Replicating Portfolios in the Insurance Industry - SOA · F3– Replicating Portfolios in the...
Transcript of Replicating Portfolios in the Insurance Industry - SOA · F3– Replicating Portfolios in the...
Investment Symposium March 2010
F3– Replicating Portfolios in the Insurance Industry
Curt Burmeister Mike Dorsel
Patricia Matson
Moderator
Hueyfang Chen
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Replicating Portfolios in the Insurance Industry
AgendaBasics of Replicating Portfoliosby Tricia Matson, FSA, MAAA
Replicating Portfolios: Advanced Approachesby Mike Dorsel, CFA, ASA
Using Trade Restrictions to Improve Your Replicating Portfoliosby Curt Burmeister
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Basics ofR li ti P tf liReplicating Portfolios
Tricia Matson, Principal Deloitte Consulting LLP
March 22, 2010
Overview
• Basics of replicating portfolios
• Uses of replios
• Industry statusy
• Approaches
• Considerations
• Candidate Assets
• Testing of Fit
• Summary
©2010. Private and confidential.4
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Basics of Replicating Portfolios
• Portfolio of assets which can be used to replicate the behaviour of life insurance liabilities under different economic scenarios
• Once a replicating portfolio of assets has been found, then under a wide range of economic conditions, the value of the replicating portfolio equals the value of the liabilities
• The RP can then be used as to estimate the MVL when market conditions change without time consuming model re-runs
• This enables companies to quickly recalculate liabilities, balance sheets, capital requirements and embedded values:– As economic conditions change– Under “what ifs” and specific scenarios– To project market consistent balance sheets
Value of replicating portfolio againstprojected liability value
©2010. Private and confidential.
o p oject a et co s ste t ba a ce s eets
Target ValueR
eplic
atin
g P
ortfo
lio
Uses of Replios
Likely initial uses: Possible future benefits:
Accelerated liability valuation can be used to make complex actuarial calculations more accessible, allowing them to be run more frequently and allowing management to monitor capital positions more closely
• Regular risk reporting/economic capital analysis
• Calculation of market consistent balance sheet
• Benchmark liability replicating portfolio to compare against actual asset portfolio (egmeasurement of basis risk, etc)
• Projecting realistic balance sheets (for
• Business planning
• Testing impact of management actions
• Articulation of risk appetite
• Solvency II
• IFRS
• Investment performance measurement
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• Projecting realistic balance sheets (for sensitivity testing, risk analysis, cost of capital analysis)
• Investment performance measurement
• Hedging strategy analysis
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Industry Status: Drivers for Change
RegulatoryPressure
Solvency II
Drivers for ChangeOpportunities• Competitive advantage• Standardized reporting • More efficient use of
resources
Rating
ERMTurbulentMarkets
Best Practices
Risky andComplex
IFRS
Real-time reportingof risk exposure and capital position
• Improved risk management and controls
• Better capital management• Improved view of economics
Challenges• Changing the cultural mindset• Ensuring global consistency • Updating policies & systems• Training personnel
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Rating Agencies &ERM
Peer Pressure
pExposures
a g pe so e• Improving internal risk
management• Understanding judgments• Avoiding over-reliance on
models• Upfront costs to adopt
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Industry Status: Global Landscape
• Significant use of replios by global insurers:– Led by large multinationals with UK and EU headquarters– Gradually expanding to other countries as their subsidiaries pave the way– Implementation underway at several domestic US insurers– Implementation underway at several domestic US insurers
• For these insurers the drivers tend to be:– The need for timely market-consistent economic capital calculations– Allocating capital appropriately across the group– Solvency II and the use test– Quick and simple representation of the liabilities for use in financial analysis, risk limit
setting and risk reporting– Identification and measurement of ALM risks
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Approaches: Three Methods for Replicating Portfolios
Balance Sheet Method Aggregate Cashflow Method Annual Cashflow Method
• Find a portfolio of assets whose total future discounted (or rolled-up) cash flows match the total discounted (or rolled-up) liability cash flows closely in a
• Find a portfolio of assets whose future cash flows by time match the liability cash flows closely in a range of scenarios for all years
• Find a portfolio of assets whose current market value matches the fair value of liabilities under a range of sensitivities
y yrange of scenarios
• One set of sufficiently varied economic scenarios (say 1000 projections)
• Can be used to update market consistent balance sheets
• Cannot project RBS
• One set of sufficiently varied economic scenarios (say 1000 projections)
• Can be used to update and project market consistent balance sheets
• Care need with some policyholder behaviour in choice of candidate assets
• Market consistent balance sheets for range of sensitivities (say 50 x 1000 projections)
• Can be used to update market consistent balance sheets
• Does not use individual cash flow information
• Many projections required
• Doesn’t capture all behaviour unless very complex sensitivities
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Base Equities up 10%
Equities down 10%
Equity volatility up 5%
Equity vol down
5%
Interest rates up
1%
… Interest rate vol down 1%
