Joint Regional Seminars Economic capital training Presented by: Supported by:
© 2011 Towers Watson. All rights reserved.
Greg Solomon, Swiss Re and Paul Carrett, UBS John Rowland, Towers Watson and Penny Fosker, Towers Watson
Objectives
Hands on introduction to economic capital
Background – what are risk based capital techniques and why these techniques were introduced How economic capital measures are used in business – why they are relevant to you
Defining the framework – the key areas of focus
Historical trends – how approaches have changed over time
Practical implementation – stepping through the development phases
Operational issues – some of the key hurdles you need to address
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Why should economic capital matter to you? Globally, accounting and regulatory regimes are moving towards principles based approaches using economic measures But also from a management perspective… …company performance will be driven by the underlying economics in the long term Recognising this is leading many companies to make strategic decisions which are informed by economic capital metrics © 2011 Towers Watson. All rights reserved. Proprietary and Confidential. For Towers Watson and Towers Watson client use only.
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What is capital?
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Objectives
Introducing and defining capital
Different approaches used for different purposes
What are risk based capital techniques
Why these techniques have been introduced
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What is capital?
Free capital
Required capital
Available capital
Assets
Capital = assets – liabilities Required capital = capital required to support the business written
Regulatory required capital
Rating agency required capital
Internal required capital
Available capital = capital available to support the business written
Technical provisions
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Why do companies hold capital?
Holding capital to support the business is a regulatory requirement…
…and it’s also essential for managing the business
Capital
Risk
Risk exposure determines capital needs Required capital is a function of the tail of the risk distribution
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How much capital is enough? How much is too much?
The market price of risk is a key driver of value creation
Value
Price depends on overall characteristics of the risk distribution
Capital utilisation has a cost and hence reduces value creation
Capital
Risk
Risk exposure determines capital needs Required capital is a function of the tail of the risk distribution © 2011 Towers Watson. All rights reserved. Proprietary and Confidential. For Towers Watson and Towers Watson client use only.
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Capital = assets - liabilities
But what do we mean by “assets” and “liabilities”?
Different definitions arise from different accounting conventions
Inclusion/exclusion of specific assets or liabilities — Exclude intangible assets
Application of different methodologies — Book value versus market value methodology — Inclusion of prudent margins in liabilities
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Different definitions – a sample overview Solvency 1
Risk based capital
Economic capital
Assets
Mix of book value and market value
Market value
Market value
Technical Provisions
Including a margin for prudence
Best estimate liability plus provision for adverse deviations
Best estimate liability plus risk margin for non-hedgeable risks
Net premium valuation using prudent valuation interest rate
Discount at risk free rate
Discount at risk free rate
No explicit allowance for value of options and guarantees
Explicit allowance for value of options and guarantees
Simple factor based approach – no direct link to risks
Sum of capital charges across specified risks
Change in net asset value under stressed conditions
Cap on allowance for reinsurance
Capital charge for each risk category calculated as risk factor x risk driver
Parameter driven stress tests or stochastic derivation, dependent on purpose and level of sophistication
No explicit allowance for value of options and guarantees Capital
Static risk factors based on industry level analysis at a selected probability of remaining solvent over a given time period
Allow for diversification within and across risk categories
Covariance factor / formula applied to allow for diversification across risk categories © 2011 Towers Watson. All rights reserved. Proprietary and Confidential. For Towers Watson and Towers Watson client use only.
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Economic capital
Risk based capital
Solvency 1
Comparing approaches… Prudent reserves Simple factor based Weak link to underlying risks
Prudent reserves and fair value assets Industry factors applied to individual risk drivers
MVA and BEL (excl TVoG) Industry factors applied to individual risk drivers
MVA and BEL (incl TVoG) Industry factors applied to individual risk drivers
MVA and BEL (incl TVoG) Industry stress tests applied across risk categories
MVA and BEL (incl TVoG) Company specific stress tests applied across risk categories
MVA and BEL (incl TVoG) Internal model approach
Increasing levels of sophistication © 2011 Towers Watson. All rights reserved. Proprietary and Confidential. For Towers Watson and Towers Watson client use only.
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Recap…
Insurers accept risk from policyholders in return for a premium
These risks need to be managed so that
Policyholder claims are paid as they fall due
The company makes a profit
Capital provides a cushion that
Reduces the likelihood that obligations to policyholders cannot be met in adverse circumstances Allows the company to continue to grow and develop
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Why have risk based capital techniques been developed?
Solvency 1 style capital requirements
Factors applied to limited risk driver proxies
…and risk management and mitigation techniques are not recognised
Lack of transparency over the actual level of solvency of the company — Due to prudence in reserving bases
…and inconsistencies between reserving strength and capital requirements — Life business:
more prudent reserves = higher capital requirement
— Non-life business:
more profitable premiums = higher capital requirement
Not responsive to changing risk profile
Risk Based Capital The amount of capital a company should hold, based on an assessment of the risks it faces © 2011 Towers Watson. All rights reserved. Proprietary and Confidential. For Towers Watson and Towers Watson client use only.
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Risk based capital versus economic capital Practice
Theory Risk based capital
Risk based capital synonymous with regulatory capital calculations
Applying industry factors to pre-defined risk drivers Allowing for diversification via application of factor or formula
Economic capital synonymous with scenario and probability distribution based approaches
Stressing the balance sheet to understand the change in the net asset value
Economic capital © 2011 Towers Watson. All rights reserved. Proprietary and Confidential. For Towers Watson and Towers Watson client use only.
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Risk based capital versus economic capital
The Solvency II Solvency Capital Requirement (SCR) is a form of risk based capital calculated on an economic basis
But it is not the only definition of economic capital Risk based capital Solvency II SCR
Economic capital © 2011 Towers Watson. All rights reserved. Proprietary and Confidential. For Towers Watson and Towers Watson client use only.
