1. Advanced (Economic) Capital
Topics
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Michel Rochette, MBA, FSA
2009 Valuation Actuary Symposium
Anaheim, CA
September 25th 2009

2. Topics
 General topics:
 Purpose and principles of capital model development
 Major components of a capital model
 Uses of a capital model
 Specialized topics:
 Approaches to building a capital model
 Validation considerations
 Calibration considerations
 Correlation in the tail: diversification
 Emerging risk considerations
25/09/2009 Enterprise Risk Advisory LL

3. Purpose
 ¨ Risk management system of an insurer for the
analysis of the overall risk situation of the insurance
undertaking, to quantify risks and determine the
capital requirement on the basis of the company
specific risk profile¨ CEA Groupe Consultatif
 Required capital is assessed in light of:
 available capital & other financial resources
 enterprise risk management processes
 strategic goals & risk appetite
 regulatory requirements
25/09/2009 Enterprise Risk Advisory LL

4. Principles
 All material risks should be covered: links to ERM
and emerging risks
 Models must be appropriate for the scale and
complexity of the firm
 Models must be dynamic and flexible
 Models must be embedded in the financial, strategic
and operational processes: Use Test in Solvency II
 Governance of models development:
 Board/top management oversight and involvement
 documentation of models, limitations & changes
 internal controls over development: auditableEnterprise Risk Advisory LL
25/09/2009

5. Major components
 Exposure models of key risks:
 financial risks & underwriting risks: assets and liabilities
models cash flows
 non financial risks: operational and business models
 strategic risks: strategic models
 Risk drivers models: ESG, catastrophic, scenarios,
stochastic, EVT, competitor, behaviour, management
actions
 Aggregation approaches: correlation with var/cov,
copulas, none
 Time horizon: short-term view versus run-off
25/09/2009 Enterprise Risk Advisory LL

6. Uses
 Investment decisions: existing and new
 Product development
 Strategic decisions
 Corporate finance decisions: financial leverage
 Hedging strategies
 External events and emerging risks
 Regulatory proposals: CP 37 & CP 56 in Solvency II
 “…widely used and plays an important role in the course
of conducting an insurer's regular business, particularly
in risk management. "
25/09/2009 Enterprise Risk Advisory LL

7. Approaches
 Top down economic and business scenarios:
 obtain an overall EC estimates for all risks combined
 Stress tests:
 judgmental and test specific risks and impact on capital
 Stochastic:
 random scenarios and obtain distribution of risks
 Insurance approach:
 Frequency, severity, recovery
 Factor based: used for regulatory
 Others:
25/09/2009 Enterprise Risk Advisory LL
 Regression, neural networks, Bayesian, fuzzy logic, EVT

8. Validation principles
 Integrates both qualitative and quantitative elements
 Provides that the models were designed, work as
planned and are implemented correctly – quality
assurance
 Analyses the predictive properties of the models:
testing against experience, backtesting
 Iterative process to assess that assumptions & data are
appropriate with a certain degree of confidence:
regular cycle
 Need independence of validation to satisfy basic risk
management principles: internal and/or external Risk Advisory LL
25/09/2009 Enterprise

9. Validation elements
 Model development, design, implementation and
operations: similar to IT systems controls in place like
COBIT
 Review of models inputs:
 assumptions & key risks
 continuous appropriate mathematics and
methodologies
 data accuracy
 Review of basic functioning of the models:
 gaps to internal standards and best industry practices
 model replication with a different set of random
25/09/2009 Enterprise Risk Advisory LL

10. Validation elements
 Historical performance:
 back testing to external sources: industry studies,
academic papers, regulatory and rating agencies’ capital
 Profit and loss attribution: comparison of actual
results to risk drivers predicted by the models. Idem
to a source of earnings analysis
 Management oversight:
 has management been using the models?
 has management put in place processes to obtain
assurance that the models are still appropriate
 Documentation and independent validationEnterprise Risk Advisory LL
25/09/2009

11. Calibration principles
 For each risk drivers, should aim to calibrate four
elements:
 level of the risk factor and its uncertainty
 trend of the risk
 inherent volatility
 calamity/catastrophic/tail
 Market conditions : impact on pro/counter cyclicality
 Frequency of calibration: at least annually and
probably more often for financial risks
 Should be performed before hedging
 Should be based on best assumption. No margin Risk Advisory LL
25/09/2009 Enterprise