Asset shares 1,000 1,050 950 1,000 1,000 970 … 1,000Cost of guarantees 50 45 57 53 45 47 … 48Guarantee charge -25 -27 -24 -25 -25 -23 … -25Cost of smoothing 5 5 10 7 4 4 … 5Other liabilities 8 8 8 8 8 8 … 8Total liability 1,038 1,081 1,001 1,043 1,032 1,006 … 1,036
S i m u l a t i o n R o l l - u p c a s h f l o w
1 1 1 52 1 1 03 1 4 54 1 2 05 1 3 3
… …1 , 0 0 0 1 2 1
Simulation 2006 2007 2008 2009 … 2026
1 6 5 10 13 … 32 6 7 11 12 … 23 7 5 6 7 … 54 5 4 15 5 … 15 4 2 3 7 … 2… … … … … … …
1,000 6 2 8 9 … 4
Data Inputs:
unless very complex sensitivities performed
Approaches: Sample Replicating Portfolio Process
Insurance Contract
Insurance Contract
Capital Market Equivalent
Capital Market Equivalent
Guaranteed Liabilities
Guaranteed Liabilities
Zero Coupon Cashflows
Zero Coupon Cashflows
Maturity guarantees
Maturity guarantees Put OptionPut Option
O ti t O ti t I t t R t I t t R t
4. Choose suitable candidate assets
Max95%75%50%25%5%Min
5. Output – updated liabilities, sensitivities or projections
3. Generate cash flows under defined scenarios
Optimisation Engine
Option to annuitiseOption to annuitise
Interest Rate Swaption
Interest Rate Swaption
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Replicating Portfolio
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Time points
1d 10d
1
234
2000
x xx xx x
x x
x x
1
23
2000
1000
Time point
Price or %
3M USD LIBOR
1
23
2000
1000
30Y USD RATE
1
23
2000
1000
RISK FACTOR N
1d 10d
Risk factor scenariosPrice
Inflation
Salary Inflation
UK Equities
Overseas Equities
UK Bonds
Cash
Index Linked
Target Value
Rep
licat
ing P
ort
folio
Value of replicating portfolio againstprojected liability value
1. Choose economic scenarios
2. Actuarial cash flow projection system
6. Validate through detailed testing program
Liability Model
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Considerations: Implementation ApproachDeloitte’s recommended implementation approach is split into a Discovery Phase and an Implementation Phase. We recommend that a pilot exercise be used to test out the methodology and technology.
Implementation Considerations:
D i i
Implementation Methodology:
Project Management and Benefits Realisation
Change Management and Transition into BAU
Discovery Phase Implementation Phase
PIL
OT
Require-ments
Definition
ProgramDesign Planning
Design Build
Deploy Technology
InfrastructureAlgorithmics Configuration
Technology Infrastructure
Algorithmics Components
Rollout
Design issues:• Governing objective• Choice of software• Dashboard – required outputs• Reporting granularity required by product• Frequency of recalibration• Required reporting frequency• Approach by product type• Allowance for non-market risk• Acceptance testing process• Allowance for new business
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Project Management and Benefits Realisation
Change Management and Transition into BAU
Discovery Phase Implementation Phase
BU
1
Require-ments
Definition
ProgramDesign Planning
Design Build
Deploy Technology
InfrastructureAlgorithmics Configuration
Technology Infrastructure
Algorithmics Components
BU
2
BU
3
Wider considerations• Design of implementation program• Information to be provided by cash flow
models• Training and communication are critical• Useful management information needed for
business buy in
As used in this presentation, “Deloitte” means Deloitte Consulting LLP, a subsidiary of Deloitte LLP. Please see www.deloitte.com/us/about for a detailed description of the legal structure of Deloitte LLP and its subsidiaries.
Considerations: Top 5 implementation challenges
Implementation challenges:
1. Buy-in from the business
• Involve in the development project• Visible senior management support required to drive the process• Link to management of the business must be demonstrated – not just an academic exercise• Implementation should produce benefits as quickly as possible• A process that produces “rough” numbers that can be refined later helps build momentum
2. Design of acceptance testing
3. Knowledge transfer and training of implementation teams
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4. Speed and efficiency of end-to-end process which is key to embedding
5. Data transfer processes• The link between live market data and both the replicating portfolio and the actual assets held is important - this
must be streamlined and accurate to allow quick revaluation• We have seen three methods used - actual assets, roll forward using indices, roll forward allowing for cashflows.
The choice varies based on systems and timescales involved and can be refined a a later date
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Considerations: Top 5 technical challenges
Technical issues:
1. Choosing and modelling appropriate candidate assets2. Policyholder behaviour and dynamic management actions3. Non-market risk4. Selecting scenarios that bring out the full nature of the liabilities5. Using a suitable optimisation routine
• Allowance for non-market risk is important when using for economic capital analysis
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• Particularly important where there is non-linearity between market and non-market risk factors
Candidate Assets
• Suitable candidate assets must be defined. The types of assets allowed would depend on the purpose of the replicating portfolio:– If the intention is to produce a replicating portfolio that can be invested in, the assets must be
tradeable.– If the replicating portfolio is to be used to provide a benchmark for asset performance, synthetic
assets such as zero coupon bonds can be used. These assets must be easily priceable given actual financial market conditions, but it is not necessary to be able to invest in them.
– More complex synthetic assets can be used, such as an asset representing the asset share mix of the liabilities, if the only purpose is to produce a portfolio that mirrors the behaviour of the liabilities.
• Care should be taken with management actions - suitable assets that capture the same effects as the actions should be used.