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Economic capital is measured by “stressing” the economic balance sheet Asset stresses include equity market declines, changes in interest rates and credit spreads, defaults
Stressing the balance sheet produces an economic loss of capital
Liability stresses include adverse reserve development, product underpricing, catastrophe, and uncollectible reinsurance, as well as asset effects
Economic Loss Stressed Capital Baseline Assets
Stressed Assets
Stressed Liabilities
Baseline Capital
Baseline Liabilities
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The basic concept of economic capital is straight forward + 0 Losses from “extreme” events are covered by economic capital up to the defined risk tolerance level
–
Risk tolerance level
Ranked outcomes – each equally likely
What level of assets is needed today to provide reasonable assurance that future obligations can be met?
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Different stakeholders have different risk tolerances 1 in ∞
1 in 1 in 2000 200
1 in 10
Mean
Ideally, a view of the whole distribution will be available
Policyholder focus Rating agency focus
Regulator focus
Investor focus
Earnings/change in value/surplus
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Current regulatory requirements in Asia Pacific Country
Assets
Technical provisions
Capital
Australia
Market
Best estimate plus margins – VIR varies with the economic environment
RBC
China
Book/market
Prudent – VIR not greater than min (7.5%, pricing rate)
Solvency 1
Hong Kong
Market
Prudent – VIR varies with the economic environment
Solvency 1
India
Book/market
Prudent – VIR varies with the economic environment
Solvency 1
Indonesia
Book/market
Prudent – VIR max 9% (IDR), 5% (USD)
RBC
Japan
Book/market
Prudent – VIR varies by policy issue year
RBC
Malaysia
Market
Best estimate plus PRADs – VIR varies with the economic environment
RBC
New Zealand
Market
Best estimate plus margins – VIR varies with the economic environment
None*
Philippines
Book
Prudent – VIR < 6%
RBC
Singapore
Market
Best estimate plus PADs – VIR varies with the economic environment
RBC
South Korea
Book/market
Prudent – VIR locked in at pricing
RBC
Taiwan
Book/market
Prudent – VIR locked in at at pricing
RBC
Thailand
Book/market
Prudent – VIR < 5%, locked in at pricing
Solvency 1
Vietnam
Book/market
Prudent – VIR < 80% of 10yr Government Bond yield, locked in at pricing
Solvency 1
* Institute of Actuaries New Zealand recommends an approach equivalent to Australian requirements. © 2011 Towers Watson. All rights reserved. Proprietary and Confidential. For Towers Watson and Towers Watson client use only.
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Future regulatory requirements in Asia Pacific… China Regulator investigating RBC and EC
India Regulator introduced EC as a supplementary measure
Singapore Review of RBC announced
Australia Introduction of ICAAP requirements from 1/1/13
Japan Revised RBC requirement effective from 31/3/12
Hong Kong Regulator investigating RBC and EC
Thailand RBC effective from 30/9/11
New Zealand Required capital effective from 31/12/11
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The role of economic capital in business
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Objectives
Economic capital and its role in risk management
Integration of economic capital into business processes
Use of economic capital in risk based pricing
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The role of economic capital in business Economic capital and its role in risk management
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Improving business performance through ERM and economic capital
ERM goes far beyond the calculation of a number © 2011 Towers Watson. All rights reserved. Proprietary and Confidential. For Towers Watson and Towers Watson client use only.
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Gearing up for an effective ERM framework Strategy/Policy • Risk strategy
Risk processes and tools
Monitoring/Reporting • Data structure
• Risk appetite
• Risk identification
• Dashboards
• Risk policies
• Capital management
• “What if” analysis
• Economic capital • ALM/hedging What types and levels of risk support strategic objectives?
• Risk-based product design • Risk-based pricing
What risk information is needed by decision makers?
• Risk optimisation • Technology • Performance management
Organisation
What data and analysis are needed to evaluate risk/reward?
Management
• Governance
• Accept risk / no action
• Roles and responsibilities
• Mitigate risk
• Risk culture
• Transfer risk • Exploit uncertainty to create value
What structure best supports effective decision making? © 2011 Towers Watson. All rights reserved. Proprietary and Confidential. For Towers Watson and Towers Watson client use only.
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An economic perspective links risk, capital and value Maximise value by relating a firm’s decisions on the risks it takes to the decisions on the capital it uses to finance its business Economic capital is the unexpected impact to value at some confidence interval over some time horizon
Value Creation
Return on Risk
Portfolio of Enterprise Risks Risk Structure
Capital Costs
Value Management
Capital Adequacy
Portfolio of Capital Resources
Risk and Capital Management How much capital do I need?
What type of capital do I need?
Capital Structure
Economic Capital © 2011 Towers Watson. All rights reserved. Proprietary and Confidential. For Towers Watson and Towers Watson client use only.
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Uses fall into different categories Calculation of capital requirements (including analysis of movement) Monitoring risk appetite, limits and controls Risk management
Capital allocation and strategic planning Business planning
Reinsurance programme Product design, underwriting and pricing M&A, re-organisations Performance management and compensation ALM, hedging
Planning
Business processes
Other reporting and key performance indicators: IFRS, regulatory, GAAP, rating agency Wider reporting
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The role of economic capital in business Integration of economic capital into business processes
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Questions are being asked about integrated, enterpriselevel risk analysis and decision-making
How much capital do we need and what return should we get on it? How do we identify the key and emerging risks within our organisation, and how do we manage them?
How can we maximise our return on capital, given our risk appetite?
How do we select our growth strategies, given our risk environment?
How do we best invest our assets, given the structure of our exposures? How much, and on what terms, should we insure and hedge? How should we report our risk management results and communicate with external audiences about our risk management programs?
How do we build a risk culture within the organisation?
How do we coordinate all of this? And how do we get started?
