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Advanced Economic Capital
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