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• The optimisation method used affects the constraints that can be put on the replicating portfolio. Such constraints could include:– Requiring all asset weights to be positive– Trading constraints - useful if the intention is to invest in the portfolio created– Requiring certain results to hold - such as the overall value of the portfolio at the start being equal to
the value of the liabilities, or the intrinsic value of guarantees to be valued correctly
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Features and Behaviors
Fixed cash flows
Candidate Assets
Zero coupon bonds
Candidate Assets
Sample liability features and behaviors and candidate assets
BasicCash Flows
Fixed cash flowsInvestment index-linked cash flowsCredited rate based on bond yieldsLongevity related
EmbeddedGuarantees
Zero coupon bondsEquity / property total return indexBond total return indexLife table amortizing bonds, mortality swaps
Equity put options Equity call options Bond put option, American style or Bermudian swaptionVanilla swaptions, quanto swaptionsForward start optionsCliquet / lookback options
Guaranteed accumulation valuesParticipation in investment profit upside (ex EIA)Guaranteed minimum credited ratesGuaranteed annuity rates, GMIBGuaranteed reinvestment terms on future premiumsRatchets / non-negative reversionary bonus
©2010. Private and confidential.
DynamicPolicyholderbehaviour
Option take-up rates depend on moneynessLapse rates increase in high marketsLapse rates increase in low marketsEquity fund lapse rate depends on interest ratesPremium persistency dependent on option value
Power law optionsUp and out optionsDown and out optionsOutside barrier optionsCompound options (options on options)
UniversalLifewith
SecondaryGuarantee
Product Features
Flexibility of premiums and death benefitsPositive performance, in particular investment, returned to policyholderMinimum credited ratesMinimum guaranteed death benefit if performance is poor
Policyholder Behavior
Lapse/disintermediationReduced lapse if in the money (ITM) guarantee (may increase with age)Premium persistencyLoans/withdrawals
Management Actions
Increase cost of insurance (COI) Reduce credited ratesIncrease expense loadsAll subject to caps/floors
Market Risk Factors
Interest ratesUp increases lapse riskDown may hit guaranteesHigher volatility raises guarantee costs
Credit riskUp may hit guarantees
Candidate Assets: Particular Replication Challenges by Product
VariableUniversal
LifeWith
Secondary Guarantee
VariableAnnuity
Fixed
Flexibility of premiums and death benefitsInvestment performance in SA fully passed to policyholderMinimum guarantees if equity performance is poorRetains some UL risks in GA
Reduced lapse if ITM guarantee (may increase with age)Premium persistencyLoans/withdrawalsFund allocation changes
Equity dropHits guaranteesReduces charge income
• Interest rates• Equity volatility increase raises
guarantee costs• Credit risk on GA
Typically single depositInvestment performance of SA fully passed to policyholderMinimum guarantees (AB/IB/DB/WB) if equity performance is poorSome $ in GA, usually small
Possibly ability to increase GMLB rider chargesReduce credited rates on GA
Single or multi depositMinimum guaranteed interest rate Reduce credited rates subject
Increase COIs Reduce credited rates on GAIncrease expense loadsAll subject to caps/floors
Reduced lapse if ITM guarantee (may increase with age) and vice versaAnnuitization ratePartial withdrawal rateReset rateFund allocation changes
Equity dropHit guaranteesReduces M&E income
• Interest rates• Equity volatility increase raises
guarantee costs• Credit risk on GA
Interest rates/creditSimilar to UL
©2010. Private and confidential.
Fixed Annuity /
Equity IndexedAnnuity
Minimum guaranteed interest rate (lower for EIA)Annuitization option (not rich)EIA includes single or multiple index optionsLegacy product a hybrid
Reduce credited rates subject to floorChange option budgeting for EIAs subject to floor
Lapse/disintermediationReduced lapse if ITM guarantee and vice versaAnnuitization
Similar to ULEquity levels for EIA
Up increases payoutsDown increases lapses
• Equity volatility increases cost of options
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Testing of Fit
• Experience is developing as more work is done in this area– “Art” as well as science– Some subjectivity in the development and acceptance of replicating portfolios
• Calculate R2 for aggregate cash flows or cash flows by term across simulations
• For cash flow method, calculate R2 for projected future balance sheets (subject to runtime constraints)
• Check the average and the standard deviations of the errors• Check whether errors are normally distributed – if not, this
might imply need for options• Graphing results can be a powerful way of providing comfort:
–Scatter graphs of cashflows or future balance sheets by simulation are effective–Graphing the errors in the replication can also be informative
Statistics
•Compare market consistent value of liabilities against market value of replicating portfolio•Check modelling of intrinsic value of guarantees only – turn volatility off•Where projecting the balance sheet forwards, these tests should be done at future time periods as well as at the projection start date
–This would require a simulation fan approach to the testing•Check how well the replicating portfolio works for out of sample stress tests / scenarios
–This is an effective way of testing the robustness of the portfolio fit
Testing approaches
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• How close should you get? It depends:– For a life business without policyholder behaviour and with only simple management actions, we have
seen as much as R2 = 99.5% obtained– Restrictions to assets that you can invest in can affect how close a match you can get
portfolio fit
Summary
• Insurance companies are increasingly using replicating portfolio techniques in the management of their business
• The key benefit opportunities are:
– Making complex actuarial investigations more practical
– Speeding up liability valuation to provide real time management information
• We expect to see much activity in this area in the next few years
©2010. Private and confidential.18
We expect to see much activity in this area in the next few years
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This presentation contains general information only and is based on the experiences and research of Deloitte practitioners. Deloitte is not, by means of this presentation, rendering business, financial, investment, or other professional advice or services. This presentation is not a substitute for such professional advice or services, nor should it be used as a basis for any decision or action that may affect your business. Before making any decision or taking any action that may affect your business, you should consult a qualified professional advisor. Deloitte, its affiliates, and related entities shall not be responsible for any loss sustained by any person who relies on this presentation.