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Company management is faced with a bewildering array of metrics Economic Capital
Traditional Embedded Value
Target Credit Ratings
Local Statutory Capital
Key Operating Ratios MarketConsistent Embedded Value Value of New Business
Book Capital
IAS
Local Accounting Rules
Internal Rate of Return
Inconsistency
Confusion
Solvency II Capital
RORAC/ RAROC
Information overload
ROE
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Economic capital is increasingly becoming a useful tool in influencing significant management decisions Capital Adequacy Assessment/Capital Management Asset/Investment Strategy (Including Hedging)
46%
Reinsurance Purchasing
46%
M&A and Divestiture
24%
Performance Measurement
23%
Incentive Compensation
21%
33%
28%
26%
24%
39%
37%
Product Design and Pricing
13%
35%
52%
Annual Business Planning
18%
28%
54%
Strategic Planning and Capital Allocation
48%
28%
35%
42% 31%
15%
Currently using EC
12%
26%
62%
Plan to use EC in the next 24 months
54%
Do not use EC and no plans to use
Towers Watson global ERM survey 2010 Q.32. (Select all that apply.) © 2011 Towers Watson. All rights reserved. Proprietary and Confidential. For Towers Watson and Towers Watson client use only.
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An economic capital framework allows risk based decisions to be put on an equal footing Traditional approach
The problem
Approach using economic capital
Pricing
Maximise ROE and/or IRR
GAAP equity subject to local accounting rules
Use economic capital as capital measure to standardise risk assessment
Diversification Benefits
Limited
“Eggs in one basket”
Standardisation of risk allows leveraging risk diversification opportunities
Capital Allocation
Local accounting
Management not informed on optimal deployment of capital
Risk transparency informs more optimal capital deployment
Hedging & Trade-off Analysis
Maximising earnings relative to capital impacts
Incents arbitrage of local accounting rules
Use economic capital to make true risk to value transparent
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Analysis can transform economic capital into a powerful management tool
Stress and sensitivity scenarios can provide valuable risk management information and facilitate discussions with senior management
“What if” analysis can be help inform risk and strategic management decisions
e.g. scenarios based on 1987 crash, Hurricane Katrina, 9/11, 2004 Indian Ocean tsunami
e.g. M&A, reinsurance strategies, asset allocation decisions
Ideally want the ability to see impact on results
Across different probabilities
At several levels of granularity (e.g. by product, risk, geography)
With and without allocation of diversification benefits
With this capability, insurers can use economic capital to support a wide range of decisions and benefit from its full potential © 2011 Towers Watson. All rights reserved. Proprietary and Confidential. For Towers Watson and Towers Watson client use only.
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Illustrative
Phased implementation depends on business benefit vs cost High
Capital requirements
Risk management Reinsurance programme
Deliv
Performance management and compensation Investment: ALM / Hedging
Business Benefit / Priority
Medium
Capital allocation
Business planning Management of participating business
Product design, underwriting and pricing Other reporting and KPIs: IFRS, Regulatory GAAP, rating agencies M&A, reorganisations
Low
Low
Medium
High
Difficulty / Cost © 2011 Towers Watson. All rights reserved. Proprietary and Confidential. For Towers Watson and Towers Watson client use only.
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Using economic capital is decision making can result in a competitive advantage “Risk comes from not knowing what you're doing.” - Warren Buffett “Risk is like fire: If controlled it will help you; if uncontrolled it will rise up and destroy you.” - Theodore Roosevelt “Any time you take a chance you better be sure the rewards are worth the risk because they can put you away just as fast for a ten dollar heist as they can for a million dollar job.” - Stanley Kubrick © 2011 Towers Watson. All rights reserved. Proprietary and Confidential. For Towers Watson and Towers Watson client use only.
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The role of economic capital in business Use of economic capital in risk based pricing
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Risk based pricing can help maximise value created by new business
Granular risk based pricing
Focused targeting and “cherry picking”
Calculation of the minimum price to charge for a product to more accurately reflect the risk and required return arising from product features, including leverage, asset risk, embedded financial options and the capital required
Identify and target areas where the company’s products are particularly profitable (and unprofitable), both in absolute terms and in their capital efficiency
Exploitation of market inefficiencies and risk synergies
An effective and dynamic risk based pricing system will allow the company to exploit opportunities arising from temporary market pricing anomalies
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Example: Stochastic pricing results show significant tail risk which leads to high economic capital 25.00% 20.00%
Expected Return
15.00% 10.00% 5.00% 0.00% -5.00% -10.00% -15.00%
Economic capital source
-20.00% Interest Rate Scenario
Product has average return of 12% over set of stochastic scenarios
A small number of scenarios have negative returns
Poor scenarios have low projected interested rates © 2011 Towers Watson. All rights reserved. Proprietary and Confidential. For Towers Watson and Towers Watson client use only.
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Example: After hedging required economic capital would be reduced 25.00% 20.00%
Expected Return
15.00% 10.00% 5.00% 0.00%
Economic capital source
-5.00% -10.00% -15.00% -20.00% Interest Rate Scenario
Average return is slightly lower over set of stochastic scenarios
Ends up being a cost for most scenarios as option expires with no value
Significantly improves tail scenarios © 2011 Towers Watson. All rights reserved. Proprietary and Confidential. For Towers Watson and Towers Watson client use only.
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Implementation – from simple methods to best practice
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Objectives
The purpose of economic capital
Defining economic capital
Defining risk distributions and loss functions
An introduction to advanced modelling
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Implementation – from simple methods to best practice What is economic capital for?
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Why do insurers calculate economic capital? United Kingdom
Malaysia
6,000
Thailand 800
1,200
750
1,150 5,500
700
5,000
4,500
650 1,050 SET Index Level
Kuala Lumpur Composite Index Level
FTSE 100 Index Level
1,100
1,000
600
550
950 500 900 450
4,000 850
3,500
800
Date
350
Date
Taiwan
Date
Hong Kong
China
25,000
3,000
7,500
22,500
2,750
7,000
20,000
2,500
6,500
SEE Composite Index Level
8,000
Hang Seng Index Level
TWSE Index Level
400
17,500
2,250
6,000
15,000
5,500
12,500
1,750
5,000
10,000
1,500
Date
Date
2,000
Date
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EX ER C
Exercise 1: Defining extreme events
IS E
That was an example of an extreme event
Discuss with your neighbours and define 5 more
Document on the sheet provided
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Other events that could lead to losses A meteorite lands on China
Cure for cancer
Improvement in longevity
Mass increase in lapse rates
Interest rates fall to zero / rise to 10%
Nuclear Armageddon
Increase in expense
SARS
Global warming
Earthquake
The Plague kills 50% of population
Increase in credit spreads
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What is economic capital?
