advanced economic capital

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Advanced (Economic) Capital Topics

Michel Rochette, MBA, FSA2009 Valuation Actuary Symposium

Anaheim, CASeptember 25th 2009

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 LLC

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


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: auditable independent review: More than peer review

Others: consistency between valuation and EC models: valuation

framework input data verifiable and controllable validation and calibration


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 approach

Confidence level: internal, regulatory, rating agencies Frequency of calculations: quarterly to monthly Valuation framework: economic, EV, EEV, MCEV Metric chosen: VAR, T-VAR, EVT


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. "


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:

Regression, neural networks, Bayesian, fuzzy logic, EVT Ideally: a combination and adapted to each risk and

complexity


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 reviews

Must go beyond the pure regulatory ticking the box


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

numbers stress testing and reverse stress testing: sensitivity of the

results models capture business environmental changes


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 validation25/09/2009 Enterprise Risk Advisory LLC

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

embedded as the purposed is to estimate required capital for the risks facing the organization

Time horizon and risk measures chosen per risk category


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% implied equity volatility of around 35%

Currency risk: usually set around +/- 20% for a well-diversified portfolio


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% range25/09/2009 Enterprise Risk Advisory LLC

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 managed

Contagion (systemic ) risk: Large FIs might be subject to additional capital if viewed as systematically important.

Strategic risk: can deplete capital and should be modeled

Reputation risk: doesn’t affect capital but value of the firm


Correlation in the tail Correlations exist at different levels:

within a risk category:

between risk categories within an entity between legal entities: should probably be zero because

of the non-fungibility of capital and the non recognition of group capital support by Solvency II


Market Risk Interest rate Equity FX

Interest rate 1

Equity 75% 1

FX 25% 25% 1

Correlation in the tail Recent experience seems to indicate otherwise

According to a recent Pimco study:


Correlation to S & P 500

Early 90s

Early 2008 2008 Meltdown% yearly loss

S & P 500 1 1 37%

High-Yield Bonds

20% -30%

80% 26%

International stocks

30% -40%

70% 45% - 55%

Real Estate 30% 60% -70% 37%

Commodities 0% -20% -30% 37%

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 › diminished reputation for the financial industry –

reputation risk and loss in value


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


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


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 EC implications25/09/2009 Enterprise Risk Advisory LLC

CONTACT

Michel Rochette, MBA, FSAEnterprise Risk Advisory, LLC

[email protected]

mailto:michel.rochette@enterprise-risk-adv

advanced economic capital

Economy & Finance