than by moments

Catastrophe model included directly in Catastrophe model included directly in aggregate loss calculation, rather than add aggregate loss calculation, rather than add PML.PML.

Additional details to be published in Additional details to be published in Summer ForumSummer Forum– ““Aggregation and Correlation of Insurance Aggregation and Correlation of Insurance

Exposure” – Meyers, Klinker and LalondeExposure” – Meyers, Klinker and Lalonde

ResultsResults

No Reinsurance With Reinsurance No Reinsurance With ReinsuranceTVaR 99% 2,665,306,927 2,431,822,820 305,543,931 245,968,540Expected Loss 1,215,000,000 1,158,671,051 121,500,000 115,867,105Reserve 999,538,735 879,134,113 99,953,873 87,913,411Capital 450,768,192 394,017,656 84,090,057 42,188,024

Internal ModelABC Insurance Company XYZ Insurance Company

No Reinsurance With Reinsurance No Reinsurance With ReinsuranceTVaR 99% 2,821,018,276 2,580,135,062 304,943,284 260,723,343Expected Loss 1,200,000,000 1,147,246,365 120,000,000 114,724,636Reserve 999,538,735 881,230,412 99,953,873 88,123,041Cat PML 143,000,000 65,000,000 14,300,000 6,500,000Capital 764,479,541 616,658,285 99,289,411 64,375,665

Proposed "Standard Formula"ABC Insurance Company XYZ Insurance Company

Next StepsNext Steps

Complete remaining sections of report (focus on Complete remaining sections of report (focus on standardized versus advanced approaches; case study standardized versus advanced approaches; case study illustrations etc.)illustrations etc.)Consider input from IAA Insurance Reg’n Committee and Consider input from IAA Insurance Reg’n Committee and interested supervisory bodies (e.g. IAIS, EC, etc.)interested supervisory bodies (e.g. IAIS, EC, etc.)Issue “discussion” draft report to Insurance Regulation Issue “discussion” draft report to Insurance Regulation Committee for email discussionCommittee for email discussionIssue revised “exposure” draft report to Insurance Issue revised “exposure” draft report to Insurance Regulation Committee on September 30 for Berlin Regulation Committee on September 30 for Berlin meetingmeetingIdentify follow-on initiatives required by the IAA and Identify follow-on initiatives required by the IAA and member associationsmember associations