Copyright © 2010 Deloitte Development LLC, All rights reserved.
©2010. Private and confidential.19
Unlocking the global potential
R li ti P tf li Ad d A h ?
Local knowledge. Global power. 20INTERNAL
Replicating Portfolios: Advanced Approaches?
Algo User GroupMarch 2010
11
Replicating Portfolios: High-level Overview
Local knowledge. Global power. 21INTERNAL
What is a replicating portfolio?
• Replicating portfolio = a portfolio of hypothetical market securities whose economic sensitivities and/or cash flowsmatch well those of a portfolio of actual assets or liabilities
• Replicating portfolios provide:– a proxy for (re-)valuing the actual asset or liability portfolio under
different market conditions– the ability to recalculate asset/liability values, balance sheets,
capital requirements and attribution analyses very quickly and efficiently
– the ability to make complex actuarial calculations more accessible
Local knowledge. Global power. 22INTERNAL
y p(through accelerated liability valuation)
– a way to avoid the need to go back to the underlying liability projection models for determining many market risk sensitivities
– a means to complete many key calculations prior to the reporting period
12
Replication: initial setup process
1. Choose Economic Scenarios
2. Actuarial Projection
System
4. Choose
Optimisation Engine 3. Liability Cash Flows Under
Defined Scenarios
Replicating Portfolio
5. Perform Validation
Local knowledge. Global power. 23INTERNAL
4. Choose Suitable
Candidate Assets
6. Risk Dashboard, Economic Capital,
MVIS attribution, etc.
Re-valuing a liability portfolio using the replicating portfolio
• New market information can be processed quickly by re-valuing the replicating portfolio
• No need to go back to the
Valuation of the replicating portfolio is quick as all replicating assets can typically be valued by closed form solution using market data directly • No need to go back to the
actuarial projection system– No new scenarios– No new liability cash flows
• Cycle for re-valuation is now measured in minutes rather than weeks!
New Market Data
Replicating Portfolio
New Value of Replicating
Portfolio
Available in minutes
Local knowledge. Global power. 24INTERNAL
Available in minutes
13
Comparison of market consistent valuation approaches
Current Process• Risk-neutral scenarios
C h fl j d f i l
Replicating Portfolio Process• Smaller set of risk-neutral scenarios plus
a wide range of other scenarios• Cash flows projected from actuarial models
• Present value obtained by discounting cash flows
• Cycle time takes many weeks or months
• Re-valuation for market changes also takes weeks!
a wide range of other scenarios• Cash flows projected from actuarial
models
• Optimization of replicating portfolio weights based on fitting cash flows and/or market sensitivities across scenarios
• Re-valuation for a wide range of small and/or large market changes obtained in minutes!
Local knowledge. Global power. 25INTERNAL
Uses of Replicating Portfolios
Local knowledge. Global power. 26INTERNAL
14
Applications of replicating portfolios
Becoming more widely used at insurance companies around the world ☺
Current uses: Economic Framework & MCEV
Risk• Risk dashboards showing realistic economic sensitivities, stress tests, solvency
positions, VaR and/or CTE levelsRisk management
purposes • Real-time ALM analytics and risk position reporting
• Ad hoc and “what-if” analyses
• Liability benchmarks for investment management
Calculation of Economic
Capital
• Results for timely capital reporting and capital management
• Proxy for MV of liabilities and assets
• Simulate joint distributions quickly to calculate capital
Attribution
• Used to develop expectation of liability asset or movement as a result of changes in market conditions
• Isolate changes in the asset or liabilities in a given reporting period
Local knowledge. Global power. 27INTERNAL
Attribution analysis of assets and liabilities
• A tool to identify changes for equity levels, interest rates, volatilities, etc. and aid in determining the changes as they relate to other items
• More efficient MVBS and MVIS reporting
• Splitting risk and return into non-hedgeable, asset management and ALM/Treasury components
Future uses include: Solvency II & IFRS
Applying different calculation/estimation techniques
Liabilities & building blocks of MVL
Estimation approach
Relative size and effort to calculate
Assets
Other Liabs
Frictional Cost
Market value of taxes
Market Value Margins
Own Credit or Liquidity
Alternative estimation techniques in addition to RPs
Non‐HLV
HLV
~90% of M
VL (si
Assets Largely IFRS fair values
Local knowledge. Global power. 28INTERNAL
HLVRPs very valuable
HLV ize and effort)
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ERC components
EUR MM FY 2008 FY 2007
AEGON Americas
AEGON NL
AEGON UK
AEGON CEE
AEGON Spain
AEGON Asia
Holdings and Other Countries
Offset AEGON NV AEGON NV AEGON NV
Investment and counterparty riskIR1 Fixed income
HY 2009
RPs can help calculate:• interest rate mismatch risk ERC• interest rate volatility risk ERC• currency mismatch risk ERC
• equity level risk ERCIR1a Spead mismatchIR2 Equity shockIR3 Alternative investmentsIR4 Counterparty riskIR5 Equity volatility
Mismatch riskMR1 Interest rateMR2 Interest rate volatilityMR3 Currency
Underwriting riskUR1C Mortality contagionUR1P Mortality and longevity level and trend
Mortality level and trendLongevity level and trend
UR2C Morbidity contagionUR2P Morbidity level and trendUR3C Persistency contagionUR3P Persistency parameterUR4C Property and casualty contagionUR4P Property and casualty parameter
O ti l i k