Economic capital is the money you hold to protect you against the impact of adverse events or combinations of adverse events happening simultaneously
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What is economic capital?
Economic capital is the money you hold to protect you against the impact of adverse events or combinations of adverse events happening simultaneously
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How much capital is enough … do I protect myself against all events? “… for insurers to consider how this liability might change in reasonably realistic adverse scenarios …” — Individual Capital Assessment, UK “… plausible adverse scenarios …” — Dynamic Capital Adequacy Testing, Canada “… on a basis that is more conservative than best estimate and that considers scenarios of adverse experience ...” — Capital Adequacy Standard, Australia
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Events can be too extreme ... outside a “risk appetite” A meteorite lands on China
Cure for cancer
Improvement in longevity
Mass increase in lapse rates
Interest rates fall to zero / rise to 10%
Nuclear Armageddon
Increase in expense
SARS
Global warming
Earthquake
The Plague kills 50% of population
Increase in credit spreads
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Another complication is that events don’t come along in isolation …
For example, equity markets fall and interest rates reduce at the same time … FTSE 100 Index Level 7,000
FTSE 100 Index Level
6,000
5,000
4,000
3,000
Date
… and, as a result, you might also experience a spike in lapse rates 25% 20% 15% 10% 5% 0% 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Month
We need to allow for these interactions
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Implementation – from simple methods to best practice Two possible approaches
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Economic capital is the answer to specific questions Question
“Technical terms”
1. What risks am I exposed to?
1.
Risk universe, risk factors
2. How might the risks I am exposed to vary?
2.
Time horizon, risk model, marginal risk distribution, dependency structure, correlation, copulas
3. Given the evolution of risks, how will this affect my business performance?
3.
Balance sheet response to risk, loss function
4. What level of impact am I concerned about?
4.
Risk measure, confidence interval, risk appetite, VaR, Tail-VaR, risk of ruin, required economic capital
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Two general approaches have emerged to measure economic capital
Liability runoff approach The level of total initial assets, less some measure of reserves for liabilities, required to pay all future policyholder benefits at the chosen confidence level
One-year mark-to-market approach The level of assets, in addition to the market value of liabilities, needed to cover a fall in the market value of net assets over a one-year time horizon at the chosen confidence level
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Each of the two main approaches has pros and cons Risk Management and Risk-Based Performance Considerations Liability Runoff
One-year Market-Consistent
+ Measures risk over period risk is held, so better for long-term decision making
+ Facilitates link between risk quantification and risk management
+ Longer-term decision making not distorted by volatility of economic assumptions over short term, i.e. stable capital requirements
+ Short-term volatility to economic assumptions may be very relevant when assessing risk management options
+ More accurately captures risks that emerge over time
+ Risk quantification and risk management linked to performance management over the typical annual performance reporting cycle
– Does not respond to short-term market fluctuations, which might impair risk management decisions
– Can lead to volatile capital requirements from one to the next period
– Can result in a timing mismatch, with shortterm performance being compared with risk and capital based on a longer term
– Fails to provide information about emergence of risk over time
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Both approaches pose certain implementation challenges Implementation Considerations One-year Market-Consistent
Liability Runoff + Relatively standard, i.e. consider the real world projection of liabilities until they run off
+ Generally easier to calibrate EC to target confidence levels over one year
– Inclusion of interim solvency assessments can add to the model complexity
+ All risks measured over the same time horizon, so consistent aggregation (and demonstration of diversification benefits) easier to achieve
– Can pose challenges in aggregation across different lines of business with different durations
– Market-consistent liability valuations can lead to stochastic-on-stochastic calculations; more simplistic approaches (e.g., stress testing) are less accurate and provide less insight into overall capital distribution; replicating portfolio and other advanced techniques may provide solutions
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Both methods can be used, but … Europe The one-year mark-to-market approach has emerged as the standard Asia Pacific The trend is towards a one-year mark-to-market approach
North America A consensus is still forming
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We will adopt a 1-year mark-to-market approach Market Value Assets
Available Economic Capital (AEC)
AEC RM BEL
Probability of outcome
Sim 1 Expected Market Value Assets
AEC RM BEL
0.5% probability
Sim 500,000
t=0
What risks am I exposed to? How might the risks I am exposed to vary?
Market Value Assets
AEC RM BEL
0.05% probability
t=1
Given the evolution of risks, how will this affect my business performance?
What level of impact am I concerned about?
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Implementation – from simple methods to best practice Getting started
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What risks am I exposed to? Total EC
Basic EC
Non-Life
Premium Reserve
Market
Currency
Health
SLT
Spread
Mortality
Interest rate
Longevity
Property
Expenses
Lapse
CAT
Operational
Counterparty
Life
Intangible
Non SLT
Lapse
Mortality
Premium Reserve
Expenses
Longevity
Disability
CAT
Lapse CAT
Equity
Disability
Concentration © 2011 Towers Watson. All rights reserved. Proprietary and Confidential. For Towers Watson and Towers Watson client use only.
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The measure of risk needs to be defined Distribution of “profit and loss” Probability of outcome
Shaded area 0.5% of distribution 99.5% value at risk
Mean value of distribution
Profit / loss
99.5% tail-value at risk
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How do I choose between VaR and Tail-VaR? Value at Risk Is the risk measure used in Solvency II and Basel II and most rating agency models
Tail-Value at Risk Used by supervisors in USA, Canada and Switzerland
Easier to implement than t-VaR
Defines the trigger point of insolvency Has a technical flaw – not a coherent risk measure – although this is not often an issue practical
Harder to implement than VaR Measures the average cost of insolvency Does not have the technical flaw faced by VaR – is a coherent risk measure
The relative simplicity of VaR has led to its emergence as the standard measure © 2011 Towers Watson. All rights reserved. Proprietary and Confidential. For Towers Watson and Towers Watson client use only.