12. Calibration by risk
 Interest rate risk:
 take into account the parallel , twists, inversion of the
term structure
 QIS4 tail up shocks: 94% at 1yr – low - to 40%
multipliers at 10yr
 interest rate volatility: usually set separately: * 1.5
 Equity risk:
 use different calibrations for publicly-traded, private
equity, hedge funds, emerging markets
 for publicly-traded: tail risk decline of 40% at 99.5%
 for hedge funds: recent decline around 20% Enterprise Risk Advisory LL
25/09/2009


13. Calibration by risk
 Credit, counterparty & asset risk:
 in a total return context, spread risk anticipates future
defaults and migration. No need for an explicit default
model
 spread risk varies by type of assets, rating and currency
 in Q1S4, spread volatility around 30% and shocks of
about 90 bps to treasuries. Probably too low given recent
experience
 concentration risk must be assessed
 for default risk: recovery assumption crucial in the 30%
to 40% range
25/09/2009 Enterprise Risk Advisory LL

14. Calibration by risk
 Life underwriting risk:
 QIS4 mortality rate increased by 15% permanent with a
2.5 additional per mille mortality catastrophe shock –
debate in light of potential pandemic
 lapse shock depends on impact. Can go as high as 100%
multiplicative
 longevity rate increased by a permanent 25%
 Operational risk: must move beyond the factor based
approach to modelling explicitly and map to insurance
coverage and other internal controls
 Liquidity risk: can be modeled and not simply
Enterprise Risk Advisory LL
25/09/2009
managed

15. Correlation in the tail
 Correlations exist at different levels:
 within a risk category:
Market Risk Interest rate Equity FX
Interest rate 1
Equity 75% 1
FX 25% 25% 1
 between risk categories within an entity
 between legal entities: should probably be zero because
of the non-fungibility of capital and the non recognition
25/09/2009 Enterprise Risk Advisory LL

16. Correlation in the tail
 Recent experience seems to indicate otherwise
 According to a recent Pimco study:
Correlation to Early Early 2008 2008 Meltdown
S & P 500 90s % yearly loss
S & P 500 1 1 37%
High-Yield 20% 80% 26%
Bonds -30%
International 30% 70% 45% - 55%
stocks -40%
Real Estate 30% 60% -70% 37%
Commodities 0% -20% -30% 37%
25/09/2009 Enterprise Risk Advisory LL

17. Correlation in the tail: lessons
 Correlations are unstable in the tail and this what EC
is trying to determine
 Independent risks become dependent in extreme
times:
 subprime business practices – operational risks ›
 enhanced defaults - credit risk ›
 market losses on securitized investments – market risk ›
 capital problems at many FIs – liquidity risk ›
 bankruptcies of many FIs – systemic risk ›
 lawsuits by investors and regulators – legal risk ›
 enhanced regulations – regulatory risk ›
25/09/2009 Enterprise Risk Advisory LL

18. Correlation in the tail: lessons
 “When people start buying an asset, the act of them
diversifying ultimately makes the asset less of a
diversifier .“ Pimco’s Head of analytics
 Rule: total diversification benefit should not be above
30%
 One potential approach is to use Clayton copulas
which measure non-linear dependency
 This is difficult as we trying to assess 1 in 200 year
events
25/09/2009 Enterprise Risk Advisory LL

19. Emerging risk
 EC must be a forward looking process , tied to ERM
and thus must anticipate emerging risks
 Risk issues and impact on EC – mostly Solvency II
 liquidity premium: not allowed in the calculation of the
market consistent value of liabilities
 discount rate: most likely the risk-free not swap rates
 group support: not allowed and impact on
diversification assumptions in EC calculation
 MVM: currently set at 6% with no diversification benefit
25/09/2009 Enterprise Risk Advisory LL

20. Emerging risk
 Environmental risks – US based:
 Fiduciary Responsibility: Legal and Practical Aspects of
Integrating ESG Issues into Institutional Investment –
UNEP FI
 NAIC is requiring insurance companies with at least 500
million in annual premiums to start estimating and
publishing an Insurer Climate Risk Disclosure Survey
starting in May 2010.
 NAIC seeks to determine "how insurers are altering their
risk-management and catastrophe-risk modeling in
light of the challenges posed by climate change. “ › direct
25/09/2009 implications
EC Enterprise Risk Advisory LL

21. CONTACT
Michel Rochette, MBA, FSA
Enterprise Risk Advisory, LLC
954-607-6969
michel.rochette@enterprise-risk-advisory.com