• equity volatility risk ERC• large and small economic sensitivities
RPs are not expected to help calculate:
RPs may also help calculate:• credit spread risk ERC
• aggregation of ERCs across risks, BUs and economies/geographies
Local knowledge. Global power. 29INTERNAL
Operational riskAfter tax gross ERCDiversification benefitsERC from shareholders' perspective
ERC from shareholders' perspectiveHoldings ERCOffset eliminationERC from policyholders' perspective
RPs are not expected to help calculate:• default and migration risk ERC
• counterparty risk ERC• mortality risk ERC• morbidity risk ERC
• policyholder behavior risk ERC• operational risk ERC
MVIS attribution
EUR MM
AEGONAmericas
AEGONNL
AEGONUK
AEGONCEE
AEGONSpain
AEGONAsia
Holdingsand OtherCountries
AEGON NVRPs can help calculate/estimate:
• economic variancesOpening Value (January 1, 2009)Value of New Business (MC VNB)Expected Existing Business Contribution(at reference rate)Experience VariancesAssumption ChangesCorrections and Model ChangesTotal Operating EarningsUnderlying Economic Variances
Interest Rate VariancesCredit VariancesChange in VOCR
• economic variances(i.e. changes in interest rates, equities, implied volatilities,
credit spreads and currencies)
RPs may also help calculate/estimate:• expected existing business contribution
• value of new business• change in liquidity premium
Local knowledge. Global power. 30INTERNAL
gEquity VariancesOther Variances
Currency Exposure VariancesTotal EarningsNon-Operational ChangesClosing Value (June 30, 2009)
RPs are not expected to help calculate/estimate:• experience variances
• assumption changes impact• non-operational changes
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MVBS projections
ASSETSFuture profits on OBS contractsInvestments for general account
Derivatives for general account
AEGON NL
AEGON UK
AEGON NV consolidated MVN HY 2009
Investments and other assets held for account of policyholder
AEGON NV consolidated MVN FY 2008
AEGON CEE
AEGON Spain
AEGON Asia
Holdings and Other
Countries + Eliminations
(amounts in EUR millions)
AEGON Americas
RPs can help calculate/estimate: H d d Li bilit V lReinsurance assets
Defined benefit assetsDeferred tax assetsOther assets and receivables for general accountCash and cash equivalents for general accountTotal assets
Non-modeled business
Total assets
EQUITY AND LIABILITIESShareholder's equityHoldings activitiesEconomic available capital
LiabilitiesInsurance contracts for account of policyholderInsurance contracts general account
• Hedged Liability Value
RPs may help calculate/estimate:• tax items
• market value margins• frictional cost
• liquidity premium
Local knowledge. Global power. 31INTERNAL
Investment contracts for account of policyholderInvestment contracts for general accountBorrowings not related to capital fundingDerivativesProvisionsDefined benefit liabilitiesDeferred tax liabilitiesOther liabilitiesAccrualsValue of own credit riskTotal liabilities
Total equity and liabilities
Other estimation techniques should be used to adjust RP values for:
• actual vs expected inforce experience• changes in assumptions
• new business volume/mix variations
The Replication/Fitting Process
Local knowledge. Global power. 32INTERNAL
17
The Familiar Elements (1)
• Actuarial Projection Models– Same models used for AeMcS
• Business Hierarchy– How are model points currently split?
• by product, issue year, …– May want to split a bit differently
• fixed vs. flexible premiums?• vary by benefit types?
– BU submits in Excel format• Group reviews & enters into system
Local knowledge. Global power. 33INTERNAL
• Group reviews & enters into system
• Product Descriptions– Product features & their relationship to risk factors– Helps guide choice of candidate instruments
Business Hierarchy Example
US
Individual Annuities
Retirement Services
FA
SPDA Newer
SPDA Older
VA
Base Contract
GMDB
Terminal Funding
Deterministic Liabs
GA Assets
401k
Local knowledge. Global power. 34INTERNAL
SPIA
GA Assets
GMAB
GMIB
GMWB
18
The Familiar Elements (2)
• Market Data– To generate economic scenarios– To value candidate instruments/assets– To generate market risk distributionsg
• Economic Scenarios– Training
• vary market risk factors (rates, index levels, vols)• both large & more representative shocks
– Out-of Sample• to test predictive value of RP• checks values between/around training scenario sprays
Local knowledge. Global power. 35INTERNAL
g p y
• Cash flows– Projected for economic scenarios outlined above– Convert to CSV format and upload into system
Training Scenarios
Stress overview DescriptionBase risk-neutral sprayInterest rate stresses up interest rate shocks (large)
up interest rate sensitivities (smaller)down interest rate shocks (large)down interest rate shocks (large)down interest rate sensitivities (smaller)
Interest rate volatility interest rate volatility shocks (large)interest rate volatility sensitivities (smaller)
Equity stresses equity shocks (large)equity sensitivities (smaller)
Equity volatility equity vol shocks (large)equity vol sensitivities (smaller)
Combined stresses combined interest rate and equity sensitivities
Local knowledge. Global power. 36INTERNAL
• Total # of interest rate training scenarios = 1500• Total # of interest rate & equity training scenarios = 2500• Separate smaller set for pure (non-optional) fee business
19
Out-of-sample Scenarios
Stress overview DescriptionChecking base value small variations in interest rates
small variations in equitiescombined interest rate and equity sensitivities
Checking interest rate variations in interest rates (e g parallel shocks)Checking interest rate movements