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What confidence interval shall I consider? Distribution of “profit and loss” Probability of outcome
TAIL PROBABILITIES AAA 1bp
AA 3bps
A 7bps
BBB 50bps
ECBBB = VaR 99.5%
Mean value of distribution
Profit / loss
ECA = VaR 99.93% ECAA = VaR 99.97% ECAAA = VaR 99.99% © 2011 Towers Watson. All rights reserved. Proprietary and Confidential. For Towers Watson and Towers Watson client use only.
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More than one event can occur simultaneously 100% correlated
-100% correlated
Positively correlated
Negatively correlated
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The approach defines capital in terms of the economic balance sheet
Free capital
Required capital
Available economic capital
Risk margin Market value of assets Market consistent value of liabilities
Time value of guarantees
Certainty equivalent liability
Discounted best estimate of liabilities
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The approach poses a computational challenge: stochastic-on-stochastic modelling Available Economic Capital (AEC) Market Value Assets
AEC RM
Scenario 1
Expected Market Value Assets
AEC
Probability of outcome
BEL
RM BEL
Scenario 100,000
Market Value Assets
AEC RM BEL
T=0
Real world
T=1
Marketconsistent © 2011 Towers Watson. All rights reserved. Proprietary and Confidential. For Towers Watson and Towers Watson client use only.
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Many life insurers implement the 1-year market-consistent approach by directly measuring the balance sheet at the chosen confidence level Normal Conditions
Stressed Conditions
AEC AEC MV Assets
RM
MV Assets
BEL
RM BEL
Required EC AEC
Normal
AEC
Stressed
Referred to as the “stress test correlation matrix” approach © 2011 Towers Watson. All rights reserved. Proprietary and Confidential. For Towers Watson and Towers Watson client use only.
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Stress test correlation matrix approach
Aggregate capital =
i
j ij C i C j
Where Ci is the capital required for the ith risk and ij is the correlation coefficient between ith and jth risk
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Example: Suppose the following impacts of stresses are measured Risk factor
Stressed value 616
Equity
7
Interest rate Mortality
775
Lapse
639
Total before diversification
2,037
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Example: Assume the following correlation matrix
Equity
Interest Rate
Mortality
Lapse
Equity
1
0.75
0.00
0.25
Interest Rate
0.75
1
0.00
0.50
Mortality
0.00
0.00
1
0.00
Lapse
0.25
0.50
0.00
1
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Example: After diversification Risk factor
Stressed value 616
Equity
7
Interest rate Mortality
775
Lapse
639
Total before diversification
2,037 (698)
Diversification Total after diversification
1,339
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Implementation – from simple methods to best practice Advanced methods
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The stress test correlation matrix approach has proved useful, but firms have started to understand its limitations Area
Stress test correlation assumption
Issue
Risks
Normally distributed
Most risks are fat‐tailed
Dependency
Correlation only captures linear dependency
Risk dependency structures vary when moving from benign to extreme conditions – “markets crash together”
Balance sheet response (1)
Assumes linear response to variations Balance sheets behave in a non‐linear way – e.g. embedded in risk financial options and guarantees vary non‐linearly with underlying market exposures
Balance sheet response (2)
Assumes separable response to variations in risk
Response to risks is not separable – e.g. annuity response to combined mortality and interest rate stress is not the sum of the two individual stresses
Fungibility of own funds and tax
Adjusted for manually outside the model if at all
Legal or regulatory restrictions prevent losses in some legal entities being supported by assets from other legal entities
Capital allocation
Not directly possible, requires ad hoc methods
Embedded and active risk management requires understanding of risk, capital consumption and value creation at the level decisions are made
Full distribution / other percentiles
Not possible without re‐run of balance sheet at target percentile
Capital at the 99.5th percentile is only one data point – best practice risk management requires understanding of impact of decisions across the risk and outcome spectrum
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Best practice firms are revisiting the general methodology and addressing the stochastic-on-stochastic modelling challenge Available Economic Capital (AEC) Market Value Assets
AEC RM
Scenario 1
Expected Market Value Assets
AEC
Probability of outcome
BEL
RM BEL
Scenario 100,000
Market Value Assets
AEC RM BEL
T=0
Real world
T=1
Marketconsistent © 2011 Towers Watson. All rights reserved. Proprietary and Confidential. For Towers Watson and Towers Watson client use only.
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Three approaches to modelling the 1 year market consistent approach have emerged
Stress test correlation matrix approach
1 year VaR
Delivery certainty
Simulation modelling of market risk, simplified modelling of insurance risk
Simulation modelling of all risks
Information gained
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This complexity has been introduced to address hidden limitations with the traditional “stress test correlation matrix” approach Area
Stress test correlation assumption
General simulation methodology
Risks
Normally distributed
Allows risks to be modelled using any marginal distribution
Dependency
Correlation only captures linear dependency
Works with complex dependency structures – e.g. copula functions
Balance sheet response (1)
Assumes linear response to variations Use of replicating models allows for full non‐linearity of the in risk balance sheet to be reflected in the calculations
Balance sheet response (2)
Assumes separable response to variations in risk
Use of replicating models allows for full non‐separability of risk to be reflected in the calculations
Fungibility of own funds and tax
Adjusted for manually outside the model if at all
Legal or regulatory restrictions can be modelled directly and reflected as balance sheet are produced for each risk outcome
Capital allocation
Not directly possible, requires ad hoc methods
Enables capital to be allocated to any level modelled in the simulation
Full distribution / other percentiles
Not possible without re‐run of balance sheet at target percentile
Automatically generates the full distribution forecast
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Looking at each component in turn Risk factor Risk marginal marginal distributions distributions
Risk factor Risk dependency dependency structure structure
Balance sheet valuation loss functions
Calculation
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Some terminology…
Risk Factors Factors that contribute to either loss frequency or loss severity Loss Functions The impacts of the changing risk factors on the balance sheet
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Risk factor marginal distributions
Risk factor dependency structure
Balance sheet valuation loss functions
Calculation
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Risks are not normally distributed
The heavy tailed distribution has a greater probability of very small and very large events The heavy tailed distribution has a lower probability of medium sized events
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Distribution of extreme events Probability
Fitting heavy tailed distribution
50% Lots of data
75%
95%
98%
percentile 99.8%
Less data Some data Little data Few events © 2011 Towers Watson. All rights reserved. Proprietary and Confidential. For Towers Watson and Towers Watson client use only.