variations in interest rates (e.g. parallel shocks)combined interest rate and equity sensitivities
Checking equity variations in equitiescombined interest rate and equity sensitivities
Checking volatilities variations in interest rate volsvariations in equity volscombined interest rate vol & equity vol sensitivities
Local knowledge. Global power. 37INTERNAL
• Should be different from training scenarios• Total # of interest rate out-of-sample scenarios = 900• Total # of interest rate & equity out-of-sample scenarios = 2200
The New Elements – Optimization Requests
• Download Excel template with multiple tabs
• Choose candidate instruments by category– ZCBs swaptions index forwards index options– ZCBs, swaptions, index forwards, index options– Exotic derivatives (e.g. path-dependent options)
• Choose optimization settings– Deterministic, Multi-deterministic, IR stochastic, IR & Equity– Optimization function
• minimize abs error vs. squared error– Cash flow bucketing
h i h fl fit i i iti l t
Local knowledge. Global power. 38INTERNAL
• emphasize cash flow fit in initial quarters– Hard/soft value constraints– Trade penalties
• minimizes large offsetting positions & resulting RPs more intuitive
• Upload filled-out Excel template into system
20
Proof of Concept: Lessons Learned
PV of Liab Cash Flows versus PV of Rep Portfolio Cash Flows by Scenario
Importance of Replicating Universe
Liabilities often contain rich, complex embedded optionsVanilla replicating instruments alone y
(all 000s)
1,000,000
2,000,000
3,000,000
4,000,000
5,000,000
6,000,000
PV o
f Lia
b C
FsR^2=0.97
Vanilla replicating instruments alone may not be sufficient to capture sensitivities with a high degree of accuracy
Define a replicating universe that is:• Generic enough to be manageable • Rich enough to capture sensitivities
sufficiently
Determine bucketing scheme
• Using single buckets will usually not
Local knowledge. Global power. 39INTERNAL
00 1,000,000 2,000,000 3,000,000 4,000,000 5,000,000 6,000,000
PV of Rep Portfolio CFs
• Using single buckets will usually not result in a good cash flow match for the first year
• In production, bucketing will at least break out first few quarters’ cash flows to ensure good cash flow match
Importance of replicating asset universe: finding a tradeoff
Vanilla Universe• Swaps• Swaptions• Zero Coupon Bonds
Caps and FloorsStructured (Complex)
• Caps and Floors• Forwards• Puts and Calls• etc
Universe
• Structures more reflective ofliability features
• plus vanilla instruments
Vanilla Universe Structured Universe
Local knowledge. Global power. 40INTERNAL
Vanilla Universe Structured Universe
Maintenance Easy Harder
Availability of instruments Typically available Often not available, require calibration
Speed of valuation Fast Slow
Stability of replicating portfolio Potentially less stable Tends to be more stable
Hedging Basis for hedge strategy Custom structures harder to apply for hedging purposes
Number of instruments Tend to use more Tend to use fewer
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Replicating Instrument Set
Instrument Group Instrument TypeCore Cash Flow ZCB s(at key rates)Vanilla InterestDerivatives
IR SwapsCaps / FloorsEuropean Swaption (Cash Settled)European Swaption (Phys. Settled)
Exotic Interest Derivatives CMS Caps / FloorsStructured Yield Curve Instruments
Vanilla Market Index Derivatives
Market Index ForwardsEuropean Calls and Puts
Exotic Market Index Derivatives
American Calls and PutsForward Starting EuropeansSi l B i O ti
Local knowledge. Global power. 41INTERNAL
Single Barrier OptionsAsian/Lookback Calls and PutsCompound Index ForwardsEuropeans on Compound Indexes
The New Elements – Replication Results
• RP Results & Goodness-of-fit– Weights x Instruments– R-squared (necessary but not sufficient) – Scatter plots (pretty, intuitive & persuasive)p (p y, p )– Max & mean absolute regret (how meaningful?)– Interest rate & equity Greeks (e.g. KRDs, Delta/Gamma)– Other specified sensitivities (e.g. parallel shifts)– PV RP cash flow vs. PV benchmark cash flow
• absolute difference & % difference• relative % change vs. base• for all training & out-of-sample scenario sprays run by BU
Local knowledge. Global power. 42INTERNAL
• Compare and choose best fitting RP– More complex business will take more time & effort– Multiple iterations (and possibly new instruments) may be needed to get
comfortable
22
Sample scatter plot
Local knowledge. Global power. 43INTERNAL
GOF Approach (1 of 5)
Risk-neutralreplio value
Risk-neutralliability value
1
2 4
3
Risk-neutralreplio value
Risk-neutralliability value
1
2 4
3
True liability valueTheoreticalreplio valueTrue liability valueTheoreticalreplio value
1. “true” value of the liabilities – Consistent with observed asset market prices. Not directly observable. Other measures are alternative approaches to estimating this value.
2. risk-neutral liability value – Discounted value of the liability cashflows produced by the liability model under a risk-neutral scenario set.
3 theoretical RP value – Theoretical market value of the assets in the replicating
Local knowledge. Global power. 44INTERNAL
3. theoretical RP value Theoretical market value of the assets in the replicating portfolio, as calculated in Algo, usually using a closed form approach. Much easier and quicker to calculate than the risk-neutral liability value (2), and so can be used more flexibly.
4. risk-neutral RP value – Discounted value of the replicating portfolio asset cashflows under the risk-neutral scenario set used to calculate the risk-neutral liability measure (2).