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Experience shock versus allowing for long term change Experience shock
Volatility around long term trend
Long term change e.g. new disease
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EX ER C IS E
Exercise 2: Fitting risk distributions
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EX ER C IS
Exposed to equity: how does equity evolve?
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EX ER C IS
Fitting a distribution…but which should we choose?
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EX ER C IS
Assessing a risk factor goodness-of-fit
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EX ER C
Risk factors - exercise
IS E
Which distribution do you choose? Exercise 2 : Risk factor calibration Task You are leading a team calibrating an economic capital model for a medium-sized Life company. You need to recommend a distribution to be used for the equity risk factor . To help with your decision, a colleague has prepared the following table of equity stresses. In addition, another colleague has fit four candidate distributions to historical data. Histograms and QQ -plots of these fits can be found in the appendix. Please consider the table and the appendix and make a recommen dation below. Table 1: Equity risk stresses Source
Stress
Regulator X’s regulatory capital assessment stress
-40%
Stress for equities in “killer scenario”
-35%
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EX ER C
Risk factors - exercise
IS E
Which distribution do you choose?
1
Recommendation I recommend the use of the Normal
(please tick one box)
Student’s T Pearson IV Variance-Gamma
distribution for modelling equity risk in the economic capital model.
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EX ER C IS
Risk factors - exercise
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Risk factor marginal distributions
Risk factor dependency structure
Balance sheet valuation loss functions
Calculation
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Dependency should allow for different behaviour in the tail United Kingdom
Malaysia
6,000
800
1,200
Hong Kong
Thailand
25,000 750
1,150 5,500
700
4,500
650 1,050
20,000 1,000
950
900 4,000
17,500
600
550
500
450
15,000
850
3,500
SET Index Level
5,000
22,500
Hang Seng Index Level
Kuala Lumpur Composite Index Level
FTSE 100 Index Level
1,100
400
800
350
12,500
Date
Date
Date
10,000
Taiwan
Hong Kong
China
8,000
25,000
3,000
7,500
22,500
2,750
Date
In benign markets, equity market fluctuations will not have a big impact on lapses, but, when markets fall, there is usually a trigger point that gives rise to mass lapses … 6,500
17,500
6,000
15,000
5,500
12,500
5,000
10,000
Date
20%
15%
10%
5%
Date
0%
SEE Composite Index Level
20,000
Hang Seng Index Level
TWSE Index Level
7,000
25% 2,500
2,250
2,000
1,750
1,500
Date
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Risk factor marginal distributions
Risk factor dependency structure
Balance sheet valuation loss functions
Calculation
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Use non-linear balance sheet models or “loss functions”
A 30% fall is not necessarily ¾ of a 40% fall 1,200
Losses
1,000 800 600 400 200 0 0%
‐10%
‐20%
‐30%
‐40%
‐50%
‐60%
Equity returns
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Use non-linear balance sheet models or “loss functions”
A 30% fall is not necessarily ¾ of a 40% fall Linear Non-linear
1,200
Losses
1,000
10% overestimation
800 600 400 200
10% underestimation
0 0%
‐10%
‐20%
‐30%
‐40%
‐50%
‐60%
Equity returns
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Replicating models – loss functions
A loss function is an interpretation of the values that would be derived if all 100,000 balance sheet runs were performed Value of Balance Sheet Loss
Values estimated by loss function
Actual values from actuarial cashflow model runs
Risk factor value
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The impact of two risks occurring at the same time is different from the sum of the individual impacts
Losses from mortality and interest rate movements Separability assumption
Actual joint stresses
Change in mortality
Change in mortality
-20% 260
-15%
-10%
-5%
0 0
-20% 0 -25 -50
100
-10%
-5%
0 0
Interest rate movement (bps)
0 -25 -50
Interest rate movement (bps)
-75
-75 360
-15%
440
-100
-100
18% underestimation
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Parametric loss functions can be fitted to stress test results from projection models Change in mortality
Change in interest rates
-10%
-£120m
-20%
-20%
Balance sheet movement non-linearity
-£260m +0.5%
+£40m
-1%
-£100m
-1%
-£440m
non-separability (multivariate non-linearity)
non-linearity
Balance sheet movement = -1,000 * Δmort2 + 1,100 * Δmort - 133,333 * Δi-rate2 + 8,667 * Δi-rate - 40,000 * Δmort * Δi-rate © 2011 Towers Watson. All rights reserved. Proprietary and Confidential. For Towers Watson and Towers Watson client use only.
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EX ER C IS E
Exercise 3: Fitting a loss function
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EX ER C
The Loss function Game!
IS E
The Loss Function Game! Play the game with your neighbour.
PLAYER A
The Loss Function Game! Play the game with your neighbour.
Each of you has to fit loss functions to three different risks. Your neighbour has the complete loss function for your risks. Unfortunately, you only have 25 hours of computer time and each run takes 5 hours, so you can only ask for 5 results.
Each of you has to fit loss functions to three different risks. Your neighbour has the complete loss function for your risks. Unfortunately, you only have 25 hours of computer time and each run takes 5 hours, so you can only ask for 5 results.
Fill in the run request form below and ask your neighbour to supply you with the results. Plot the results on the charts and sketch your estimated loss functions.
Fill in the run request form below and ask your neighbour to supply you with the results. Plot the results on the charts and sketch your estimated loss functions.
Meet your neighbour
Stress
Result
Stress
Result
…………
…………
Run 1:
…………
…………
Run A:
Run 2:
…………
…………
Run B:
…………
…………
Run 3:
…………
…………
Run C:
…………
…………
Run 4:
…………
…………
Run D:
…………
Run 5:
…………
…………
Run E:
…………
PLAYER B
Don’t cheat! ………… …………
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EX ER C
The Loss function Game!
IS E
Loss with respect to spread stress
300
200
Loss function value
100
0
-100
-200
-300 -0.4
-0.2
0
0.2
0.4
Spread stress
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EX ER C
The Loss Function Game! – How to play
IS E
PLAYER A
PLAYER B
Turn to Page 1
Turn to Page 2
Take 2 minutes to consider the 3 risks
Player A will ask you for some results from your graphs
Request 5 different runs from Player B. Write the stresses in the spaces on side 1 of your sheet.
Estimate the loss function results from your graph and given them to Player A
Sketch the loss functions you think best fit the 3 risks. Turn to Page 2, swap roles and repeat!
Turn to Page 1, swap roles and repeat! © 2011 Towers Watson. All rights reserved. Proprietary and Confidential. For Towers Watson and Towers Watson client use only.
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EX ER C IS
The Loss Function Game!
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Risk factor marginal distributions
Risk factor dependency structure
Balance sheet valuation loss functions
Calculation
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A simulation approach models capital by business unit and risk factor Capital by Business Unit
Capital by Risk Factor
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Using this modelling approach, insurers can understand risk drivers and monitor against a risk appetite Split of Economic Capital
Counterparty risk Operational risk
Insurance risk
Diversification effect Equity Real Estate
ALM -Risk
Interest Rate
Business Unit Economic Capital
Risk Category Interest rates
BU1
BU2
BU3
BU4
BU5
Other
Total
535
397
170
296
985
465
1,322 1,322
98
448
320
393
71
50
689 689
Other market risk
242
341
382
625
697
658
1,277 1,277
Insurance
591
664
284
258
755
293
1,262 1,262
Operational
131
92
78
827
554
171
1,026 1,026
12
57
8
42
18
25
849
963
603
Equity
Counterparty Total
1,177 1,177
1,529 1,529
876 876
79 2,550 2,550
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Implementation – historic trends
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Objectives
Results from Towers Watson’s global ERM survey
How economic capital methodology has changed over time…
…and how it varies currently
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The Towers Watson global ERM survey
Biennial survey of enterprise risk management (ERM) in the insurance sector Largest and longest standing survey for the insurance industry
First survey run in 2000
465 participants globally in 2010, 99 from Asia Pacific
Covers multiple areas of risk management and measurement, including
Performance, priorities and challenges
Governance and organisation
Risk appetite, limits and reporting
Economic capital methodology
Solvency II (for European headquartered participants)
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The proportion of respondents calculating economic capital globally has increased from 57% in 2008 to 65% in 2010
2010
Global
65%
2008
25%
57%
2006
28%
65%
2010
10%
15%
19%
59%
16%
32%
9%
Asia Pacific ex Japan 2008
53%
Currently calculate
24%
Plan to calculate
24%
Do not calculate and no plans
Towers Watson global ERM survey 2006, 2008 and 2010. Does your organisation calculate economic capital? © 2011 Towers Watson. All rights reserved. Proprietary and Confidential. For Towers Watson and Towers Watson client use only.
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Globally, one year approaches are most favoured… … alternative risk assessment periods are most often used by P&C insurers
Global
2010
68%
2008
68%
2006
15%
13%
56%
2010
14%
12%
14%
14%
3%
5%
18%
81%
14%
5%
Asia Pacific ex Japan 2008
60%
1 year
2 to 5 years
10%
Run-off
25%
5%
Other
Towers Watson global ERM survey 2006, 2008 and 2010. Over what period do you assess risk in calculating economic capital? © 2011 Towers Watson. All rights reserved. Proprietary and Confidential. For Towers Watson and Towers Watson client use only.
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Companies that use a fixed time period to calculate economic capital most commonly use a market-consistent terminal balance sheet Global
Asia Pacific ex Japan
Market-consistent balance sheet (mark to market or fair value)
57% 56%
24%
17%
Regulatory balance sheet
60% 60%
GAAP or IFRS balance sheet
23%
GAAP or IFRS balance sheet
Market-consistent balance sheet (mark to market or fair value)
14% 13%
26%
Regulatory balance sheet
27%
16%
Other
3%
Other
0% 0%
4%
2010
2008
Towers Watson global ERM survey 2008 and 2010. If you use a fixed time period to calculate economic capital, what basis do you use for the terminal balance sheet? © 2011 Towers Watson. All rights reserved. Proprietary and Confidential. For Towers Watson and Towers Watson client use only.
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The proportion of insurers using the VaR measure is higher in Asia Pacific (ex Japan) than globally Global
Asia Pacific ex Japan 72%
Value at risk (VaR) or risk of ruin (RoR)
67%
84%
Value at risk (VaR) or risk of ruin (RoR)
70%
39%
Tail value at risk (TVaR) or conditional tail expectation (CTE)
Economic cost of ruin (ECoR)
Tail value at risk (TVaR) or conditional tail expectation (CTE)
20% 21% 37%
4% Economic cost of ruin (ECoR)
5% 11%
11% 20%
3% 0%
4% Other
Other
6% 14%
2010
2008
3% 10%
2006
Towers Watson global ERM survey 2006, 2008 and 2010. What primary measure of risk tolerance do you use to calculate economic capital? © 2011 Towers Watson. All rights reserved. Proprietary and Confidential. For Towers Watson and Towers Watson client use only.
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More than 50% of the respondents to the 2010 survey use simple correlation aggregation approaches Global
Asia Pacific ex Japan 54%
Correlation matrix
55% 56%
Simulation-based aggregation and structural models
None
32%
57%
Correlation matrix
50%
Simulation-based aggregation and structural models
32% 26%
9% 6%
22% 30%
None
11% 10%
Other
11% 10%
10%
Other
5% 7% 7%
2010
2008
2006
Towers Watson global ERM survey 2008 and 2010. What methodology do you use for aggregating risk at the corporate level? © 2011 Towers Watson. All rights reserved. Proprietary and Confidential. For Towers Watson and Towers Watson client use only.
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In summary
Standards for economic capital calculation have emerged over time… …but approaches still vary by region and by type and size of company
There is no single “right” answer!
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Implementation – how you can get there
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Objectives
An example of a practical, phased approach to implementation
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Hypothetically … what are we aiming for? Key design decisions1 Time horizon
1 year
Measure of risk
Value at risk (VaR)
Risks included
Market, insurance, operational
Level of confidence to target
Complete distribution
1. Key design decisions for time horizon and measure of risk for hypothetical requirements based on most common responses made by Asia Pacific companies to relevant questions in Towers Watson global ERM survey 2010.