23
GOF Approach (2 of 5)
Risk-neutralreplio value
Risk-neutralliability value
1
2 4
3
Sampling error
Parameterization error
Risk-neutralreplio value
Risk-neutralliability value
1
2 4
3
Sampling error
Parameterization error
Risk-neutralreplio value
Risk-neutralliability value
1
2 4
3
Risk-neutralreplio value
Risk-neutralliability value
1
2 4
3
Sampling error
Parameterization error
True liability valueTheoreticalreplio value
Replication error
True liability valueTheoreticalreplio valueTrue liability valueTheoreticalreplio valueTrue liability valueTheoreticalreplio value
Replication error
• replication error – Caused by a replication being imperfect, with the RP not producing exactly the same cashflows as the liability model.
• sampling error – Due to the use of random scenarios in a risk-neutral valuation. D th b f i i
Local knowledge. Global power. 45INTERNAL
Decreases as the number of scenarios increases.• parameterization error – Limitation of the Economic Scenario Generator
(“ESG”), caused by the impracticality of creating a set of economic scenarios capable of accurately pricing all market instruments. The scenarios cannot be calibrated to the full set of economic parameters observable in the market. In particular, there are practical limits to the portion of full implied volatility surfaces for equity and interest options to which one can calibrate.
GOF Approach (3 of 5)
Risk-neutralreplio value
Risk-neutralliability value
2 4
Sampling error
Revised comparison
Risk-neutralreplio value
Risk-neutralliability value
2 4
Sampling error
Revised comparison
Replication error
True liability value Theoreticalreplio value
1 3
Parameterization error
Original comparison
Replication error
True liability value Theoreticalreplio value
1 3
Parameterization error
Original comparison
Local knowledge. Global power. 46INTERNAL
• The most intuitive comparison is between risk-neutral liability value (which many actuaries think is equal to the true liability value) and the theoretical RP value, since this is analogous to comparing ones “old” results to the “new” results.
• However, a preferable comparison is available, between the risk-neutral liability value and the risk-neutral RP value.
24
GOF Approach (4 of 5)
Risk-neutralreplio value
Risk-neutralliability value
2 4
Sampling error
Control variate dj f
Risk-neutralreplio value
Risk-neutralliability value
2 4
Sampling error
Control variate dj f
Replication error
True liability value Theoreticalreplio value
1 3
Parameterization error
adjustment factor
Replication error
True liability value Theoreticalreplio value
1 3
Parameterization error
adjustment factor
Local knowledge. Global power. 47INTERNAL
• New estimated liability value = RN liab value + (Theo RP value - RN RP value)
• New estimated liability value = (RN liab value - RN RP value) + Theo RP value
• New estimated liability value ≈ Theo RP value
GOF Approach (5 of 5)
Risk-neutralreplio value
Risk-neutralliability value
2 4
Sampling error
Parameterization
Revised comparison
Risk-neutralreplio value
Risk-neutralliability value
2 4
Sampling error
Parameterization
Revised comparison
Replication error
True liability value
Theoreticalreplio value
1
3
Parameterization error
Instrument valuation error
Original comparison
Replication error
True liability value
Theoreticalreplio value
1
3
Parameterization error
Instrument valuation error
Original comparison
Local knowledge. Global power. 48INTERNAL
• instrument valuation error – Caused by errors in the market data and/or valuation formulas for the assets in the replicating portfolio. Minimized through appropriate pre-optimization validation procedures.
25
The New Elements – Scaling Factors
• Should also adjust RP for non-market risk elements– Inforce
• Actual vs. expected actuarial experience• Actuarial assumption changes
– New business• Volume sold• Demographic mix sold
• Suggested approaches– Replicate business in materially distinct pieces
• inforce vs. new business• different sub-products?
Local knowledge. Global power. 49INTERNAL
• components of MVL (e.g. HLV, taxes, margins, LP)?– Scale each RP, using ratio of
• Current level of a volume driver (specific to product and risk type)• Projected value of same driver (to current date, using models at replication date)
– Calculated all projected RP values on an “aged” basis
The New Elements – Market Risk Reporting
• Market risk reports available – At any level of the business hierarchy– For assets, liabs or the difference
• VaR reports & market risk ERCs– Market risk ERCs ≈ 99.5% VaR for each risk factor
• CTE measures also readily available– Aggregate by applying copula (VCV matrix) to results
• consistent with current process
Local knowledge. Global power. 50INTERNAL
• Stress/Sensitivity Scenarios & MVIS attribution– Can help isolate MVIS economic variance sub-lines– Could also be used to populate risk disclosures– Predefined set for capturing risk dashboard
26
Using Trade Restrictions to ImproveUsing Trade Restrictions to Improve Your Replicating Portfolios
Curt BurmeisterVice President, Risk Solutions
Finding a Good Replicating Portfolio
Common Choices• Candidate Instrument Universe• Scenario Set• Objective Function • Constraints
Common Problems• Too many candidate instruments• Poor out-of-sample performance• Large offsetting trades
© 2010 Algorithmics Incorporated. All rights reserved. 52
• Hard to interpret results