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…therefore we need…
Stochastic asset liability models to calculate the market consistent balance sheet
Risk models for all underlying risks
Data to support calibration and parameterisation of risk models
Modelling and aggregation techniques that allow for interactions across and between risk categories with non-linearity and non-separability Models that run quickly enough to produce results at all points on the distribution
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…but we have…
Deterministic liability cashflow models
Project liabilities on best estimate assumptions
Investment return assumptions do not vary by period
Single risk discount rate
Assets values determined according to current GAAP requirements
But (usually) easily convertible to market value
A simple asset model capable of re-valuing assets under stressed conditions The knowledge that the three key risks underlying our business are interest rate risk, lapse risk and mortality risk A reasonable amount of data (and the relevant skills) that allows us to develop (allowing for judgement where relevant)
Probability distributions underlying these three risks
A simple correlation matrix of dependencies
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What might a sensible development path look like?
Getting from what we have now… …to what we need… …to support our aims An example approach
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Using a phased implementation approach – Step 1
Step 1: Certainty equivalent value of liabilities
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Using a phased implementation approach – Step 2
Step 1: Certainty equivalent value of liabilities
Step 2: Market value of assets and liabilities
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Using a phased implementation approach – Step 3
Step 1: Certainty equivalent value of liabilities
Step 2: Market value of assets and liabilities
Step 3: Extend risks to cover other insurance and market risks
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Using a phased implementation approach – Step 4
Step 1: Certainty equivalent value of liabilities
Step 2: Market value of assets and liabilities
Step 3: Extend risks to cover other insurance and market risks
Step 4: Allow for non-separability on an approximate basis
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Using a phased implementation approach – Step 5
Step 1: Certainty equivalent value of liabilities
Step 2: Market value of assets and liabilities
Step 5: Extend risks to cover operational risks
Step 3: Extend risks to cover other insurance and market risks
Step 4: Allow for non-separability on an approximate basis
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Using a phased implementation approach – Step 6
Step 1: Certainty equivalent value of liabilities
Step 6: Employ advanced modelling techniques
Step 2: Market value of assets and liabilities
Step 5: Extend risks to cover operational risks
Step 3: Extend risks to cover other insurance and market risks
Step 4: Allow for non-separability on an approximate basis
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Implementation – operational issues
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Objectives
Model and process governance arrangements
Achieving buy-in
Implementation constraints
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Implementation – operational issues Operationalising the system
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Making the system operational Define overall strategy Provide guidance on use of economic capital Ensure on-going appropriateness of methodology, design etc
Business owner
Development team
Production team
Implement the strategy Develop supporting models and reporting Validate and document system
Perform calculations Analyse and report results
Use results to manage the business Input into methodology and design, challenge the approach Use results to monitor risk taking activity
Users
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Senior management support is crucial
Economic capital is used as a tool to help management make better decisions
Senior management need to be actively involved in defining requirements
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Reliable results are essential if they are to be used to manage the business Testing / Validation
Initial and on-going Feed results back into the methodology/model development cycle Not just around the mean – test results/validity of model across the distribution
Business requirements – underlying principles of model, purpose of model, limitations Detailed specification – could be used to re-build a consistent model Testing and validation – testing completed and reasonableness of results User manual Guide for senior management
Documentation / Explanation
Accurate, complete and appropriate underlying data Internal / external loss data, market data, in-force policy data Expert judgement
Data / Parameterisation
Systems and processes
Stable, secure, controlled and auditable system Streamlined, systemised and automated processes Reproducible results
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A continuing cycle of improvement Known issues / testing and validation
Best practice methodology and approaches Model change programme Business uses
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Implementation – operational issues Achieving buy-in
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Use top-down and bottom-up communication to secure internal buy-in
Top-down communication from senior management plus tailored training programmes
Rationale for the decision to implement economic capital
The overall economic capital methodology
Short-term and long-term implementation plans
Modelling requirements
Using the results in decision making
The impact on processes
Bottom-up communication gives business managers the opportunity to react and provide feedback on top-down communication
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How much and when to disclose?
Upside of announcing strong enterprise risk management and economic capital implementation
versus Downside of making disclosures too early in the process
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Implementation – operational issues Implementation constraints
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What are the biggest challenges companies face? What are your biggest challenges in implementing or using economic capital? 49%
Availability of resources
56% 44% 44%
Approach / methodology
44%
Data (e.g. lack of, integrity)
39% 35%
Technology (e.g. run times)
30% 33%
Management buy-in
44% 21%
Relevancy (if regulation N/A) Other
31% 5% 3%
Global
Asia Pacific (ex Japan)
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Do you have the right skill set?
New concepts, new methodologies and new tools
Significant one-off effort… — Initial development requirements – methodology, model, validation, documentation — New processes — Training
…plus on-going needs — On-going maintenance – methodology, model, validation, documentation,
processes — On-going training requirements — Production and analysis of results — Use in decision making
Import or grow the required skills? © 2011 Towers Watson. All rights reserved. Proprietary and Confidential. For Towers Watson and Towers Watson client use only.
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Do you have the systems you need?
What do you have now…
…and what do you want from your system?
Are current systems adaptable to meet new and on-going requirements? Is there an opportunity to radically change the way actuarial reporting and processing systems are operated? Internally or externally developed software solutions?
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What’s your timeframe and budget for implementation?
Time and financial constraints are significant factors in implementation…
…and expected time and cost can depend on many factors
Size, diversity and complexity of your business
Nature of financial models already in place
New hardware and software requirements
Complexity of the proposed methodology being implemented
Phasing of implementation
Availability of data
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In summary…
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A successful economic implementation…
…is a journey …is not just about the numbers …can lead to better informed decisions… …and aid value creation
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Disclaimer This presentation has been prepared for general information purposes only and does not constitute professional advice. The information, opinions and illustrations contained here-in are derived from various sources and have not necessarily been independently verified. Views expressed are those of the presenters, and do not necessarily represent the views of any particular company.
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