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Variable Annuity Portfolio – # Policies by GMDB type
~15000 Total Policies
Policy Date ROP Roll-up Ratchet Combo Total
< 2002 2428 1057 1960 664 6109
2002-2005 2165 444 879 1583 5071
2005-2007 1389 0 682 2147 4218
Total 5982 1501 3521 4394 15398
© 2010 Algorithmics Incorporated. All rights reserved. 53
Variable Annuity Portfolio – # Policies by ITM Band
1: MGDB Guarantee / Account Value < 0.92: 0.9 ≤ MGDB Guarantee / Account Value ≤ 1.13: 1.1 ≤ MGDB Guarantee / Account Value
ITM Band ROP Roll-up Ratchet Combo Total
1 4391 455 984 361 6192
2 1396 419 2241 3587 7645
3 195 627 296 446 1567
Total 5982 1501 3521 4394 15398
© 2010 Algorithmics Incorporated. All rights reserved. 54
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Variable Annuity Cash Flows
Scenario dependent cash flows include Market Indices
1. guaranteed minimum death benefit 2. general account release3. commissions4. expenses5. mortality/expense charge6. revenue sharing7. surrender charges8. per policy fees
1. US Interest Rate Curve2. Russell 1000 3. S&P 5004. Nasdaq 1005. MSCI EAFE Index 6. MSCI Emerging Market Free7. MSCI REIT Index8. Lehman US Aggregate
© 2010 Algorithmics Incorporated. All rights reserved. 55
gg g
Replicating Universe and Optimization Setup
366 Replicating Instruments• Zero Coupon Bonds• Swaptions (physical settlement),
E it F d ( h i d )• Equity Forwards (on each index)• European Equity Options (on each index)
500 ScenariosSet A = 250 (used for optimization)Set B = 250 scenarios (used for out-of-sample testing)
© 2010 Algorithmics Incorporated. All rights reserved. 56
20 years of Annual Cash Flows
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Annual Variable Annuity Cash Flows
© 2010 Algorithmics Incorporated. All rights reserved. 57
Try #1 - Unconstrained Problem
Match Linear (PV cash flows)
Solve optimization using scenario set A
Evaluate the results under scenario sets A & B
© 2010 Algorithmics Incorporated. All rights reserved. 58
30
Match Linear (PV Cash flow)
© 2010 Algorithmics Incorporated. All rights reserved. 59
R2 = 1.000 R2 = .299
Trading Budget Efficient Frontier
Construct an efficient frontier by adding a trading budget constraint and then solving the same problem with varying budget levels
© 2010 Algorithmics Incorporated. All rights reserved. 60
31
Another “Perfect” Solution – Min Units
© 2010 Algorithmics Incorporated. All rights reserved. 61
R2 = 1.000 R2 = .647
Out-of-Sample Evaluation
Evaluate the efficient frontier of replicating portfolios under scenario set B
© 2010 Algorithmics Incorporated. All rights reserved. 62
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Best Out-of-Sample Solution (1.9K Units)
© 2010 Algorithmics Incorporated. All rights reserved. 63
R2 = .984 R2 = .953
Match Linear - R2 versus Units Traded
© 2010 Algorithmics Incorporated. All rights reserved. 64
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Trade Penalties Also …
Reduce the number of instruments in the replicating portfolio
Make the replicating portfolio easier to interpret
Eliminate large offsetting positions
© 2010 Algorithmics Incorporated. All rights reserved. 65
Perfect Replication – Min Units
© 2010 Algorithmics Incorporated. All rights reserved. 66
34
Total Instruments Traded
© 2010 Algorithmics Incorporated. All rights reserved. 67
Best Out-of-Sample Solution (1.9K Units)
© 2010 Algorithmics Incorporated. All rights reserved. 68
35
Trade Restrictions
Can also be use to evaluate and compare different objective functions
© 2010 Algorithmics Incorporated. All rights reserved. 69
Match Quadratic - R2 versus Units Traded
© 2010 Algorithmics Incorporated. All rights reserved. 70
36
Match Linear versus Match Quadratic
© 2010 Algorithmics Incorporated. All rights reserved. 71
Match Linear (PV Cashflow) Set A
© 2010 Algorithmics Incorporated. All rights reserved. 72
37
Decisions for Constructing Trade Restrictions
Units or Value
Budget or Penalty
Size of weight, budget, or penalty
© 2010 Algorithmics Incorporated. All rights reserved. 73
References
Brodie, J., Daubechies,I., De Mol, C., Giannone, D. and I. Loris (2008), “Sparse and stable Markowitz portfolios,” European Central Bank Working Paper Series No. 936 (available at www.ecb.europa.eu)
DeMiguel V Garlappi L Nogales F J and R Uppal (2008) “A Generalized Approach toDeMiguel, V., Garlappi, L., Nogales, F.J. and R. Uppal (2008), A Generalized Approach to Portfolio Optimization: Improving Performance By Constraining Portfolio Norms.” London Business School.
Gotoh, J.-Y. and A. Takeda (2009), “On the Role of the Norm Constraint in Portfolio Selection,” Department of Industrial and Systems Engineering Discussion Paper Series ISE 09-03, Chuo University.
Hesterberg, T., Choi, N.H., Meier, L. and C. Fraley (2008), “Least angle and l1 penalized regression: A review,” Statistics Surveys 2, 61-93.
© 2010 Algorithmics Incorporated. All rights reserved. 74
Tibshirani, R. (1996), “Regression shrinkage and selection via the lasso,” Journal of the Royal Statistical Society Series B, 58, 267-288.
Wang, H., Li, G. and G. Jiang (2007), “Robust regression shrinkage and consistent variable selection through the LAD-lasso,” Journal of Business & Economic Statistics, 25:3, 347-355.
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Q & AQuestions?
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Q & AQuest o s